{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -3, 1, -4],\n [2, 3, 1, 2],\n [2, 3, 1, 2],\n [2, -3, -5, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 4, 6, 3],\n [10, 3, -2, -2],\n [32, 6, 8, -10],\n [4, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -8, -16, -16],\n [-6, 4, 8, 8],\n [9, -6, -12, -12],\n [-3, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 2, -2, -6],\n [-8, -4, 4, 12],\n [-6, -3, 3, 9],\n [8, 4, -4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-6, 6, 0, -6],\n [6, -6, 0, 6],\n [-2, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -6, -3, 6],\n [-12, 6, 3, -6],\n [-4, 2, 1, -2],\n [12, -6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 6, 0, -8],\n [-17, 2, 2, -6],\n [24, 11, -14, 4],\n [-2, 10, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -16, -16, 8],\n [0, 0, 0, 0],\n [-1, 4, 4, -2],\n [-2, 8, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 2, 6, -8],\n [-2, -1, 7, 2],\n [2, 4, -3, 0],\n [-4, -2, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 8, -12, 8],\n [6, 4, -6, 4],\n [-12, -8, 12, -8],\n [-3, -2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 10, 16, -8],\n [-12, -8, -6, 5],\n [1, 3, 4, -1],\n [-12, -15, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -12, -16, -8],\n [-3, 9, 12, 6],\n [1, -3, -4, -2],\n [3, -9, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -8, 20, 8],\n [8, 4, -24, -8],\n [-15, -18, 10, 8],\n [-3, 0, 14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[17, -6, -8, -2],\n [13, 16, 12, -4],\n [-8, 19, 18, -1],\n [-15, -5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -6, -22, 6],\n [14, 0, 0, -8],\n [-2, 12, 5, -2],\n [5, 9, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -20, -22, 8],\n [5, -1, 2, 0],\n [-2, 11, 5, -6],\n [2, 23, 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 4x4 matrix:\n[[-2, 2, -3, -2],\n [-9, 9, -9, -7],\n [0, 0, 18, 8],\n [12, -12, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -10, 15, 0],\n [-5, 6, -9, -7],\n [-3, 2, -3, 1],\n [-9, 10, -15, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -3, 3, -3],\n [8, -2, 2, -2],\n [12, -3, 3, -3],\n [-16, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 0, 3, 12],\n [6, 0, 2, 8],\n [9, 0, 3, 12],\n [9, 0, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -9, -9, -2],\n [13, 21, 21, 10],\n [5, 0, 0, -1],\n [-14, -18, -18, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 9, 3, 0],\n [-4, -3, -1, 0],\n [8, 6, 2, 0],\n [-12, -9, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, 6, 17, 1],\n [10, 2, 10, 0],\n [-4, 7, -4, 3],\n [-12, -5, -12, -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 4x4 matrix:\n[[3, -3, -3, 7],\n [9, -16, -9, -7],\n [-9, 11, 9, -13],\n [0, 4, 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[[11, -5, 8, 17],\n [13, -3, 1, 22],\n [-15, -2, -3, -6],\n [28, 10, -17, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, -6, 3, 12],\n [16, -8, 4, 16],\n [4, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, 16, 12, -10],\n [4, 0, 2, -3],\n [-15, -12, -18, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 1, -8, 2],\n [0, 8, -22, 15],\n [-10, -4, 6, -15],\n [-6, 8, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 8, 4, -2],\n [-1, 6, 8, 0],\n [15, -18, 6, 9],\n [12, -8, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -7, 5, 2],\n [4, -4, -22, 6],\n [-4, 0, 14, -14],\n [-2, 12, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, 6, -12, 12],\n [-8, 8, -16, 16],\n [8, -8, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -2, -8, -4],\n [0, 0, 0, 0],\n [-16, 4, 16, 8],\n [-12, 3, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, -16, 0],\n [8, 8, -2, -6],\n [-14, -13, 2, 10],\n [0, -8, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 0, 2, 0],\n [-2, 0, 2, 0],\n [-8, 0, 8, 0],\n [2, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 0, 7, -16],\n [-6, 0, -5, -16],\n [-7, 20, 12, 11],\n [-10, 0, 8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -8, 16, 22],\n [48, -48, 12, 4],\n [-12, 12, -14, -25],\n [36, -36, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 10, 4, -14],\n [-24, -3, 3, -15],\n [16, 8, 4, -2],\n [28, 6, 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[[-13, 21, 21, -9],\n [16, -4, 25, 2],\n [9, -4, 13, -1],\n [16, -4, 25, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -8, -8, -16],\n [-6, 4, 4, 8],\n [-3, 2, 2, 4],\n [-6, 4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -10, -18, 13],\n [-23, 3, 7, -9],\n [7, 0, 16, -12],\n [14, 1, -3, 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[[-6, 5, 2, -2],\n [8, -6, -5, 5],\n [10, -13, 13, -13],\n [24, -20, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -17, 8, -22],\n [-14, -11, 12, -30],\n [-15, 6, 15, -21],\n [-22, 15, 17, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -4, 6, -3],\n [-8, -8, -6, 6],\n [6, 4, 9, -7],\n [-6, -8, 0, 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[[-13, 24, -15, 19],\n [13, -28, 16, -20],\n [0, -12, 3, -3],\n [1, 2, -15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -15, 13, -6],\n [-14, -2, 12, -14],\n [10, 6, -12, -2],\n [13, 2, -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[[-18, -4, -16, -6],\n [-9, -12, -12, 9],\n [-12, -16, -16, 12],\n [6, -12, 0, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -6, 2, 0],\n [10, -6, -6, 14],\n [-24, 15, 1, -20],\n [4, 0, -6, 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[[4, -4, 4, 2],\n [8, -8, 8, 4],\n [-4, 4, -4, -2],\n [8, -8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 4, -2, -6],\n [24, -4, 6, 10],\n [-1, -8, -13, -2],\n [-14, 4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 1, 0],\n [0, 0, -3, 0],\n [0, 0, -2, 0],\n [0, 0, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 6, -4, 0],\n [2, -6, 4, 0],\n [-2, 6, -4, 0],\n [4, -12, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 10, -32, 14],\n [2, 1, -27, 23],\n [6, -3, 9, 3],\n [-2, -18, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -7, -7, -28],\n [-25, -4, -24, 6],\n [14, 13, 17, 17],\n [-2, 3, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 4, 4, -1],\n [0, -12, -12, 3],\n [0, -12, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 22, -3, 4],\n [8, -26, 2, -4],\n [-6, 0, 6, 3],\n [24, 13, 11, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 2, -12, 6],\n [0, 12, -32, 12],\n [4, -4, 4, 0],\n [-4, 13, -28, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, 9, -12],\n [12, 12, -9, 12],\n [12, 12, -9, 12],\n [12, 12, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 0, -6, 0],\n [1, 0, 2, 0],\n [-3, 0, -6, 0],\n [4, 0, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 4, -1, -6],\n [-4, -10, -24, 8],\n [2, 6, 14, -2],\n [-1, -6, -19, 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[[-12, 11, 0, 8],\n [20, -6, -22, 4],\n [-22, 11, 21, 2],\n [-19, 15, 20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -6, -2, 2],\n [3, 3, 1, -1],\n [3, 3, 1, -1],\n [-6, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 6, 2, -8],\n [4, 12, 4, -16],\n [2, 6, 2, -8],\n [1, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, -6, 0, 9],\n [0, -4, 0, 6],\n [0, 8, 0, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -3, 4, -1],\n [9, -6, 0, -3],\n [12, -3, 12, 0],\n [8, -7, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 4, 0, 0],\n [-1, 0, -2, 2],\n [12, 10, -9, -14],\n [28, 30, -27, -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[[0, -9, 8, -18],\n [-18, 12, -8, -12],\n [8, -6, 6, 4],\n [-18, 26, -21, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [4, 8, -6, -6],\n [-8, -16, 12, 12],\n [-4, -8, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 2, 11, 13],\n [16, -2, 3, -11],\n [20, -8, 4, -16],\n [8, -12, -25, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 4, -4, 8],\n [-15, -6, 12, -12],\n [-11, -4, 9, -8],\n [6, 4, -4, 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[[-3, 5, -2, 8],\n [-6, -11, 3, -12],\n [6, -1, 1, -4],\n [9, 18, -5, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 4, 4, 4],\n [-1, 13, 11, 10],\n [-4, 1, -1, -2],\n [-6, -7, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, 4, -12, 12],\n [12, 4, -12, 12],\n [12, 4, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -15, 3, 10],\n [-7, 0, 3, -10],\n [13, 15, 0, -6],\n [11, 3, -18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 12, -12, -8],\n [8, -6, 6, 4],\n [12, -9, 9, 6],\n [-12, 9, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 0, -6, 4],\n [-3, 0, 9, -6],\n [3, 0, -9, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 8, 10, -13],\n [4, -6, -14, 13],\n [-3, -2, 4, 0],\n [7, -8, -22, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -2, -2, -2],\n [-9, -3, -3, -3],\n [-12, -4, -4, -4],\n [-12, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-4, -2, -2, 2],\n [0, 0, 0, 0],\n [8, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -8, 4, 16],\n [-3, -5, 16, 10],\n [20, 12, 0, -24],\n [11, 9, -12, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 5, -4, 5],\n [-12, 12, 16, -12],\n [-6, -3, 12, -12],\n [2, 1, -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[[-9, -12, 0, -3],\n [12, 16, 0, 4],\n [6, 8, 0, 2],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 3, 4, 2],\n [0, 0, 0, 0],\n [16, -12, -16, -8],\n [-16, 12, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 0, 6, 10],\n [6, 12, -6, 6],\n [12, 14, -10, 2],\n [-2, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, -5, -7, -5],\n [0, -2, -1, -4],\n [0, 10, -1, -10],\n [10, 8, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 3, -6, -12],\n [-9, 3, -6, -12],\n [3, -1, 2, 4],\n [-9, 3, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -7, -2, 1],\n [11, 1, 6, 7],\n [1, 3, 2, 1],\n [2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -4, 14, 20],\n [-11, 12, 0, 16],\n [10, -4, 13, -8],\n [0, 0, -14, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 13, -2, 32],\n [18, -4, -8, 16],\n [24, -8, -22, 8],\n [0, -13, 6, -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[[-7, 2, -6, 9],\n [-9, -3, -9, 18],\n [5, -7, 3, 0],\n [18, -20, 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 4x4 matrix:\n[[-28, -44, 40, 12],\n [28, 20, -16, 6],\n [-1, 11, -14, -14],\n [18, 10, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 9, 9, -3],\n [6, -6, -6, 2],\n [12, -12, -12, 4],\n [12, -12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -13, 9, 10],\n [4, -14, 12, 8],\n [4, 16, 4, -12],\n [10, 34, -6, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, -8, 1],\n [15, -1, 15, -18],\n [-3, -11, -11, 22],\n [1, 9, 7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 6, 22, -25],\n [10, -27, -4, -2],\n [-12, -13, -2, 1],\n [14, -17, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 6, 11, -6],\n [-5, 3, 1, 3],\n [11, -3, 8, -15],\n [-3, 3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 5, -9, -3],\n [7, 2, 2, 4],\n [28, 3, 11, 7],\n [-41, -10, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -8, 4, -2],\n [-6, 8, -4, 2],\n [12, -16, 8, -4],\n [9, -12, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -12, -9, -2],\n [-4, 4, -3, -2],\n [-20, 16, -3, -4],\n [-8, 8, -6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -9, 3, -12],\n [8, 12, -4, 16],\n [2, 3, -1, 4],\n [-8, -12, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 14, -14, -10],\n [0, 10, -8, -8],\n [12, 3, 6, -6],\n [4, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 10, 4, 0],\n [-16, -16, -8, 0],\n [12, -8, -6, 0],\n [-28, -13, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 0, -4, 6],\n [-24, -2, -8, 6],\n [8, 7, -14, -10],\n [0, -1, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 9, 3, 6],\n [-4, -12, -4, -8],\n [4, 12, 4, 8],\n [3, 9, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -1, -1, 2],\n [2, -1, -1, 2],\n [-6, 3, 3, -6],\n [8, -4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -15, -18, 9],\n [2, 1, 3, 3],\n [6, -5, -3, 9],\n [8, -14, -15, 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, 19, -1, 3],\n [22, 7, -9, 21],\n [-4, -24, 5, 7],\n [-4, 6, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 6, 6, 6],\n [-6, -6, -6, -6],\n [-2, -2, -2, -2],\n [-2, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 6, -6, -2],\n [-9, -12, -8, 4],\n [-25, -9, -1, -13],\n [6, 18, 2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -16, -16, 12],\n [3, -12, -12, 9],\n [0, 0, 0, 0],\n [-4, 16, 16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, 4, 16],\n [18, 14, 7, 12],\n [9, 6, 3, 0],\n [-4, -2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -9, -3, 9],\n [-4, 12, 4, -12],\n [-4, 12, 4, -12],\n [-2, 6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, -8, -4],\n [4, -13, -1, 1],\n [0, 0, 0, 0],\n [4, -13, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -2, -12, 7],\n [-6, -16, -16, 8],\n [12, -1, 8, -5],\n [-18, 15, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 2, 10, 0],\n [-3, 1, -9, 1],\n [-9, -17, 13, -7],\n [0, -8, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 5, -1, -11],\n [-12, 2, -10, -20],\n [9, -6, 6, 21],\n [-3, 11, 1, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 2, 15, -16],\n [-10, 8, 11, -10],\n [2, -18, 18, -24],\n [-10, -6, 22, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -4, 1, -4],\n [12, -20, -2, 0],\n [-9, 21, 2, 1],\n [18, -14, -3, 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 4x4 matrix:\n[[4, 4, -12, -12],\n [-2, -2, 6, 6],\n [1, 1, -3, -3],\n [-4, -4, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 18, 20, -6],\n [10, 10, 4, 1],\n [4, -36, 0, -10],\n [5, 5, -14, 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[[9, -3, -3, -15],\n [17, 19, -12, -5],\n [4, 13, -4, 15],\n [5, 4, -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[[3, 14, -3, 1],\n [-2, -22, 6, -10],\n [-1, 2, 0, 9],\n [-3, -13, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -4, 0],\n [-16, 20, -20, -16],\n [-4, -7, 1, -4],\n [12, -15, 15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 0, 2, -8],\n [-18, -6, -10, -8],\n [-18, -3, -6, 0],\n [-12, 1, 0, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [6, -8, 4, -2],\n [14, -4, 12, 10],\n [-2, -12, -4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 11, 13, 4],\n [0, -11, -13, -11],\n [6, 22, 10, -16],\n [-10, -2, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, -16, -3, -4],\n [0, -5, -1, 0],\n [-4, -11, 5, 12],\n [-8, 8, -9, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -9, 12, 12],\n [0, 0, 0, 0],\n [-9, -9, 12, 12],\n [6, 6, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 4, 4, 20],\n [13, 0, 5, 11],\n [12, 4, 9, 0],\n [-5, 7, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 11, 15, 8],\n [-2, -6, -6, -4],\n [-14, 10, 18, 8],\n [13, -13, -21, -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[[3, 2, 4, 2],\n [-12, -8, -16, -8],\n [-9, -6, -12, -6],\n [12, 8, 16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, -15, 12, 11],\n [4, 20, 8, -16],\n [20, 4, -20, -2],\n [-1, 11, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -9, -12, 0],\n [-1, -3, -4, 0],\n [-1, -3, -4, 0],\n [-2, -6, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, -9, -6, 0],\n [-12, 18, 12, -6],\n [2, -12, -8, 8],\n [-29, -3, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, -6, 6],\n [0, 4, 6, -6],\n [3, 3, 2, -3],\n [-6, -2, 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[[21, -10, -8, 5],\n [-5, -6, 6, -7],\n [12, 0, -11, 5],\n [6, 20, 2, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, -8, 9],\n [0, 6, -3, 9],\n [0, -8, 4, -12],\n [0, -2, 4, -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[[20, 10, -19, 8],\n [-8, -6, 8, -2],\n [0, 10, -2, -6],\n [-8, 14, 4, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-9, 6, 6, 9],\n [-6, 4, 4, 6],\n [-9, 6, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, 0, 9],\n [7, -3, 0, 12],\n [16, -4, 0, 21],\n [-9, 1, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -2, 2, 2],\n [-8, 4, -4, -4],\n [12, -6, 6, 6],\n [-16, 8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -6, -8, 6],\n [-4, 3, 4, -3],\n [16, -12, -16, 12],\n [12, -9, -12, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -2, 3, -3],\n [0, 0, 0, 0],\n [2, -2, 3, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, 16, 1, -10],\n [5, 30, -1, 9],\n [8, 16, -9, -12],\n [6, -2, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 9, 3, -9],\n [8, -6, -2, 6],\n [4, -3, -1, 3],\n [4, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 16, -13, 5],\n [-8, -4, -9, -3],\n [4, 0, 8, -16],\n [0, 4, 1, -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[[0, -2, -2, -2],\n [-4, -2, 0, -8],\n [-8, 0, 4, -12],\n [4, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 0, -16, -12],\n [0, 0, 0, 0],\n [-4, 0, 8, 6],\n [2, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -2, 6, -8],\n [-4, -1, 3, -4],\n [-4, -1, 3, -4],\n [4, 1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 17, 5, 5],\n [-3, 5, -14, -3],\n [12, 28, -4, -4],\n [2, -14, 22, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -2, 3, 4],\n [-6, 6, -9, -12],\n [2, -2, 3, 4],\n [-4, 4, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 16, -12, -12],\n [-3, 4, -3, -3],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, -5, 26, -4],\n [-17, 11, -11, -2],\n [11, -4, 15, -12],\n [0, -16, -12, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 0, -16, -2],\n [2, 18, 8, -14],\n [-1, 6, 16, -3],\n [-3, -3, 20, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -3, -12, 0],\n [0, -3, -12, 0],\n [0, -4, -16, 0],\n [0, 3, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 11, 20, 6],\n [1, -1, -9, -18],\n [8, 12, -2, -19],\n [-11, -5, 3, -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 4x4 matrix:\n[[1, 3, -3, -9],\n [3, 1, -1, -9],\n [-4, 0, -5, -11],\n [11, 17, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 9, -16, -21],\n [-3, 3, -12, -2],\n [3, -3, 16, -3],\n [-12, -7, -16, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -12, -9, 3],\n [4, -4, -3, 1],\n [0, 0, 0, 0],\n [8, -8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 4, 16, 0],\n [8, -2, -8, 0],\n [0, 0, 0, 0],\n [8, -2, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 10, 2, -2],\n [0, -15, -3, 3],\n [6, 2, -2, -22],\n [5, -5, -3, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[29, -22, -5, -13],\n [7, -10, 4, 0],\n [10, 12, -33, -25],\n [-15, 10, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 1, 1, 3],\n [-9, -3, -3, -9],\n [-9, -3, -3, -9],\n [6, 2, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 28, -20, 0],\n [7, -8, 2, -13],\n [0, 24, -20, -10],\n [-4, 32, -24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 6, -6, 8],\n [-1, -3, 3, -4],\n [-14, 14, -6, 20],\n [-4, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 0, -8, -4],\n [8, 0, 4, 2],\n [0, 0, 0, 0],\n [-4, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-4, 2, 4, -2],\n [12, -6, -12, 6],\n [-12, 6, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 11, 15, -4],\n [8, 22, 28, 4],\n [0, -12, -14, -6],\n [-10, -11, -15, 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[[-8, 16, 5, -19],\n [-30, 0, -12, 14],\n [12, 0, 3, -9],\n [0, 14, 5, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 2, -6, 4],\n [-1, 1, -3, 2],\n [-2, -4, -6, -2],\n [-4, -5, -12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[21, 19, -24, -4],\n [-21, -21, 21, 3],\n [0, 8, 19, -13],\n [16, 14, -22, 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 4x4 matrix:\n[[-20, -17, -19, 0],\n [-4, -18, 7, 0],\n [13, 20, 10, 0],\n [2, 15, -10, 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[[17, 20, 2, 23],\n [8, 6, 2, 2],\n [7, 6, 4, 4],\n [18, 14, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 13, 12, 8],\n [8, -2, 3, 2],\n [28, -9, 9, 6],\n [8, -10, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 4, -8, 16],\n [-3, -3, 6, -12],\n [2, 2, -4, 8],\n [-2, -2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -4, 3, 0],\n [16, -16, 12, 0],\n [-12, 12, -9, 0],\n [-8, 8, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[33, 0, 27, -15],\n [-7, 16, -3, 19],\n [-11, 6, -9, -1],\n [16, -10, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -4, 1, 3],\n [0, 0, 0, 0],\n [-2, 8, -2, -6],\n [-4, 16, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -12, -8, -4],\n [-11, 10, 6, 6],\n [4, -2, -1, -2],\n [14, -16, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 3, 15, 6],\n [-9, -6, 15, -6],\n [10, 5, 4, -6],\n [5, 4, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -2, 0, 8],\n [-12, 4, 0, -16],\n [-3, 1, 0, -4],\n [-3, 1, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -3, 2, 0],\n [-18, -10, -8, -13],\n [12, -8, 10, -2],\n [2, -29, -14, -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[[-2, 9, 8, 8],\n [-2, 8, 4, 20],\n [-13, -2, -5, 1],\n [15, -15, -15, 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 4x4 matrix:\n[[2, 0, 3, -3],\n [6, 0, 9, -9],\n [-4, 0, -6, 6],\n [-8, 0, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 4, 4, 4],\n [0, 0, 0, 0],\n [-6, -8, -8, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -8, -4, 4],\n [-4, 2, 1, -1],\n [16, -8, -4, 4],\n [8, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, 16, -6, -2],\n [20, -17, -5, 5],\n [6, -5, 11, 0],\n [2, -6, -10, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 5, 8, -7],\n [0, -4, -4, 4],\n [0, -6, -6, 6],\n [5, -3, -18, 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[[14, -3, -3, -8],\n [8, 0, -3, -11],\n [0, 3, -1, -5],\n [4, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, 1, 7, -6],\n [-20, -2, 14, 10],\n [-2, 17, -4, -16],\n [20, -20, -8, 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 4x4 matrix:\n[[16, 12, 4, 8],\n [-4, -3, -1, -2],\n [-4, -3, -1, -2],\n [12, 9, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -3, -12, -12],\n [-6, -3, -12, -12],\n [-8, -4, -16, -16],\n [-4, -2, -8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 12, 8, -12],\n [-24, 10, 17, -17],\n [-4, -6, 5, -1],\n [4, 10, -9, 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 4x4 matrix:\n[[26, -17, 3, 12],\n [17, -8, 7, 3],\n [24, -12, 2, 14],\n [0, -6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 2, -3, 7],\n [18, -18, 12, 2],\n [12, -4, 0, 12],\n [6, 4, -6, 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 4x4 matrix:\n[[4, 0, 6, 8],\n [-2, 0, -3, -4],\n [-8, 0, -12, -16],\n [8, 0, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-3, 0, -3, -3],\n [-6, 0, -6, -6],\n [3, 0, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -8, 20, 0],\n [7, -37, 4, 22],\n [15, -21, 12, 6],\n [4, 21, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 8, -6, -6],\n [-3, -4, 3, 3],\n [6, 8, -6, -6],\n [12, 16, -12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 2, 13, -4],\n [-21, -12, -6, 24],\n [7, 8, -8, -12],\n [-9, -10, -3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 16, -12, -4],\n [-2, -4, 3, 1],\n [-2, -4, 3, 1],\n [-4, -8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 9, 0, -12],\n [-25, -9, 0, 16],\n [-6, -11, 0, 12],\n [-21, -6, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 8, 6, -16],\n [-22, 22, -12, -8],\n [-4, 16, 12, -32],\n [-19, 21, -5, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 3, 2, -3],\n [17, -3, -10, 9],\n [-18, 4, 4, -5],\n [-7, 3, -10, 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 4x4 matrix:\n[[-11, 8, 0, -12],\n [-2, 2, -3, 0],\n [-1, -2, 15, -12],\n [-4, 8, -28, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 1, -10, -8],\n [15, 13, 12, 13],\n [-8, 0, 15, 19],\n [-12, -16, -13, -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 4x4 matrix:\n[[-8, -4, 0, 0],\n [22, 14, -6, 9],\n [20, 12, -4, 6],\n [22, 14, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 12, 28, -11],\n [6, 16, 24, -8],\n [2, 4, 8, -3],\n [-1, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -4, -12, -8],\n [6, 2, 6, 4],\n [-12, -4, -12, -8],\n [12, 4, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -4, 5, -1],\n [15, -12, 15, -3],\n [14, -10, 14, -4],\n [-8, 0, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -12, 6, 4],\n [22, -29, -7, 7],\n [14, -4, -18, -12],\n [-9, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -3, -3, -12],\n [9, -3, -3, -12],\n [3, -1, -1, -4],\n [-6, 2, 2, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 12, -12, 12],\n [-6, -3, -6, 0],\n [9, -8, 14, -10],\n [3, -6, 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[[-2, -1, -3, -1],\n [4, 2, 6, 2],\n [2, 1, 3, 1],\n [6, 3, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 9, 8, -10],\n [6, 15, 16, 2],\n [14, 6, 8, -4],\n [-1, 9, 10, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -3, -2, 1],\n [21, 21, -1, -1],\n [9, 18, -8, 4],\n [-9, 7, -7, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 0, -6, 3],\n [-3, 12, 2, -13],\n [1, 0, 2, -1],\n [4, -12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -9, 3, -6],\n [1, -3, 1, -2],\n [-4, 12, -4, 8],\n [-1, 3, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 6, 3, -4],\n [-2, -3, 0, 0],\n [-12, 12, 15, -20],\n [2, 3, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, 1, 2],\n [-8, 8, -2, -4],\n [22, -4, 4, -1],\n [-16, -8, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -5, -11, 1],\n [20, 7, 16, -2],\n [-4, -2, -2, -2],\n [20, 7, 16, -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 4x4 matrix:\n[[-3, -2, -6, 4],\n [-9, 27, -1, 5],\n [0, -18, 3, -6],\n [-9, -9, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -3, 2, -5],\n [12, 6, -10, -3],\n [9, 3, -7, -5],\n [-12, -16, 17, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -8, 12, -14],\n [-11, -12, 3, -6],\n [6, 8, 6, -4],\n [19, 20, -9, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 9, -6, -3],\n [-12, -12, 8, 4],\n [9, 9, -6, -3],\n [12, 12, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 1, 7, 6],\n [-12, -4, -12, -8],\n [20, 4, -20, -24],\n [-7, -2, -2, 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[[7, 6, 3, 10],\n [-8, -18, -10, -18],\n [5, 15, 16, 21],\n [-18, -14, -4, -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[[8, 3, 1, -4],\n [10, 6, -5, 10],\n [-13, 2, 1, -9],\n [-12, -9, 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[[3, 4, 2, -4],\n [-12, 0, -8, 16],\n [-21, 12, -14, 28],\n [6, 4, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 12, 0, -16],\n [12, 12, 0, -16],\n [-6, -6, 0, 8],\n [6, 6, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 3, 6, 3],\n [2, -1, -2, -1],\n [2, -1, -2, -1],\n [4, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -4, -8, 18],\n [8, -4, -8, 12],\n [2, 0, 0, 3],\n [0, 4, 8, 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 4x4 matrix:\n[[18, -4, 4, -9],\n [-8, 4, 16, 24],\n [-6, 0, -12, -9],\n [-4, 2, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -5, 5, 3],\n [-13, 5, -12, -8],\n [14, -1, 15, 9],\n [12, 7, 14, 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 4x4 matrix:\n[[-12, 4, 12, 4],\n [-9, 3, 9, 3],\n [9, -3, -9, -3],\n [-3, 1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 8, 15, -16],\n [0, 8, 18, -18],\n [-24, -6, -3, 5],\n [-3, 22, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -4, 12, 24],\n [20, -8, -6, 8],\n [18, -34, 2, -4],\n [-2, 10, 0, 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[[-6, 3, 6, 6],\n [4, -2, -4, -4],\n [2, -1, -2, -2],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[29, -5, 19, -1],\n [-7, -5, -7, 3],\n [5, -17, -4, 7],\n [-5, -10, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 4, -2, 0],\n [-1, 2, -1, 0],\n [0, 0, 0, 0],\n [-2, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 5, -8, -5],\n [10, -1, 10, 4],\n [-7, -11, -16, -1],\n [4, -3, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-36, 8, -5, -11],\n [16, -21, -3, 19],\n [16, -13, -6, 14],\n [14, 4, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 9, 6, -12],\n [-2, 18, 2, -16],\n [7, -7, -3, 8],\n [9, -11, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 12, -8, 16],\n [-4, -12, 8, -16],\n [1, 3, -2, 4],\n [2, 6, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 8, -5, -2],\n [-11, 6, 5, 16],\n [9, -10, 1, -8],\n [-24, -26, 10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, -12, 3],\n [8, -4, 12, 12],\n [-6, 3, -1, -11],\n [14, -7, 9, 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 4x4 matrix:\n[[8, -2, -8, -8],\n [12, -3, -12, -12],\n [0, 0, 0, 0],\n [4, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 4, 2, 2],\n [2, 16, 2, 8],\n [9, -12, -12, -6],\n [3, 12, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -16, -2, 17],\n [-21, -12, 21, 3],\n [7, 26, 2, -30],\n [9, 24, 3, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 10, -4, -4],\n [3, 20, -32, 22],\n [21, -8, 8, 2],\n [-8, 14, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 5, -8, 4],\n [-2, 14, -6, -6],\n [7, -13, -1, 11],\n [-5, -1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 0, 2, 8],\n [0, 0, 0, 0],\n [-8, 0, 2, 8],\n [-4, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -16, -10, 0],\n [-13, 11, 7, -1],\n [-20, 16, 10, 0],\n [-20, 16, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -12, 18, -3],\n [-10, 6, 11, 6],\n [-14, -4, -12, 6],\n [-17, -3, -23, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -6, -8, -4],\n [-7, -14, -18, -5],\n [-12, -8, -8, 12],\n [9, 13, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -4, -8, -4],\n [0, -16, -22, -12],\n [0, 6, 12, 6],\n [0, -4, -13, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 0, 2, 3],\n [3, 0, -6, -9],\n [2, 0, -4, -6],\n [-4, 0, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 9, -9, 0],\n [-9, -9, 10, 0],\n [-6, -6, 0, 0],\n [-3, -3, 4, 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[[-3, 2, 1, 4],\n [-6, 4, 2, 8],\n [4, 0, 4, -16],\n [12, -8, -4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, -4, 4],\n [-16, -16, 8, -8],\n [-8, -8, 4, -4],\n [8, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 6, 0, -2],\n [2, 9, 8, -15],\n [-14, 12, -6, 5],\n [0, 3, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -10, 6, 4],\n [10, -10, 22, -12],\n [8, 16, -10, -6],\n [11, 10, 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[[6, 6, 0, -6],\n [-2, -9, 1, 6],\n [-14, 0, -2, 6],\n [-4, 3, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 7, -5, -12],\n [12, -10, -16, 12],\n [-12, 2, 14, 0],\n [-12, 10, 16, -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 4x4 matrix:\n[[1, -4, 1, -4],\n [4, -16, 4, -16],\n [1, -4, 1, -4],\n [1, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 0, 0, -5],\n [-20, -8, 16, 6],\n [13, 5, -10, -5],\n [-8, -2, 4, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 12, 12, 12],\n [3, -4, -4, -4],\n [3, -4, -4, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -14, -25, -13],\n [5, 14, 25, 13],\n [-6, 12, 2, 14],\n [-8, -8, -24, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 6, 6, 8],\n [-4, 12, 12, 16],\n [-1, 3, 3, 4],\n [4, -12, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -12, 12, -4],\n [4, 6, -6, 2],\n [6, 9, -9, 3],\n [8, 12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 4, 16, -16],\n [16, -4, -16, 16],\n [8, -2, -8, 8],\n [4, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -4, -8, 4],\n [0, 0, 0, 0],\n [-9, 6, 12, -6],\n [3, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 0, 6, -3],\n [0, -12, -6, 3],\n [8, -8, -2, 1],\n [-4, -10, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 0, 0, -1],\n [6, 0, 0, -2],\n [3, 0, 0, -1],\n [9, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, -14, -10, -8],\n [-24, 23, 1, 10],\n [-21, 5, 1, -2],\n [-16, -2, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 8, 2, -2],\n [-16, 16, 4, -4],\n [-16, 16, 4, -4],\n [-16, 16, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-1, 3, 2, 1],\n [-3, 9, 6, 3],\n [2, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -8, 0, -4],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 0, -6, -9],\n [0, 0, 0, 0],\n [-4, 0, 8, 12],\n [1, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 0, 5, -9],\n [-2, -2, -4, 12],\n [-1, 3, -4, 0],\n [-2, 4, -7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, 5, -13, -20],\n [-12, 23, -15, -8],\n [-15, -6, -4, -14],\n [17, -13, 10, 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[[2, 6, 6, -8],\n [-1, -3, -3, 4],\n [1, 3, 3, -4],\n [4, 12, 12, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -9, 3, 12],\n [-13, -19, -15, 4],\n [10, 15, 11, -4],\n [-8, -9, -13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -3, 4, 8],\n [-4, 14, 7, 12],\n [17, 4, 4, -5],\n [-4, -9, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 1, -2, -4],\n [-3, 3, -6, -12],\n [-3, 3, -6, -12],\n [-3, 3, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, -2, -12],\n [-14, 10, -10, -4],\n [-8, 4, -4, -12],\n [17, -9, 9, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, 3, 1],\n [12, -6, -9, -3],\n [-4, 2, 3, 1],\n [-4, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -9, -9, -6],\n [0, -12, -12, -8],\n [0, 12, 12, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -6, 6, -3],\n [0, -2, 2, -1],\n [0, 4, -4, 2],\n [0, -2, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -2, -5, -3],\n [-9, 12, 3, 9],\n [-10, 15, 6, 12],\n [8, -14, -8, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -8, 16, 4],\n [-9, -6, 12, 3],\n [-6, -4, 8, 2],\n [-6, -4, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 10, 10, 20],\n [1, -4, 9, 7],\n [8, 0, -19, -10],\n [3, 0, -21, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 0, -18, 11],\n [-10, -4, -14, 12],\n [-14, 14, -10, -4],\n [1, -3, 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[[9, 15, 8, 0],\n [-18, -24, -14, 9],\n [13, 17, 10, -7],\n [-1, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -6, -12, -12],\n [6, -4, -8, -8],\n [-6, 4, 8, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 16, 17, -19],\n [4, 11, 6, -10],\n [8, 1, -3, 1],\n [4, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -8, 28, -4],\n [-2, 4, -4, -4],\n [-12, 15, 0, -24],\n [-4, -4, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -12, -5, 2],\n [-6, 18, -3, 3],\n [-28, 4, 11, -6],\n [12, 0, -7, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 12, 4, 4],\n [3, 3, 1, 1],\n [-3, -3, -1, -1],\n [-9, -9, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 12, 1, 0],\n [0, 4, 0, -1],\n [-2, 8, -2, -8],\n [4, -32, 4, 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, -8, 4, 8],\n [12, -12, 6, 12],\n [8, -8, 4, 8],\n [-8, 8, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -1, -3, 3],\n [12, -3, -9, 9],\n [-12, 3, 9, -9],\n [12, -3, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -12, 12, -16],\n [2, 6, -9, 19],\n [10, 12, -9, 5],\n [-4, -6, 6, -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 4x4 matrix:\n[[-6, 15, -6, -3],\n [-2, -1, 2, -7],\n [1, -10, 6, -7],\n [5, -14, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 16, 18, -8],\n [-4, -13, -7, 2],\n [16, -15, 13, -6],\n [16, 20, 20, 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[[-2, -4, -8, 7],\n [20, -32, 8, -4],\n [11, -20, 2, 0],\n [-8, 20, 4, -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[[3, 0, 9, 9],\n [-1, -4, -3, -6],\n [0, 0, 0, 0],\n [4, 0, 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[[6, 8, 8, -8],\n [12, 16, 16, -16],\n [0, 0, 0, 0],\n [6, 8, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 2, -8, -10],\n [3, -8, 0, 10],\n [-4, 14, -5, -5],\n [5, -4, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -7, -3, -1],\n [2, -3, -2, -4],\n [10, -10, 4, 12],\n [-4, 1, -1, -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 4x4 matrix:\n[[-20, 24, 8, 28],\n [20, -24, -8, -28],\n [-7, 10, 6, 5],\n [-5, 6, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 4, 5, -8],\n [8, 0, -6, 0],\n [12, 2, -11, -4],\n [-8, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -20, -3, 27],\n [2, 0, -12, 8],\n [1, 0, -6, 4],\n [2, 3, -17, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 16, 2, -8],\n [8, -10, -8, -4],\n [-8, 4, 8, 8],\n [8, 2, -8, -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 4x4 matrix:\n[[2, 0, -1, 1],\n [-6, 16, 2, -3],\n [-5, -4, -3, 9],\n [5, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -8, 28, -8],\n [0, 0, 0, 0],\n [-3, -3, 12, 3],\n [2, -6, 22, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -2, -4, 6],\n [10, 4, -6, 9],\n [26, -15, 22, 23],\n [10, -3, 6, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -2, 2, -4],\n [8, -4, 4, -8],\n [4, -2, 2, -4],\n [-6, 3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 8, -11, 18],\n [5, -6, 11, -15],\n [-17, -15, 10, 4],\n [12, 9, -15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 8, 11, -4],\n [-9, 2, -7, -4],\n [-7, 11, -6, -12],\n [-11, 10, -9, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 11, -10, -3],\n [-9, -8, -1, 1],\n [12, -11, 10, 3],\n [-3, -16, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, -3, 4, 0],\n [0, 3, -4, 0],\n [0, 12, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 9, -3, 3],\n [6, -6, 2, -2],\n [3, -3, 1, -1],\n [3, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, -12, -9, 3],\n [-4, -8, -6, 2],\n [6, 12, 9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -17, 6, 6],\n [-3, 15, -6, 0],\n [-3, 15, 2, -8],\n [2, -9, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, 1, -2],\n [0, 4, -5, -8],\n [0, 12, -10, -4],\n [0, 0, -2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -4, 21, -40],\n [23, 2, 1, 12],\n [24, 6, -2, 6],\n [8, 8, -22, 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[[-3, 6, 9, -9],\n [-4, 8, 12, -12],\n [2, -4, -6, 6],\n [-3, 6, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 12, 17, -14],\n [1, 3, 0, -12],\n [3, 9, 9, -18],\n [1, 3, 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[[-2, 11, -2, 2],\n [-4, 8, -4, -2],\n [-14, 0, -14, -19],\n [2, 10, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 1, 12, -4],\n [3, 3, 14, -7],\n [-3, -3, 4, 7],\n [6, -6, -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[[3, 18, 9, 3],\n [20, 8, 4, -4],\n [-4, 4, 2, 2],\n [-18, -10, -5, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [-4, 4, 4, 4],\n [-12, 12, 12, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 11, 3, -7],\n [9, 13, 3, -5],\n [-11, -12, -2, 0],\n [-6, 3, 3, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 6, -1, 11],\n [-15, -6, 0, -11],\n [-1, 6, -1, 10],\n [28, 0, -5, 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[[-3, -18, -3, 9],\n [-1, -18, 1, -1],\n [-7, -2, -3, 13],\n [10, 4, 4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 4, -12, 12],\n [12, 3, -9, 9],\n [8, 2, -6, 6],\n [-4, -1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, 11, 8, 18],\n [-12, -20, -20, -24],\n [11, -5, -10, 2],\n [9, 1, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 4, 2, 8],\n [0, -6, 3, -24],\n [-3, 3, -2, 16],\n [16, -8, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-29, 4, 7, -20],\n [7, -24, 17, 11],\n [-7, 8, 0, -10],\n [-12, -8, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, -1, 0, -2],\n [0, 4, 0, 8],\n [0, -4, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 0, 3, 0],\n [11, 17, 4, 36],\n [-8, -2, -4, -14],\n [-16, 4, -4, 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[[-21, -3, -20, -10],\n [-15, 15, -4, 16],\n [-6, 0, -4, -2],\n [24, -17, 10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -4, -3, 3],\n [-16, 16, 12, -12],\n [-8, 8, 6, -6],\n [-12, 12, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 8, 0, -2],\n [-6, -7, 10, -7],\n [4, 2, -12, 10],\n [8, 11, -10, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 1, 3, -3],\n [-6, -3, -9, 9],\n [20, 10, -2, -6],\n [4, 2, -18, 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 4x4 matrix:\n[[-16, -7, 8, -4],\n [7, -10, -12, 7],\n [-10, -3, 2, -5],\n [19, -2, -20, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 4, 16, 8],\n [12, -4, -16, -8],\n [6, -2, -8, -4],\n [3, -1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 8, -14, 4],\n [14, -8, 14, -4],\n [9, 6, -3, -6],\n [2, 10, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [6, 9, -9, 9],\n [-8, -12, 12, -12],\n [8, 12, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 0, 16, 12],\n [2, 8, -4, -1],\n [0, 0, 0, 0],\n [16, 4, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -4, -4, 8],\n [5, -5, 15, -6],\n [2, 9, -16, 2],\n [-10, 0, -10, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -12, 20, -8],\n [-16, 4, -12, 4],\n [12, 15, -13, 7],\n [8, -20, 28, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -9, -3, 3],\n [-6, -9, -3, 3],\n [2, 3, 1, -1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-8, -4, 4, 6],\n [12, 6, -6, -9],\n [12, 6, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -2, 1, -1],\n [0, 0, 0, 0],\n [1, -2, 1, -1],\n [-2, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 7, -7, 5],\n [-1, 2, -2, 1],\n [-1, 1, -1, 2],\n [-4, 6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -6, 5, 14],\n [6, -4, 10, -4],\n [-9, -4, -5, -7],\n [-6, -6, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 5, -3, 8],\n [6, -3, 3, -5],\n [6, -3, 3, -5],\n [-2, -7, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 9, -12, 12],\n [2, 6, -8, 8],\n [3, 9, -12, 12],\n [2, 6, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, 0, -20, -14],\n [-10, -11, -6, -7],\n [0, -23, 10, 1],\n [0, -19, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -1, 7, 12],\n [-18, -3, -3, 8],\n [4, 2, -2, -15],\n [2, 1, 5, -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[[-9, 8, -13, 3],\n [5, -23, 20, -18],\n [-3, 25, -16, 20],\n [2, -6, -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 4x4 matrix:\n[[10, 19, -9, -3],\n [-6, 11, -17, -27],\n [8, 0, 14, 12],\n [14, 13, 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[[-9, -10, 1, -1],\n [6, -2, -10, 4],\n [-4, 10, 16, -6],\n [2, 8, 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[[1, 2, -3, 3],\n [0, 0, 0, 0],\n [3, 6, -9, 9],\n [-3, -6, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, -3, 3, 15],\n [-8, 12, 7, -8],\n [7, 12, 16, 16],\n [-10, 6, 0, -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 4x4 matrix:\n[[-12, 16, -8, -4],\n [9, -12, 6, 3],\n [6, -8, 4, 2],\n [3, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, 2, -10],\n [-12, -4, 2, -6],\n [4, 8, -14, 2],\n [-6, -8, 9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 2, -9, -4],\n [8, -2, 9, 4],\n [8, 0, 6, 4],\n [4, 2, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -4, 2, 1],\n [0, 0, 0, 0],\n [-4, -8, 4, 2],\n [8, 16, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -4, -8, 16],\n [12, -8, 24, 12],\n [-8, -8, 4, 22],\n [-12, -8, 0, 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 4x4 matrix:\n[[6, -7, -1, -5],\n [1, -6, 0, -7],\n [14, -20, -17, 11],\n [-3, 1, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, 0, 4, 24],\n [-6, -4, -1, -8],\n [9, 20, 2, 22],\n [-2, 8, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 9, -3, -12],\n [-6, -9, 12, 3],\n [-3, -3, 7, -2],\n [-2, -9, 0, 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[[-3, -27, 25, -13],\n [5, 5, 17, -17],\n [-8, -2, 9, -12],\n [0, 6, -25, 22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -6, 0, 4],\n [8, -12, 0, 8],\n [2, -3, 0, 2],\n [8, -12, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 4, 12, 12],\n [-16, 4, 12, 12],\n [-12, 3, 9, 9],\n [-4, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -10, -24, -26],\n [-9, 6, -7, -21],\n [-15, 12, 6, -18],\n [-2, -14, -20, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -4, 1, 4],\n [-2, -16, 10, -4],\n [-2, -2, 2, -3],\n [4, -24, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -2, -14, -3],\n [3, -6, -7, -2],\n [1, 2, -1, 0],\n [-12, 0, 20, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, -4, -6, 6],\n [0, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 8, 5, -11],\n [8, 16, 4, -4],\n [10, 20, 7, -11],\n [-14, -28, -10, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -2, -1, 2],\n [3, 2, 1, -2],\n [-9, 2, 1, -2],\n [13, -2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, 6, -4],\n [-2, 0, -3, 2],\n [-2, 0, -3, 2],\n [8, 0, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 14, -2, 7],\n [0, 4, 0, 3],\n [-3, 14, -2, 7],\n [-3, 18, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 9, 9, -9],\n [-12, -9, -9, 9],\n [-12, -9, -9, 9],\n [8, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-8, 16, -4, -8],\n [6, -12, -9, 12],\n [-12, 24, 10, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, 0, -8],\n [10, -2, 12, -10],\n [15, -4, 14, -5],\n [-4, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -6, 0, 0],\n [4, 2, -4, -4],\n [8, 0, -8, -8],\n [-16, -8, 16, 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[[-14, -12, 8, 2],\n [-4, -12, -2, -2],\n [-12, 4, 14, 6],\n [16, 8, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, 2, 2],\n [4, -4, 1, 1],\n [-4, 4, -1, -1],\n [16, -16, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 3, 9, -9],\n [-8, 8, 8, 6],\n [0, 0, 12, -17],\n [-8, 6, 2, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[30, -4, -6, 29],\n [-4, -13, -7, -2],\n [31, -9, -8, 28],\n [3, 13, 6, 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[[19, 5, 8, -2],\n [7, 14, 17, -17],\n [-7, 3, 12, -14],\n [13, -5, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 20, -12, 24],\n [0, 3, -19, -5],\n [7, -8, 0, -12],\n [6, -9, 17, -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[[16, 14, -19, 21],\n [5, 4, 1, 9],\n [-18, -18, 19, -31],\n [7, 8, -9, 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[[0, 0, 0, 0],\n [4, 4, 16, -4],\n [-3, -3, -12, 3],\n [-4, -4, -16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, -8, 8],\n [0, 0, 0, 0],\n [-12, 0, 8, -8],\n [6, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 10, 12, -4],\n [-3, 6, 11, -2],\n [18, -20, 14, 12],\n [-12, 14, -6, -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 4x4 matrix:\n[[10, -15, -3, 3],\n [-11, 18, 7, -12],\n [-8, -6, -10, 6],\n [-9, 12, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 3, -6, 0],\n [-6, 2, -8, 2],\n [12, 4, 8, -8],\n [9, -3, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -9, -9, 22],\n [-7, -8, -12, -3],\n [-6, -1, -9, 16],\n [-4, -2, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-17, -1, 2, 3],\n [-6, -14, 1, 11],\n [6, 0, -16, 2],\n [-20, -4, 22, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 9, -9, -9],\n [-16, 12, -12, -12],\n [4, -3, 3, 3],\n [16, -12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 17, -4, -5],\n [-1, -6, 6, 1],\n [4, -4, 8, 0],\n [-11, -10, 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[[16, 16, 0, -8],\n [-16, -16, 0, 8],\n [-12, -12, 0, 6],\n [8, 8, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -2, -6, -6],\n [6, 2, 6, 6],\n [-3, -1, -3, -3],\n [9, 3, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 13, 14, 6],\n [-5, 1, 14, 22],\n [11, -12, 10, 18],\n [-1, 2, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 12, 12, -9],\n [0, 12, 12, -9],\n [0, 12, 12, -9],\n [0, 12, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -6, 14, -6],\n [21, 2, 4, -13],\n [13, 1, 11, 0],\n [-5, -2, 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[[0, 3, 2, -1],\n [0, 0, 0, 0],\n [0, -3, -2, 1],\n [0, 12, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 9, -12, -5],\n [-3, 7, 0, -7],\n [0, -16, 12, 12],\n [-6, 14, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -10, 12, -2],\n [-4, -10, 4, 6],\n [8, 8, -8, 0],\n [-8, -8, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 4, 4, -2],\n [12, 16, 16, -8],\n [-3, -4, -4, 2],\n [12, 16, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 16, 8, 8],\n [-12, -8, 16, -4],\n [-6, -16, 12, -8],\n [6, 4, -8, 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 4x4 matrix:\n[[9, -3, 9, 3],\n [0, 0, 0, 0],\n [-12, 4, -12, -4],\n [3, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 14, 6, 7],\n [-16, 9, 1, -3],\n [-4, -8, -1, 4],\n [-20, 12, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 3, 9, 0],\n [-9, 12, 6, -12],\n [-12, 7, 11, -4],\n [6, -17, -1, 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[[-9, 15, -9, 12],\n [10, -8, 20, -4],\n [-3, 16, 12, 15],\n [-6, 3, -21, 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[[10, 2, -4, -6],\n [-7, -9, 4, 9],\n [-15, -3, 6, 9],\n [14, -20, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 6, 11, -12],\n [2, -8, 3, 7],\n [10, 4, 13, -20],\n [0, -1, 1, -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, 3, 2, -1],\n [12, -9, -6, 3],\n [-4, 3, 2, -1],\n [-16, 12, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, -16, -16],\n [0, -6, 12, 12],\n [0, -8, 16, 16],\n [0, -8, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -9, 0, -9],\n [-12, -12, 0, -12],\n [-12, -12, 0, -12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 7, 8, 12],\n [2, 12, 10, 18],\n [-9, 5, -8, -8],\n [-6, -5, -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[[-2, -14, -8, 18],\n [0, 6, 24, 2],\n [13, 13, 4, 0],\n [8, 9, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -6, 10, -10],\n [4, 5, -9, 9],\n [12, 7, -11, 11],\n [-8, -6, 10, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, -12, 3],\n [-12, 0, -12, 3],\n [-4, 0, -4, 1],\n [12, 0, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-4, 3, -2, 4],\n [8, -6, 4, -8],\n [-8, 6, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -9, -6, -3],\n [12, -9, -6, -3],\n [-8, 6, 4, 2],\n [-12, 9, 6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -1, -4, 0],\n [0, 1, 4, 0],\n [0, 2, 8, 0],\n [0, -4, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 0, 0, 6],\n [-6, 0, 0, -9],\n [4, 0, 0, 6],\n [-2, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 10, -3, 5],\n [-25, -31, 3, 10],\n [-22, -22, 4, 2],\n [2, -6, -4, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 6, -17, -2],\n [15, 9, -3, -18],\n [18, 9, 0, -20],\n [10, 6, -2, -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[[9, -10, 13, -14],\n [2, -12, 14, -12],\n [-8, -18, 19, -12],\n [14, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 4, 0, -12],\n [6, -2, -18, 12],\n [-1, -3, 3, 8],\n [-3, 1, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[22, -2, 14, -1],\n [-14, -9, 3, 8],\n [-35, 5, -24, 2],\n [-10, -5, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [8, 2, 8, -2],\n [-16, -4, -16, 4],\n [16, 4, 16, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -14, -1, 11],\n [11, 2, 3, 16],\n [12, 12, -2, -3],\n [-13, 2, 3, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, 2, -2],\n [1, -1, 1, -1],\n [-4, 4, -4, 4],\n [-2, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -3, -5, 6],\n [-7, -8, 8, -15],\n [-4, 27, -6, 11],\n [-10, -4, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 2, -5, -1],\n [-2, 1, -5, -2],\n [10, 3, 21, -18],\n [14, 4, 20, 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[[10, 11, -1, -4],\n [1, -4, 5, -14],\n [-2, -1, -1, 4],\n [0, -6, 6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -9, -6, -5],\n [-6, 6, -10, -6],\n [-6, 15, 2, 3],\n [-6, 15, 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[[2, -6, 5, -4],\n [3, 9, 3, -15],\n [1, 15, -2, -11],\n [4, 0, 7, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 1, 3, 3],\n [-32, 4, 4, -4],\n [0, -9, -3, 15],\n [-2, 10, 2, -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[[2, -1, 3, -1],\n [6, -3, 9, -3],\n [-2, 1, -3, 1],\n [-8, 4, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 10, 2, -2],\n [8, 4, 12, 16],\n [-8, 10, 2, -2],\n [-8, 12, 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[[22, 0, -4, 22],\n [12, -2, 0, 12],\n [4, 3, -4, 4],\n [6, 21, -24, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 8, 0, -6],\n [4, -8, 0, 6],\n [8, -16, 0, 12],\n [4, -8, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -3, 1, 3],\n [-1, -3, 1, 3],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, 8, -1],\n [23, 9, -27, 5],\n [-6, 2, 6, -5],\n [-19, -5, 23, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, 21, 19],\n [-6, 11, -25, -12],\n [-6, 7, 1, 6],\n [8, 4, -10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -10, -3, -13],\n [-6, -9, -3, -9],\n [3, 6, 3, -3],\n [0, 3, 3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, -6, -20],\n [8, -4, 3, -5],\n [-4, 2, -3, -1],\n [2, -1, -9, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 24, -12, 37],\n [-3, 6, -4, 9],\n [-2, -8, -2, -8],\n [3, 12, 6, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 5, 5, 3],\n [4, 7, 7, 3],\n [32, -4, -4, 0],\n [4, -7, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 5, -7, 0],\n [-22, 2, -4, -6],\n [-25, -1, 0, -7],\n [4, -20, 28, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 9, 0, 6],\n [-12, -9, 0, -6],\n [-12, -9, 0, -6],\n [16, 12, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -12, -4, 16],\n [-12, 0, -9, -12],\n [4, -6, -8, 0],\n [2, 9, 18, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 11, 17, 0],\n [-6, -1, -4, -3],\n [2, -16, -4, 10],\n [-26, -7, -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[[-8, 20, -14, -14],\n [2, 0, 1, 1],\n [2, -6, 4, 4],\n [-5, 13, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, -10, 1, 7],\n [20, 16, -2, -8],\n [16, 12, -1, -10],\n [-7, -6, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -7, 4, 6],\n [-8, 5, 12, 5],\n [-2, 5, -12, -10],\n [4, -6, 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, -11, 32, -25],\n [-8, 3, -20, 9],\n [-26, 5, -29, 19],\n [18, 3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 24, 18, -10],\n [8, 24, 12, -2],\n [-8, 0, 12, -16],\n [8, 16, 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[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [4, -3, -2, 2],\n [-12, 9, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -8, -12, -6],\n [-16, -8, 12, 14],\n [7, 13, 9, 1],\n [15, 13, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -4, -8, 6],\n [2, 2, 12, -7],\n [-2, -4, -20, 12],\n [-4, -2, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -6, 4, 4],\n [-12, -12, 8, 8],\n [9, 9, -6, -6],\n [3, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 9, -9, -6],\n [-16, 12, -12, -8],\n [16, -12, 12, 8],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 6, -1, 1],\n [13, 4, 1, 3],\n [-3, -14, 9, 3],\n [28, 14, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 4, 8, -4],\n [-17, 10, 15, -3],\n [4, 16, 8, -4],\n [-8, 14, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 9, 9, 9],\n [1, 3, 3, 3],\n [0, 0, 0, 0],\n [-1, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, -4, 6, -4],\n [-10, 0, 4, -2],\n [4, 8, -4, -4],\n [15, -20, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 5, 5, -3],\n [8, -8, -2, 0],\n [-10, 14, -4, 6],\n [-25, 19, 16, -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 4x4 matrix:\n[[20, 9, -4, -12],\n [0, 11, -4, 8],\n [-20, 3, -2, 24],\n [-14, -22, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -16, 12, -8],\n [4, 4, -3, 2],\n [0, 0, 0, 0],\n [16, 16, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 2, 19, 3],\n [-12, -3, 1, -9],\n [2, -2, -8, 6],\n [-8, -11, -24, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 4, 21, -1],\n [6, 5, 29, -2],\n [-6, -3, 9, -6],\n [3, 5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 6, 2, 3],\n [3, 4, 0, -1],\n [-12, -11, 1, 5],\n [12, 6, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, 6, 12, -8],\n [2, 0, -12, 14],\n [4, 16, -8, 10],\n [4, 4, -8, 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[[-16, -12, 0, -12],\n [0, -7, 2, 1],\n [-6, -15, 3, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [16, -8, 4, -12],\n [0, -2, 4, 6],\n [-12, 3, 3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 3, 0, -6],\n [12, -3, 0, 6],\n [-16, 4, 0, -8],\n [-16, 4, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 4, 8, -8],\n [12, 3, 6, -6],\n [0, 0, 0, 0],\n [-4, -1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 3, 0, 0],\n [-8, -2, 0, 0],\n [0, 0, 0, 0],\n [-8, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 12, 16, -4],\n [-4, 3, 4, -1],\n [4, -3, -4, 1],\n [16, -12, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 4, 4, -6],\n [-1, 2, 2, -3],\n [-3, 6, 6, -9],\n [-4, 8, 8, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 19, 14, 8],\n [-3, -5, -3, -4],\n [-2, 7, 8, 16],\n [-12, -17, -10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 1, 2, 3],\n [-3, -3, 0, 6],\n [5, 1, 2, 6],\n [5, -1, -1, -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 4x4 matrix:\n[[-8, 3, 3, 9],\n [-8, -6, -12, -3],\n [16, 0, 24, 20],\n [-8, -9, -15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -8, 6, 2],\n [-6, -8, 6, 2],\n [-3, -4, 3, 1],\n [-6, -8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, 8, -6],\n [-3, 9, -3, -12],\n [0, -4, -2, 11],\n [-4, 4, -8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -8, -16, -8],\n [4, 2, 4, 2],\n [16, 8, 16, 8],\n [-4, -2, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 3, 11, -11],\n [-2, 0, 5, -8],\n [-6, 14, -2, -12],\n [-6, 4, -11, 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[[-10, 6, -10, -1],\n [-2, 4, 12, 18],\n [4, -4, 6, 15],\n [-6, 8, -4, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, 19, 4, -9],\n [16, 6, 3, -15],\n [-14, -19, -4, 9],\n [8, 28, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -6, -8, -5],\n [15, -16, -5, -10],\n [11, 16, -13, -30],\n [-10, 22, 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 4x4 matrix:\n[[0, 8, -16, -12],\n [0, 0, 0, 0],\n [0, 6, -12, -9],\n [0, -6, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -8, 4, -28],\n [8, -2, -11, 8],\n [17, -8, -24, 7],\n [0, 6, 19, 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 4x4 matrix:\n[[-12, 12, 8, 0],\n [3, -3, -2, 0],\n [9, -9, -6, 0],\n [-3, 3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 5, 9, -12],\n [9, -3, 0, -9],\n [-2, 8, 6, 6],\n [-10, 7, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, 7, -1, 7],\n [-6, -2, 6, 2],\n [21, -13, -1, -15],\n [-6, -2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 11, -6, 6],\n [6, -6, -5, -9],\n [-6, 14, -9, 3],\n [-12, -8, 15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 9, 12, 9],\n [6, -9, -12, -9],\n [-6, 9, 12, 9],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -7, -5, 5],\n [-2, -10, -14, 2],\n [4, 0, 8, 6],\n [3, 19, 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[[-22, -25, 15, 24],\n [9, 15, -5, -10],\n [9, 15, -5, -10],\n [-14, -14, 12, 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[[6, 6, -4, -4],\n [0, 0, 0, 0],\n [-12, -12, 8, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, -5, 4, -8],\n [-9, -7, 8, -8],\n [6, -2, -2, -4],\n [8, -6, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -13, 8, -13],\n [10, -28, -2, -11],\n [7, -10, -6, 3],\n [-11, -4, 2, -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 4x4 matrix:\n[[16, 8, 16, 0],\n [16, 8, 16, 0],\n [-4, -2, -4, 0],\n [12, 6, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -16, 2, 12],\n [1, 14, -11, -13],\n [2, -12, 6, 9],\n [-14, 6, 16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, -8, -4],\n [-9, 0, -6, -3],\n [3, 0, 2, 1],\n [3, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 12, 12, 12],\n [-12, 16, 16, 16],\n [6, -8, -8, -8],\n [-12, 16, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 4, -6, 8],\n [-9, -32, 0, -28],\n [-9, 6, 5, -2],\n [-3, 4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -8, 6, 8],\n [0, -16, 12, 16],\n [0, -8, 6, 8],\n [0, 8, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 4, -7, -16],\n [12, -6, 16, 20],\n [-12, 10, -19, -12],\n [3, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -1, -13, -8],\n [11, -4, 8, 5],\n [-17, -8, 14, -18],\n [3, 6, -16, 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[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-4, -8, -4, -16],\n [-4, -8, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-19, -6, 14, -12],\n [-18, -10, 12, -12],\n [-14, 4, 14, -6],\n [-19, -9, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -8, 11, 12],\n [-20, -27, 7, -22],\n [-24, -20, 26, 0],\n [12, 6, -19, -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[[3, 3, 3, -12],\n [-1, -1, -1, 4],\n [0, -12, 0, 8],\n [4, 4, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, 1, -2],\n [0, 0, 0, 0],\n [0, 2, 1, -2],\n [0, 8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 7, -10, -7],\n [4, 24, 8, 16],\n [-8, 12, -13, -7],\n [3, -5, -13, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 5, 36, -1],\n [17, 11, 8, 15],\n [-21, -5, -12, 13],\n [-9, -3, 24, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 0, -9, 12],\n [4, 0, -3, 4],\n [0, 0, 0, 0],\n [4, 0, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -5, -7, -5],\n [-7, -1, -14, 25],\n [6, 0, 9, -4],\n [-7, 3, -15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 4, 8, -12],\n [-1, 1, 2, -3],\n [-4, 4, 8, -12],\n [-3, 3, 6, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 0, -3, 6],\n [-4, 6, 20, 20],\n [2, -3, -10, -10],\n [0, -4, -16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, 8, 5],\n [-11, 3, 8, 10],\n [0, 0, 14, 8],\n [17, 3, -13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 11, 11, 11],\n [7, -13, -12, -11],\n [1, -4, -6, -1],\n [-13, 7, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 4, -3, 2],\n [-9, 0, -19, -10],\n [0, -18, 4, -14],\n [-3, -15, -3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -12, 9, -12],\n [9, -8, 3, -11],\n [-3, 4, -2, 5],\n [0, -8, 6, -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 4x4 matrix:\n[[-12, 12, -9, 6],\n [-16, 16, -12, 8],\n [-8, 8, -6, 4],\n [-12, 12, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -3, -17, -9],\n [-3, 9, -12, -9],\n [-2, 18, -10, -10],\n [2, -12, 9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 5, 11, 0],\n [8, -7, -7, 4],\n [-18, -6, 12, 14],\n [4, -5, -3, 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[[-16, 13, 14, -12],\n [-14, 17, 7, -6],\n [6, -2, -1, 0],\n [10, -19, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -10, -7, 8],\n [-13, 8, 7, 2],\n [10, -12, -10, 0],\n [22, 4, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 0, 8, 5],\n [-2, -6, 8, 8],\n [5, 0, -8, -5],\n [-5, 0, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -15, 7, -3],\n [0, -10, 6, -4],\n [-1, 14, -8, 5],\n [-1, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -16, 16, -4],\n [-11, 10, -8, 6],\n [-7, 14, -16, 0],\n [-6, 22, -28, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 6, -28, 18],\n [9, 0, 18, -9],\n [-12, 24, -16, 12],\n [-16, 8, -24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -3, 2, -2],\n [6, -6, 4, -4],\n [-3, 3, -2, 2],\n [12, -12, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 2, 0, 2],\n [-15, 6, 4, 1],\n [12, 12, 16, -8],\n [-6, 15, 16, -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[[0, 9, -3, 0],\n [0, -12, 4, 0],\n [0, -3, 1, 0],\n [0, -9, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, -6, 8],\n [0, 0, 12, -16],\n [0, 0, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-2, 4, 6, -2],\n [2, -4, -6, 2],\n [-2, 4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -16, -8, 16],\n [4, -16, -8, 16],\n [-2, 8, 4, -8],\n [1, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -7, 4, -3],\n [-6, 9, 2, 1],\n [-9, -4, 3, -2],\n [-9, 1, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 4, -12, -16],\n [6, 20, 18, -2],\n [21, -7, 8, 15],\n [-6, -20, -18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 12, -9, -3],\n [-1, 4, -3, -1],\n [-3, 12, -9, -3],\n [-1, 4, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, 31, -11, 19],\n [-15, 11, 7, 8],\n [-6, 11, -7, 6],\n [12, -4, -14, -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[[6, 9, -3, 0],\n [-2, -3, 1, 0],\n [2, 3, -1, 0],\n [-6, -9, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 9, 6, -12],\n [-2, -3, -2, 4],\n [2, 3, 2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -4, -8, -4],\n [1, -1, -2, -1],\n [1, -1, -2, -1],\n [-4, 4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 2, 1, 0],\n [4, 20, 8, 16],\n [0, 6, 3, 0],\n [-3, -15, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, -10, -8, 4],\n [-12, -5, -8, 0],\n [15, 0, 10, 13],\n [-2, -7, 8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 3, -3, 4],\n [-4, 6, -6, 8],\n [-6, 9, -9, 12],\n [6, -9, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 7, -4, -4],\n [-13, -19, 28, -2],\n [15, 9, 0, -9],\n [0, -8, 20, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 4, 1, 2],\n [0, 0, 0, 0],\n [-3, 4, 1, 2],\n [6, -8, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 20, -4, -4],\n [4, -28, 12, 8],\n [1, -7, 3, 2],\n [7, -13, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 6, -3, -5],\n [9, -9, 3, 12],\n [-24, 0, -4, 12],\n [-12, 3, -3, 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, -6, -21, 14],\n [13, -8, 5, -14],\n [-19, -10, -11, 18],\n [7, 22, 11, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[32, 2, -2, -11],\n [-4, -22, 20, -14],\n [28, 10, -8, -4],\n [-8, 16, 12, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-6, -4, 4, 6],\n [3, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -6, 12, -12],\n [-2, -4, 8, -8],\n [0, 0, 0, 0],\n [2, 4, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -1, -4, 0],\n [5, 5, 11, 3],\n [7, 7, 10, 6],\n [-4, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -9, 0, 0],\n [0, -6, 0, 0],\n [0, 0, 0, 0],\n [0, -6, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 10, -12, -8],\n [4, 4, 8, -16],\n [-16, 8, -16, 0],\n [-2, 4, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -9, 3, -20],\n [-5, 10, -8, 9],\n [-10, 3, -9, 6],\n [1, 8, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 3, -3, 6],\n [4, 4, -4, 8],\n [-2, -2, 2, -4],\n [-4, -4, 4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -9, 14, 1],\n [-16, -5, -10, -11],\n [16, 5, 10, 11],\n [28, -7, 22, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 4, -8, 8],\n [11, -8, 7, -11],\n [-4, 12, 12, 4],\n [-20, 20, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 9, -16, 20],\n [13, 0, 9, -6],\n [3, 3, -1, 2],\n [-9, -1, -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[[-3, 10, 13, 4],\n [9, -16, -9, -9],\n [-1, -6, -16, 0],\n [9, -24, -25, -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 4x4 matrix:\n[[-3, 0, -3, -9],\n [4, 0, 4, 12],\n [1, 0, 1, 3],\n [4, 0, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 0, 0, 2],\n [4, 0, 0, -8],\n [1, 0, 0, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, 12, 10, -8],\n [-8, -16, 2, -14],\n [-10, -18, 1, -16],\n [-14, -6, -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 4x4 matrix:\n[[-12, 12, 4, -8],\n [3, -3, -1, 2],\n [-9, 9, 3, -6],\n [-9, 9, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 6, 9, 0],\n [2, 4, 6, 0],\n [-1, -2, -3, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 21, -12, 18],\n [0, 0, 0, 0],\n [9, 5, -8, 0],\n [-15, -3, 12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 4, 0, 3],\n [16, 4, 0, 3],\n [-16, -24, -20, 2],\n [8, 4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 3, -21, -9],\n [8, 4, 6, 6],\n [1, -7, 15, 3],\n [12, 6, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -6, 8, -8],\n [12, -9, 6, -6],\n [8, 18, -20, 20],\n [16, 4, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, -15, -11, 0],\n [-22, -14, -5, 4],\n [-1, 10, 10, 5],\n [-28, -22, -12, 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[[-3, 9, 0, -6],\n [2, -6, 0, 4],\n [0, 0, 0, 0],\n [-4, 12, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -9, 0, 2],\n [-13, -13, -16, 0],\n [23, 8, 4, 7],\n [16, 26, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 2, -26, -12],\n [12, -11, -1, 3],\n [8, -2, 26, 18],\n [12, 6, -24, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 11, 8, -17],\n [7, -13, -6, 12],\n [6, -3, -10, 9],\n [8, -10, 5, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, 2, -2],\n [4, 0, -4, 4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 2, 12, 8],\n [-14, -10, -20, -16],\n [20, 12, 32, 24],\n [-14, -10, -20, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [12, -14, -7, 18],\n [-20, -4, -6, 3],\n [28, 2, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -12, 8, 0],\n [-15, -12, 0, 12],\n [-8, -7, -6, 16],\n [-4, -4, -8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -1, -1, 4],\n [4, 6, 18, -28],\n [5, 0, -3, 1],\n [-7, -8, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 0, 4, -4],\n [10, 0, 8, -14],\n [14, 0, 16, -10],\n [-5, 0, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -20, 4, 12],\n [12, 16, -4, -12],\n [3, 4, -1, -3],\n [18, 8, -4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 22, 16, 7],\n [-6, -14, 8, -19],\n [2, -6, -8, -11],\n [-1, 5, 5, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -3, -19, 1],\n [5, 6, -2, -12],\n [3, 2, -3, 2],\n [9, 3, 21, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, -12, 15, -3],\n [-4, -2, 0, -18],\n [-20, -10, 11, -13],\n [-16, -8, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, -5, -10, 5],\n [3, -3, -6, 3],\n [16, -7, -14, 7],\n [-2, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 0, 4, 2],\n [12, 4, 12, 16],\n [-7, -1, 1, -2],\n [-20, -4, -4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 5, -4, -2],\n [-3, 11, -1, -1],\n [-5, -2, -5, -18],\n [-3, 4, 1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 4, 12, -19],\n [-2, -2, -4, 8],\n [-19, -3, -22, 24],\n [8, -4, 4, 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[[5, 17, -11, -2],\n [-12, 4, 4, 2],\n [14, 22, -18, -4],\n [-13, -25, 19, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -14, 0, -5],\n [6, -14, 1, -6],\n [-23, 8, -10, 11],\n [19, -4, 14, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [14, -6, -12, -8],\n [8, -24, -16, 0],\n [2, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -2, 0, 13],\n [-4, 2, 2, -16],\n [-4, 2, -2, -10],\n [8, -4, 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 4x4 matrix:\n[[-12, 16, -4, -4],\n [3, -4, 1, 1],\n [-3, 4, -1, -1],\n [12, -16, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, -10, -20, 8],\n [-7, 8, 4, -4],\n [5, -2, 4, 0],\n [4, 0, 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[[0, -9, 18, -9],\n [6, -18, 27, -14],\n [7, -9, 10, -1],\n [4, -3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -6, -4, 10],\n [2, 25, -7, -20],\n [-11, 3, -20, 7],\n [-12, -9, -6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 0, 8, -8],\n [-4, 0, 0, 4],\n [-18, 0, -20, 18],\n [6, 0, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -6, -3, 0],\n [-4, -8, 0, 4],\n [-4, -6, 3, 6],\n [-3, -6, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 6, -6, 9],\n [-3, -2, 2, -3],\n [-6, -4, 4, -6],\n [-6, -4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -10, 6, -14],\n [12, 10, -6, 14],\n [12, 14, -6, -2],\n [-2, 1, 1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -2, -2, -2],\n [6, 3, 3, 3],\n [8, 4, 4, 4],\n [-4, -2, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 1, 1, -2],\n [-8, -2, -2, 4],\n [-8, -2, -2, 4],\n [8, 2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 2, -1, -1],\n [12, 6, -3, -3],\n [-16, -8, 4, 4],\n [4, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -6, 3, 6],\n [12, -20, 2, 12],\n [8, -16, 1, 9],\n [2, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -2, 15, 3],\n [-6, -4, 6, 0],\n [-3, -6, 21, 3],\n [11, 6, -5, 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 4x4 matrix:\n[[-8, -4, -8, -2],\n [-4, -2, -4, -1],\n [-8, -4, -8, -2],\n [-12, -6, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -7, -4, -5],\n [13, -2, -7, 5],\n [12, 10, 20, 18],\n [-9, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, 14, -2],\n [8, -7, 7, -3],\n [0, 0, 0, 0],\n [8, -4, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, -12, -3],\n [8, 0, 16, 4],\n [-6, 0, -12, -3],\n [2, 0, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -4, -10, -5],\n [-12, 2, 6, 3],\n [-24, 2, 12, 6],\n [28, -3, -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[[-6, -6, -1, 16],\n [21, 21, 13, -19],\n [-19, -19, -16, 15],\n [14, 14, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[29, -2, -14, 17],\n [33, -5, -15, 19],\n [1, 9, -1, -1],\n [-2, -15, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 4, 2, 1],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-8, -16, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 16, 0, 16],\n [2, 4, 0, 4],\n [0, 0, 0, 0],\n [8, 16, 0, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 6, -2, -3],\n [4, 9, -3, -6],\n [3, -7, -7, -9],\n [6, 2, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 12, 3, -3],\n [-4, 4, 1, -1],\n [16, -16, -4, 4],\n [-16, 16, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 10, -5, 7],\n [28, -12, 7, 15],\n [13, -1, -8, 18],\n [10, 2, -11, 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[[-12, -16, 12, 0],\n [-6, -4, 8, -8],\n [0, -6, -3, 12],\n [12, 0, -20, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 6, -1, 5],\n [18, 3, -14, 4],\n [2, 10, 3, -4],\n [-8, 1, 4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -8, 0, -1],\n [0, 0, -2, 3],\n [12, 12, 5, -6],\n [8, 8, -6, 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[[-20, 8, 20, -20],\n [11, 10, -3, 3],\n [-8, -4, 4, -4],\n [-9, 0, 7, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, -4, 3],\n [0, 6, -12, 9],\n [0, 4, -8, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, -4, 4],\n [0, 0, 0, 0],\n [0, 4, -8, 8],\n [0, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, -10, 1],\n [-6, -8, 4, -10],\n [-3, -9, 7, 2],\n [-1, -1, 19, -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 4x4 matrix:\n[[4, 3, 2, 4],\n [-8, -6, -4, -8],\n [4, 3, 2, 4],\n [-8, -6, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -16, 10, 8],\n [15, -3, 21, 15],\n [3, -9, 12, 9],\n [-4, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -1, -9, 5],\n [17, -2, 17, -10],\n [-14, 7, -14, 9],\n [3, 5, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 2, 1, -3],\n [-4, -4, -2, 6],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 14, 7, -6],\n [-10, 4, -1, -6],\n [0, -16, -11, -10],\n [4, -20, -7, 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[[2, -24, 0, -4],\n [5, 20, 8, 6],\n [-9, -12, -12, -6],\n [-1, -28, -4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -3, -9, 12],\n [-9, -3, -9, 12],\n [0, 0, 0, 0],\n [-6, -2, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 12, 6, -15],\n [-9, 18, 0, -21],\n [9, -9, -9, 12],\n [-12, 9, 15, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 9, 12, 0],\n [-6, 6, 8, 0],\n [3, -3, -4, 0],\n [3, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[25, 8, 2, -8],\n [-18, -5, -2, 6],\n [13, -8, 10, -8],\n [-12, 3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, 10, 2],\n [-24, -12, -4, 12],\n [-2, -2, -3, 1],\n [10, 1, -9, -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 4x4 matrix:\n[[3, -9, 0, -12],\n [-1, 3, 0, 4],\n [3, -9, 0, -12],\n [4, -12, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, 4, 4, -12],\n [-2, 0, -8, -8],\n [8, -2, 8, 16],\n [10, -4, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -6, -2, 6],\n [6, 6, 2, -6],\n [-12, -12, -4, 12],\n [9, 9, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -12, 0, -12],\n [-9, 9, 0, 9],\n [-6, 6, 0, 6],\n [-12, 12, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 12, 18, 6],\n [-24, -15, -8, -14],\n [22, 10, 0, 18],\n [-10, 2, 8, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 0, 4, -1],\n [5, -10, -19, 8],\n [1, 13, 24, -1],\n [-2, -4, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -16, -12, -8],\n [-10, 0, 6, 0],\n [10, -10, -9, -5],\n [0, -10, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 8, -4, 4],\n [-8, 4, -2, 2],\n [4, -2, 1, -1],\n [-12, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -2, 0, -6],\n [8, 2, 0, 6],\n [-16, -4, 0, -12],\n [-4, -1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [16, 16, 0, -7],\n [4, 4, -7, 7],\n [8, 8, 6, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 22, 17, 22],\n [-7, 10, 1, 10],\n [12, 20, 22, 20],\n [-5, -1, -4, -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 4x4 matrix:\n[[12, 8, 18, -8],\n [2, 13, 10, -13],\n [8, 2, 10, -2],\n [0, -20, -12, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, -4, 0],\n [0, 0, 0, 0],\n [9, 9, -6, 0],\n [3, 3, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[18, 12, -18, 0],\n [-6, -4, 6, 0],\n [-2, 12, -3, -10],\n [16, 16, -18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 9, 18, 12],\n [-5, -1, 1, 5],\n [7, 10, 18, -6],\n [-3, 2, 2, -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[[2, 0, 9, 6],\n [0, 0, -6, -8],\n [1, 0, 6, 5],\n [-1, 0, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-23, 13, -4, -1],\n [9, -3, 12, 3],\n [-11, 8, -1, -5],\n [13, -23, -12, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -7, -8, -4],\n [-2, 9, 25, 15],\n [-1, 1, 4, -8],\n [7, 13, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, -28, -18, 2],\n [15, 21, 15, -3],\n [-14, -16, -12, -8],\n [-9, -8, -18, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -6, -6, 0],\n [-8, 8, 8, 0],\n [2, -2, -2, 0],\n [-2, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 0, 0, -4],\n [4, 0, 0, 1],\n [0, 0, 0, 0],\n [4, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 8, -16, -12],\n [0, 1, -6, -5],\n [-4, 6, 4, 5],\n [-20, 3, 14, 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[[-6, 9, 21, -3],\n [12, 9, -3, 21],\n [-4, -3, 1, -7],\n [16, 12, -4, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 8, 16, -12],\n [1, 2, 4, -3],\n [-1, -2, -4, 3],\n [1, 2, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -4, 8, 12],\n [6, -2, 4, 6],\n [-3, 1, -2, -3],\n [3, -1, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-25, -2, -21, -15],\n [4, 1, 0, 2],\n [10, -3, 6, 4],\n [0, 4, 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[[12, -8, -4, 16],\n [2, -12, 6, 0],\n [8, -16, 4, 8],\n [-6, 4, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, -8, -6, 2],\n [6, 8, 6, -2],\n [-12, -16, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 8, -6, -2],\n [12, -15, 15, 15],\n [0, -3, 6, 12],\n [12, -10, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 2, 10, 1],\n [1, 4, 0, -3],\n [0, 1, -1, -1],\n [3, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, -21, 23, -10],\n [-9, -15, 23, -12],\n [-14, 10, 0, 11],\n [17, 5, -10, -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[[5, 0, -1, 12],\n [5, 0, 1, 13],\n [1, 3, -4, 11],\n [15, -12, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -12, 3, 3],\n [-16, -16, 4, 4],\n [-16, -16, 4, 4],\n [12, 12, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -4, -2, -14],\n [8, 2, 6, -8],\n [-1, -7, -6, -17],\n [9, 0, 5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -6, 4, 4],\n [8, -6, 14, -4],\n [9, -3, 12, -6],\n [7, 1, 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[[2, -17, -13, -15],\n [2, -17, -13, -15],\n [6, -15, -12, -18],\n [6, -11, -9, -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[[3, -2, -3, 1],\n [-12, 8, 12, -4],\n [0, 0, 0, 0],\n [-3, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -6, 9, -6],\n [3, 2, -3, 2],\n [-6, -4, 6, -4],\n [-6, -4, 6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -2, -1, -13],\n [14, -4, 0, -24],\n [5, 10, -13, -1],\n [12, -2, -4, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 11, 9, 5],\n [3, -8, -6, -4],\n [-4, -1, 3, -3],\n [-5, 4, 6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, -1, 2],\n [-12, 6, 3, -6],\n [11, -3, 11, 3],\n [2, 2, 16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-4, -10, -14, 6],\n [-2, -5, -7, 3],\n [8, 20, 28, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 8, -4, 8],\n [9, 14, 11, -2],\n [-15, -10, -13, 6],\n [-6, -6, -6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -12, 0, 9],\n [0, 8, 0, -6],\n [0, 12, 0, -9],\n [0, -16, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -3, 9, 9],\n [0, 0, 0, 0],\n [-6, -12, 6, 16],\n [-9, -6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -9, 12, -9],\n [-3, 3, -4, 3],\n [6, -6, 8, -6],\n [-9, 9, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -5, -6, -12],\n [1, 0, 19, 0],\n [-4, 21, -1, 9],\n [7, -15, -4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -7, 7, -9],\n [10, 6, 4, 12],\n [3, 1, 10, 6],\n [3, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, 12, -3, -9],\n [6, -12, 3, 9],\n [-8, 16, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -11, 14, -6],\n [-17, -8, 2, -12],\n [26, 5, 7, 22],\n [9, -9, 21, 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 4x4 matrix:\n[[5, -1, 14, 12],\n [-1, 1, -8, -6],\n [7, 3, -9, -3],\n [13, 3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 8, 4, -4],\n [-6, 6, -7, 12],\n [9, 2, 9, -15],\n [-9, 8, -14, 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[[-15, 15, -2, -4],\n [-18, 9, 3, -12],\n [-6, 18, -8, 8],\n [12, 4, -8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 4, -1, -4],\n [-2, -8, 2, 8],\n [-4, -16, 4, 16],\n [3, 12, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 4, 8, 6],\n [-24, 4, 8, 12],\n [-22, 2, 4, 12],\n [4, -9, -18, 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 4x4 matrix:\n[[4, 8, 1, -12],\n [-6, -4, -7, 16],\n [-4, -6, 2, 4],\n [-4, -6, 9, -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[[0, -16, -6, 24],\n [3, 4, -12, 5],\n [18, 15, 6, -3],\n [-15, -30, 2, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-28, -12, 0, 0],\n [0, 0, 12, 0],\n [-6, 11, 2, 10],\n [24, 13, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -14, -17, 15],\n [3, -2, 5, -10],\n [3, 5, 5, -3],\n [11, 4, 10, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 9, -9, 12],\n [0, -6, 6, -8],\n [0, 0, 0, 0],\n [0, -6, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 5, -3, -7],\n [-18, 10, -6, -14],\n [-14, -2, -2, -18],\n [6, -7, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -4, 18, -12],\n [6, -8, 11, -9],\n [2, 4, 7, -3],\n [4, -16, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 13, -3, -6],\n [20, -9, -1, 8],\n [-20, 11, -1, -7],\n [0, -2, 2, -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 4x4 matrix:\n[[2, 3, 0, -3],\n [14, 12, 0, -16],\n [-13, -6, 0, 12],\n [7, -3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -2, 3, -1],\n [-9, 10, -11, -1],\n [5, -2, 3, -1],\n [-10, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -3, 0, 9],\n [-16, -8, 3, 9],\n [10, 5, -1, -10],\n [-10, -5, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -1, 2, 2],\n [-3, 1, -2, -2],\n [3, -1, 2, 2],\n [-12, 4, -8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, 0, 0],\n [4, 0, 0, 0],\n [-4, 0, 0, 0],\n [4, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -9, 10, -8],\n [1, 19, 1, -1],\n [2, 14, 3, -7],\n [-10, 6, -14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 8, 8, 8],\n [0, 0, 0, 0],\n [0, -6, -6, -6],\n [0, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -6, -6, 12],\n [0, 0, 0, 0],\n [-2, -2, -2, 4],\n [-8, -8, -8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -4, -16, -4],\n [-2, 4, 10, -6],\n [-1, -5, -14, 5],\n [-5, -4, -13, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 16, -4, -16],\n [-2, -4, 1, 4],\n [0, 0, 0, 0],\n [8, 16, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 20, -12, -14],\n [11, -5, 4, 3],\n [-16, 12, -8, -8],\n [-5, -6, 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[[10, -11, -11, 11],\n [-3, -13, 5, 4],\n [14, 2, -2, 0],\n [-3, -13, 5, 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 4x4 matrix:\n[[-6, 12, -18, -8],\n [-8, 16, -5, 2],\n [0, 0, -12, -8],\n [0, 0, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -8, 18, 14],\n [-15, -8, 14, 18],\n [-11, -14, 6, 22],\n [0, -14, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 14, 17, 12],\n [-6, 2, -12, 17],\n [5, 0, 19, -18],\n [0, 2, 30, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 3, 2, 4],\n [3, 11, 12, 11],\n [-15, 8, -4, -10],\n [10, -17, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [4, 0, -12, 8],\n [4, 0, -12, 8],\n [-2, 0, 6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 3, 9, -6],\n [-3, 3, 9, -6],\n [-3, 3, 9, -6],\n [1, -1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 2, 13, -7],\n [3, 3, -5, 7],\n [-3, 3, 2, 2],\n [-9, -1, 11, -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[[-12, 0, -3, -12],\n [28, 9, 13, 7],\n [4, 6, 5, -10],\n [-32, -12, -16, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 4, -12, -12],\n [-12, 7, 4, 14],\n [12, 5, -10, -8],\n [8, -6, -2, -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, -1, 2, 10],\n [-7, 13, 14, -10],\n [-5, 7, 10, 2],\n [-4, 6, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -1, 5, 10],\n [-12, -15, 0, -12],\n [12, 13, 0, 11],\n [3, -7, 5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -12, -3, 0],\n [-8, 16, 4, 0],\n [-6, 12, 3, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[19, 0, -1, 23],\n [-4, 9, 4, 7],\n [20, -6, -4, 16],\n [-8, 9, 4, 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 4x4 matrix:\n[[-6, 10, 15, -19],\n [-15, -4, -10, 7],\n [4, 0, 8, -12],\n [3, 12, 2, 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[[12, 7, 0, -14],\n [-2, 0, 14, 14],\n [-13, -8, -5, 11],\n [-10, -7, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 3, -5, -3],\n [-8, 12, 20, 0],\n [12, 4, -4, -4],\n [16, -2, -10, -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[[1, -1, 3, 0],\n [4, -4, 12, 0],\n [-4, 4, -12, 0],\n [-2, 2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 6, -18, -12],\n [-15, 9, 0, 18],\n [-6, -6, 12, 4],\n [17, -3, -9, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -3, 12, 0],\n [8, -2, 8, 0],\n [-16, 4, -16, 0],\n [12, -3, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -18, 17, -1],\n [22, -16, 2, 26],\n [-6, -3, 9, -9],\n [-17, 8, 6, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 5, 9, -17],\n [8, -7, -5, 17],\n [11, -1, 4, -4],\n [8, 1, 9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -10, -8, -9],\n [6, -13, -2, -14],\n [3, 6, -14, 9],\n [15, 4, 16, 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[[3, 12, -9, 9],\n [-3, -12, 9, -9],\n [1, 4, -3, 3],\n [4, 16, -12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 12, -10, -4],\n [8, 2, 4, -2],\n [16, -2, 16, -6],\n [-20, 4, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [-4, 0, -3, 4],\n [-8, 0, -6, 8],\n [8, 0, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 5, 5, 4],\n [-15, -8, 10, 0],\n [20, -12, -12, -8],\n [11, -7, -7, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 13, 2, -4],\n [-18, -15, 2, -4],\n [-21, -25, 1, 3],\n [-3, -27, -9, 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 4x4 matrix:\n[[-9, -6, -9, -9],\n [-6, -4, -6, -6],\n [-12, -8, -12, -12],\n [-9, -6, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -2, 1, 2],\n [-4, -25, 18, 14],\n [14, 16, -11, -10],\n [4, -19, 14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -4, 12, -8],\n [-16, 18, -28, 0],\n [-16, 6, 6, -6],\n [24, -16, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 1, 0, -5],\n [4, 10, 14, 13],\n [0, 4, 6, 7],\n [8, -4, -8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 4, -6, 2],\n [-4, -8, 12, -4],\n [2, 4, -6, 2],\n [1, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 4, -4, -28],\n [-9, -9, 6, 12],\n [9, -6, -6, -12],\n [-4, 10, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[17, 5, -6, -3],\n [4, 5, 10, 25],\n [14, -7, -6, -27],\n [-3, -11, 7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 16, 20, -28],\n [-5, 4, 13, -13],\n [-13, -16, -8, 19],\n [-24, -12, 13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 9, -15, 0],\n [5, 2, 7, 6],\n [4, -13, 5, -10],\n [-7, -3, -14, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -6, 9, -9],\n [-6, -6, 9, -9],\n [0, 0, 0, 0],\n [4, 4, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -6, 2, 16],\n [18, 9, -3, -24],\n [8, 4, -4, 0],\n [-12, -6, 2, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 2, 0, -8],\n [-2, -2, 0, 8],\n [1, 1, 0, -4],\n [1, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 9, -9, 0],\n [9, 9, -9, 0],\n [3, 3, -3, 0],\n [-3, -3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -1, 3, -2],\n [10, 16, -12, 2],\n [-14, 6, 6, -18],\n [-16, 1, 9, -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[[-16, -4, 4, -10],\n [-13, -1, 1, -10],\n [8, 11, -11, 4],\n [14, -1, 1, 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 4x4 matrix:\n[[4, -6, -3, 1],\n [4, -6, 0, 16],\n [-16, 24, 12, -4],\n [-8, 12, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [6, 3, -3, -12],\n [2, 1, -1, -4],\n [-4, -2, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, -4, 14, 14],\n [-16, -5, 10, 10],\n [4, -25, 5, 5],\n [4, 17, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, 4, 12, -1],\n [-13, 4, 4, -12],\n [-12, 4, 0, -16],\n [7, 1, 8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 8, 4, 4],\n [6, -4, -2, -2],\n [-6, 4, 2, 2],\n [9, -6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -3, 0, 6],\n [12, 14, -13, 3],\n [-8, -6, 9, 5],\n [6, 3, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, -4, -6],\n [-16, 8, -8, -12],\n [4, -2, 2, 3],\n [-8, 4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -15, -22, 14],\n [-10, -13, 4, 20],\n [-2, -11, -6, 18],\n [12, 18, 25, -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[[-12, 0, 8, 12],\n [6, 0, -4, -6],\n [6, 0, -4, -6],\n [-12, 0, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 21, 28, -12],\n [4, -3, -4, 12],\n [2, 4, 12, -4],\n [2, -3, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 0, -2, -3],\n [-1, -3, -5, 6],\n [0, -4, -4, 12],\n [4, 0, 8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -9, -21, -6],\n [4, -1, -25, 8],\n [-10, -7, 5, 22],\n [-28, -16, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -6, -2, -4],\n [-16, -12, -4, -8],\n [-16, -12, -4, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 3, 0, -3],\n [4, -3, 0, 3],\n [12, -9, 0, 9],\n [-12, 9, 0, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 10, -12, 7],\n [-28, 16, -22, 5],\n [4, -5, -1, 11],\n [36, -17, 31, -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[[8, 4, -6, -4],\n [4, 2, -3, -2],\n [-8, -4, 6, 4],\n [4, 2, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -4, 0, -8],\n [6, -3, 0, -6],\n [-6, 3, 0, 6],\n [-4, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, 2, 1],\n [2, -2, 2, 1],\n [-6, 6, -6, -3],\n [-4, 4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, -9, -7, 15],\n [20, 9, 7, -15],\n [-6, -9, 21, -6],\n [10, 12, -24, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 4, -9, -6],\n [-9, -8, -7, 2],\n [-6, -12, -3, 6],\n [-7, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, -8, -8, 0],\n [0, 0, 0, 0],\n [0, -16, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-8, -6, -6, -2],\n [8, 6, 6, 2],\n [-12, -9, -9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 18, 14, -10],\n [-1, 18, 14, -10],\n [6, -10, -7, 4],\n [13, -10, -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[[-2, 10, 1, -5],\n [5, -8, 15, -27],\n [7, 9, -28, 5],\n [7, 2, -21, 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 4x4 matrix:\n[[-8, -12, -4, -4],\n [8, -22, -26, -8],\n [4, -12, -20, -12],\n [-6, -16, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 4, 5, 19],\n [7, 17, 19, 20],\n [-2, 4, 14, 15],\n [-3, -5, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 5, 13, -7],\n [13, 7, 19, -13],\n [-7, 2, -8, -10],\n [9, 6, 15, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -5, 3, -5],\n [-3, 8, -1, 5],\n [7, 15, -3, -7],\n [-1, -11, 7, -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[[16, -5, 2, 14],\n [-16, 13, 12, -14],\n [-16, -2, -8, -4],\n [0, -1, -8, -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[[-4, 0, 3, -4],\n [0, -16, -5, 24],\n [7, 13, 14, -5],\n [-1, -15, -9, 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[[-4, 2, 2, 1],\n [12, -6, -6, -3],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -12, 6, -12],\n [-12, 7, 0, 8],\n [8, -4, 2, -4],\n [-12, 1, -18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -16, -10, -4],\n [1, 16, 7, 2],\n [-7, -12, -24, -14],\n [3, -4, 8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -8, -6, -12],\n [4, -4, -12, -12],\n [-8, 0, 12, 8],\n [-4, 2, 9, 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 4x4 matrix:\n[[0, 8, 0, -16],\n [0, 6, 0, -12],\n [-3, 1, 2, 6],\n [3, 1, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -1, -3, 4],\n [7, -12, -1, 13],\n [-4, 8, 4, -12],\n [-2, 3, -1, -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[[7, -5, -14, -12],\n [-1, -13, -10, -6],\n [18, 10, -16, -18],\n [-10, -18, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-6, 8, -4, -6],\n [-3, 4, -2, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, 3, -4],\n [0, 6, 9, -12],\n [0, 8, 12, -16],\n [0, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -3, -13, 0],\n [6, -9, -6, 4],\n [4, -14, -2, 9],\n [-10, 19, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 12, 4, 12],\n [12, 9, -19, 9],\n [0, 0, 4, 0],\n [-4, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 2, 1, -3],\n [2, 2, 1, -3],\n [8, 8, 4, -12],\n [4, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 8, -12, 8],\n [-4, 2, -3, 2],\n [-4, 2, -3, 2],\n [12, -6, 9, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, -4, 4],\n [-16, -12, 16, 8],\n [0, 12, 0, -24],\n [-10, 6, 10, -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, 0, 13, -13],\n [3, -6, 9, 3],\n [-9, 8, -1, -11],\n [-15, 10, 7, -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[[-9, 15, 19, -6],\n [0, -3, -7, 3],\n [3, -4, -4, 1],\n [-9, 15, 19, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -6, 0, 2],\n [12, -9, 0, 3],\n [12, -9, 0, 3],\n [8, -6, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -2, -2, -7],\n [5, -6, 6, 9],\n [17, -18, -2, -3],\n [-7, 6, 3, 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[[-13, -5, -11, -5],\n [7, -8, 2, 8],\n [3, -5, 5, -7],\n [-1, -24, 2, -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 4x4 matrix:\n[[6, 6, 2, 4],\n [12, 12, 4, 8],\n [-9, -9, -3, -6],\n [-3, -3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, -2, 8],\n [-12, 8, 4, -16],\n [9, -6, -3, 12],\n [-3, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -1, -1, 4],\n [-3, -3, -3, 12],\n [-2, -2, -2, 8],\n [4, 4, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -4, 18, 8],\n [9, -26, 24, 16],\n [7, -16, 16, 14],\n [7, -24, 28, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 8, -8, 0],\n [0, 6, -6, 0],\n [0, 4, -4, 0],\n [0, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, 3, -32, 2],\n [20, 0, 36, -4],\n [10, -3, 8, -1],\n [6, -18, -3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 4, -8, 16],\n [9, 8, 2, -16],\n [14, 10, 4, -24],\n [-11, -11, -2, 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[[2, 11, 4, -4],\n [-20, -7, -20, -5],\n [-14, 5, -14, -8],\n [-16, 7, -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[[6, -12, -8, -10],\n [12, -12, -12, -8],\n [-3, 0, 2, -1],\n [12, -15, -13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -6, -4, 10],\n [-8, -12, 12, -12],\n [-26, 12, 9, -16],\n [2, 18, -13, 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, 5, -7, 9],\n [12, 1, -11, 15],\n [-3, 7, 5, -7],\n [12, 2, -10, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 4, -16, 14],\n [-12, 1, -9, -2],\n [1, -3, 22, -4],\n [-22, -3, -19, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 14, -6, 1],\n [10, 18, -2, -3],\n [-2, 2, 6, -5],\n [2, -2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 0, 2, 2],\n [8, 0, 4, 4],\n [0, 0, 0, 0],\n [8, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 9, -5, 7],\n [-8, -9, -4, 7],\n [6, 3, 4, 8],\n [4, 6, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 2, 2, -2],\n [-2, -2, -2, 2],\n [-6, -6, -6, 6],\n [2, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -28, -6, 4],\n [2, 1, -13, -13],\n [-1, 16, 9, 1],\n [8, 13, -4, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 6, 12, -13],\n [0, 0, 18, -15],\n [-4, 3, -15, 11],\n [4, -3, 15, -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 4x4 matrix:\n[[7, -4, -9, -9],\n [-5, 8, 3, 3],\n [-3, 0, 5, 5],\n [6, -12, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, -1, 8, -4],\n [10, 1, 17, 9],\n [-5, -3, 4, -2],\n [-11, 2, -7, -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[[-13, -18, 10, 14],\n [-13, -19, 15, 6],\n [23, 10, -10, -18],\n [-11, 2, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -3, -3, -1],\n [6, -6, -6, -2],\n [3, -3, -3, -1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 20, -1, 7],\n [8, -20, -5, -5],\n [8, -20, 4, -18],\n [-16, 4, -17, 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[[-7, -10, 5, 6],\n [1, 0, -5, 12],\n [4, 6, -2, -6],\n [-16, -20, 20, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 20, 1, 7],\n [8, -14, 0, -7],\n [9, 1, -8, 7],\n [-1, -14, 9, -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 4x4 matrix:\n[[-2, 6, -2, -6],\n [-2, 6, -2, -6],\n [12, 20, 8, 4],\n [2, 8, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -24, -6, -3],\n [-8, 8, 6, 11],\n [8, -16, -4, -2],\n [-13, 28, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -14, 11, 15],\n [-8, -4, -2, -2],\n [16, 18, -9, -13],\n [1, -7, 10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 5, -9, 1],\n [6, 16, -22, 2],\n [9, 17, 2, 8],\n [20, -2, -16, -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 4x4 matrix:\n[[0, -4, -12, 12],\n [0, 1, 3, -3],\n [0, 1, 3, -3],\n [0, 3, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, 0, -8],\n [13, -9, 6, -18],\n [-6, 0, -9, 9],\n [-9, 3, -9, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -5, -6, 0],\n [7, 4, 10, -5],\n [2, -5, -12, 3],\n [2, 11, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, -19, -13, -23],\n [-24, 6, 5, 18],\n [3, -9, 6, -5],\n [8, 16, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -2, 8, -4],\n [-3, -3, 12, -6],\n [-1, -1, 4, -2],\n [2, 2, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -1, -2, -2],\n [8, -2, -4, -4],\n [-16, 4, 8, 8],\n [-12, 3, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-16, -8, -4, 16],\n [12, 6, 3, -12],\n [8, 4, 2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 8, 16, 12],\n [-6, -6, -12, -9],\n [-2, -2, -4, -3],\n [2, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, 8, -4],\n [0, -8, 16, -8],\n [0, 6, -12, 6],\n [0, -2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-8, -16, -4, 8],\n [4, 8, 2, -4],\n [2, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -3, -2, -4],\n [0, -3, -3, -9],\n [-6, -9, -7, -17],\n [-9, -6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 6, -10, 4],\n [-8, 10, -6, -20],\n [16, 12, -20, 8],\n [-8, -2, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 9, -12, 3],\n [4, -12, 16, -4],\n [4, -12, 16, -4],\n [1, -3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 9, -3, -14],\n [-26, 0, -8, 20],\n [-29, -1, 2, 27],\n [-4, -10, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 11, -8, 4],\n [3, -6, 9, -6],\n [-2, -11, 11, 2],\n [-5, 1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -12, 9, -9],\n [6, -18, 9, -15],\n [0, -6, 0, -6],\n [4, 6, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -3, 3, -1],\n [-3, 20, 12, 26],\n [26, 6, -12, 1],\n [-5, -13, -9, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 12, -3, -6],\n [4, -4, 1, 2],\n [0, 0, 0, 0],\n [-8, 8, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -6, 7, 1],\n [6, 9, -5, 1],\n [-13, 12, 9, 12],\n [4, -12, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -1, -11, 3],\n [15, 3, -3, 18],\n [4, 0, -4, 3],\n [-12, 4, 28, 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 4x4 matrix:\n[[20, 9, -7, 10],\n [0, 5, 5, -6],\n [32, -12, -12, 8],\n [-10, 8, -4, 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, -12, -15, 0],\n [-8, 12, 12, -4],\n [-7, 6, -3, -14],\n [-1, 3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -16, 7],\n [4, -4, -16, 7],\n [24, 32, -12, 0],\n [4, 12, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 8, 16, -16],\n [0, 0, 0, 0],\n [4, 4, 8, -8],\n [8, 8, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -1, -5, -2],\n [3, -1, -8, -3],\n [-3, 1, 8, 3],\n [-24, 8, -20, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 12, -12, 4],\n [-4, 6, 10, -6],\n [6, 6, -10, 4],\n [-2, -12, 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[[2, 6, -4, 14],\n [12, 4, -8, 4],\n [2, 6, -4, 14],\n [-7, 3, 2, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, 8, 7, 5],\n [-1, -16, -11, 14],\n [3, -12, -1, 13],\n [16, -7, -6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -4, -7, 15],\n [8, 2, 2, 8],\n [-4, 6, -6, -8],\n [10, 0, 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 4x4 matrix:\n[[-7, -15, -2, 9],\n [1, -5, 8, -3],\n [-1, 24, 0, -9],\n [-12, -28, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 1, -5, -10],\n [-20, -7, 13, -7],\n [0, -2, -2, -22],\n [-12, -4, 8, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -8, -4, -8],\n [-1, -4, -2, -4],\n [-1, -4, -2, -4],\n [-1, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 3, 2, -2],\n [4, -3, -2, 2],\n [-12, 9, 6, -6],\n [8, -6, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 1, -8, -24],\n [4, -8, -20, -4],\n [3, -3, -12, -12],\n [-4, 3, 15, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, 1, -3],\n [4, 8, 0, -16],\n [-4, -10, 1, 13],\n [-1, 2, -2, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 3, 3, -3],\n [-6, 6, -12, 12],\n [-2, -12, 3, -3],\n [-6, -6, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, 3, -6],\n [-4, 0, 2, -4],\n [-6, 0, 3, -6],\n [2, 0, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 2, 0, 3],\n [6, -6, 0, -9],\n [4, -4, 0, -6],\n [-2, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [4, -8, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 12, 29, 4],\n [20, -7, 8, 4],\n [-18, 0, -13, 8],\n [12, -1, 16, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 7, 24, -21],\n [0, 6, 32, -26],\n [-3, 4, 2, -3],\n [-12, 6, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [6, 0, -9, -3],\n [0, 0, 0, 0],\n [4, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, 20, -14, -6],\n [-2, -13, -7, -6],\n [12, 17, -1, 2],\n [11, 1, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -16, 16, 12],\n [-6, -8, 8, 6],\n [3, 4, -4, -3],\n [6, 8, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, -6, 9],\n [0, -6, 6, -9],\n [0, -2, 2, -3],\n [0, 4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 4, 4, 10],\n [-9, 4, -11, 3],\n [8, -3, -3, -16],\n [0, 2, 7, 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[[7, 2, -2, -14],\n [7, 2, -2, -14],\n [-7, -2, 2, -2],\n [-1, 6, 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[[3, -9, 3, 3],\n [-4, -3, -4, 5],\n [3, 6, 3, -6],\n [2, 14, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 8, -12, 16],\n [0, 4, -6, 8],\n [0, -4, 6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -9, 2, 5],\n [2, 9, -8, -11],\n [-4, 12, -4, -8],\n [-2, 6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 3, 0, 4],\n [4, -2, -6, 4],\n [18, 11, -3, 18],\n [14, 13, 3, 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, -2, -2, 1],\n [-12, -8, -8, 4],\n [9, 6, 6, -3],\n [-3, -2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, -10, -1, -1],\n [-8, -3, 1, 1],\n [-14, -5, 6, 6],\n [-17, 0, 13, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 4, 8, 4],\n [-3, -1, -2, -1],\n [-3, -1, -2, -1],\n [6, 2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 2, 2, 6],\n [-4, -1, -1, -3],\n [-16, -4, -4, -12],\n [-4, -1, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -2, 4, -8],\n [4, -2, 4, -8],\n [-4, 2, -4, 8],\n [2, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, 3, 6],\n [6, -6, 3, 6],\n [2, -2, 1, 2],\n [2, -2, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -2, 0, -2],\n [12, -3, 0, -3],\n [16, -4, 0, -4],\n [-16, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 3, 12, -6],\n [4, -2, -8, 4],\n [4, -2, -8, 4],\n [8, -4, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, -2, 2],\n [-12, 8, 4, -4],\n [-9, 6, 3, -3],\n [3, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -4, 8, 8],\n [-8, 4, -8, -8],\n [0, 0, 0, 0],\n [8, -4, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 4, -10, -6],\n [8, -7, -23, -9],\n [-2, -1, 20, 9],\n [-11, 15, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 12, -4, -16],\n [-4, -15, 4, 13],\n [-16, -21, 3, 0],\n [16, 6, 2, 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[[0, 0, 0, 0],\n [-4, -2, 0, -6],\n [8, 4, 0, 12],\n [4, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -4, 2, 19],\n [-12, -19, 17, -16],\n [-13, -22, 28, -3],\n [6, -4, -4, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 28, -8, -20],\n [-13, -4, -12, 16],\n [10, -7, 8, -1],\n [-17, 12, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 3, 4, 2],\n [-2, 6, 8, 4],\n [4, -12, -16, -8],\n [4, -12, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -13, -6, 1],\n [-4, 20, 16, -12],\n [9, 5, -1, 2],\n [5, 9, 1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, 0, 8],\n [-6, -6, 0, -6],\n [-2, -2, 0, -2],\n [6, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 2, 3, -3],\n [-2, -2, -3, 3],\n [0, 0, 0, 0],\n [-8, -8, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -5, -3, 10],\n [-10, -7, -3, 8],\n [10, 8, 2, -2],\n [10, 9, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 6, -6, -2],\n [12, -12, 12, 4],\n [-12, 12, -12, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 4, -2, -1],\n [0, 0, 0, 0],\n [-2, -8, 4, 2],\n [3, 12, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -18, -5, -1],\n [-7, 22, 15, -1],\n [31, 12, -19, 19],\n [13, 28, 7, 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[[-1, 19, -19, 9],\n [-2, -22, 2, -12],\n [5, -8, 19, 6],\n [-4, 7, -24, -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[[12, 4, -12, 8],\n [0, 0, 0, 0],\n [-9, -3, 9, -6],\n [3, 1, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 2, 3, -1],\n [-12, -16, 8, -32],\n [-2, -4, -1, -3],\n [-6, 0, 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 4x4 matrix:\n[[1, 3, 4, -2],\n [1, 3, 4, -2],\n [3, 9, 12, -6],\n [2, 6, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -5, 3, 3],\n [7, 4, -10, -8],\n [12, 9, -5, -13],\n [8, 5, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -12, 20, 2],\n [-8, 10, -16, -3],\n [6, -14, 25, -1],\n [-4, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 6, -8, 2],\n [21, -4, 11, 10],\n [-15, 4, -9, -6],\n [-1, 6, -13, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 3, 4, 0],\n [-6, 6, 8, 0],\n [-12, 12, 16, 0],\n [-3, 3, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -12, -11, -13],\n [-6, 4, 5, 7],\n [10, 12, 8, 7],\n [2, -12, -11, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 24, -16, -12],\n [16, -21, 20, -2],\n [-13, 2, -10, -30],\n [-14, -10, -12, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 7, -14, 12],\n [-20, -9, 13, -14],\n [-12, -5, 8, -8],\n [-16, -4, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -14, -2, 12],\n [12, 22, -2, -20],\n [-9, -18, 0, 16],\n [6, -4, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [19, 8, -11, 5],\n [15, 5, -9, 3],\n [-25, 0, 17, 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[[9, -6, 3, -12],\n [-3, 2, -1, 4],\n [-6, 4, -2, 8],\n [12, -8, 4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 14, 18, 16],\n [8, -2, 6, 0],\n [-7, -22, -4, -40],\n [7, -5, -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[[8, -8, -4, -4],\n [16, -16, -8, -8],\n [4, -4, -2, -2],\n [-8, 8, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 18, 6, 0],\n [4, 8, 2, -6],\n [1, 14, 5, 3],\n [0, 16, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, -8, 32, -20],\n [-16, 0, -24, 16],\n [2, -4, 4, -2],\n [-13, 2, -20, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 4, -24, 4],\n [-6, -14, 0, -8],\n [9, 21, 0, 12],\n [9, 21, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, -2, -1],\n [0, 0, 4, 2],\n [0, 0, -8, -4],\n [0, 0, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 16, -4, -8],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -8, 20, -6],\n [-16, 12, -12, 0],\n [-11, -13, 12, -5],\n [12, -4, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -6, -6, 6],\n [-2, -3, -3, 3],\n [-8, -12, -12, 12],\n [8, 12, 12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -2, -6, 8],\n [0, -1, -3, 4],\n [0, 4, 12, -16],\n [0, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 8, -6, -4],\n [-3, -12, 9, 6],\n [-4, -16, 12, 8],\n [4, 16, -12, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 0, 10, -4],\n [4, -4, -1, 4],\n [-6, 3, 15, -15],\n [10, -7, -16, 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[[7, 4, 11, -3],\n [10, 2, -16, 0],\n [-4, -8, -8, -10],\n [-3, -1, 18, -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[[0, -4, -5, -2],\n [-4, 8, -1, 10],\n [2, -6, -2, -6],\n [-1, -5, -9, -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[[26, -6, 12, -6],\n [-12, 0, 12, 8],\n [-6, -8, -10, 8],\n [16, -14, -10, 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 4x4 matrix:\n[[15, 0, 8, 14],\n [-3, -2, -5, 1],\n [15, 2, -9, 24],\n [5, 4, -20, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 22, -11, -1],\n [8, -16, -12, 16],\n [11, -12, 2, -15],\n [-2, -6, 7, 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[[-16, 21, 14, 20],\n [30, -27, 1, 5],\n [-22, 12, -10, -12],\n [-15, 18, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -6, 9, -3],\n [-3, -6, 9, -3],\n [-3, -6, 9, -3],\n [3, 6, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, 9, 6],\n [12, -5, 4, 1],\n [-24, 15, 2, 13],\n [20, -8, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 2, 7, -9],\n [-8, 6, -5, 7],\n [8, -2, 9, -7],\n [8, -4, 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 4x4 matrix:\n[[2, 8, -2, 4],\n [0, 0, 0, 0],\n [1, 4, -1, 2],\n [3, 12, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 7, -23, 3],\n [24, 16, -16, 17],\n [4, 9, 1, 11],\n [12, 10, -13, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 15, -16, -2],\n [-12, 10, -1, 10],\n [8, -4, -10, -8],\n [16, -1, -6, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 3, -1, 3],\n [22, -9, -7, -8],\n [0, 3, -4, 2],\n [0, -12, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -2, 3, 0],\n [-4, 10, -1, 6],\n [-12, 2, -10, -3],\n [12, -2, 10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 3, -15, 13],\n [-16, 0, 16, -12],\n [12, -15, 3, -11],\n [4, -9, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, -9, 0, 0],\n [0, 6, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -11, 16, 0],\n [8, 24, 8, -14],\n [13, 26, 0, -16],\n [7, -11, 24, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 12, -3, 3],\n [-12, -16, 4, -4],\n [12, 16, -4, 4],\n [-6, -8, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -8, -6, 15],\n [3, 15, 0, -9],\n [4, 2, 4, -8],\n [1, -13, 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[[0, -8, 16, -4],\n [-6, -2, 0, 4],\n [12, 14, -20, -3],\n [12, 6, -4, -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[[-1, -2, 5, 2],\n [13, -2, -1, 6],\n [-8, 5, -8, -8],\n [24, -1, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -15, -18, 3],\n [0, 8, 9, 1],\n [1, -5, -6, 1],\n [-3, -9, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -12, -4, -20],\n [1, 5, -1, -8],\n [11, 13, -9, -10],\n [-13, -3, 7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -12, 12, 12],\n [12, 12, -12, -12],\n [0, 0, 0, 0],\n [4, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -9, -2, 5],\n [18, -10, -12, 8],\n [-8, -9, -2, 5],\n [8, 9, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 12, 16, 12],\n [10, -6, -2, -6],\n [12, -6, 2, -6],\n [15, -9, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -12, -3, 0],\n [4, -16, 0, 8],\n [-13, 4, 4, 6],\n [2, -2, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 4, 16, 0],\n [0, 2, 8, 0],\n [0, -4, -16, 0],\n [0, -2, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, 0, -6],\n [0, -8, -2, -6],\n [8, -8, -2, -14],\n [2, -16, -4, -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 4x4 matrix:\n[[6, 3, -4, -1],\n [-4, 0, 6, 4],\n [-4, -6, -4, -6],\n [12, 9, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -2, 6, 0],\n [-12, 4, 16, 16],\n [15, 0, -21, -12],\n [8, 4, -12, 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[[-9, -6, 14, 3],\n [-10, 2, 11, -6],\n [-6, 6, -4, -6],\n [3, 1, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 2, -1, 22],\n [4, -1, -8, -18],\n [7, -18, -11, 10],\n [12, -4, 9, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -3, -9, 6],\n [16, -4, -12, 8],\n [16, -4, -12, 8],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 4, 0, -2],\n [-2, -8, 0, 4],\n [1, 4, 0, -2],\n [3, 12, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, -2, 2],\n [-4, -4, -2, 2],\n [-4, -4, -2, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -5, 6, -28],\n [23, 7, -11, -32],\n [-9, 10, 17, 9],\n [7, -7, -15, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 0, 18, -6],\n [-2, 6, 20, -8],\n [-1, 3, 10, -4],\n [3, 21, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 4, -4, 0],\n [-6, 0, 6, -12],\n [4, -4, -2, 12],\n [-4, 8, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-8, -12, 8, 16],\n [-6, -9, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -13, -24, -18],\n [-1, 5, 10, 8],\n [1, 1, 3, 3],\n [14, -10, -10, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 2, -1, -4],\n [-8, -4, 2, 8],\n [-12, -6, 3, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -7, 0, -10],\n [0, 6, -2, 14],\n [-2, -7, 0, -10],\n [4, 8, 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[[-18, 15, -9, 0],\n [0, 1, 10, -3],\n [2, 16, -2, -4],\n [16, -10, -10, 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 4x4 matrix:\n[[13, 1, -10, 12],\n [-16, 4, 12, -12],\n [-13, -1, 10, -12],\n [-10, 11, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 0, 0, 2],\n [-4, 0, 0, -1],\n [-4, 0, 0, -1],\n [-4, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 1, -9, -1],\n [-1, 5, -13, -9],\n [-9, -3, 25, 19],\n [-3, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, -4, 6],\n [9, 0, 6, -9],\n [12, 0, 8, -12],\n [-3, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -4, 8, -8],\n [-7, -13, 8, -8],\n [-2, -2, 4, -4],\n [8, 16, -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[[6, 9, 3, -6],\n [-12, -5, -10, 8],\n [-2, 3, -1, -6],\n [-2, -6, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 1, 3, 1],\n [12, -4, -12, -4],\n [-9, 3, 9, 3],\n [-12, 4, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -12, -16, 4],\n [-4, -6, -8, 2],\n [-8, -12, -16, 4],\n [-8, -12, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 0, 8, 2],\n [-1, 3, -1, 5],\n [-7, 11, -5, 18],\n [-12, 6, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 8, -8, 0],\n [6, 16, 4, 10],\n [-9, -20, 3, -10],\n [-12, -24, 10, -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[[20, 0, 0, 20],\n [6, 4, -4, 6],\n [-9, 24, -24, -9],\n [-7, 12, -12, -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[[3, -18, -15, -19],\n [3, -10, -11, -13],\n [3, -2, -9, -10],\n [6, 24, 8, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, -4, -1, 10],\n [-2, -12, 5, 2],\n [16, 12, -1, -16],\n [6, -20, 11, -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[[-10, -10, 10, 10],\n [12, 21, -12, -3],\n [7, 11, -7, -3],\n [-10, -20, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -4, 4, 4],\n [12, 3, -3, -3],\n [16, 4, -4, -4],\n [-8, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 0, 4, 20],\n [-10, 4, -2, 4],\n [3, -2, 3, 6],\n [-13, 13, -5, 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 4x4 matrix:\n[[17, -4, 0, 20],\n [-2, -6, 6, -6],\n [-19, 10, -11, -18],\n [3, 8, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -13, -2, -4],\n [-2, -4, -3, -1],\n [-14, -4, -7, -7],\n [-37, 13, -3, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-17, -10, -10, -9],\n [-17, -26, -5, -9],\n [-5, -2, 1, -9],\n [-6, 4, 0, -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[[-8, 0, 6, -2],\n [-4, -12, -4, 0],\n [-20, -12, 8, -4],\n [7, -3, -7, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 10, -4, 2],\n [-3, -15, 2, -1],\n [-4, -4, -8, 4],\n [-4, -7, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -19, 4, 17],\n [2, 14, 4, -10],\n [-1, -7, -2, 5],\n [2, 11, 0, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 20, 14, -10],\n [-1, -14, -5, 7],\n [2, 0, -4, 0],\n [2, 0, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-8, -4, -16, -8],\n [-8, -4, -16, -8],\n [2, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 2, 14, 4],\n [4, -4, 8, 4],\n [7, -7, -3, -1],\n [3, -3, -7, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 8, -4, 16],\n [-1, 2, -1, 4],\n [-1, 2, -1, 4],\n [-3, 6, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 12, 4, 16],\n [22, 12, 32, 10],\n [10, -8, -4, -2],\n [20, -9, 13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 6, 6, 3],\n [3, 6, 6, 3],\n [-1, -1, 4, 4],\n [4, 4, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 1, 0, 4],\n [-12, -4, 0, -16],\n [-3, -1, 0, -4],\n [9, 3, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 15, -13, -11],\n [15, 10, 17, -16],\n [6, -2, -10, 4],\n [9, -27, -3, 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[[-2, -3, 2, 3],\n [8, 12, -8, -12],\n [6, 9, -6, -9],\n [-8, -12, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-4, -8, 8, -2],\n [4, 8, -8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -10, 10, -8],\n [4, 4, 2, 2],\n [-20, -8, -14, -2],\n [-8, -8, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 1, -14, 10],\n [1, -1, 3, -3],\n [4, 6, 4, 4],\n [1, -1, 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[[-5, 8, 6, -3],\n [2, -9, -12, 7],\n [2, -24, -8, 11],\n [5, -12, -10, 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[[-17, 20, -2, -10],\n [12, 3, -18, 2],\n [3, 17, -24, -4],\n [-2, 18, 4, -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[[3, -10, -6, 9],\n [0, -6, 0, 0],\n [3, -6, -6, 9],\n [1, -10, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-28, 0, -7, 1],\n [-22, -2, 6, -8],\n [-1, 3, -8, 5],\n [23, -8, 9, 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 4x4 matrix:\n[[2, -4, 3, -1],\n [2, -4, 3, -1],\n [2, -4, 3, -1],\n [4, -8, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 0, -6, 20],\n [-4, 0, -4, -8],\n [0, 0, 5, 2],\n [16, 0, -4, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 12, -16, 16],\n [18, 11, -8, -2],\n [25, 16, -12, -2],\n [-21, -15, 12, 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[[-31, 2, 6, -22],\n [-2, 2, 12, 10],\n [18, 0, 5, 21],\n [16, 0, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 0, 9, 0],\n [-10, 4, 4, 4],\n [9, 0, -9, 0],\n [-9, 6, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 15, -10, 2],\n [12, 18, -12, 0],\n [-18, 0, 0, -9],\n [-8, -15, 10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-12, 9, 6, -3],\n [-12, 9, 6, -3],\n [16, -12, -8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -10, 19, 5],\n [28, -21, 4, 1],\n [4, -6, -13, -1],\n [-14, -7, 11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 16, 8, -4],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-4, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 2, 0, 0],\n [-8, 18, -20, 10],\n [-1, 4, -4, 2],\n [-1, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 6, -2, 16],\n [12, -17, 14, -12],\n [-10, 6, -7, -4],\n [6, 9, -3, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 4, -2, 3],\n [-7, 20, -6, -5],\n [6, -6, 4, -3],\n [12, 6, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, -15, -8, -5],\n [-10, -6, -2, -8],\n [12, 4, 0, 12],\n [-6, -2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 9, -9, 4],\n [-1, 2, -4, 2],\n [16, -20, 4, 0],\n [-2, 4, -8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 10, 2, -8],\n [6, -13, -5, 14],\n [2, -7, -3, 8],\n [-4, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -5, -6, 5],\n [-9, -5, 1, 5],\n [-11, -7, -9, 11],\n [1, -2, -7, 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[[4, -2, 2, 8],\n [-6, 3, -3, -12],\n [2, -1, 1, 4],\n [-8, 4, -4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -11, -3, 0],\n [12, 3, 0, 9],\n [-16, -4, 0, -12],\n [0, 17, 4, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -4, -1, 4],\n [4, -8, -2, 8],\n [0, 0, 0, 0],\n [-8, 16, 4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -7, 5, 2],\n [18, 16, -14, -8],\n [16, 22, -14, -4],\n [6, -3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -3, 10, 10],\n [-6, -4, 15, 15],\n [-3, -4, 8, 7],\n [-10, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -12, -12, 3],\n [0, -12, -12, 3],\n [0, 8, 8, -2],\n [0, -8, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 5, -5, -5],\n [-11, -17, 3, -11],\n [-8, -14, 12, 10],\n [-2, -2, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 0, -12, 12],\n [-4, 0, 16, -16],\n [0, 0, 0, 0],\n [3, 0, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 16, -4, 8],\n [-6, -8, 2, -4],\n [-6, -8, 2, -4],\n [3, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -2, 16, 13],\n [0, -3, -12, 3],\n [6, 1, 2, -6],\n [-2, 3, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 1, -19, 12],\n [-6, -1, 19, -12],\n [10, -2, -6, 20],\n [6, -1, -5, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 6, -4, 4],\n [-4, 3, -2, 2],\n [4, -3, 2, -2],\n [8, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 4, -21, 8],\n [-14, -16, -2, 8],\n [-5, -16, 4, -13],\n [-23, -24, -8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -14, 4, 0],\n [8, -8, 2, -4],\n [0, -12, 4, 8],\n [28, -19, 4, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 8, 0, 0],\n [15, 6, -9, -3],\n [5, 2, -3, -1],\n [0, 14, 9, 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 4x4 matrix:\n[[-23, 10, -32, 17],\n [14, 0, 26, -16],\n [-7, 6, -9, 4],\n [-6, 16, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -4, -12, -16],\n [-8, -2, -6, -8],\n [-12, -3, -9, -12],\n [16, 4, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 10, 12, -4],\n [-1, 8, 7, -4],\n [1, -11, 2, 16],\n [1, 1, -14, -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[[4, 21, 25, 9],\n [4, 9, 11, 5],\n [4, -3, -3, 1],\n [8, 12, 15, 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 4x4 matrix:\n[[-2, 4, 10, 12],\n [14, -4, 14, 12],\n [-4, 4, 6, 8],\n [-6, 0, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 12, 15, 17],\n [5, -12, 0, -7],\n [-5, -4, -10, -9],\n [1, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -1, 3, 1],\n [-4, 4, -4, -12],\n [0, 0, 6, -6],\n [1, -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[[-16, -16, -4, 16],\n [-2, -3, -3, 3],\n [2, 3, 3, -3],\n [-16, -16, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 12, -3, -12],\n [10, -13, 4, 17],\n [8, -9, 3, 13],\n [4, -15, 3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 9, 6, -9],\n [-4, -12, -8, 12],\n [-2, -13, -3, 7],\n [-2, 8, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 16, -9, 11],\n [-2, -18, 2, -8],\n [-13, 0, 13, -7],\n [-11, -8, 11, -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 4x4 matrix:\n[[0, -10, 2, 16],\n [-10, -10, 14, 2],\n [-4, -1, 5, -4],\n [-5, 0, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, 0, -10],\n [0, 0, 0, 0],\n [20, -1, 2, -18],\n [-12, -6, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -7, -2, 4],\n [2, -14, -4, 8],\n [14, -8, 2, -14],\n [1, -7, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 0, -16, -22],\n [7, -8, 8, 1],\n [-1, 4, 2, -1],\n [-9, -4, -14, 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[[7, -6, 1, -1],\n [4, -14, -8, -15],\n [8, -2, -4, 14],\n [-6, 12, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 6, -8, 8],\n [-3, -3, 4, -4],\n [-12, -12, 16, -16],\n [-12, -12, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 4, -4, -2],\n [0, 0, 0, 0],\n [-6, 6, -6, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[24, 4, 40, -16],\n [-3, 7, 5, 7],\n [1, -3, -11, -1],\n [-1, 5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, 19, 10, 7],\n [-2, -1, -10, 2],\n [12, -14, -20, -2],\n [-14, 15, 18, 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 4x4 matrix:\n[[1, -4, -1, -3],\n [-3, 12, 3, 9],\n [2, -8, -2, -6],\n [1, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 2, 3, 10],\n [7, 10, -17, -6],\n [7, -2, 0, -10],\n [9, 6, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, 12, -2, -4],\n [-19, 4, -14, 12],\n [-3, -12, -18, 24],\n [-11, 4, -6, 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, 12, 0, 3],\n [0, -12, 0, -3],\n [0, -8, 0, -2],\n [0, 16, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, -4, 1],\n [0, 0, -12, 3],\n [0, 0, -4, 1],\n [0, 0, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -14, 26, 20],\n [-14, -2, 2, 20],\n [-8, -8, 32, 32],\n [8, -11, -6, -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[[7, 1, -3, 3],\n [4, -2, 6, 3],\n [2, -4, 12, 3],\n [0, 8, -24, -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[[-24, 8, 4, -20],\n [-3, 1, -2, -3],\n [3, -1, 12, 5],\n [-3, 1, -17, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -3, 3, -2],\n [3, -3, 3, -2],\n [-12, 12, -12, 8],\n [6, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -6, -8, 2],\n [0, -6, -8, 2],\n [0, -3, -4, 1],\n [0, -3, -4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -8, 2, 8],\n [4, 4, -1, -4],\n [0, 0, 0, 0],\n [-4, -4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -6, -3, -3],\n [12, 0, 2, -4],\n [-4, -4, -4, 2],\n [-24, -6, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -7, 7, -20],\n [-7, 3, -3, 4],\n [5, -3, 3, -8],\n [-9, 5, -5, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -8, 8, -17],\n [-5, -14, -4, -5],\n [-3, -10, -4, -2],\n [3, 18, 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 4x4 matrix:\n[[0, 12, 9, 6],\n [0, 0, 0, 0],\n [0, 8, 6, 4],\n [0, -8, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 2, 9, -6],\n [-6, -2, 9, 3],\n [-20, 8, 15, -9],\n [2, -2, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, -2, 0],\n [-2, -4, 1, 0],\n [0, 0, 0, 0],\n [8, 16, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 0, 4, 4],\n [0, 3, 3, -9],\n [2, 1, 3, -1],\n [-3, 0, -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, 20, 0, 8],\n [-6, 18, 2, 4],\n [-1, 4, 1, 0],\n [-7, 19, 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 4x4 matrix:\n[[-6, -6, 12, -3],\n [6, 6, -12, 3],\n [-4, -4, 8, -2],\n [-8, -8, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -12, -4, -16],\n [-6, 6, 2, 8],\n [0, 0, 0, 0],\n [-6, 6, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -16, -16, -16],\n [-16, 16, 16, 16],\n [-8, 8, 8, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -1, -12, -13],\n [0, -10, -12, -22],\n [-10, -10, 6, -4],\n [-11, -9, 9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 12, -12, 3],\n [-16, 16, -16, 4],\n [4, -4, 4, -1],\n [-16, 16, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [8, -16, 12, 12],\n [-8, 16, -12, -12],\n [-8, 16, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, 9, -24, -9],\n [-6, 2, -2, 8],\n [-4, 1, 9, 24],\n [16, 0, 1, -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[[13, -3, 2, 12],\n [-11, -3, -4, -6],\n [7, -9, -2, 12],\n [10, 18, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, -4, -4],\n [18, -6, 13, 13],\n [-4, 4, -6, -6],\n [-8, 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[[-8, -11, 6, -11],\n [10, 13, -12, 13],\n [-6, -8, 6, -8],\n [-1, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 4, -4, 3],\n [-9, 20, 0, 25],\n [-6, 12, -2, 14],\n [0, 6, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 14, 4, 4],\n [-7, -1, 4, 4],\n [18, -10, -8, -8],\n [10, 3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 2, -4, -4],\n [4, 6, -12, -18],\n [-2, -1, 2, 11],\n [2, 2, -4, -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 4x4 matrix:\n[[32, 4, 20, 4],\n [3, 3, -9, 10],\n [-12, 0, -15, 1],\n [6, 0, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [2, 0, 6, 6],\n [-4, 0, -12, -12],\n [1, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -3, -4, 1],\n [-6, 9, 12, -3],\n [-8, 12, 16, -4],\n [8, -12, -16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, 20, -7, -4],\n [-4, -1, -17, 9],\n [6, -6, 8, -2],\n [-8, 19, -13, -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 4x4 matrix:\n[[7, -13, 20, -2],\n [8, -8, 16, -8],\n [7, -5, 16, -10],\n [6, -6, 18, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, 8, -8],\n [0, 0, 0, 0],\n [8, 8, 8, -8],\n [8, 8, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 9, -2, -4],\n [-21, -5, -5, 16],\n [-7, -11, -1, 12],\n [22, -6, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -1, 3, 1],\n [-3, 1, -3, -1],\n [9, -3, 9, 3],\n [-12, 4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 3, -8, -2],\n [-4, -12, 4, -8],\n [-5, -4, -1, -4],\n [-1, -3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -8, -2, -4],\n [6, -8, -2, -4],\n [3, -4, -1, -2],\n [6, -8, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -8, -6, 8],\n [6, -2, -16, 16],\n [-8, -13, -10, 6],\n [4, 19, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 2, 4, -6],\n [4, -1, -2, 3],\n [-4, 1, 2, -3],\n [12, -3, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 8, 8, 0],\n [-9, -8, 1, 9],\n [0, 0, 0, 0],\n [3, -12, -15, -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[[28, 4, 17, 7],\n [-12, -16, 3, 13],\n [8, 12, -2, -14],\n [4, 9, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 4, -1, 3],\n [3, 4, -1, 3],\n [-3, -4, 1, -3],\n [-12, -16, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -13, -2, -14],\n [-13, 13, -8, -1],\n [-7, -3, -4, 12],\n [-15, 7, 8, 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[[2, -1, -3, -3],\n [-8, 4, 12, 12],\n [6, -3, -9, -9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 7, 12, -19],\n [-14, -7, 9, 5],\n [-3, 2, 1, -24],\n [2, 14, 14, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -2, 6, -2],\n [4, -20, -16, 17],\n [-2, 0, 2, 1],\n [2, 2, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 4, 1, 3],\n [-7, -28, 18, 4],\n [-1, 20, -12, -2],\n [13, 20, -14, -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[[-1, -4, -4, -4],\n [3, 12, 12, 12],\n [3, 12, 12, 12],\n [1, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -12, -11, 13],\n [-9, 16, 15, -17],\n [7, -8, -5, 11],\n [-2, 12, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 8, -8, -6],\n [-9, -16, -16, -3],\n [-11, -14, 2, 8],\n [9, 14, 14, 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[[0, 0, 0, 0],\n [0, 2, -6, 2],\n [0, -1, 3, -1],\n [0, -3, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, 4, 12],\n [-3, 0, 3, 9],\n [-2, 0, 2, 6],\n [-2, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -11, -4, 17],\n [-1, 11, 4, -17],\n [11, 5, 10, 7],\n [3, 2, 3, 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[[-1, -1, -3, -1],\n [2, 2, 6, 2],\n [-1, -1, -3, -1],\n [1, 1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 7, 8, -11],\n [-9, 9, 17, -15],\n [-1, 7, 11, -17],\n [-8, 4, 7, -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[[0, -4, 6, -8],\n [0, 2, -3, 4],\n [0, 2, -3, 4],\n [0, 8, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -6, 15, 18],\n [-8, 15, -9, -13],\n [10, 1, 7, 1],\n [-8, 7, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 5, 1, -4],\n [12, 15, 3, -12],\n [-8, -12, 12, -6],\n [16, 2, -24, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 3, 8, -4],\n [13, 17, -9, -22],\n [-3, -5, 16, 8],\n [-7, -11, 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 4x4 matrix:\n[[-4, 4, 4, 8],\n [-2, 2, 2, 4],\n [-2, 2, 2, 4],\n [-8, 8, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -12, 0, 9],\n [12, -16, 0, 12],\n [12, -16, 0, 12],\n [9, -12, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 11, 10, -1],\n [-4, -2, -4, 4],\n [0, 6, 8, 0],\n [14, 6, 8, -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 4x4 matrix:\n[[4, 0, -4, -14],\n [4, -2, 0, -23],\n [6, 2, -10, -12],\n [2, -7, 3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -4, 6, 6],\n [-3, -6, 9, 9],\n [-1, -2, 3, 3],\n [-2, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 4, -12, 4],\n [14, -3, 9, 2],\n [-16, 2, -6, -3],\n [4, 4, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, -9, 6],\n [-2, 2, 3, -2],\n [-6, 6, 9, -6],\n [-6, 6, 9, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -8, -24, -32],\n [6, -6, 0, 0],\n [4, 4, 12, 16],\n [8, -8, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 18, 1, -11],\n [-8, -2, 0, 4],\n [1, -11, 9, 22],\n [2, -7, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 1, -7, -19],\n [15, 25, 15, 3],\n [17, 25, 13, 1],\n [14, 15, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 14, -16],\n [-6, 9, 5, -4],\n [-4, 6, 8, -8],\n [12, -18, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 2, -14, -5],\n [-8, -2, -6, -10],\n [6, 19, 7, 20],\n [4, -23, -7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -9, -6, -9],\n [8, 12, 8, 12],\n [-4, -6, -4, -6],\n [-4, -6, -4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -4, -2, 0],\n [2, 15, 15, -4],\n [2, 3, -1, -2],\n [2, 4, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 20, -2, 16],\n [-8, -16, 0, -12],\n [-8, 4, -4, 5],\n [-4, -8, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 10, -4, 6],\n [13, -13, 3, -8],\n [-16, 11, -1, 11],\n [-8, 15, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -7, 11, 0],\n [-1, 0, 4, -19],\n [0, -1, -2, 20],\n [-13, 7, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 12, -12, -9],\n [-12, 12, -12, -9],\n [8, -8, 8, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, 15, -12, 9],\n [-10, -14, 10, 12],\n [-12, -4, 4, -16],\n [-7, -5, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -1, -3, -3],\n [-2, 2, 6, 6],\n [-2, 2, 6, 6],\n [3, -3, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 3, -8, 12],\n [-25, -11, -4, -12],\n [12, 4, 16, -8],\n [-24, -10, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -12, -1, -6],\n [6, -6, -2, -4],\n [2, -3, 2, 0],\n [1, -3, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 12, 6, -22],\n [-14, 18, 3, 5],\n [-6, -4, 1, 10],\n [18, 0, -9, -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[[22, -6, 16, -8],\n [-10, -2, -12, -7],\n [-12, 8, -4, 15],\n [12, -4, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 12, -17, 15],\n [14, -18, 3, 7],\n [-8, 15, -15, 11],\n [-15, 15, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 9, 14, 1],\n [8, 8, 13, -3],\n [-6, -1, -1, -4],\n [-2, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -9, 12, -3],\n [8, 12, -16, 4],\n [-4, -6, 8, -2],\n [6, 9, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -8, 8, 8],\n [-3, -12, 12, 12],\n [1, 4, -4, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, 10, -16, -12],\n [9, 2, -8, -8],\n [3, 9, -6, -1],\n [-12, -11, 14, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 19, 12, -2],\n [-2, -8, 5, -8],\n [7, -4, 11, -1],\n [-2, -17, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[19, -10, -21, 11],\n [-10, -14, 7, -5],\n [11, -14, -13, 7],\n [21, -6, -22, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 15, -25, 21],\n [11, 7, -7, 1],\n [-16, -8, -7, 15],\n [-8, -4, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -12, -20, -24],\n [-11, 4, 10, 8],\n [27, -16, -4, 8],\n [4, -14, -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[[18, -5, -12, 1],\n [6, -15, -9, 12],\n [-8, -12, 0, 12],\n [-24, -4, 12, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-19, 10, 2, -6],\n [-8, 12, 8, -20],\n [-19, 6, 4, -1],\n [-24, 8, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 22, -2, 4],\n [-18, 28, -2, 2],\n [-5, 11, 13, 4],\n [7, -15, -16, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -9, 9, 3],\n [12, 24, -12, 0],\n [0, 6, -38, 22],\n [-6, -3, 21, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 10, 8, 2],\n [-16, 10, 8, 2],\n [16, -13, -14, -5],\n [-12, 5, 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[[12, -9, -6, -9],\n [4, -3, -2, -3],\n [-4, 3, 2, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -4, 8, -8],\n [6, -6, 7, -7],\n [6, 0, 5, -5],\n [-2, 13, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 0, 6, -6],\n [2, 0, -4, 4],\n [3, 0, -6, 6],\n [-1, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 8, -2, 20],\n [0, 8, 2, -4],\n [12, 8, -4, 32],\n [-4, -16, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -4, 4, 1],\n [-9, -12, 12, 3],\n [3, 4, -4, -1],\n [-3, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 9, 3, 18],\n [-4, -12, -2, 6],\n [-4, -4, -1, -3],\n [-15, -17, -4, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -8, -16, -16],\n [-13, -10, 4, 0],\n [15, 11, 4, 7],\n [-3, -1, -20, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 12, -16, 0],\n [8, -12, 16, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 2, 6, -2],\n [-9, 3, 9, -3],\n [-9, 3, 9, -3],\n [12, -4, -12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, -36, 20],\n [9, 1, -29, 19],\n [8, -5, -11, -6],\n [-6, -2, 4, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 6, -9, -12],\n [16, 8, -12, -16],\n [18, 10, -7, -6],\n [9, 6, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 4, 12, 0],\n [8, -4, -12, 0],\n [-6, 3, 9, 0],\n [-6, 3, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -3, -4, 5],\n [-5, -3, -3, 5],\n [12, 8, -5, -8],\n [13, 4, -15, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 3, -12, 3],\n [0, -2, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, -3, 6],\n [6, 12, 9, -2],\n [-6, -6, -6, 4],\n [4, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 12, 0, -12],\n [12, 12, 0, -12],\n [-8, -8, 0, 8],\n [-12, -12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -4, -5, 17],\n [3, 4, -1, -3],\n [0, 0, 0, 0],\n [0, 10, 2, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, 16, 0],\n [-12, -12, -16, 0],\n [-9, -9, -12, 0],\n [-12, -12, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -4, 3, -2],\n [20, -12, -11, 0],\n [-14, 6, 13, 16],\n [-1, -10, 23, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 14, 5, 22],\n [0, 8, 8, 16],\n [-12, 8, -4, 8],\n [6, -12, -6, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, -11, 2, 4],\n [-19, -18, 2, 4],\n [-10, -6, -4, -8],\n [-10, -6, -4, -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[[-5, 3, -9, -2],\n [-8, 1, -10, -2],\n [11, 4, 5, 2],\n [-12, -11, -14, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -4, -22, 4],\n [-17, 10, 1, 0],\n [-5, 0, 0, 31],\n [15, -6, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, -8, -8],\n [1, 1, 2, 2],\n [-4, -4, -8, -8],\n [3, 3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, -9, -3],\n [-6, 0, 9, 3],\n [-4, 0, 6, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -14, -2, -12],\n [-3, 5, -1, 9],\n [4, -6, 2, -13],\n [5, -13, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -2, 2, -1],\n [-9, 12, 6, -9],\n [-16, 8, 16, -16],\n [2, -16, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 0, -10, 8],\n [0, 2, 9, -4],\n [13, 20, 25, 12],\n [7, 12, 19, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -2, -14, 18],\n [20, -32, -14, 22],\n [-4, -2, -24, 28],\n [12, -12, 11, -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[[22, -11, 5, 16],\n [-20, 11, -13, 4],\n [6, -21, -2, 8],\n [-21, 11, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, -4],\n [0, 0, 0, 3],\n [0, 0, 0, 0],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 12, 5, -20],\n [-12, 0, -4, -8],\n [-12, -12, -11, 8],\n [-6, 12, 5, -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[[21, 4, 18, -24],\n [2, 10, 1, -8],\n [-3, -20, 6, 12],\n [-3, -8, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [3, -3, -9, 0],\n [2, -2, -6, 0],\n [1, -1, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -5, 6, 3],\n [-4, -16, -12, -12],\n [7, -4, 1, 9],\n [-11, -15, -11, -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[[3, -1, -3, 4],\n [-6, 2, 6, -8],\n [0, 0, 0, 0],\n [12, -4, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, 0, 13, 8],\n [-8, 22, -26, -16],\n [-8, -2, -11, 2],\n [-12, 18, -29, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -5, 3, 1],\n [-5, 5, -15, -3],\n [-10, 9, -12, -2],\n [-15, 9, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 4, -2, -2],\n [18, -4, -1, 3],\n [4, -8, 22, -2],\n [-7, -6, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -16, 0, 0],\n [-4, 14, 3, -4],\n [-12, -14, 9, -12],\n [-4, -14, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[15, -12, -14, -1],\n [9, -12, -10, -5],\n [0, 12, 4, 11],\n [10, -16, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-2, 4, 6, -8],\n [-2, 4, 6, -8],\n [-2, 4, 6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -6, 3, 0],\n [-19, -6, 2, 3],\n [-17, 2, -4, 9],\n [-2, 16, -8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -4, 6, 7],\n [1, 8, 3, 1],\n [-3, 6, 1, -4],\n [-4, -2, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 20, 11, 8],\n [-4, 16, 8, 8],\n [-3, 0, 1, -2],\n [15, -12, -10, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 5, 23, -4],\n [-19, -1, -15, 9],\n [5, 0, 12, -13],\n [-16, 1, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 4, 8, -12],\n [-14, 23, -14, -16],\n [7, -7, 7, 2],\n [-20, 24, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 3, -3, -1],\n [-2, 3, -3, -1],\n [-6, 9, -9, -3],\n [-8, 12, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 0, -2, -22],\n [12, 12, -3, 24],\n [-11, 16, 14, -4],\n [-9, 16, 0, -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[[10, -26, -2, -34],\n [7, -7, 5, -11],\n [1, -8, -5, -10],\n [4, -10, -4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, 6, -2],\n [0, 0, 0, 0],\n [12, -12, 12, -4],\n [9, -9, 9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -18, -8, -6],\n [10, -14, 4, 16],\n [1, -5, -2, -2],\n [-11, 5, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[25, -25, -2, -26],\n [14, -19, -10, -8],\n [5, -2, 0, -6],\n [-12, 14, 9, 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[[2, 6, 12, 0],\n [8, -6, 6, -6],\n [17, -19, 4, -14],\n [4, 12, 24, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 16, -8, 12],\n [6, -12, 6, -9],\n [6, -12, 6, -9],\n [-8, 16, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 6, -6, 4],\n [8, 6, -6, 4],\n [-4, -3, 3, -2],\n [-8, -6, 6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -2, -10, 8],\n [-7, 9, 1, 12],\n [9, -15, -9, -12],\n [9, -15, -9, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -12, -12],\n [3, -3, -9, -9],\n [-1, 0, -4, -3],\n [2, 1, 15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 0, -4, -8],\n [8, 0, 4, 8],\n [-12, 0, -6, -12],\n [4, 0, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -1, 28, -6],\n [-3, -3, -24, 9],\n [-3, -6, 12, 0],\n [2, 6, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -8, 12, -6],\n [0, -6, 13, 5],\n [0, 2, 19, 5],\n [0, -8, -3, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 9, 6, -9],\n [3, -9, -6, 9],\n [4, -12, -8, 12],\n [-1, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, 16, 4],\n [-1, 0, -4, -1],\n [-2, 0, -8, -2],\n [-3, 0, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -4, -12, -4],\n [-8, 1, 5, -1],\n [-18, 5, 11, 0],\n [8, -3, -5, -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 4x4 matrix:\n[[-4, -2, 0, 6],\n [6, 3, 0, -9],\n [8, 4, 0, -12],\n [-6, -3, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 9, 8, -6],\n [0, 9, 12, 9],\n [-6, -12, -12, 3],\n [-14, -19, -16, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -6, -12, 9],\n [-9, 3, -6, 21],\n [-21, 8, -22, 0],\n [5, 16, -2, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 0, -2, -4],\n [8, 2, -9, -4],\n [6, 6, -16, -2],\n [4, -1, -4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 3, 0, 4],\n [3, 9, 0, 12],\n [-2, -6, 0, -8],\n [-2, -6, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -1, -13, -6],\n [13, 13, 19, 5],\n [-15, -15, 12, 21],\n [6, 6, -11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 4, -4, -28],\n [6, 1, 6, 18],\n [-6, -9, -12, -12],\n [4, 14, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -8, -6, -2],\n [12, -16, -12, -4],\n [-9, 12, 9, 3],\n [12, -16, -12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -8, 4, -4],\n [-8, -16, 8, -8],\n [-4, -8, 4, -4],\n [4, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -20, -3, 3],\n [-2, 12, -3, 3],\n [4, 6, 5, 6],\n [-3, -2, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -24, 14, 3],\n [9, 16, -10, -9],\n [-9, 12, -6, 9],\n [-3, 4, -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[[1, 0, 1, 0],\n [-3, 0, -3, 0],\n [-1, 0, -1, 0],\n [3, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, -2, -1],\n [0, 0, 0, 0],\n [0, -8, 8, 4],\n [0, 4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -12, -6, 0],\n [2, -10, -12, 6],\n [16, 11, -5, 9],\n [8, 16, 8, 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 4x4 matrix:\n[[-1, -4, 4, -4],\n [4, 16, -16, 16],\n [3, 12, -12, 12],\n [1, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -12, -12, -6],\n [4, -16, -16, -8],\n [4, -16, -16, -8],\n [3, -12, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -8, 16, 12],\n [-3, -2, 4, 3],\n [-3, -2, 4, 3],\n [6, 4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 2, -1, 5],\n [5, -8, 1, -11],\n [-9, 0, 3, -9],\n [4, 8, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -12, -8, -12],\n [9, 9, 6, 9],\n [9, 9, 6, 9],\n [-3, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -11, 2, -11],\n [-6, 18, 5, 18],\n [-4, 13, 4, 13],\n [6, -3, 5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 8, -12, -10],\n [-2, -25, 12, -13],\n [14, 16, -18, 4],\n [4, -6, -14, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 9, -12, 6],\n [0, -12, 16, -8],\n [0, 9, -12, 6],\n [0, 9, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -14, 5, 6],\n [12, 8, -15, -4],\n [-20, -21, 16, 4],\n [4, -7, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-12, 3, 3, 3],\n [-16, 4, 4, 4],\n [12, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, -16, 6, 12],\n [-15, -3, 3, -9],\n [1, -25, 11, 9],\n [-2, 14, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 1, -3, 4],\n [0, 0, 0, 0],\n [2, 1, -3, 4],\n [-6, -3, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -3, 5, -3],\n [0, 8, -10, -12],\n [-4, -6, 7, 12],\n [-2, -13, 16, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 1, -5, 1],\n [0, -16, 4, 12],\n [8, 12, -5, -16],\n [3, -9, 1, 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[[0, 0, 0, 0],\n [4, -3, 2, -1],\n [4, -3, 2, -1],\n [16, -12, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 14, 6, -7],\n [-6, -16, -6, 11],\n [2, 4, 2, -1],\n [0, -2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -8, 4, 4],\n [0, 0, 0, 0],\n [1, 2, -1, -1],\n [-4, -8, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, -6, 6, 6],\n [0, 0, 0, 0],\n [0, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 10, 12, 5],\n [4, 6, 6, 2],\n [2, 3, 3, 1],\n [6, 4, 6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -1, 6, -9],\n [0, -7, 18, 4],\n [-1, -1, 1, -1],\n [13, -7, 11, 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[[-16, -12, -4, -8],\n [12, 9, 3, 6],\n [0, 0, 0, 0],\n [-4, -3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 18, 9, 6],\n [9, -19, -7, -3],\n [-2, 2, -4, -6],\n [7, -15, -6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 2, 3, 0],\n [-4, 8, 12, 0],\n [1, -2, -3, 0],\n [-3, 6, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -2, 12, -9],\n [-4, -7, 3, 5],\n [-16, 0, 12, -14],\n [-16, -4, 12, -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 4x4 matrix:\n[[0, -6, 2, -2],\n [-8, 8, 4, 0],\n [-16, 10, 10, -2],\n [-16, 16, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 5, 2, 0],\n [-6, 10, 8, 10],\n [0, 0, 0, 0],\n [9, -15, -12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 0, 9, -6],\n [0, 0, 0, 0],\n [-2, 0, -3, 2],\n [8, 0, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -7, -4, 1],\n [0, 9, 6, -3],\n [0, -14, 10, 2],\n [2, -1, 3, -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[[16, 19, -28, 6],\n [-1, 3, 5, 8],\n [4, -19, 8, -11],\n [-13, 11, -15, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [-12, -4, 13, -2],\n [-11, 1, 9, -10],\n [20, 4, -20, 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 4x4 matrix:\n[[21, -3, -6, -3],\n [-1, 3, 0, -5],\n [-6, 8, 1, -12],\n [2, 4, -1, -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 4x4 matrix:\n[[8, -2, -6, 0],\n [-12, 3, 11, -4],\n [16, -4, -12, 0],\n [4, -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[[-1, 12, 5, -11],\n [-5, -20, 1, 9],\n [-1, 12, 5, -11],\n [-3, 6, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -7, 1, 1],\n [-27, 21, -18, 15],\n [4, -4, 4, -2],\n [-14, 22, -1, 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[[-13, 8, 7, 20],\n [19, -8, -25, 4],\n [-9, 4, 11, 0],\n [3, -2, -1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 5, -14, -1],\n [1, -1, -10, 1],\n [-4, -18, -4, 7],\n [2, 14, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 3, 9, 9],\n [-16, -4, -12, -12],\n [-4, -1, -3, -3],\n [-4, -1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -4, -15, 7],\n [4, 0, 17, -1],\n [-6, -4, -2, 14],\n [-8, -6, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -18, -24, 0],\n [16, 10, -4, 16],\n [8, 11, 10, 4],\n [0, -1, -2, 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, 10, 2, 3],\n [-7, -4, -2, -3],\n [-2, -5, 2, 3],\n [-10, -7, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 3, 10, 0],\n [-5, 15, 8, -14],\n [-3, 9, 0, -10],\n [0, 0, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 4, -20, -24],\n [12, -22, 2, 6],\n [-2, 2, 8, 9],\n [4, -4, -16, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, 0, 1],\n [5, -10, -3, -6],\n [10, -20, 12, 9],\n [6, -12, 12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -9, 5, 10],\n [-28, 12, -8, -6],\n [0, -3, 10, -17],\n [-6, -3, 14, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -8, 8, -8],\n [-1, -4, 4, -4],\n [-1, -4, 4, -4],\n [4, 16, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 17, 1, 9],\n [6, 2, -12, -12],\n [-16, -7, 3, 13],\n [19, -4, 10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -18, 0, 4],\n [-6, 12, -6, 6],\n [3, 1, -5, 21],\n [-6, 15, 0, -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 4x4 matrix:\n[[-9, 0, -3, -6],\n [-3, 0, -1, -2],\n [9, 0, 3, 6],\n [-3, 0, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 12, -12, -12],\n [0, 0, 0, 0],\n [-9, -9, 9, 9],\n [12, 12, -12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 2, -8, -8],\n [-1, -1, 4, 4],\n [0, 0, 0, 0],\n [1, 1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 4, 10, -22],\n [-3, 8, -13, 0],\n [0, -4, 2, 6],\n [1, 6, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 12, 12, -12],\n [-12, 12, 12, -12],\n [4, -4, -4, 4],\n [4, -4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-31, -20, 8, -11],\n [-6, -1, 8, -7],\n [0, -4, -10, 8],\n [-2, 0, -4, 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[[20, -2, 1, 2],\n [-9, 10, 0, 10],\n [-2, 10, -2, 16],\n [-4, 18, 16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -4, -20, 16],\n [2, 16, 0, 16],\n [-15, -10, -22, 12],\n [3, -6, 6, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -12, -2, -2],\n [-16, 8, -16, 6],\n [20, -20, 24, -28],\n [4, 4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 10, -6, -34],\n [-1, -20, -12, 2],\n [10, 9, 13, 9],\n [2, -16, 0, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 1, -2, -3],\n [-4, 4, -8, -12],\n [2, -2, 4, 6],\n [-4, 4, -8, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 11, -9, -13],\n [-5, 9, -12, -11],\n [5, 7, -6, 7],\n [2, -2, 12, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-2, -4, -4, 0],\n [-2, -4, -4, 0],\n [-6, -12, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -8, -8, 10],\n [-7, 10, -14, 18],\n [10, 4, 4, 4],\n [7, -2, 13, -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[[-6, 0, -6, 2],\n [-3, 0, -3, 1],\n [3, 0, 3, -1],\n [-3, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 8, -4, -1],\n [12, 0, 0, -12],\n [2, 8, -4, 2],\n [-3, -12, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -5, -4, 9],\n [5, 40, 26, -20],\n [-33, -19, -12, -1],\n [-6, -33, -22, 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[[-16, 10, 2, 7],\n [-16, 6, 6, 13],\n [-4, 7, -4, -5],\n [12, -17, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, -4, -6],\n [6, -3, 6, 9],\n [-6, 3, -6, -9],\n [4, -2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -12, -9, 12],\n [4, -2, -8, 0],\n [-6, 9, -16, -16],\n [-12, 9, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 1, -13, -16],\n [5, 7, -1, 8],\n [-1, -7, 10, 4],\n [4, -4, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 14, -16, -2],\n [5, -5, -8, 11],\n [3, 6, -12, 3],\n [-5, 0, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -16, -8, 4],\n [9, 12, 6, -3],\n [-12, -16, -8, 4],\n [-9, -12, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -10, 5, -8],\n [1, 19, -22, 4],\n [-8, 11, -12, 2],\n [-6, -26, 28, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 2, 14, 13],\n [-4, 2, -10, -15],\n [-2, 6, 0, -10],\n [0, 2, 2, -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 4x4 matrix:\n[[2, -2, 4, 8],\n [4, -4, 8, 16],\n [-1, 1, -2, -4],\n [2, -2, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 4, -12, -16],\n [-14, 14, 6, 8],\n [24, -20, -12, -16],\n [8, 12, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 16, 12, 12],\n [5, 5, 6, 1],\n [9, 13, 12, 7],\n [14, 8, 15, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, 2, 3],\n [-16, 16, -8, -12],\n [12, -12, 6, 9],\n [16, -16, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 8, -8, 2],\n [10, -12, 4, 0],\n [-4, 8, -8, 2],\n [-12, 8, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 0, 7, -1],\n [10, -8, -20, -2],\n [-2, -8, 8, -6],\n [3, -24, 3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, -4, -3],\n [-8, 0, -8, -6],\n [-8, 0, -8, -6],\n [16, 0, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -6, -3, 9],\n [6, -4, -2, 6],\n [6, -4, -2, 6],\n [-9, 6, 3, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -12, 16, -8],\n [-2, 6, -8, 4],\n [1, -3, 4, -2],\n [-3, 9, -12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 2, 8, -8],\n [2, 2, 8, -8],\n [3, 3, 12, -12],\n [2, 2, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -2, 6, 11],\n [-11, 7, -8, 7],\n [12, 0, -4, -14],\n [11, -7, 8, -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[[-5, 4, -1, -1],\n [10, -8, 2, 2],\n [3, -2, -3, -3],\n [3, -3, 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[[7, -4, -20, -2],\n [-6, 0, 8, 4],\n [-12, 3, 24, 6],\n [-4, 1, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, -12, -16, -20],\n [-15, -10, -12, -16],\n [5, 0, 8, 4],\n [-4, 8, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -15, 4, 22],\n [-6, 2, -24, 0],\n [-9, 12, 0, -18],\n [-3, 3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 2, 6, -6],\n [-8, 5, 7, 13],\n [-3, -6, -12, -3],\n [10, 6, 14, -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[[2, -7, -12, 3],\n [-10, -9, 4, -9],\n [-2, -7, -14, 3],\n [-8, -18, -4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -6, -3, 2],\n [4, 5, -17, 7],\n [-2, -2, 5, -2],\n [-20, -14, 8, -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 4x4 matrix:\n[[7, 9, 7, -13],\n [8, 10, 10, -18],\n [12, 16, 8, -16],\n [4, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -6, 10, 8],\n [3, -2, 6, 0],\n [-1, 6, -10, -8],\n [5, -6, 14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, 8, -16],\n [-15, -8, 1, -16],\n [-4, -5, 8, 6],\n [-6, -18, 17, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, -8, -4],\n [8, -16, 16, 8],\n [-2, 4, -4, -2],\n [8, -16, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -6, 4, 2],\n [10, 14, -6, -13],\n [-16, -20, 8, 20],\n [2, -3, 8, 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[[6, 6, 6, -3],\n [-8, -8, -8, 4],\n [6, 6, 6, -3],\n [-4, -4, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -3, -3, -3],\n [12, -9, -9, -9],\n [0, 0, 0, 0],\n [12, -9, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -2, 14, -18],\n [4, -3, 9, -12],\n [-6, 2, -14, 18],\n [-4, -7, -11, 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 4x4 matrix:\n[[22, -6, -13, 17],\n [-4, 3, 10, 2],\n [-24, 9, 6, -22],\n [0, -9, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 4, -3, 0],\n [-8, -12, -21, 6],\n [-1, -16, -9, 12],\n [-1, -4, 0, 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[[0, -3, 1, -1],\n [0, -3, 1, -1],\n [0, -9, 3, -3],\n [0, 6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 4, -28, 20],\n [-6, -3, 21, -15],\n [-6, 0, 12, -12],\n [8, 3, -25, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 4, -6, -4],\n [6, -6, 9, 6],\n [-6, 6, -9, -6],\n [8, -8, 12, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -4, 4, -7],\n [-9, 8, 4, -1],\n [0, 6, 12, -12],\n [-6, 8, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -7, 9, -1],\n [9, -28, 24, 17],\n [8, -10, 9, 12],\n [-13, 4, -5, -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 4x4 matrix:\n[[7, 2, -17, -11],\n [4, 2, -4, -9],\n [9, -19, 3, 12],\n [-15, 2, 5, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -5, -11, -6],\n [-4, 7, 0, -7],\n [-8, 9, 10, 1],\n [4, -6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 12, 0, 0],\n [-6, 2, 0, -6],\n [8, -17, 0, -12],\n [12, -24, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 7, 8, -9],\n [-14, -10, -12, 10],\n [-16, -4, -4, 8],\n [1, 10, 13, -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 4x4 matrix:\n[[3, 4, 2, -4],\n [0, -2, -13, 5],\n [14, 18, 5, -17],\n [5, 8, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 3, 0, -4],\n [8, -4, 4, 16],\n [7, -11, 2, 20],\n [-11, 13, -4, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -8, -8, 4],\n [-12, 12, 12, -6],\n [-8, 8, 8, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 12, 4, 12],\n [7, -3, -7, -9],\n [-9, 3, 11, 13],\n [8, 0, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 2, 0, 0],\n [9, 6, 0, 0],\n [3, 2, 0, 0],\n [-12, -8, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [6, -6, -12, 3],\n [-6, 6, 12, -3],\n [-8, 8, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -6, 4, 6],\n [6, -9, -4, -1],\n [0, 0, 8, 8],\n [-4, 6, 24, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -4, 0, 1],\n [5, 6, 4, -25],\n [8, -15, 1, 11],\n [3, 9, 3, -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[[3, -3, 12, 0],\n [12, 0, 12, -12],\n [-9, -5, 6, 14],\n [-12, -3, -3, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -6, 6, -3],\n [3, -2, -8, -11],\n [3, 4, -2, 4],\n [-1, 6, 8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, 3, 1],\n [-2, -4, -3, 1],\n [4, 16, 12, -2],\n [-6, 16, 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 4x4 matrix:\n[[-5, 7, 20, -7],\n [1, -8, -16, 2],\n [6, 5, 4, 1],\n [-3, -3, -12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 1, 2, 4],\n [-8, 4, 8, 16],\n [8, -4, -8, -16],\n [6, -3, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -4, 6, -2],\n [-7, -10, 15, 2],\n [8, 0, 0, 2],\n [5, 14, -21, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, -3, -15],\n [-6, 4, 3, -7],\n [16, -8, -14, 6],\n [6, -1, -12, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 6, 24, 8],\n [1, -6, -18, -10],\n [-4, -8, -28, -12],\n [3, 6, 21, 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[[15, 0, 9, 0],\n [-11, 13, -8, -18],\n [4, 6, 2, -28],\n [1, 12, -1, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 0, 3, -1],\n [-2, -5, 6, -12],\n [5, 9, -7, 7],\n [2, -8, 8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 0, 6, -6],\n [2, -2, 10, 0],\n [9, -3, 11, 4],\n [-16, 4, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 1, 0, 3],\n [6, 3, 0, 9],\n [-2, -1, 0, -3],\n [4, 2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 6, -2, 0],\n [0, 9, -3, 0],\n [0, 6, -2, 0],\n [0, -3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 2, -8, 3],\n [-9, -1, -19, 19],\n [2, -4, 10, -3],\n [-3, -8, 7, 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[[14, -5, 5, 1],\n [-8, 6, -8, -6],\n [-6, 0, -1, -5],\n [-14, 6, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 0, 3, -3],\n [-2, 0, -6, 6],\n [1, 0, 3, -3],\n [-2, 0, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -21, 6, 23],\n [-1, -23, 0, 27],\n [-25, 25, -20, -25],\n [11, -23, 12, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[21, 6, -1, -29],\n [-18, -12, 3, 9],\n [-22, -4, 6, 30],\n [-6, -3, 6, 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, 20, -25, 11],\n [8, -24, 28, -12],\n [-5, -6, 2, 0],\n [-10, 16, -22, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -5, -6, 1],\n [-15, -18, -9, -2],\n [6, 10, 12, -2],\n [9, 11, 6, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 4, 2, 0],\n [-6, -6, -3, 0],\n [-4, -4, -2, 0],\n [6, 6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-6, 8, 2, -4],\n [3, -4, -1, 2],\n [9, -12, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 8, 4, -4],\n [-14, 7, 0, -2],\n [9, -12, 15, -3],\n [17, -11, 5, 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[[13, 4, 3, -9],\n [13, 2, 6, -8],\n [-3, -2, 2, 2],\n [2, 4, -3, -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[[-15, 3, 5, 1],\n [-15, 3, 5, 1],\n [-9, -3, 7, -1],\n [18, -6, -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[[-1, 0, -2, 4],\n [-9, -8, -2, 10],\n [-16, -16, 0, 12],\n [-24, -28, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 0, 0, -3],\n [-9, 0, 0, -9],\n [0, 0, 0, 0],\n [-9, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 0, -4, 6],\n [12, 27, 12, -4],\n [8, 17, 2, -24],\n [16, 12, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -16, -8, 16],\n [-8, 16, 8, -16],\n [4, -8, -4, 8],\n [-4, 8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, 1, 2],\n [-8, -8, 4, -8],\n [-8, -20, 8, -12],\n [6, 9, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -6, -1, -4],\n [-2, 12, 14, -18],\n [4, 0, 2, -8],\n [3, 13, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -10, 11, -9],\n [3, -8, 0, -5],\n [4, -4, -2, -2],\n [-11, -4, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -12, -16, 8],\n [-6, -8, -9, 3],\n [-12, 4, 2, -14],\n [-12, -8, -8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -8, -1, -1],\n [6, 14, 8, -2],\n [-9, -17, -9, 2],\n [9, -3, -6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 10, 6, -3],\n [24, 22, -4, 28],\n [2, -2, -8, -2],\n [-2, -19, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -2, -2, 4],\n [2, 2, 2, -4],\n [2, 2, 2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 0, 10, 10],\n [-8, 0, -4, -4],\n [12, 0, 10, 10],\n [4, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -2, 0, 4],\n [16, 4, 0, -8],\n [4, 1, 0, -2],\n [-4, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 3, 12, -12],\n [3, -3, -12, 12],\n [4, -4, -16, 16],\n [-3, 3, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -18, 0, -15],\n [-4, -8, -28, -8],\n [5, 10, 26, 3],\n [-4, -8, -18, 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[[10, -4, 14, -12],\n [2, -3, 4, -3],\n [3, 12, -3, 0],\n [-15, 6, -21, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, -4, -4, 1],\n [4, 4, 4, -1],\n [16, 16, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -9, 1, -6],\n [1, -12, -2, 2],\n [-5, 0, -2, 6],\n [4, 12, 4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -1, -2, 4],\n [-3, 1, 2, -4],\n [6, -2, -4, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 0, -8, -4],\n [6, 0, 4, 2],\n [-6, 0, -4, -2],\n [6, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -9, 6, 3],\n [12, -4, -16, -28],\n [-7, 9, 1, 8],\n [0, 4, -5, -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[[4, 2, -10, 12],\n [8, 4, -16, 16],\n [-2, -1, 8, -12],\n [10, 5, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -4, -8, -14],\n [3, 9, 8, 2],\n [4, 2, 24, 6],\n [6, 21, -8, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 14, -14, 22],\n [5, 18, -6, 13],\n [0, 10, -6, 10],\n [10, -18, 16, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, 9, 3],\n [-2, -4, -21, -15],\n [8, -22, -16, -4],\n [-6, 17, 9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 23, -3, 6],\n [-4, 19, -9, 5],\n [-2, 10, 12, 3],\n [4, 2, 12, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 9, -5, 9],\n [4, 7, -11, 3],\n [-4, -7, 11, -3],\n [7, 1, -13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -8, -4, -16],\n [1, -11, 8, -13],\n [4, 4, 2, 8],\n [1, 5, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -6, -6, -6],\n [2, 2, 2, 2],\n [4, 4, 4, 4],\n [2, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 4, -8, -8],\n [12, 16, -2, -2],\n [12, 16, 8, 8],\n [9, 12, 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[[15, -20, -5, -9],\n [9, -9, -2, 20],\n [-3, 7, 2, 24],\n [0, 0, 0, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 12, -3, 9],\n [4, 4, -1, 3],\n [-8, -8, 2, -6],\n [12, 12, -3, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 13, -12, 2],\n [-6, -7, 4, 2],\n [-12, -15, 12, 0],\n [-4, -4, 0, 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[[-3, -9, 3, -6],\n [-3, -9, 3, -6],\n [4, 12, -4, 8],\n [-1, -3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, -16, -4, -4],\n [0, -12, -3, -3],\n [0, -16, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 0, -16, 12],\n [5, 10, -12, 2],\n [2, -4, -2, 4],\n [9, -4, -12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -8, 16, -16],\n [7, -3, 8, -10],\n [-12, 8, -12, 20],\n [1, 6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 4, -2, 4],\n [10, -6, -7, -4],\n [7, -2, 16, -5],\n [-12, 8, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 2, -4, 0],\n [-1, -5, 2, 1],\n [4, -4, -24, 4],\n [1, -7, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, -13, 2, -10],\n [18, -18, 0, -8],\n [10, -8, 22, -1],\n [20, -22, 2, -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[[6, 10, 2, 14],\n [3, 3, -1, -1],\n [27, 17, -7, -4],\n [-3, 12, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -6, -4, -1],\n [8, 24, 16, -20],\n [4, 12, 8, -10],\n [4, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 4, -2, -4],\n [0, -2, 1, 2],\n [0, -8, 4, 8],\n [0, -8, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 2, -2, -1],\n [-4, -2, 2, 1],\n [-16, -8, 8, 4],\n [-12, -6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -14, 7, 3],\n [7, 9, 20, -12],\n [-14, 15, -1, -3],\n [-22, 11, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 18, 2, -21],\n [-20, -20, 0, 24],\n [-9, -9, 4, 12],\n [-9, -9, 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[[-4, -4, -3, 0],\n [16, 16, 12, 0],\n [-16, -16, -12, 0],\n [16, 16, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 5, 12, -11],\n [-11, -9, 7, 5],\n [24, 5, -27, -4],\n [-5, 2, 10, 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[[9, 12, 12, 15],\n [-6, -2, -8, -8],\n [-9, 2, 8, 0],\n [8, 7, 24, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -1, 2, -4],\n [3, 1, 3, -4],\n [0, 0, 0, 0],\n [-4, -4, 8, -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 4x4 matrix:\n[[-2, 4, -4, -6],\n [-3, 6, -6, -9],\n [1, -2, 2, 3],\n [-4, 8, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, -21, 1, -18],\n [-1, -3, -6, 4],\n [-4, -12, -24, 16],\n [-16, -3, 13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -2, -6, -2],\n [2, 1, 3, 1],\n [2, 1, 3, 1],\n [-8, -4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 12, 6, 9],\n [-10, -8, -10, 18],\n [8, 2, 3, -17],\n [-17, -8, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -8, 6, 0],\n [-1, -4, 3, 0],\n [-4, -16, 12, 0],\n [3, 12, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 3, -12, 9],\n [0, 0, 0, 0],\n [-9, 3, -12, 9],\n [12, -4, 16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 13, -10, -10],\n [-13, 18, -14, -13],\n [2, 1, 0, -5],\n [-7, 14, -10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -14, -12, -6],\n [3, 0, 8, 11],\n [-6, -6, -4, -1],\n [18, 20, 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[[13, -7, -13, 0],\n [-1, -5, 1, -8],\n [1, 5, -1, 8],\n [-11, -1, 11, -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 4x4 matrix:\n[[15, -9, -18, 0],\n [-9, 3, 10, 2],\n [-3, -3, 2, 4],\n [3, -3, -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[[16, -7, -18, -9],\n [16, -10, -12, -18],\n [-4, 1, 6, 0],\n [-12, 5, 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[[-1, -8, 14, -3],\n [-5, -8, 22, -11],\n [4, 2, -16, 12],\n [-1, 28, -34, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, -4, 16],\n [3, 0, -3, 12],\n [4, 0, -4, 16],\n [-3, 0, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 16, -8, -12],\n [-16, -16, 8, 12],\n [-4, -4, 2, 3],\n [8, 8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -2, 4, -8],\n [6, -4, 5, -13],\n [8, 1, -6, 8],\n [2, -4, 7, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 14, -6, 12],\n [-5, -15, 5, -16],\n [9, 13, -2, 19],\n [3, 11, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -3, -3, 21],\n [5, -23, -5, 3],\n [-7, 8, 9, 9],\n [4, 8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-6, 4, 0, 2],\n [3, -2, 0, -1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, 3, -3],\n [-4, 4, -2, 2],\n [2, -2, 1, -1],\n [6, -6, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 20, 6, 14],\n [-6, 7, 4, 1],\n [8, -8, 2, -2],\n [-11, 15, 11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -3, 9, -3],\n [0, 0, 0, 0],\n [-12, -4, 12, -4],\n [9, 3, -9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 4, -16, 0],\n [-8, -2, 8, 0],\n [-8, -2, 8, 0],\n [-8, -2, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -2, 1, -11],\n [-10, -18, 14, -6],\n [-4, -3, 3, 5],\n [-18, -10, 20, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, 9, -9],\n [4, 0, -6, 6],\n [-4, 0, 6, -6],\n [-8, 0, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -9, 3, -9],\n [6, 12, 2, 10],\n [-6, -12, -2, -10],\n [-2, 9, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 0, -4, 16],\n [-12, 0, 3, -12],\n [0, 0, 0, 0],\n [-8, 0, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -2, 1, 1],\n [2, -4, 2, 2],\n [-2, 4, -2, -2],\n [2, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 8, -20, 20],\n [6, 11, -5, -13],\n [0, -10, 10, 2],\n [-8, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -1, 1, 19],\n [-1, 0, 0, -4],\n [-5, 4, -6, -19],\n [1, 2, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 0, 4, -3],\n [4, 0, 8, -2],\n [-4, 0, 16, -10],\n [-12, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -1, 4, -4],\n [-3, -1, 4, -4],\n [-9, -3, 12, -12],\n [9, 3, -12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 14, -16, -3],\n [-12, -12, 7, -10],\n [2, 22, -10, 1],\n [6, 0, -10, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -2, 1, -1],\n [12, 0, 9, -9],\n [-11, -1, -10, 10],\n [-21, -3, -21, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -7, 18, -2],\n [-10, -10, 22, -4],\n [13, 13, 0, 14],\n [-13, -13, 13, -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[[0, -1, -2, 0],\n [-7, 0, 10, -15],\n [-6, -8, -1, 9],\n [-18, -10, 10, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -4, 6, 2],\n [16, 8, -12, -4],\n [12, 6, -9, -3],\n [-16, -8, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -15, -6, 9],\n [-10, -18, -12, 10],\n [-1, 8, -4, -6],\n [15, 13, 22, -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[[-4, -2, 0, 2],\n [-8, -4, 0, 4],\n [2, 1, 0, -1],\n [-8, -4, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -5, -10, -3],\n [12, 10, 0, 8],\n [-8, -6, 2, -5],\n [0, 4, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 1, -4, 7],\n [-4, 4, -16, -4],\n [-2, -1, 4, 5],\n [-4, 1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 5, -5, 11],\n [0, 5, -5, 11],\n [6, 9, 3, 9],\n [1, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -4, 6, 10],\n [-4, -2, -6, 4],\n [-9, -13, -5, 8],\n [-14, -20, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -10, -11, 24],\n [-4, 4, -14, 12],\n [12, -18, 6, 14],\n [-10, 15, -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[[0, 2, -6, -6],\n [21, -10, 9, 16],\n [21, -11, 12, 19],\n [-12, 6, -6, -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[[-13, 1, -8, 20],\n [11, 4, 10, 8],\n [17, 7, 16, -4],\n [3, 12, 10, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -3, 3, -6],\n [9, -5, 5, -14],\n [19, -4, -6, -8],\n [0, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -1, 1, 1],\n [6, 6, 2, 10],\n [-1, -13, 1, -11],\n [1, -14, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 5, 12, -4],\n [0, -8, -16, 0],\n [-3, 1, 0, 4],\n [3, -9, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -6, -6, 6],\n [-11, 15, 12, -9],\n [16, -20, -12, 4],\n [3, -5, -6, 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 4x4 matrix:\n[[0, 2, -6, -3],\n [4, 4, -12, -4],\n [-7, -5, 21, 7],\n [1, 9, -13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -6, 6, -27],\n [-2, -14, -8, 8],\n [-10, -1, 11, -2],\n [11, 7, -4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 2, -2],\n [-2, 8, 4, 0],\n [-1, 4, -1, 3],\n [-4, 16, 4, 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[[11, 16, -18, 3],\n [31, -2, 16, -31],\n [-2, 16, -4, -2],\n [3, -5, 23, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -2, 4, -6],\n [-16, 4, -8, 12],\n [8, -2, 4, -6],\n [-16, 4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 7, -18, 16],\n [-17, -8, 17, -13],\n [-1, -7, -3, -1],\n [-24, 12, -6, 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 4x4 matrix:\n[[-16, 13, -1, 8],\n [15, -12, -6, -3],\n [17, -13, -2, -10],\n [-6, 3, -3, 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 4x4 matrix:\n[[-8, -8, 6, 8],\n [4, 4, -3, -4],\n [0, 0, 0, 0],\n [-4, -4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, 20, 6, -11],\n [-13, 24, 2, -15],\n [1, 14, -3, -3],\n [-16, 18, 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[[0, -2, 8, -6],\n [0, 4, -16, 12],\n [0, 1, -4, 3],\n [0, 1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, -4, 4],\n [-8, 4, -4, 4],\n [-16, 8, -8, 8],\n [-16, 8, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -9, -18, 7],\n [-2, 4, 9, -14],\n [-4, -2, 8, 22],\n [2, 6, 12, -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[[-1, -20, -8, 15],\n [-15, 5, 16, -3],\n [-14, 0, 14, 12],\n [-1, -10, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 6, -3, 6],\n [16, -8, 4, -8],\n [-4, 2, -1, 2],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -17, 7, -8],\n [-22, 6, 24, 19],\n [0, 14, -10, 4],\n [-14, 14, 8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -15, 14, -2],\n [-1, 3, -2, 0],\n [5, -12, 8, -2],\n [7, 15, -14, 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[[-15, -4, -4, -6],\n [10, 8, 8, 2],\n [6, 8, 8, 0],\n [-1, -12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 0, -2, 11],\n [-2, 1, -5, 14],\n [29, 2, -11, -11],\n [-5, 22, 5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 6, 0, 8],\n [11, 25, 6, 29],\n [14, 4, 4, 5],\n [-19, 1, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, -6, 0, 8],\n [-8, 2, -5, -1],\n [-12, 2, -11, 1],\n [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 4x4 matrix:\n[[2, 5, 0, 2],\n [-4, -17, -17, -5],\n [-2, 20, 11, -7],\n [1, -9, -1, 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 4x4 matrix:\n[[-24, 5, -25, -7],\n [4, -16, -4, 0],\n [-5, -6, -9, -2],\n [10, -1, 11, 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[[8, -6, 2, -2],\n [4, -3, 1, -1],\n [0, 0, 0, 0],\n [-4, 3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 8, 6, 4],\n [-13, 0, 1, -10],\n [-4, 14, 10, 12],\n [15, -7, -6, 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[[-18, 10, -10, 6],\n [-3, -3, -18, 15],\n [-3, 3, 3, -3],\n [9, -5, 5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 3, 3, 0],\n [-20, 3, 5, 0],\n [-2, 2, -8, 0],\n [18, -4, 2, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [-12, 0, 0, 9],\n [-4, 0, 0, 3],\n [-16, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -6, 0, 9],\n [-16, 8, 0, -12],\n [4, -2, 0, 3],\n [8, -4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -2, -6, -8],\n [-3, -3, -9, -12],\n [-3, -3, -9, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 2, 6, 2],\n [-8, 2, 6, 2],\n [-16, 4, 12, 4],\n [16, -4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 14, -7, -7],\n [-2, 8, -3, -9],\n [5, -10, 5, -4],\n [-11, 18, -10, 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, 8, -3, 17],\n [5, -5, 1, 6],\n [-7, 4, 0, -10],\n [-14, 11, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -2, -10, -4],\n [-4, -2, 2, 4],\n [-5, -11, -2, 8],\n [-5, 0, 1, 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[[14, -4, -10, 1],\n [-4, 0, -4, -6],\n [4, -2, -8, -4],\n [8, -4, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -7, 4, -5],\n [-7, 5, -5, -2],\n [9, -9, 8, 1],\n [-2, -14, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 6, 9, 9],\n [-12, -6, -9, -9],\n [-12, -6, -9, -9],\n [-16, -8, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 4, -1, -1],\n [-24, -12, 16, -16],\n [23, 1, -7, 8],\n [-9, 7, 7, -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 4x4 matrix:\n[[4, 8, -2, -8],\n [-4, -8, 2, 8],\n [8, 16, -4, -16],\n [8, 16, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[22, -4, 20, 8],\n [-25, 0, -22, -4],\n [12, -9, 12, 12],\n [-20, -10, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -12, -20, -15],\n [19, -13, 3, -2],\n [23, -5, 1, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, 4, -4],\n [0, -4, 4, -4],\n [0, 4, -4, 4],\n [0, -6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 8, 4, -16],\n [-3, 0, 12, -6],\n [-7, -8, 8, 10],\n [3, 6, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, 4, 11, 11],\n [-8, -12, 12, 17],\n [-4, -6, -4, -4],\n [15, 12, 7, 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[[-4, -8, -8, 4],\n [6, 12, 12, -6],\n [-2, -4, -4, 2],\n [-6, -12, -12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -4, 6, 4],\n [3, -14, 13, 10],\n [6, -4, -8, 7],\n [-11, -12, 11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 0, -2, 8],\n [-19, 20, -19, 11],\n [-3, 0, -3, 12],\n [6, -8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, -2, 4],\n [8, 3, -13, 2],\n [8, 24, -22, 20],\n [0, 4, 4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, -1, 2],\n [-7, -4, 12, 4],\n [2, 6, -1, -6],\n [-12, -8, 20, 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 4x4 matrix:\n[[-12, -12, -8, 12],\n [0, 0, 0, 0],\n [9, 9, 6, -9],\n [9, 9, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, 0, 6],\n [-3, 2, 0, 3],\n [-6, 4, 0, 6],\n [-9, 6, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -4, 6, 4],\n [4, 1, 16, 20],\n [4, 1, 16, 20],\n [0, -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[[12, -3, -21, -15],\n [-16, 4, 16, 16],\n [8, -2, -11, -9],\n [12, -3, -15, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -2, -4, -6],\n [0, 0, 0, -12],\n [0, 0, 0, -16],\n [0, 0, 0, -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[[-11, 4, 7, 10],\n [15, -7, -10, -13],\n [11, -4, -7, -10],\n [7, -18, -9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 21, -10, 5],\n [6, 15, 2, -13],\n [-2, -5, 2, -5],\n [1, 4, -2, 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[[6, -22, 2, -8],\n [8, 12, 0, 22],\n [-11, 3, -1, -15],\n [-11, 23, -1, 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 4x4 matrix:\n[[4, 8, -4, -6],\n [-4, -8, -14, -3],\n [-2, -4, -10, -3],\n [-10, -20, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -4, -8, 8],\n [-2, -2, 6, 4],\n [6, -8, -4, 16],\n [-8, 6, 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[[8, 8, 6, -7],\n [12, 24, 18, -3],\n [-10, -16, -12, 5],\n [-13, -20, -15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, -14, 8, 2],\n [-7, 0, -2, -4],\n [-6, -16, 6, -4],\n [0, -22, 11, 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[[0, 12, 6, -9],\n [-6, 18, 10, -16],\n [-1, -17, -9, 18],\n [14, 14, 6, -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[[14, 13, -12, -11],\n [-9, -9, 7, 7],\n [11, 15, -13, -9],\n [-19, -1, 17, 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[[8, -2, -8, 6],\n [0, 0, 0, 0],\n [-12, 3, 12, -9],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 12, -4, 8],\n [16, -4, -12, -12],\n [-4, 1, 3, 3],\n [12, -3, -9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-36, -4, -5, -1],\n [-12, 12, 1, 5],\n [-8, 5, 1, 11],\n [8, 16, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 16, 0, -4],\n [-16, -8, -4, 8],\n [-2, 8, -2, 1],\n [12, 12, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -14, -5, -2],\n [8, 17, 0, 1],\n [-2, -1, 13, 3],\n [2, 0, -17, -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[[-2, 6, 16, 1],\n [10, 2, 16, -5],\n [-8, -8, -32, 4],\n [-12, 0, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -3, -14, -17],\n [3, 11, -29, -18],\n [3, 0, 3, 3],\n [-7, -6, -13, -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[[0, 5, -3, -1],\n [0, 6, -4, -4],\n [0, -8, 2, -18],\n [0, -6, 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[[4, -2, -3, -3],\n [16, -8, -12, -12],\n [0, 0, 0, 0],\n [-16, 8, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 6, -6, -8],\n [-9, -9, 9, 12],\n [6, 6, -6, -8],\n [-3, -3, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, -3, 9],\n [2, -2, -1, 3],\n [-1, 10, 2, -6],\n [4, -10, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -4, -3, 3],\n [6, 25, 9, -18],\n [-6, -8, -6, 6],\n [10, 19, 11, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 4, 9, -9],\n [6, -10, -12, -2],\n [-3, -1, 0, -3],\n [-12, -1, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -2, 0, -4],\n [0, 1, 0, 2],\n [0, -2, 0, -4],\n [0, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 10, 2, 8],\n [2, 17, -8, 7],\n [2, 8, -6, 2],\n [9, 9, -21, -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 4x4 matrix:\n[[-1, -2, 4, -1],\n [0, 0, 0, 0],\n [-1, -2, 4, -1],\n [4, 8, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 4, 2, -1],\n [-2, -4, -2, 1],\n [-6, -12, -6, 3],\n [-4, -8, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, -4, -6, 2],\n [-18, -16, -20, 4],\n [-12, -1, -6, 5],\n [1, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 6, -4, -2],\n [-12, 0, 3, 3],\n [-4, -9, -2, -5],\n [16, 6, -2, 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[[5, -15, -3, -16],\n [18, 2, 20, 12],\n [26, -6, 8, 20],\n [13, 2, 7, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -5, 9, 4],\n [-3, 7, -3, -4],\n [-31, 26, 10, -2],\n [17, -3, -23, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -8, 10, 8],\n [4, 16, -14, -14],\n [-16, 16, 1, -9],\n [-20, 16, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -17, -23, -2],\n [-16, 5, 0, 5],\n [12, 15, 30, 1],\n [-8, 17, 23, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 0, 12, 0],\n [-4, 0, -12, 0],\n [0, 0, 0, 0],\n [-3, 0, -9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -9, -5, 1],\n [4, -18, 0, -4],\n [-20, -10, 10, 6],\n [-16, -3, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -20, -3, -13],\n [-16, 0, 12, -28],\n [-14, 8, 12, -20],\n [-10, -8, 6, -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[[0, 0, 0, 0],\n [0, -4, -16, -12],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 1, 2, 3],\n [-8, 4, 8, 12],\n [6, -3, -6, -9],\n [2, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 3, 4, 0],\n [-4, 12, 16, 0],\n [2, -6, -8, 0],\n [1, -3, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 13, 6, -3],\n [3, -3, 4, -5],\n [-6, -16, -22, 2],\n [-3, 19, 23, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -6, 12, 5],\n [6, 3, -11, -16],\n [24, 20, -20, -2],\n [20, 16, -38, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -3, 1, 3],\n [0, -4, 4, 13],\n [8, -1, -5, -1],\n [-2, 10, 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[[-18, 16, 9, -9],\n [21, -18, -12, 9],\n [18, -16, -9, 9],\n [-1, -2, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [3, 1, 2, 2],\n [0, 0, 0, 0],\n [-6, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -9, 12, 3],\n [-8, 6, -8, -2],\n [16, -12, 16, 4],\n [8, -6, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -1, 1, -2],\n [0, 0, 0, 0],\n [4, 1, -1, 2],\n [4, 1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, 2, 4],\n [-3, 6, 12, -6],\n [2, -4, -8, 4],\n [0, -6, 6, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 8, 6, 6],\n [-2, 2, 5, 1],\n [10, -19, -16, -14],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 6, -6, 2],\n [6, -8, 3, -4],\n [-12, 10, -15, 2],\n [12, -12, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [4, 4, 4, 4],\n [0, 0, 0, 0],\n [2, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 7, 11, 7],\n [-4, -2, -4, -3],\n [6, 1, -3, 0],\n [8, 10, 15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -8, -2, -4],\n [4, -16, -4, -8],\n [4, -16, -4, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -12, 0, 12],\n [-6, -8, 6, 12],\n [4, 6, 0, -6],\n [-7, -10, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 12, -6, 0],\n [-3, 4, -2, 0],\n [12, -16, 8, 0],\n [-9, 12, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -2, -4, 0],\n [8, 4, 8, 0],\n [8, 4, 8, 0],\n [4, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -5, -2, 3],\n [-8, 1, 3, 0],\n [-8, -13, 13, 12],\n [-8, -13, 13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, -4, 8],\n [9, 9, -6, 12],\n [-9, -9, 6, -12],\n [6, 6, -4, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -8, -6, -6],\n [-4, 4, 3, 3],\n [12, -12, -9, -9],\n [16, -16, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -1, -1, -1],\n [6, -10, 14, -6],\n [3, 3, -9, 1],\n [6, -10, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 8, 4, -8],\n [8, -4, -2, 4],\n [12, -6, -3, 6],\n [12, -6, -3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -1, 0, 4],\n [0, -1, 0, 4],\n [0, 3, 0, -12],\n [0, 2, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 11, -2, -7],\n [-15, -21, -3, 9],\n [-2, 5, -10, -9],\n [-2, -8, 6, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 4, -12, -6],\n [7, 1, 9, -1],\n [-2, 2, 3, 0],\n [-4, 19, -6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 0, 8, 6],\n [4, 0, -8, -6],\n [-2, 0, 4, 3],\n [-4, 9, -13, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 2, 4, 1],\n [-12, 8, 16, 4],\n [9, -6, -12, -3],\n [3, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, 14, 15, 28],\n [7, 6, 30, 19],\n [6, 0, -9, 7],\n [-12, -1, 3, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -3, 9, -3],\n [-3, -3, 9, -3],\n [-3, -3, 9, -3],\n [2, 2, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 12, 12, -12],\n [20, 8, -4, 18],\n [-4, -12, -10, 15],\n [-2, -16, -23, 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 4x4 matrix:\n[[12, -6, 9, 6],\n [0, 9, 6, 12],\n [-12, 9, -7, -2],\n [-4, 2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 5, -14, 4],\n [-19, -9, 6, 12],\n [5, 1, 8, -10],\n [-25, -11, 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[[-2, 12, -18, 3],\n [22, 20, -16, 26],\n [26, 20, -14, 29],\n [0, -12, 16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -3, -3, -1],\n [0, 0, 0, 0],\n [-2, 3, 3, 1],\n [-4, 6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, -4, 6, 13],\n [0, 10, 11, 0],\n [-3, -14, -13, 3],\n [11, 18, 11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -2, 3, 3],\n [-2, 14, -4, -20],\n [2, -10, -2, 14],\n [0, 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[[-4, -16, 12, 0],\n [4, 16, -12, 0],\n [2, 8, -6, 0],\n [3, 12, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -16, 4],\n [0, 2, -4, 1],\n [0, 6, -12, 3],\n [0, 6, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -4, 1, 4],\n [8, 16, -12, 0],\n [5, 6, -4, -1],\n [4, -8, 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[[-11, -20, 1, 10],\n [-5, -19, 8, 4],\n [8, 9, -1, 0],\n [16, 15, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -1, -12, -15],\n [12, 12, 22, 10],\n [8, -16, -17, 1],\n [-24, 14, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [1, 4, 1, -3],\n [-3, -12, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -12, 0, -3],\n [-5, 10, -4, 9],\n [0, -11, 18, 24],\n [8, 2, 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, -12, 3, -9],\n [6, -12, 3, -9],\n [-2, 4, -1, 3],\n [-4, 8, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 1, -4, 26],\n [0, -13, -8, 10],\n [-2, 1, 3, -8],\n [-4, -1, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -16, 2, 2],\n [-5, -1, 20, 15],\n [5, -7, -16, -11],\n [15, -15, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 9, -4, 9],\n [6, 0, -3, 0],\n [0, 9, -3, 9],\n [-8, 12, 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[[-1, -10, 15, -2],\n [-2, 20, 0, 1],\n [-4, -12, 24, -6],\n [-2, -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 4x4 matrix:\n[[2, -11, 4, 2],\n [-2, 4, -2, 1],\n [-14, 7, -8, 16],\n [-2, -3, 0, 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 4x4 matrix:\n[[14, 2, -1, 6],\n [-16, 28, 2, 15],\n [-1, 15, -7, 18],\n [23, -5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-21, 9, 8, -18],\n [-12, 4, 4, -10],\n [15, -7, -6, 13],\n [-6, 10, 6, -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 4x4 matrix:\n[[-12, 14, 8, -20],\n [9, -7, -7, 13],\n [-7, 7, 3, -15],\n [-6, 7, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -3, 1, 0],\n [4, -12, 4, 0],\n [-3, 9, -3, 0],\n [-4, 12, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -2, -6, 8],\n [-1, -1, -3, 4],\n [-1, -1, -3, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 13, -6, -5],\n [-11, -7, -21, 5],\n [10, 10, 18, -6],\n [-8, -6, -15, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-4, -16, 12, -4],\n [2, 8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -6, 5, 4],\n [24, 8, -12, -16],\n [-6, -9, 0, 18],\n [-16, 5, 11, 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[[3, 1, -1, 1],\n [-6, -2, 2, -2],\n [-6, -2, 2, -2],\n [-3, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -8, -6, 7],\n [6, -14, -24, 1],\n [-11, -1, 8, 7],\n [1, -14, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -4, -9, -4],\n [16, -6, -6, -16],\n [-2, 0, -6, 8],\n [-4, 2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -8, -12, 0],\n [-2, -4, -6, 0],\n [-1, -2, -3, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 13, 9, 5],\n [3, 9, 4, 3],\n [12, 0, 16, -6],\n [6, 6, 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[[4, -16, -12, -8],\n [0, 15, 0, 3],\n [-2, -7, 6, 1],\n [-5, -25, -37, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [2, -4, 0, -1],\n [-4, 8, 0, 2],\n [-2, 4, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, 6, 8, -13],\n [12, 17, 0, 3],\n [-18, -29, 1, -6],\n [-4, -2, 0, -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[[-3, -8, 4, 1],\n [8, 4, 0, -28],\n [0, -9, 9, -12],\n [1, 8, -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[[-9, -6, 18, -9],\n [-4, -6, 3, 6],\n [12, 8, -24, 12],\n [-3, -6, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 2, 14, -9],\n [11, 5, -4, -3],\n [-6, 2, 14, -9],\n [10, 6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 4, -3, 3],\n [2, 24, -12, 20],\n [-8, 0, 9, 1],\n [16, -4, 7, 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 4x4 matrix:\n[[1, -4, -5, -4],\n [-1, 4, 8, 5],\n [8, -32, -4, -20],\n [-6, 24, 6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 12, 0, 3],\n [2, -8, -4, 10],\n [1, -4, -1, 2],\n [-3, 12, -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[[8, 8, 8, 8],\n [-12, -12, -12, -12],\n [4, 4, 4, 4],\n [-16, -16, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 3, -9, -6],\n [0, -4, 12, 8],\n [0, -4, 12, 8],\n [0, 4, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -2, 0, 16],\n [-5, -2, 12, 0],\n [-7, 20, 12, 4],\n [11, 2, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-6, 6, 6, 2],\n [3, -3, -3, -1],\n [12, -12, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -2, 5, 2],\n [12, 14, -24, -6],\n [-11, 12, -5, 10],\n [3, -12, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 6, -4, 6],\n [12, 12, -8, 12],\n [3, 3, -2, 3],\n [12, 12, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 2, -2, -8],\n [16, -4, 4, 16],\n [12, -3, 3, 12],\n [-4, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -2, 12, -7],\n [-2, 3, 12, -5],\n [8, -13, 3, 3],\n [-10, 9, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -17, -23, -3],\n [14, -2, -8, -10],\n [-6, 1, 13, 5],\n [-24, -10, 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 4x4 matrix:\n[[3, 1, 2, -4],\n [-9, -3, -6, 12],\n [-3, -1, -2, 4],\n [6, 2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -5, 2, -14],\n [-2, -4, 4, 8],\n [3, -4, 2, -8],\n [-1, -2, 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[[-8, -4, 8, 0],\n [-6, -3, 6, 0],\n [-4, -2, 4, 0],\n [8, 4, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 6, 20, 12],\n [-2, 1, 17, 14],\n [9, -4, -14, -10],\n [-5, 1, -2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-9, -12, -12, -3],\n [-3, -4, -4, -1],\n [3, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 15, -14, -5],\n [2, -18, 26, 2],\n [7, -33, 31, 7],\n [-5, 9, -6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -4, 15, 4],\n [-6, -5, 5, -1],\n [-6, -4, 2, -4],\n [3, -25, -8, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 1, -11, 0],\n [15, -11, -10, -15],\n [7, -6, -1, -8],\n [-6, 8, 18, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, 6, -15, 0],\n [-1, 4, -5, -5],\n [-8, -8, 4, 16],\n [-6, 4, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -5, 0, 1],\n [-18, 18, -1, -2],\n [-4, 4, 2, -4],\n [4, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 3, 4, -3],\n [-6, 18, 24, 10],\n [0, 24, 32, 16],\n [0, -12, -16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 3, -3, 0],\n [4, -1, 1, 0],\n [0, 0, 0, 0],\n [-4, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -4, -6, -2],\n [6, -6, -9, -3],\n [-4, 4, 6, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 16, 14, 0],\n [-9, -4, 27, -34],\n [5, 16, 4, 12],\n [-1, 16, 23, -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[[0, 2, 2, -4],\n [3, -8, -3, 6],\n [-12, 16, -4, 8],\n [-9, 15, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 12, 12, 9],\n [-1, -4, -4, -3],\n [-1, -4, -4, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -2, -5, 7],\n [-8, 4, 12, -11],\n [12, 0, -10, 9],\n [-6, -10, -1, 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 4x4 matrix:\n[[0, 3, 4, 11],\n [-12, 15, 12, 3],\n [10, -11, -8, 3],\n [-3, 0, -2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 10, 5, 6],\n [9, -4, -11, 3],\n [2, -2, -3, 0],\n [1, 4, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -1, 2, -6],\n [-3, -1, 3, -3],\n [-9, -1, 1, -9],\n [12, 3, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 6, -2, 8],\n [2, 6, -2, 8],\n [4, 12, -4, 16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -20, -10, -12],\n [1, -6, -11, -2],\n [-6, 12, 12, 6],\n [0, -8, -18, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -3, -3, -3],\n [-10, 14, 18, -6],\n [9, -9, -9, -9],\n [14, -16, -18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 4, -8, 2],\n [0, 10, -22, 2],\n [-4, 6, -14, 0],\n [16, 1, 1, 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[[10, 8, 0, 2],\n [8, 4, 2, 4],\n [1, -4, 4, 5],\n [-2, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -4, 5, -21],\n [-28, 28, -14, -6],\n [-12, -1, -23, -10],\n [16, -12, -8, 32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 1, 0, 1],\n [-8, -4, 0, -4],\n [0, 0, 0, 0],\n [-6, -3, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, 2, 0],\n [3, -3, 1, 0],\n [0, 0, 0, 0],\n [3, -3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 1, -11, -15],\n [5, -18, -26, -13],\n [-2, 21, 9, -10],\n [1, 17, 13, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 5, 3, 0],\n [8, 4, 24, 24],\n [-4, -2, -12, -12],\n [0, 3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -8, 8, -8],\n [0, 16, -16, 16],\n [0, 0, 0, 0],\n [0, 12, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 9, -6, -3],\n [-12, 9, -6, -3],\n [12, -9, 6, 3],\n [8, -6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, 6, -2],\n [0, -4, 6, -2],\n [0, 8, -12, 4],\n [0, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -8, -14, 6],\n [4, -12, -24, 11],\n [-10, 12, 15, -5],\n [12, -8, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 8, 12, 7],\n [1, 14, 11, 6],\n [-4, 18, 4, -2],\n [7, -16, -19, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -5, 7, -4],\n [-7, -8, 4, 21],\n [1, -4, -7, -9],\n [-1, -9, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 10, 12, 2],\n [-5, -6, 12, -14],\n [-1, 18, -12, 18],\n [15, -8, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 4, -10, -10],\n [-44, -5, 38, 17],\n [24, 6, -24, -2],\n [-16, 4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, 4, -12],\n [2, 0, -2, 1],\n [6, 1, -7, 6],\n [0, 3, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, 12, -8, 4],\n [0, 0, 0, 0],\n [3, -9, 6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 0, -12],\n [4, 8, 12, -24],\n [-2, 4, 2, 4],\n [-4, 16, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 0, -4, -6],\n [-16, 0, 8, 12],\n [-4, 0, 2, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[18, 5, -14, 16],\n [0, -2, -6, -6],\n [-20, 0, 36, 4],\n [-4, -3, -12, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -3, -1, 3],\n [-6, 9, 3, -9],\n [6, -9, -3, 9],\n [8, -12, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 2, -13, 3],\n [-6, 0, -9, 3],\n [9, 6, -12, 0],\n [-10, -8, 19, -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[[4, 0, 12, 16],\n [1, -2, -2, -4],\n [-2, 4, 4, 8],\n [6, 0, 18, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -18, 14, -2],\n [-5, 10, -33, -6],\n [1, 20, 23, -16],\n [4, 1, 2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 8, 3, 10],\n [20, 2, 12, 13],\n [2, 14, 9, 15],\n [6, 10, 9, 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[[-14, 8, -12, -4],\n [-16, 8, -8, 8],\n [-4, 4, -12, -20],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -8, 4, -4],\n [2, 2, -1, 1],\n [-4, -4, 2, -2],\n [2, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 10, 5, -30],\n [-12, 16, 4, -28],\n [9, 4, 7, -28],\n [3, -20, -7, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 1, 0, 6],\n [-1, -12, -8, 4],\n [3, 13, 6, -4],\n [-6, -2, -6, 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[[-9, -12, 12, 6],\n [-12, -16, 11, 8],\n [-12, -16, 20, 8],\n [9, 12, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -3, -1, 7],\n [7, 20, 16, -7],\n [-12, -5, 1, 24],\n [-1, 2, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -8, 12, 8],\n [0, 0, 0, 0],\n [6, 6, -9, -6],\n [4, 4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -16, 12, 10],\n [0, 14, -8, -11],\n [-2, 8, -6, -5],\n [-17, 5, -15, 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, -9, -9, 4],\n [-10, -5, -4, 1],\n [-6, -2, 9, -5],\n [7, 17, 19, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -9, 3, 12],\n [0, -11, 3, 6],\n [-10, -4, 2, 14],\n [-2, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -4, 2, 9],\n [7, -4, 10, 11],\n [0, 0, 0, 0],\n [3, -6, -15, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 12, -12, -12],\n [6, 6, -12, -6],\n [10, -14, 4, 14],\n [10, -2, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 2, 2, 1],\n [0, 6, 6, 3],\n [0, -8, -8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [4, 8, 0, 12],\n [0, 0, 0, 0],\n [3, 6, 0, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 4, -8, 0],\n [-8, 4, -8, 0],\n [4, -2, 4, 0],\n [12, -6, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -2, 8, -8],\n [12, -4, 8, -16],\n [6, -2, 4, -8],\n [-10, 2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 15, 2, -10],\n [-1, -11, -8, 12],\n [-4, 1, -5, 3],\n [6, -9, 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[[-4, -4, 12, -12],\n [1, -3, -4, 3],\n [1, 1, -3, 3],\n [-4, -12, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, -6, 6, -4],\n [-3, -3, 3, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, -6, -8, 2],\n [-6, -6, 12, -2],\n [-2, 16, -14, 6],\n [4, 1, -5, 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[[4, 0, 0, -8],\n [4, 0, 0, -8],\n [-4, 0, 0, 8],\n [6, 0, 0, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -13, 8, 4],\n [-1, 10, 1, -1],\n [10, -12, 8, -2],\n [-8, -9, -4, 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[[0, 2, -2, 2],\n [0, 1, -1, 1],\n [0, 3, -3, 3],\n [0, 3, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -10, 10, -5],\n [8, -2, 8, -7],\n [1, -4, 1, 1],\n [0, -10, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 16, -16, 8],\n [8, 4, -8, -4],\n [-8, -1, 6, 7],\n [-8, 2, 4, 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[[-14, -18, 14, 2],\n [-16, -16, 16, -8],\n [6, 10, -6, -6],\n [-4, -12, 4, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -6, 5, -6],\n [7, -2, -11, 4],\n [5, -5, -6, -1],\n [-6, 6, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -2, -7, 3],\n [-5, -1, 3, -1],\n [5, -16, -17, 9],\n [-15, -3, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -12, 12, -8],\n [4, 12, -12, 8],\n [4, 12, -12, 8],\n [-3, -9, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -16, 8, 0],\n [-1, 4, -2, 0],\n [-2, 8, -4, 0],\n [-4, 16, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -1, 4, 1],\n [-16, -4, 16, 4],\n [8, 2, -8, -2],\n [-16, -4, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -3, -1, -3],\n [-2, 6, 2, 6],\n [2, -6, -2, -6],\n [-2, 6, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 8, 10, -5],\n [7, -5, 9, -7],\n [3, -2, 5, -7],\n [-5, 4, -6, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 1, 5, 6],\n [1, -8, 3, 8],\n [-11, -11, 2, 3],\n [-10, 3, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 6, -3, 6],\n [2, -4, 2, -4],\n [12, 8, 4, 8],\n [-6, 4, -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[[12, -3, 6, 6],\n [-4, 1, -2, -2],\n [-8, 2, -4, -4],\n [-12, 3, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -8, -6, -2],\n [-3, 4, 3, 1],\n [-12, 16, 12, 4],\n [-6, 8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 6, 4, 4],\n [16, -12, -8, -8],\n [8, -6, -4, -4],\n [-12, 9, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 9, 15, -3],\n [2, 14, 10, -3],\n [-18, -4, 4, 27],\n [13, 0, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 4, -4, -16],\n [-9, 3, -3, -12],\n [-4, -8, 16, 0],\n [1, 2, -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, 0, 0, 0],\n [12, 9, 0, -3],\n [-8, -6, 0, 2],\n [16, 12, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -6, -6, 12],\n [-6, -4, -4, 8],\n [12, 8, 8, -16],\n [6, 4, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, 8, -2, -3],\n [5, 2, -2, -3],\n [13, 7, -4, -6],\n [1, 4, 2, 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, -4, -4, -4],\n [3, -6, -6, -6],\n [4, -8, -8, -8],\n [1, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 1, 4, -2],\n [-6, 3, 6, -12],\n [-12, 0, 12, 12],\n [1, 2, -1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, -2, 6],\n [0, 0, 0, 0],\n [-4, 2, -1, 3],\n [8, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 4, 12, 4],\n [16, -4, -12, -4],\n [-4, 1, 3, 1],\n [4, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -1, -14, -3],\n [3, 8, 7, 0],\n [-9, 3, -8, 3],\n [-7, 4, -4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -12, 4, 4],\n [7, -9, -1, 7],\n [-9, 12, 1, -9],\n [5, -6, -1, 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[[2, 10, 3, 15],\n [-12, 4, -6, -8],\n [0, -6, 6, -16],\n [-18, 18, -15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [1, 1, 3, 1],\n [3, 3, 9, 3],\n [-1, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 6, 0, 8],\n [0, 0, 0, 0],\n [-2, -6, 0, -8],\n [-3, -9, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 12, 0, 6],\n [-12, 3, 0, 6],\n [-30, 17, -12, 20],\n [18, -7, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 16, 8, 0],\n [-3, 4, 2, 0],\n [-9, 12, 6, 0],\n [-12, 16, 8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 25, -28, -4],\n [0, -3, 8, -2],\n [0, -24, 8, 13],\n [-10, -15, 24, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 16, -10, -6],\n [0, -12, 6, 6],\n [12, 10, -1, -9],\n [12, 4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 0, 1, -4],\n [-8, 0, 4, -16],\n [2, 0, -1, 4],\n [-6, 0, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, 3, -2],\n [16, -12, 12, -14],\n [16, -10, 12, -13],\n [20, -18, 15, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -4, -1, -4],\n [-14, 13, 2, 18],\n [4, -28, -12, -8],\n [-1, 7, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 8, 1, -15],\n [14, -2, -16, -6],\n [-11, -12, -9, 15],\n [-16, -4, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -2, -4, -6],\n [-2, 1, 3, 1],\n [3, -3, -8, -5],\n [9, -3, -10, -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[[4, 18, 5, -3],\n [1, -25, -2, -10],\n [-7, -1, 18, 0],\n [-5, 27, 17, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 10, -10, 4],\n [6, 11, -11, -4],\n [12, 2, -2, -16],\n [8, -12, 12, -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[[-4, 20, 7, 6],\n [0, 4, -1, -2],\n [1, -8, -1, 0],\n [-3, 28, 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, -5, -15, -9],\n [16, -9, -13, -12],\n [-2, 4, -6, 4],\n [22, -7, -13, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -10, -11, 15],\n [-4, 3, 17, -15],\n [-4, 0, -3, -2],\n [7, -1, -11, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 4, 2, -8],\n [0, 0, 0, 0],\n [-12, 8, 4, -16],\n [6, -4, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 6, -3, 3],\n [-4, 0, -5, -5],\n [-4, 4, 4, 8],\n [-4, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 8, 11, -1],\n [2, -18, 7, -3],\n [-6, 6, 10, 0],\n [-6, 14, 9, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -6, -1, -3],\n [6, 2, 7, -11],\n [-3, 0, -2, 10],\n [0, 12, 10, -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[[12, -3, -3, -6],\n [4, -1, -1, -2],\n [4, -1, -1, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -8, -3, 10],\n [-6, 4, 9, 0],\n [0, 0, -9, -6],\n [-6, 4, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -1, 0, -3],\n [-9, 3, 0, 9],\n [-12, 4, 0, 12],\n [9, -3, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -1, 13, -7],\n [-20, -12, -6, 11],\n [-24, -18, -18, 20],\n [4, 10, -13, 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 4x4 matrix:\n[[16, 16, 16, -16],\n [-8, -8, -8, 8],\n [-2, 0, -2, 0],\n [-10, -12, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -5, 8, -5],\n [3, -6, 9, -9],\n [6, -5, 8, -5],\n [-16, 4, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, -8, 6],\n [-8, -8, 8, -6],\n [8, 8, -8, 6],\n [-8, -8, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 8, -14, -4],\n [-6, 4, -10, -2],\n [2, 4, -2, -2],\n [-4, 4, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 10, -24, 9],\n [-8, 12, -17, 4],\n [-16, 14, 1, -7],\n [-10, 6, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 2, -24, 20],\n [4, 24, 5, -1],\n [-16, -1, -13, 17],\n [14, 12, 28, -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[[9, 2, -11, -1],\n [-6, 8, -10, -6],\n [-18, 10, 4, -10],\n [-21, 7, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 0, 0, 0],\n [1, 30, -16, 13],\n [8, -12, 10, -7],\n [-3, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -4, 8, -2],\n [-2, 4, -8, 2],\n [4, -8, 16, -4],\n [-4, 8, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -4, -5, 5],\n [5, 1, 12, 21],\n [-5, 2, -5, -5],\n [-7, 2, -7, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 6, -10, -7],\n [-6, -9, 1, -7],\n [6, 9, -5, 2],\n [-2, -3, 3, 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[[8, 7, -8, -4],\n [-4, -2, 4, -4],\n [-6, -5, 6, 2],\n [4, 1, -4, 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[[21, 24, -1, -6],\n [18, 20, -6, -6],\n [6, 9, -2, 12],\n [0, -3, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -1, 2, 1],\n [-8, -4, 8, 4],\n [-20, 4, -8, 0],\n [6, 23, -27, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, -12, 4, 16],\n [0, -3, 1, 4],\n [0, -9, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, 2, -4],\n [4, 8, 2, -4],\n [-8, -16, -4, 8],\n [4, 8, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 13, -8, 15],\n [-14, 2, 0, 6],\n [-12, -3, 3, 0],\n [2, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -6, 8],\n [7, 1, 1, -14],\n [6, -2, 11, -8],\n [-7, -5, 9, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -20, -5, -15],\n [-12, 10, -15, -7],\n [5, 1, -1, 6],\n [1, 8, 7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, 8, -2, 9],\n [8, -16, -12, 0],\n [36, 10, 2, -1],\n [-30, 4, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -12, -11, -20],\n [29, -4, -1, -8],\n [10, -5, -5, -10],\n [14, 9, 9, 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[[-4, 14, -8, 7],\n [-8, 2, 2, -11],\n [-8, 7, -2, -7],\n [2, 5, -3, 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[[0, 0, 0, 0],\n [3, -6, 9, 3],\n [-2, 4, -6, -2],\n [-1, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, 5, 10, -20],\n [6, 1, -3, 24],\n [8, 3, -1, -12],\n [21, 7, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, 4, -12],\n [30, 5, 4, -10],\n [-4, 12, -24, 0],\n [15, -1, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 13, 13, 24],\n [9, -3, 9, 12],\n [-3, -10, -9, -17],\n [-16, 20, -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[[-5, -18, -16, 10],\n [20, 8, -4, 0],\n [15, 6, -3, 0],\n [-12, 8, 16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, -20, -10, -17],\n [12, 0, 40, 4],\n [5, 14, 18, 7],\n [2, -2, 16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 6, -6, -6],\n [0, 4, -2, -3],\n [0, 0, 4, 8],\n [-7, 3, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -10, -29, 21],\n [-22, 22, 22, -4],\n [-2, 1, 4, -4],\n [4, 6, 26, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-3, -9, 0, 0],\n [1, 3, 0, 0],\n [-1, -3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -12, -2, 16],\n [1, -3, -13, -1],\n [-22, -18, -20, 22],\n [10, 6, 9, -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[[8, 6, -8, 2],\n [0, 3, 8, 1],\n [-4, -6, -4, -2],\n [0, -3, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 2, -8, -6],\n [6, -2, -4, 0],\n [-3, -5, 8, 9],\n [1, -1, 0, 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[[-4, 2, -8, -2],\n [0, 5, 8, 1],\n [-8, 4, -16, -4],\n [3, 6, 18, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -2, 3, 1],\n [-2, -4, 6, 2],\n [0, 0, 0, 0],\n [3, 6, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -2, -12, 0],\n [8, 6, -8, -4],\n [12, 9, -12, -6],\n [-12, 2, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 1, -14, 5],\n [12, -5, 10, -1],\n [-14, -4, 4, -4],\n [-1, 8, -2, -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[[-10, 12, 24, -16],\n [-18, 7, 16, -10],\n [-4, -21, 4, -8],\n [-6, 11, 16, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -18, 9, 7],\n [0, 0, 0, 0],\n [13, -7, 12, 15],\n [-8, -13, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 8, -8, 4],\n [12, -8, 8, -4],\n [6, -4, 4, -2],\n [-9, 6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -6, 6, 6],\n [12, -16, 11, 2],\n [12, -25, 19, 8],\n [-12, 14, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -1, -9, 8],\n [8, 14, 2, 8],\n [22, 12, -18, 4],\n [10, -2, -18, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -10, 7, -18],\n [-8, 10, -11, 6],\n [12, -6, 5, 6],\n [-8, -2, -4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 6, 12, -9],\n [4, -4, -8, 6],\n [4, 2, -16, 10],\n [2, -8, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 3, -15, 4],\n [12, -5, 19, -5],\n [10, -10, 8, -6],\n [-9, 9, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -20, -1, 5],\n [8, 24, -14, 22],\n [10, -4, -14, 28],\n [-8, -4, 21, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 12, -1, -4],\n [8, 3, 16, -1],\n [11, -6, 13, 2],\n [9, -9, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -16, -4, 8],\n [-4, 2, 9, 0],\n [-8, 4, 18, 0],\n [-4, 6, -7, -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 4x4 matrix:\n[[7, -3, -9, -5],\n [-8, -4, -12, -11],\n [16, 0, 0, 4],\n [4, 4, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -12, 6, 0],\n [6, 8, -4, 0],\n [-9, -12, 6, 0],\n [12, 16, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -6, 4, -8],\n [0, 9, -6, 12],\n [0, 8, -6, 7],\n [0, 10, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 2, 3, 0],\n [4, 4, 6, 0],\n [8, 8, 12, 0],\n [-6, -6, -9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 2, -8, -3],\n [9, 14, 5, 7],\n [1, -10, -5, -9],\n [-1, -22, 13, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -4, 4, -2],\n [0, -8, 8, -4],\n [0, 0, 0, 0],\n [0, -12, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -5, -20, -18],\n [-9, -6, -24, -21],\n [11, 6, 24, 20],\n [-3, 1, 4, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -8, -8, 4],\n [-9, 12, 12, -6],\n [-12, 16, 16, -8],\n [-12, 16, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -12, -16, -18],\n [4, 28, 16, 10],\n [0, -12, -8, -6],\n [2, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 0, -4, 7],\n [12, -8, -24, 18],\n [6, -7, -12, 0],\n [-6, 6, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 3, 6, -6],\n [-8, 2, 4, -4],\n [-4, 1, 2, -2],\n [-8, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 7, 13, 19],\n [-3, 11, 14, 23],\n [-20, 9, 21, 33],\n [37, 0, -15, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -3, 1, 1],\n [6, 9, 3, -15],\n [-1, 9, 1, -11],\n [-6, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 0, 1, 14],\n [8, -8, -2, 4],\n [10, -8, -7, -2],\n [-16, 18, 4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 10, 0, -4],\n [-4, -8, 8, 9],\n [-8, 4, 8, 8],\n [-13, -8, 18, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -5, -1, -18],\n [-1, 6, 6, -3],\n [14, 9, 12, -6],\n [-3, -10, -11, 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[[-2, 8, 8, -6],\n [2, -8, -8, 6],\n [-3, 12, 12, -9],\n [-1, 4, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 16, 0, -16],\n [17, -18, -6, -10],\n [-3, 10, -3, 15],\n [8, 8, -9, 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[[-22, 25, 9, -8],\n [-20, 16, 20, -16],\n [15, -15, -11, 9],\n [6, 7, 19, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 3, 0, 1],\n [0, 3, 0, 1],\n [-2, -8, 2, -10],\n [-3, 9, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -4, 6, 0],\n [-9, 6, -9, 0],\n [12, -8, 12, 0],\n [-9, 6, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -16, 18, -2],\n [8, -16, 16, 0],\n [-10, 16, -18, 2],\n [0, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -14, -6, -8],\n [12, 16, 4, 2],\n [16, 20, 6, 5],\n [-16, -20, -6, -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[[-16, 16, -5, -10],\n [-6, -6, 13, -6],\n [-8, 0, -24, 0],\n [16, 5, -2, 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[[-2, -6, -16, 4],\n [-16, 9, 22, 0],\n [-14, -6, 20, 12],\n [-13, -3, 28, 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 4x4 matrix:\n[[-18, -3, 6, -10],\n [3, 3, -3, -3],\n [-14, -2, 5, -6],\n [-8, -20, 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[[2, 6, 6, -8],\n [-2, -6, -6, 8],\n [-2, -6, -6, 8],\n [4, 12, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -7, -17, 17],\n [-9, 4, -1, 1],\n [-8, 9, -1, 1],\n [-14, 5, -15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -6, 0, -18],\n [4, -10, 4, -16],\n [-5, 6, 0, 12],\n [4, 2, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 8, 0, -6],\n [-8, -8, 0, 6],\n [12, 12, 0, -9],\n [12, 12, 0, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -5, -2, -2],\n [-7, 10, -9, -9],\n [4, -5, -2, -2],\n [-7, 9, 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[[12, -24, -13, -28],\n [0, 12, 4, 16],\n [-16, 4, 8, 0],\n [-16, 25, 15, 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[[0, 0, 0, 0],\n [8, 8, -4, 0],\n [-8, -8, 4, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 8, 22, 5],\n [12, 0, 0, 18],\n [-24, -8, -32, 4],\n [14, 6, 14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -12, 9, -6],\n [0, -16, 12, -8],\n [0, 8, -6, 4],\n [0, -16, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -6, 4, -4],\n [-4, -6, 4, -4],\n [4, 6, -4, 4],\n [8, 12, -8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -22, 12, -3],\n [10, -20, 3, -7],\n [-14, -6, 12, -6],\n [2, 22, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 4, -3, 4],\n [2, -4, 3, -4],\n [-4, 8, -6, 8],\n [-8, 16, -12, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 2, -5, -6],\n [-12, 15, -6, 0],\n [-16, 12, -2, 4],\n [-12, 19, -9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 4, -2, -1],\n [-2, -4, 2, 1],\n [4, 8, -4, -2],\n [2, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-18, -20, -8, -10],\n [6, 4, -2, 8],\n [-2, -4, -4, 2],\n [9, 14, 11, -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, 4, 10, -5],\n [7, -4, -6, -1],\n [1, 3, 7, -3],\n [-8, -4, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, -4, 0],\n [-2, 2, 1, 0],\n [-2, 2, 1, 0],\n [-6, 6, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 10, -7, -11],\n [-10, 11, -1, 7],\n [-4, -13, 19, 4],\n [26, -5, -3, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 7, 1, -6],\n [15, -9, -2, 3],\n [-15, 7, 8, 5],\n [27, -6, -21, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -3, 9, 3],\n [-2, -2, 6, 2],\n [1, 1, -3, -1],\n [-1, -1, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -8, -2, -2],\n [1, 16, -1, 1],\n [-6, -9, 12, -3],\n [-1, -40, 9, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 16, -4, 0],\n [14, 10, -1, -12],\n [7, 2, -23, -2],\n [-15, -5, -7, 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[[-4, -2, -1, 2],\n [-16, -8, -4, 8],\n [8, 4, 2, -4],\n [-4, -2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 10, -7, 5],\n [8, -10, 14, 2],\n [1, -14, 13, -9],\n [7, -8, 13, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 6, -10, 0],\n [-3, -1, 2, -6],\n [4, 16, 4, 28],\n [-3, -21, 12, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 8, -2, 0],\n [-8, 24, -8, -8],\n [4, -22, 8, 10],\n [-12, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 6, 9, -8],\n [-6, -12, -13, 6],\n [6, 0, -3, 6],\n [0, 12, 16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 6, 2, -2],\n [-3, -3, -1, 1],\n [-9, -9, -3, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -5, 12, 4],\n [-12, 16, 12, 16],\n [6, -3, 24, 12],\n [-20, 22, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -18, 2, -7],\n [0, -12, 8, -10],\n [-10, -2, -7, 5],\n [10, -4, 11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 9, 15, 20],\n [-16, -2, -16, 4],\n [-4, -1, -5, 0],\n [16, -10, -8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 34, 7, 10],\n [23, 14, -5, 13],\n [10, 12, 0, 5],\n [16, 8, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 0, -16, -8],\n [12, 0, -12, -6],\n [4, 0, -4, -2],\n [-12, 0, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 14, -7, 12],\n [9, 0, 0, 3],\n [-1, -4, 2, -3],\n [16, 10, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [12, 12, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 8, -2, -8],\n [0, 0, 0, 0],\n [-4, 4, -1, -4],\n [12, -12, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 12, 0, -4],\n [-14, -10, 16, 6],\n [0, 0, 0, 0],\n [-10, -2, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 16, 0, -12],\n [17, 12, 4, -25],\n [5, 12, -2, -1],\n [-11, -12, -1, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 32, -8, 8],\n [4, -16, 12, 4],\n [-4, 0, 8, 8],\n [-5, -4, 15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -1, 20, 6],\n [21, 1, 2, 19],\n [15, 4, -8, 7],\n [12, 2, 1, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 0, 4, 16],\n [-20, -9, -11, -17],\n [-16, -3, -6, -15],\n [16, 6, 8, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, 8, -8],\n [6, -3, -12, 12],\n [2, -1, -4, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -1, -3, 0],\n [-3, 1, 3, 0],\n [-9, 3, 9, 0],\n [-6, 2, 6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -3, -1, 2],\n [12, -12, -4, 8],\n [12, -12, -4, 8],\n [-6, 6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 2, 0, 1],\n [7, 3, -7, -5],\n [29, 10, -12, -9],\n [-5, -6, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -23, -9, -1],\n [-1, 10, 11, 8],\n [17, -21, -3, 13],\n [-1, -3, 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, -2, -3, 0],\n [-4, 10, 9, -8],\n [1, -4, -3, 4],\n [-4, -8, 0, 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 4x4 matrix:\n[[6, -8, -2, 6],\n [-6, 8, 2, -6],\n [-6, 8, 2, -6],\n [3, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -8, 2, 8],\n [0, -12, 0, 0],\n [-9, 28, -3, -12],\n [9, -28, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, -8, -6],\n [1, -1, -4, -3],\n [-3, 3, 12, 9],\n [-4, 4, 16, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 9, 9, -9],\n [-12, 12, 12, -12],\n [-6, 6, 6, -6],\n [-12, 12, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 6, -4, -8],\n [11, 9, -10, -16],\n [-1, 0, -4, -4],\n [-8, -6, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 4, -5, 11],\n [7, -4, 3, -7],\n [14, -8, 6, -14],\n [-12, 0, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 2, 4, -10],\n [-3, 7, 0, 1],\n [-7, 8, -5, 14],\n [-7, 13, -2, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 8, 6, -2],\n [-4, -8, -6, 2],\n [-4, -8, -6, 2],\n [-8, -16, -12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -6, -10, 8],\n [-2, 10, 0, -5],\n [-22, -13, 6, -16],\n [-10, -13, 18, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -18, 12, -4],\n [-20, -4, -28, 16],\n [20, 4, 4, -20],\n [-21, 27, -21, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -1, 3, -1],\n [0, 3, -9, 3],\n [0, 2, -6, 2],\n [0, -4, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, 18, 0],\n [12, -16, 10, 0],\n [12, 4, 20, 0],\n [12, -20, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 8, -8, 2],\n [3, 4, -4, 1],\n [-6, -8, 8, -2],\n [6, 8, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 8, -8, -8],\n [-12, -8, 8, 8],\n [-6, -4, 4, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 4, 2, 3],\n [16, -6, -21, -22],\n [-28, -10, 18, 21],\n [8, 20, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -2, -8, -6],\n [12, -3, -12, -9],\n [-12, 3, 12, 9],\n [16, -4, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 8, -4, 16],\n [-4, -1, 3, 0],\n [19, -2, -9, -12],\n [-14, 1, 7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 13, -15, 15],\n [-8, -17, 11, -11],\n [-6, -9, 5, -5],\n [-10, -10, 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[[-5, -2, 5, 1],\n [-3, 3, -11, 9],\n [10, -2, 10, -14],\n [8, -4, 16, -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 4x4 matrix:\n[[4, -4, -4, 8],\n [7, 3, 5, 0],\n [-14, -6, -10, 0],\n [-12, -8, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -1, -1, 3],\n [-6, 2, 2, -6],\n [-9, 3, 3, -9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 6, 8, 6],\n [0, -12, -16, -12],\n [0, 6, 8, 6],\n [0, -6, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 2, 0, -2],\n [12, -4, 0, 4],\n [-3, 1, 0, -1],\n [6, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -2, -3, -1],\n [3, -2, -3, -1],\n [-6, 4, 6, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 6, 3, -9],\n [9, -6, -3, 9],\n [12, 0, 0, 0],\n [10, -8, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -3, 12, -9],\n [-1, -1, 4, -3],\n [-4, -4, 16, -12],\n [4, 4, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -6, -4, 12],\n [8, -5, 20, -4],\n [-12, 15, 0, -24],\n [12, -9, 24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 0, 9, 3],\n [-12, 0, -12, -4],\n [6, 0, 6, 2],\n [-3, 0, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -2, -1, -2],\n [4, -14, 11, -14],\n [8, -16, 12, -16],\n [-20, -2, 5, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 3, -6, -4],\n [12, -2, 20, 8],\n [-6, -4, 10, 6],\n [9, -1, 13, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -3, -9, 12],\n [-2, 1, 3, -4],\n [0, 0, 0, 0],\n [6, -3, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 6, 6, -6],\n [6, -6, -6, 6],\n [3, -3, -3, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 18, -5, 7],\n [4, 11, -2, 4],\n [-4, 24, -13, 11],\n [4, -10, 7, -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, 0, 10, -12],\n [-18, -14, 2, 20],\n [28, 20, 0, -32],\n [0, -8, 14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 10, 0, -6],\n [3, 15, 0, -9],\n [-1, -5, 0, 3],\n [-8, 14, 0, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, -20, -13],\n [3, -3, -4, -4],\n [5, -5, -8, -7],\n [-2, 2, 12, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, -4, -1],\n [8, -4, 8, 2],\n [-12, 6, -12, -3],\n [-12, 6, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, 4, -2],\n [-8, 8, -8, 4],\n [4, -4, 4, -2],\n [4, -4, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -11, 1, 6],\n [7, 4, -10, 8],\n [-7, -11, 3, 4],\n [17, 23, -11, -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[[0, 12, 8, 8],\n [0, 6, 4, 4],\n [0, -12, -8, -8],\n [0, 9, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -6, -8, 4],\n [4, -3, -4, 2],\n [8, -6, -8, 4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -9, -16, 2],\n [-1, -3, -24, -2],\n [7, -9, -2, 4],\n [-16, 18, -10, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 16, 4, 8],\n [1, 4, 1, 2],\n [-3, -12, -3, -6],\n [-4, -16, -4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 12, -24, 3],\n [-12, -18, 14, -1],\n [3, 1, -17, 1],\n [-12, -5, -7, 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[[0, 3, 1, -1],\n [0, -6, -2, 2],\n [0, 12, 4, -4],\n [0, -12, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 2, -2, -1],\n [-12, 8, -8, -4],\n [-9, 6, -6, -3],\n [9, -6, 6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -18, 5, 3],\n [-6, -22, -5, 2],\n [13, 29, -3, 6],\n [-8, -20, 4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -18, 6, -4],\n [-7, 15, -4, 3],\n [3, 6, -10, 16],\n [-12, 27, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 23, -2, -20],\n [24, 6, -4, -8],\n [10, 30, 0, -24],\n [-6, 1, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -8, -8, -12],\n [-3, -13, -11, -1],\n [2, 2, 5, -3],\n [21, -13, 3, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 6, -4, 0],\n [-8, -12, 8, 0],\n [8, 12, -8, 0],\n [6, 9, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 2, -22, -4],\n [3, 7, -2, -4],\n [12, -4, -16, 0],\n [-6, 2, 8, 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 4x4 matrix:\n[[-2, -4, 0, -8],\n [2, 4, 0, 8],\n [-1, -2, 0, -4],\n [-4, -8, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 9, 27, 23],\n [13, 7, 12, 13],\n [7, 3, 1, 5],\n [-4, -16, -44, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -5, 1, 8],\n [-1, 7, -3, -8],\n [1, -7, 3, 8],\n [2, 8, -4, -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[[-13, 6, -15, -3],\n [-9, -6, -3, -3],\n [15, -1, 13, 4],\n [11, 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[[-6, 6, 5, -7],\n [9, 9, 21, -6],\n [12, 0, 9, 3],\n [4, 12, 22, -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[[-3, 1, -3, 9],\n [-5, -11, 7, -1],\n [14, 31, -16, -5],\n [2, 15, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -3, 0, -4],\n [-9, 9, 0, 12],\n [-3, 3, 0, 4],\n [12, -12, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -2, 2, 15],\n [-6, -4, 9, 29],\n [-19, -9, -2, -12],\n [3, 14, 7, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, 2, -4],\n [-6, 4, 2, -4],\n [6, -4, -2, 4],\n [-9, 6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 4, 7, -2],\n [-15, -24, -15, -15],\n [-4, -4, 2, -7],\n [-5, -8, -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[[20, -2, 4, -5],\n [3, -1, 2, 13],\n [-11, 5, -10, -7],\n [18, -5, 10, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 16, 16, -12],\n [8, 14, 18, -11],\n [-2, -16, 16, -1],\n [12, 6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 3, 3, -9],\n [4, -4, -4, 12],\n [-1, 1, 1, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 8, 16, -8],\n [-2, -4, -8, 4],\n [4, 8, 16, -8],\n [-4, -8, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 12, -9, -12],\n [-5, -14, 1, 8],\n [-7, 7, -5, -14],\n [-5, -1, 1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 0, -8, 12],\n [0, 0, 0, 0],\n [6, 0, 4, -6],\n [12, 0, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -16, -16, -16],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 10, -2, -2],\n [12, -4, 16, 4],\n [-15, 3, -17, 9],\n [12, 15, 15, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, 4, 7],\n [2, 13, 5, -16],\n [0, -9, -3, 15],\n [10, 17, 9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [16, -12, 0, 0],\n [12, -9, 0, 0],\n [4, -3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -20, 20, 32],\n [16, -2, -2, 0],\n [-4, -2, 3, 4],\n [-16, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -9, 6, 0],\n [6, 8, -2, -8],\n [5, 6, 1, -12],\n [6, 8, -2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 16, 12, -2],\n [-11, 4, 3, -4],\n [1, -8, -6, 2],\n [15, -8, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 1, -3, -1],\n [5, -3, 6, 1],\n [-13, 26, -3, 10],\n [-18, 26, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -12, -8, 1],\n [-32, 20, -8, 20],\n [-16, 3, -22, 23],\n [12, -8, 4, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -12, 4, 8],\n [9, 9, -3, -6],\n [9, 9, -3, -6],\n [12, 12, -4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -8, -4, 9],\n [-16, 0, -16, -12],\n [-5, -12, 4, 3],\n [2, -12, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -1, 12, -6],\n [-15, -3, -17, -10],\n [17, -12, -15, 20],\n [-6, 3, 24, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -6, 6, -9],\n [0, -2, 3, -4],\n [3, -19, 15, -2],\n [2, -6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -9, 12, -9],\n [2, -3, 4, -3],\n [4, -6, 8, -6],\n [-4, 6, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 9, -12, -3],\n [-4, -6, 8, 2],\n [-8, -12, 16, 4],\n [2, 3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -20, -16, -6],\n [-2, 8, 4, -6],\n [-1, 18, 12, -3],\n [1, -25, -17, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 12, -6, 0],\n [0, 0, 0, 0],\n [4, 8, -4, 0],\n [-8, -16, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -3, 12, -6],\n [-2, 2, -8, 4],\n [1, -1, 4, -2],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 1, -4, -1],\n [-5, -2, 1, -2],\n [2, 6, 6, 10],\n [-30, -6, 14, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -14, -8, 10],\n [-1, -8, -2, -11],\n [1, 4, 2, -1],\n [-1, -4, -2, 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 4x4 matrix:\n[[0, -12, 12, 9],\n [0, 16, -16, -12],\n [0, -12, 12, 9],\n [0, -12, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -3, 9, 0],\n [6, -3, 9, 0],\n [6, -3, 9, 0],\n [-2, 1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, -6, 4],\n [2, -1, 3, -2],\n [6, -3, 9, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -1, 2, 1],\n [2, 2, -4, -2],\n [4, 4, -8, -4],\n [-4, -4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 7, 6, 11],\n [5, -4, 14, 9],\n [-3, 1, -2, 13],\n [4, -3, 4, 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 4x4 matrix:\n[[-14, 18, 3, -16],\n [1, 8, -3, 16],\n [4, -6, -9, -8],\n [-3, -10, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -8, 8, -8],\n [12, 16, -16, 16],\n [-12, -16, 16, -16],\n [6, 8, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-8, -4, 4, -16],\n [-8, -4, 4, -16],\n [2, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 4, 10, -2],\n [2, -8, -2, 1],\n [-8, 22, 13, -4],\n [-8, 14, 17, -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[[-10, -1, 1, 0],\n [26, 10, 23, -32],\n [14, -8, 5, -8],\n [-4, -11, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 4, 4, -4],\n [12, -16, -16, 16],\n [0, 0, 0, 0],\n [-9, 12, 12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 1, 2, -1],\n [0, 4, 8, -4],\n [0, -1, -2, 1],\n [0, -2, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -12, -9, -3],\n [0, -12, 5, 7],\n [24, 0, 28, 20],\n [16, -8, 22, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 6, 6, 2],\n [0, 12, 12, 4],\n [0, 3, 3, 1],\n [0, -3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, 4, 0],\n [8, -4, 8, 0],\n [-4, 2, -4, 0],\n [16, -8, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 15, -11, -8],\n [0, 24, -16, -12],\n [-2, -21, 13, 10],\n [2, -3, 3, 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[[3, -3, 3, -4],\n [-12, 12, -12, 16],\n [0, 0, 0, 0],\n [-12, 12, -12, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 21, 24, 4],\n [0, -15, -1, 11],\n [12, 6, -2, -10],\n [15, 6, 15, 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 4x4 matrix:\n[[0, 14, 8, 2],\n [28, 2, 0, 13],\n [-20, 2, 24, -29],\n [-26, 0, 10, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -13, -6, -15],\n [2, 0, 4, -14],\n [20, -9, 14, 9],\n [9, 9, 8, 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, 8, -4, 4],\n [-17, 0, -5, -7],\n [4, -3, 4, 2],\n [22, -8, 14, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -1, 2, -3],\n [0, 0, 0, 0],\n [0, 3, -6, 9],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 5, 15, 12],\n [-4, -2, -6, -16],\n [6, 1, 15, 0],\n [-16, 7, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 20, -4, 12],\n [-14, 17, -13, 0],\n [8, -14, 22, 12],\n [12, -11, -1, -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[[20, -9, 1, 6],\n [-18, 8, 0, 1],\n [-10, 0, -4, -12],\n [-6, 2, 2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -10, 6, 1],\n [5, -2, -2, 13],\n [3, -6, 6, -9],\n [-16, 20, -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[[-14, 2, -4, -4],\n [-8, 0, -8, -4],\n [1, -3, -14, -4],\n [19, -1, 14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -12, 6, 25],\n [0, 16, 2, -20],\n [2, 8, 4, -6],\n [-2, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, -8, 0],\n [2, -1, 2, 0],\n [2, -1, 2, 0],\n [-4, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, -2, -2],\n [-1, -9, -4, 2],\n [-11, 9, 10, 4],\n [-3, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 11, 11, 4],\n [-3, -10, 20, 17],\n [15, 14, 4, -1],\n [6, 1, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 5, 1, 13],\n [-4, -4, -2, -10],\n [-4, -2, 2, -6],\n [4, -2, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -8, 18, -18],\n [0, 0, 0, 0],\n [-3, 6, -6, 6],\n [5, 6, -14, 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[[-13, -7, -8, 3],\n [19, 5, 10, -6],\n [28, 18, 20, -5],\n [-22, -20, -18, 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[[0, -2, 8, -4],\n [5, -12, -2, 1],\n [-3, 7, 2, -1],\n [1, 1, -14, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, -8, -16, 16],\n [12, 8, -8, -8],\n [1, 5, 5, -11],\n [24, -15, -7, 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[[0, 14, -4, 6],\n [16, -17, -20, 21],\n [23, -3, -21, 12],\n [-19, -1, 8, 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[[6, 7, 12, -13],\n [-5, -5, -9, 10],\n [-4, 2, 0, 2],\n [-4, -8, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -9, -13, -8],\n [-6, -6, -18, -18],\n [4, 8, 16, 20],\n [7, 5, 21, 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[[-2, 14, -6, -6],\n [8, 33, -26, -29],\n [19, 1, 7, -11],\n [14, 11, 2, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -26, -14, 2],\n [4, -2, -7, 8],\n [33, 15, 0, 3],\n [-10, 11, 19, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -16, -9, 15],\n [-1, -4, 0, -3],\n [5, 12, 2, 3],\n [7, 16, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -17, -5, -13],\n [-6, -13, -4, -10],\n [-6, -2, -2, -2],\n [-12, -4, -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[[0, 3, 6, 12],\n [0, -1, -2, -4],\n [0, -2, -4, -8],\n [0, 4, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 12, 0, -8],\n [-11, 7, -4, 14],\n [0, -3, -3, 16],\n [1, -5, -4, 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 4x4 matrix:\n[[14, 1, 12, -2],\n [0, 22, 14, -8],\n [-4, 20, 20, -4],\n [2, -4, -13, -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 4x4 matrix:\n[[-6, -6, 3, -9],\n [-2, -2, 1, -3],\n [-8, -8, 4, -12],\n [6, 6, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -5, 1, 3],\n [26, 0, -8, -2],\n [-20, -6, -1, 2],\n [9, -12, -9, 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[[-1, -10, 3, -7],\n [2, 0, -6, -6],\n [-2, -6, 6, 0],\n [2, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -6, 0, -4],\n [16, 12, 0, 8],\n [16, 12, 0, 8],\n [8, 6, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, 4, 7, -20],\n [6, 1, 3, 0],\n [-2, -1, -1, 8],\n [10, 4, 5, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 0, 14, 2],\n [-2, 3, 25, 4],\n [3, 9, 12, 3],\n [1, 6, 15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -9, 0, 9],\n [4, -6, 0, 6],\n [4, -6, 0, 6],\n [4, -6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -13, 7, 6],\n [-4, 1, 1, 2],\n [6, -15, 16, -9],\n [20, -14, 0, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -3, -6, -6],\n [4, 2, 4, 4],\n [-6, -3, -6, -6],\n [6, 3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -5, -3, -8],\n [8, 5, 7, 0],\n [-12, -5, -7, -11],\n [-8, -4, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, 24, 16],\n [-2, 0, 12, 8],\n [3, 12, 0, 0],\n [1, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, 0, 4, 6],\n [-9, -6, -2, -1],\n [1, -4, -2, -3],\n [-8, -1, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 6, 19, 15],\n [0, 4, -26, -10],\n [8, -14, 23, 7],\n [-6, 10, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -2, 8, 0],\n [0, 0, 0, 0],\n [-9, -3, 12, 0],\n [9, 3, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -4, 4, 12],\n [-14, 13, 6, -3],\n [-6, -4, 8, -3],\n [3, -9, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 8, -2, 11],\n [-6, 11, 2, 11],\n [2, -4, -7, 4],\n [8, -16, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -5, -8, -10],\n [-12, 9, 24, 6],\n [0, 3, 0, 12],\n [-10, 7, 20, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 12, 3, -12],\n [0, 0, 0, 0],\n [-3, 4, 1, -4],\n [6, -8, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 12, -6],\n [0, 0, -8, 4],\n [0, 0, 8, -4],\n [0, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 17, -10, -12],\n [-8, -14, 16, 12],\n [4, 9, -4, -6],\n [8, 13, -18, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -6, 3, 0],\n [-8, 8, -4, 0],\n [8, 4, -2, 0],\n [-4, -4, 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[[-6, -10, -3, 7],\n [-18, 16, 21, -7],\n [10, 4, -20, 0],\n [-10, -5, 5, 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 4x4 matrix:\n[[4, 5, 31, 4],\n [16, 7, 20, 3],\n [6, -1, -30, -4],\n [-4, -7, -13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 6, 9, 3],\n [10, 6, -29, -7],\n [-14, -3, -6, -19],\n [-14, 7, 2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 12, 0, 8],\n [5, 8, -4, 6],\n [18, -11, -32, 6],\n [-1, 27, 24, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 6, 8, -12],\n [-22, -6, 12, 16],\n [-14, -6, 2, 14],\n [-5, -17, 10, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 0, 3, -9],\n [-3, 0, 1, -3],\n [0, 0, 0, 0],\n [9, 0, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -12, -8, -4],\n [3, 9, 6, 3],\n [-1, -3, -2, -1],\n [2, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -4, -20, 4],\n [-9, -19, -17, 1],\n [6, -10, 4, 6],\n [13, 9, 18, -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, 6, 5, 18],\n [-6, 6, 1, 17],\n [8, -8, -18, -21],\n [-8, 8, 18, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -4, 8, 0],\n [-16, -8, 16, 0],\n [12, 6, -12, 0],\n [8, 4, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -4, -2, -2],\n [9, -4, -2, -2],\n [13, -8, -9, -4],\n [11, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 12, -9, 9],\n [0, 13, -11, 6],\n [3, -1, 2, 3],\n [-2, -8, 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[[1, -13, -9, -2],\n [-9, 15, 23, -4],\n [-2, 4, -10, 2],\n [3, 9, -9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -3, -9, -6],\n [-8, -4, -12, -8],\n [8, 4, 12, 8],\n [6, 3, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[28, 18, -2, 18],\n [-16, 0, 26, -6],\n [5, -3, -10, 0],\n [1, 15, -3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 0, 4, -12],\n [24, -10, -5, 8],\n [32, -20, -2, -8],\n [8, -4, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [4, 1, -3, -1],\n [-8, -2, 6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 4, -1, 0],\n [-6, 12, 3, 12],\n [4, -16, -3, -14],\n [-11, 10, 4, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 0, 3, -32],\n [-25, -5, -17, -22],\n [12, 3, 12, -6],\n [-2, 4, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -6, 2, -4],\n [-8, 0, 6, 2],\n [14, 6, -8, 2],\n [-9, 3, 8, 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, 28, 24, -12],\n [11, 6, 4, -12],\n [6, 8, 0, -6],\n [-2, -6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 6, -10, -20],\n [3, 0, 1, -4],\n [6, -6, 15, 0],\n [-2, -4, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -1, 8, -10],\n [-12, 8, -2, 2],\n [-12, 5, -9, 11],\n [-14, 7, -8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -9, -1, -1],\n [0, 28, 12, -20],\n [0, -21, -9, 15],\n [12, -16, -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[[-3, -6, -6, -6],\n [-2, -4, -4, -4],\n [-3, -6, -6, -6],\n [-2, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -2, -4, -11],\n [-7, 5, -1, 2],\n [-2, 6, -6, -8],\n [-14, 2, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -4, 16, 12],\n [-12, -3, 12, 9],\n [8, 2, -8, -6],\n [16, 4, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 6, -2, -4],\n [-7, -5, -7, 0],\n [6, -5, 6, 5],\n [24, 19, 24, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 2, -20, -14],\n [-16, -8, 0, 16],\n [-3, -15, 8, 6],\n [12, 16, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 4, 7, 9],\n [-36, -4, -19, -9],\n [-10, 2, -2, -3],\n [40, 4, 20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 6, 8, -2],\n [-1, -3, -1, 1],\n [8, 0, -6, 0],\n [-16, 12, 19, -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[[2, -1, 0, -3],\n [16, -6, 12, -18],\n [-9, 4, -3, 12],\n [-1, 1, 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[[0, 0, 0, 0],\n [0, -1, 3, -4],\n [0, 3, -9, 12],\n [0, 2, -6, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 24, 14, -24],\n [3, 0, -5, 0],\n [0, 12, 17, -12],\n [-7, -4, 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 4x4 matrix:\n[[0, 8, -14, -15],\n [0, -13, 2, 3],\n [0, 1, 0, -1],\n [0, 9, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 0, 2, 2],\n [21, 12, 17, 21],\n [12, 6, 8, 12],\n [5, 6, 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 4x4 matrix:\n[[4, 0, -2, -2],\n [-6, 0, 3, 3],\n [0, 0, 0, 0],\n [-4, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-36, 2, -9, 12],\n [-12, -12, -6, 9],\n [4, 14, -13, -18],\n [4, 9, 22, 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[[-2, -1, -3, -2],\n [6, 6, 9, 4],\n [6, -9, 9, 14],\n [0, 6, 0, -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 4x4 matrix:\n[[-2, 6, 16, -14],\n [22, -6, 12, -4],\n [16, -4, 0, 6],\n [0, 4, 16, -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[[2, 4, 4, 3],\n [-6, -12, -12, -9],\n [-2, -4, -4, -3],\n [-4, -8, -8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -24, -10, -11],\n [-2, 1, -1, 4],\n [-14, 24, 10, 11],\n [-8, 16, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 3, 2, 9],\n [2, 2, -10, -11],\n [0, 0, 4, 6],\n [-1, -1, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 7, 9, 18],\n [-8, -14, -6, -9],\n [-8, -8, 7, 9],\n [-4, 7, 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[[16, 16, -8, -16],\n [-8, -8, 4, 8],\n [-16, -16, 8, 16],\n [-12, -12, 6, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -8, -16, -8],\n [0, -2, -4, -2],\n [0, 4, 8, 4],\n [0, -4, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 21, 14, -7],\n [8, 24, 16, -4],\n [-18, -9, -6, -16],\n [8, 6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 30, 24, -16],\n [-6, 4, -13, 10],\n [-4, 6, 8, -20],\n [-2, 8, 11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -4, -7, -8],\n [-6, 4, 1, -16],\n [-8, 0, -4, -16],\n [6, 4, 7, 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 4x4 matrix:\n[[6, -5, -1, -12],\n [12, -10, -2, -24],\n [-14, 1, 13, -4],\n [12, 2, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -15, 6, 12],\n [19, -3, -20, -14],\n [0, -3, 7, 4],\n [11, -9, -17, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -5, 2, -8],\n [5, 0, 11, 6],\n [-3, 3, -21, -6],\n [-17, -8, 1, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -12, 9, 9],\n [-2, -4, 3, 3],\n [2, 4, -3, -3],\n [4, 8, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 4, -12, -18],\n [10, 2, 8, -2],\n [-4, -4, 0, 12],\n [-3, 3, -6, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 4, 6, 10],\n [-1, -1, 11, 11],\n [2, 2, 10, 26],\n [1, 10, -4, -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, 13, -10, 13],\n [19, 17, -12, 9],\n [-18, -4, 5, -15],\n [-6, 7, 15, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -3, 0, 9],\n [-13, -8, -15, 6],\n [-8, 2, -6, 6],\n [-2, 23, -3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 4, -20, -12],\n [12, 4, 8, 36],\n [0, 2, -4, 10],\n [10, 2, 8, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 3, -6, 0],\n [5, 3, -2, 2],\n [5, 3, -2, 2],\n [-4, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 20, 12, -7],\n [0, 0, -1, -4],\n [3, 4, 6, 13],\n [-3, -4, -6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -3, 1, 9],\n [-8, -12, -16, 12],\n [-10, 1, 8, 7],\n [-4, -2, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -9, 2, 11],\n [8, 11, 6, -5],\n [6, 5, 2, -3],\n [11, -16, -4, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 3, -8, 10],\n [6, -9, 3, 12],\n [4, 15, -6, 9],\n [-6, 13, -6, -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 4x4 matrix:\n[[6, 6, -6, -8],\n [-3, -3, 3, 4],\n [0, 0, 0, 0],\n [12, 12, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -2, 5, 1],\n [-7, 8, -2, -9],\n [-10, 0, 7, -4],\n [-3, -18, 0, 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[[-4, 0, 2, 3],\n [-4, 0, 2, 3],\n [8, 0, -4, -6],\n [-8, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 8, -24, -28],\n [-1, 6, -8, -11],\n [-2, 12, -16, -22],\n [0, -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[[0, 6, -12, 6],\n [0, 4, -8, 4],\n [0, 2, -4, 2],\n [0, 6, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 13, -4, -7],\n [-9, 9, -12, 9],\n [-4, 16, -8, -4],\n [3, -3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -9, -9, -6],\n [0, 0, 0, 0],\n [6, -9, -9, -6],\n [-6, 9, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -16, 8, -8],\n [16, 16, -8, 8],\n [-4, -4, 2, -2],\n [-8, -8, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -11, -3, 3],\n [-5, -8, 16, 5],\n [-1, 10, -22, -13],\n [-6, 2, -6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -11, -13, -6],\n [-3, 18, 13, -2],\n [0, 10, 8, 0],\n [3, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -12, -4, -8],\n [16, -12, -4, -8],\n [12, -9, -3, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 3, 4, 4],\n [0, 0, 0, 0],\n [-4, -12, -16, -16],\n [-3, -9, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, 18, -6, -8],\n [0, -5, -20, 8],\n [7, -8, -14, 13],\n [8, -12, -11, 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[[12, 0, 16, 4],\n [9, 0, 12, 3],\n [3, 0, 4, 1],\n [-9, 0, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 3, 3, 3],\n [-2, -1, -1, -1],\n [-2, -1, -1, -1],\n [-2, -1, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 16, -28, -24],\n [-10, 24, -22, -8],\n [-1, 4, 9, 8],\n [2, 8, 14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 9, -17, -9],\n [0, -3, 7, 3],\n [11, 6, 1, -6],\n [-6, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 8, -6, 4],\n [-8, -1, 6, 17],\n [16, 10, -12, -10],\n [8, 0, -6, -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 4x4 matrix:\n[[12, 0, 8, -8],\n [12, 0, 8, -8],\n [3, 0, 2, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-23, -1, -8, -7],\n [3, 7, 13, 9],\n [0, 4, 6, 4],\n [12, 9, 14, 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[[8, -16, -8, -12],\n [-4, 2, 3, 5],\n [-2, 4, 2, 3],\n [-8, -8, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, -4, 8],\n [5, 2, 2, -4],\n [-16, 8, -4, 8],\n [9, 0, 3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 6, 2, -2],\n [12, 9, 3, -3],\n [8, 6, 2, -2],\n [-16, -12, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 0, 16, 16],\n [-8, 0, -12, -20],\n [-6, 0, -4, 0],\n [6, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 2, 8, -2],\n [-4, -4, -16, 4],\n [-4, -4, -16, 4],\n [-4, -4, -16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 3, 13, 6],\n [-4, 11, 11, 12],\n [-2, -1, 9, 12],\n [10, 11, 18, 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 4x4 matrix:\n[[17, -7, -5, 10],\n [13, -7, 11, -8],\n [-14, 6, 2, -6],\n [-1, -1, 13, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 0, 1, 1],\n [6, 0, 2, 2],\n [12, 0, 4, 4],\n [12, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 1, 5, -3],\n [-21, 11, 15, -3],\n [8, 0, -8, -2],\n [7, 1, -3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 8, 0, -8],\n [2, -4, 0, 4],\n [-2, 4, 0, -4],\n [2, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -14, 14, 16],\n [3, 5, 1, -1],\n [6, 10, 2, -2],\n [-15, -17, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -4, 4, 1],\n [-24, -8, 8, -14],\n [0, 0, 0, 0],\n [-20, -4, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [3, 1, -4, -3],\n [-6, -2, 8, 6],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 3, 0, 0],\n [-9, 9, 0, 0],\n [-12, 12, 0, 0],\n [-12, 12, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -8, 6, -4],\n [1, 4, -3, 2],\n [-1, -4, 3, -2],\n [-2, -8, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -6, 0, 8],\n [0, 0, 0, 0],\n [-3, 9, 0, -12],\n [-3, 9, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-25, 5, 2, -12],\n [1, -3, 3, 3],\n [-22, 6, 0, -12],\n [28, -4, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 1, 3, 1],\n [8, 4, 12, 4],\n [-6, -3, -9, -3],\n [8, 4, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [8, 6, 2, -6],\n [8, 6, 2, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 22, -20, 6],\n [0, 16, -12, 4],\n [0, 19, -16, 5],\n [0, 16, -19, 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 4x4 matrix:\n[[4, -14, -10, -4],\n [4, -15, -13, 0],\n [6, -22, -18, -2],\n [1, -1, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -9, 3, 6],\n [8, -12, 4, 8],\n [0, 0, 0, 0],\n [-4, 6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 8, 8, 4],\n [3, 2, 2, 1],\n [12, 8, 8, 4],\n [9, 6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 17, 12, 9],\n [-1, -3, -3, -1],\n [-2, 4, -1, -1],\n [5, -11, 7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 4, 26, -6],\n [-14, -4, -16, -14],\n [-11, 2, -12, -2],\n [-13, 4, -9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 17, 2, 10],\n [4, -8, -8, 5],\n [2, -10, -4, -2],\n [3, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -1, 0, 1],\n [3, -5, 9, -7],\n [2, -5, 6, -3],\n [1, 1, 3, -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 4x4 matrix:\n[[-5, -8, -4, 2],\n [-2, -2, 8, -1],\n [9, 12, -12, 0],\n [-5, -8, -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[[-4, 6, -2, -8],\n [2, -3, 1, 4],\n [-6, 9, -3, -12],\n [2, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -8, -6, 8],\n [-6, -5, -9, 5],\n [-6, -9, -9, 9],\n [6, 9, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 0, 0, 2],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [12, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -8, 12, -16],\n [-9, 24, -16, 12],\n [3, 0, 2, -6],\n [4, -24, 8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -16, 8, 10],\n [-1, 4, -2, -6],\n [3, -12, 6, 12],\n [1, -4, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 6, 4, 8],\n [-14, 9, 6, 4],\n [-14, 9, 6, 4],\n [-17, 12, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, 2, -4],\n [-2, 1, 1, -2],\n [-2, 1, 1, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 21, -3, 12],\n [-3, 3, -2, 1],\n [-18, 0, -11, -5],\n [-3, -15, -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[[-16, -16, -4, 0],\n [4, 4, 1, 0],\n [-12, -12, -3, 0],\n [16, 16, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -6, -11, 4],\n [10, -7, -12, 1],\n [-2, -8, -22, 4],\n [4, -2, -1, -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[[-30, 28, -18, 0],\n [5, -17, 12, -10],\n [-28, 2, 6, -20],\n [-25, 8, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -12, 1, -1],\n [-9, 15, -1, 1],\n [-18, 14, 18, -14],\n [-4, 3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [16, 16, 16, 4],\n [-16, -16, -16, -4],\n [16, 16, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [3, 3, -2, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, -8, -16, 8],\n [-15, -6, -20, 2],\n [-4, -6, -16, -8],\n [-1, -7, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 3, 6, -12],\n [-3, 3, 6, -12],\n [-3, 3, 6, -12],\n [-3, 3, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -11, 7, -2],\n [-17, -11, 7, -10],\n [-6, 8, -4, -24],\n [-16, -13, 9, -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 4x4 matrix:\n[[4, 8, -2, 2],\n [-8, -16, 4, -4],\n [-2, -4, 1, -1],\n [2, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, 1, -6, -5],\n [16, -8, 11, 4],\n [-6, 6, -4, -2],\n [-14, -4, 1, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -2, 3, 1],\n [-9, -6, 4, 4],\n [-3, -3, 15, 1],\n [12, 6, -18, 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[[4, 16, -16, 12],\n [1, 4, -4, 3],\n [4, 16, -16, 12],\n [3, 12, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 6, 8, 8],\n [-1, 3, 4, 4],\n [-2, 6, 8, 8],\n [-3, 9, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -12, 12, 16],\n [4, -3, 4, -1],\n [-2, 6, -7, -3],\n [-16, -6, 4, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 6, 0, 2],\n [5, 9, 6, -5],\n [1, 15, 18, -19],\n [11, 0, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -16, 0, -11],\n [0, -10, -18, -8],\n [14, -8, 8, -5],\n [-10, 10, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -6, 0, 8],\n [-6, -9, 0, 12],\n [-6, -9, 0, 12],\n [-8, -12, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, 7, -1, -5],\n [0, 5, -10, -11],\n [7, 2, -11, -10],\n [10, -5, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -6, 6, -10],\n [2, -10, 2, -6],\n [-10, 1, 4, -5],\n [6, 19, -8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 11, 18, 0],\n [0, 6, 4, -8],\n [0, 14, 12, -15],\n [0, 17, 22, -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[[-16, 0, 8, 16],\n [0, -16, 8, 8],\n [-8, 8, 0, 4],\n [-8, 4, 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[[16, 4, 12, 4],\n [16, 4, 12, 4],\n [8, 2, 6, 2],\n [8, 2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 9, -6, 12],\n [-16, 12, -8, 16],\n [-8, 6, -4, 8],\n [16, -12, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 2, 0, -11],\n [4, 15, -2, 9],\n [6, 10, 9, -10],\n [14, 12, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -4, -8, 8],\n [12, -3, -6, 6],\n [-12, 3, 6, -6],\n [-4, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -16, 13, -10],\n [20, -4, 17, -8],\n [2, -17, 22, -13],\n [-6, -5, 10, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 6, -4, 6],\n [0, 6, -4, 6],\n [0, -3, 2, -3],\n [0, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 8, 12, 16],\n [-8, -8, -12, -16],\n [0, 0, 0, 0],\n [2, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 4, -6, 8],\n [-12, -2, 1, 3],\n [-16, 16, -4, 4],\n [-3, -18, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 5, 9, -2],\n [-28, -10, -13, 14],\n [16, 6, 8, -8],\n [-8, -5, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 9, -6, 3],\n [12, 9, -6, 3],\n [-12, -9, 6, -3],\n [8, 6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 24, 19, 16],\n [8, 0, 5, -10],\n [-2, 5, -4, 14],\n [-12, -7, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-3, 3, 3, -2],\n [12, -12, -12, 8],\n [9, -9, -9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -5, -15, 4],\n [-19, 4, 9, -5],\n [3, 7, 24, -9],\n [19, -2, -2, 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[[-6, 12, 3, -9],\n [-6, 12, 3, -9],\n [6, -12, -3, 9],\n [-8, 16, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -3, -4, -2],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-8, -12, -16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 12, -3, -9],\n [-6, 8, -2, -6],\n [0, 0, 0, 0],\n [9, -12, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -2, -4, -13],\n [-8, -8, -4, -18],\n [0, -19, 21, -4],\n [-6, 17, -15, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -2, 2, -6],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-12, -3, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 0, 2, -3],\n [2, 0, -4, 6],\n [-1, 0, 2, -3],\n [4, 0, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 12, 8, 6],\n [6, -4, 1, 6],\n [-4, -8, -4, -12],\n [11, -18, -6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, 4, -3],\n [12, -20, 28, -17],\n [-8, 2, 4, 0],\n [4, -4, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, 4, 2, 12],\n [-2, -4, -7, 3],\n [14, 28, -5, -3],\n [6, -12, 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[[0, -8, -6, 1],\n [12, 4, 0, 4],\n [4, 4, 2, 1],\n [5, -1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, 2, -2, -6],\n [6, -8, 8, 13],\n [-2, -4, 4, 4],\n [1, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, 8, -8, 8],\n [-15, 12, -16, 12],\n [-3, 10, 12, 10],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 6, 21, 1],\n [1, 1, 4, 3],\n [13, 9, -3, -5],\n [0, -6, -9, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 16, 0, 4],\n [3, 12, 0, 3],\n [-1, -4, 0, -1],\n [-1, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 4, 0, -8],\n [18, 0, -12, -2],\n [18, -10, -2, 18],\n [-14, 8, 12, -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 4x4 matrix:\n[[9, -3, -7, -5],\n [6, -1, -5, -2],\n [3, 7, -5, 9],\n [9, -18, -2, -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 4x4 matrix:\n[[-2, -6, 10, 2],\n [-2, -14, 16, 2],\n [-2, -14, 16, 2],\n [0, 16, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -4, 11, -10],\n [-3, 2, 7, -5],\n [8, -12, 8, -10],\n [4, -6, 4, -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[[3, -1, 12, -11],\n [-7, 1, 9, -11],\n [-7, 1, 9, -11],\n [1, 5, 12, -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[[-6, 8, -18, 9],\n [5, -6, 13, -6],\n [-16, 16, -32, 12],\n [1, 3, -1, 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 4x4 matrix:\n[[-10, 10, 1, 9],\n [16, -4, -23, 5],\n [-16, -24, -6, 4],\n [22, 6, -18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, -19, 9, 1],\n [-6, -9, -3, -23],\n [10, 5, -6, -6],\n [-28, 10, -12, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -4, 2, 3],\n [1, -2, 3, 3],\n [-8, -8, 28, 24],\n [4, -8, 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[[-8, -4, -4, 16],\n [-8, -4, -4, 16],\n [8, 4, 4, -16],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -16, 0, 16],\n [-1, 4, 0, -4],\n [1, -4, 0, 4],\n [3, -12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 13, 12, 14],\n [17, 5, 9, -17],\n [-7, -5, 6, 7],\n [-18, -20, -15, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 9, 20, 0],\n [-8, 12, 8, -28],\n [6, -9, -16, 6],\n [-4, 6, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 0, -24, -8],\n [-24, 0, 24, 8],\n [-20, 0, 20, 2],\n [0, 0, 0, -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 4x4 matrix:\n[[2, 0, -2, 8],\n [-1, 0, 1, -4],\n [4, 0, -4, 16],\n [-1, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 5, -2, 12],\n [32, -4, 12, -32],\n [-4, 1, 3, 4],\n [12, 20, 24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -3, 6, 21],\n [-1, -1, -14, 3],\n [3, 1, -2, 13],\n [-3, -11, 22, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -20, 10, 20],\n [0, -8, 4, 8],\n [-6, 24, -12, -24],\n [9, -20, 10, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 12, 16, 8],\n [0, -6, -8, -4],\n [0, 3, 4, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 2, -9, 2],\n [24, -12, -6, 8],\n [16, 2, -9, 2],\n [20, -8, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, -15, -9, 1],\n [-15, -15, -3, 2],\n [2, -14, 18, 20],\n [-4, 10, -21, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 3, -3, -9],\n [4, -6, -10, -14],\n [-2, 3, 5, 7],\n [0, 0, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -8, -9, 13],\n [-3, 5, 18, -9],\n [-16, -20, -14, 8],\n [-20, -14, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -4, -18, -2],\n [-14, -12, 16, -10],\n [2, -26, -12, -14],\n [-8, -26, 2, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 3, 1, 7],\n [-2, -3, -14, -13],\n [-2, -1, 9, 11],\n [5, 5, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, -3, -1],\n [10, -2, -15, -7],\n [-20, 14, 5, -1],\n [22, -14, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 4, 2, 3],\n [-4, -3, -4, -3],\n [-13, -11, -18, -12],\n [-28, -16, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 16, -3, 14],\n [0, -16, 0, -16],\n [0, 0, 0, 0],\n [-6, 8, -18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -16, -16, 8],\n [-12, 12, 12, -6],\n [-12, 12, 12, -6],\n [-4, 4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 12, -16, -12],\n [4, 14, -18, -18],\n [-13, 4, -5, -10],\n [-7, -4, 21, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 22, 16, -4],\n [9, -11, -8, 2],\n [-3, 2, -4, 1],\n [3, -1, 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[[0, 0, 0, 0],\n [-9, -12, 12, -12],\n [3, 4, -4, 4],\n [9, 12, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 0, 0, 0],\n [-4, 0, 0, 0],\n [-8, 0, 0, 0],\n [2, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 9, 9, -9],\n [4, 3, 3, -3],\n [16, 12, 12, -12],\n [-12, -9, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 17, -16, 0],\n [2, -2, 4, 0],\n [-3, 5, -8, 0],\n [2, 18, -16, 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 4x4 matrix:\n[[12, 16, -4, -12],\n [6, 8, -2, -6],\n [-3, -4, 1, 3],\n [-3, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -2, 0, 8],\n [3, -1, 0, 4],\n [-9, 3, 0, -12],\n [-6, 2, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -4, -4, 12],\n [4, -2, -2, 6],\n [-6, 3, 3, -9],\n [6, -3, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -2, -2, 2],\n [-3, 14, -19, -8],\n [9, -2, 4, 10],\n [9, -2, -13, 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, -8, 0, -2],\n [-7, -9, -1, -2],\n [-5, -5, -8, 3],\n [0, -2, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -4, -4, -2],\n [-1, 16, -11, 17],\n [6, 0, -6, 2],\n [-4, 4, 1, 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[[16, 14, 5, -2],\n [0, -14, 7, 2],\n [-10, -24, 3, 1],\n [-6, -21, 6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 14, -10, 14],\n [-3, 2, -6, -20],\n [5, -8, -2, -2],\n [-12, 5, 21, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -7, 14, 6],\n [6, 2, -8, -2],\n [-1, 5, 8, -3],\n [9, 11, -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[[-4, 6, -6, 8],\n [6, 7, -3, 0],\n [-6, 17, -15, 18],\n [-4, 6, -6, 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 4x4 matrix:\n[[0, 6, -6, -18],\n [-1, -3, 1, 4],\n [2, 10, -6, -20],\n [-1, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 12, 0, -6],\n [0, 16, 0, -8],\n [0, 4, 0, -2],\n [0, 8, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 4, 4, 4],\n [4, 2, 2, 2],\n [-12, -6, -6, -6],\n [12, 6, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 3, -1, -4],\n [0, 0, 0, 0],\n [8, -6, 2, 8],\n [-4, 3, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 24, -10, -12],\n [4, 32, -4, -12],\n [-4, -8, -20, -6],\n [-4, -12, -16, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -6, -6, -4],\n [8, -12, -12, -8],\n [-2, 3, 3, 2],\n [-4, 6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-6, -6, 6, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 18, 7, -6],\n [-3, -5, 6, -13],\n [-3, 16, -1, 8],\n [-12, 7, 15, -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[[8, -8, 0, 0],\n [-6, 6, -2, -4],\n [20, -20, -4, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -12, -16, -8],\n [-5, 12, 20, 16],\n [4, 6, 8, 4],\n [2, 16, 24, 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[[-14, -2, -12, 20],\n [11, 0, 9, -14],\n [11, 8, -12, -20],\n [12, -6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -16, 19, 7],\n [-2, 1, -3, 3],\n [-2, 8, 2, -6],\n [-3, -10, -7, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [16, 12, -16, 4],\n [8, 6, -8, 2],\n [-16, -12, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, -13, -22, 17],\n [-15, 13, 14, -5],\n [12, -4, -24, 4],\n [-15, 15, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -8, 4, 4],\n [1, 4, -10, -6],\n [6, 4, 10, 4],\n [3, 0, 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 4x4 matrix:\n[[8, 4, 8, -8],\n [16, -4, -8, -8],\n [16, 2, 4, -12],\n [4, -7, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 10, 3, -17],\n [-21, -12, 6, 9],\n [-11, -5, 27, -11],\n [4, 2, 21, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 1, -12, 7],\n [-5, 7, -14, -1],\n [-2, 10, -8, -10],\n [0, -6, 2, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 0, -2, 4],\n [2, 0, 2, -4],\n [6, 0, 6, -12],\n [-2, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -7, 0, 0],\n [-1, 1, -12, 8],\n [6, 0, 7, 0],\n [19, -15, 1, -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 4x4 matrix:\n[[-28, 2, 16, 37],\n [0, -9, -9, -9],\n [-8, 1, 5, 11],\n [-8, -6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 12, -12, -4],\n [2, -12, 6, -12],\n [10, 6, 0, 4],\n [2, 30, -20, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-22, 16, 28, -8],\n [8, -4, 6, -2],\n [-12, 8, 8, -2],\n [2, 6, 25, 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, 8, -10, 0],\n [5, 11, 1, -13],\n [1, 0, 4, -2],\n [12, -7, 14, -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 4x4 matrix:\n[[-2, 0, 0, -10],\n [26, 6, -8, -6],\n [18, 1, -3, -6],\n [-18, -8, 9, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -1, -10, 6],\n [-2, -10, -10, 12],\n [1, 13, 10, -11],\n [4, 22, 10, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-4, 8, -12, 8],\n [0, 0, 0, 0],\n [1, -2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -5, 7, -17],\n [-6, -3, 9, -21],\n [-8, 17, 5, -7],\n [8, -14, -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[[13, -6, -6, 3],\n [6, -2, -2, 6],\n [12, -8, -8, -12],\n [15, -8, -8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, -24, 20, -21],\n [21, 25, -24, 36],\n [-5, -2, 2, -1],\n [-11, -22, 19, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -6, 10, 0],\n [3, -10, 8, 6],\n [-4, 0, -14, 2],\n [-4, 6, 16, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, 12, -18, -6],\n [13, 2, 11, -25],\n [-6, 4, -7, 1],\n [-3, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -2, -3, 15],\n [-6, -5, 13, -15],\n [-13, 2, -2, -18],\n [-8, -12, 20, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 8, 4, 8],\n [-10, 7, 4, 10],\n [-5, 4, 3, 10],\n [-11, 6, 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 4x4 matrix:\n[[3, -9, -12, -12],\n [-4, 12, 16, 16],\n [4, -12, -16, -16],\n [2, -6, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 2, -10, -12],\n [11, 1, -18, -20],\n [9, 3, -15, -18],\n [5, -17, -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 4x4 matrix:\n[[11, 4, 18, 1],\n [10, 16, -15, 4],\n [15, 18, -1, 1],\n [4, 12, -22, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 10, -20, 8],\n [-10, 2, 9, 3],\n [-6, -9, 37, -5],\n [20, -22, 16, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 19, -5, -3],\n [4, 1, 23, 17],\n [8, 2, 20, 14],\n [2, -19, -8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -8, -4, 16],\n [-9, -5, -10, 4],\n [4, 12, 16, -16],\n [-12, -3, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -8, -4, -6],\n [8, 8, 4, 6],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 6, 4, -9],\n [-10, 2, 16, -3],\n [-1, 8, 12, -12],\n [1, 4, 4, -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[[22, -6, 0, 10],\n [-4, 12, 32, 16],\n [25, -5, -4, -9],\n [-15, 5, -2, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 8, 20, 24],\n [1, -4, -7, -8],\n [-12, 0, 9, 12],\n [25, 12, 0, -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[[2, 2, 6, -7],\n [-10, -28, 8, -10],\n [-3, -21, 3, -15],\n [5, 17, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [1, 1, 0, 3],\n [-3, -3, 0, -9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -12, -8, 12],\n [0, 12, 8, -12],\n [0, -9, -6, 9],\n [0, 6, 4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 12, -12, 4],\n [-13, 10, 14, 6],\n [-4, 16, -14, -10],\n [11, -14, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 8, -4, 8],\n [12, -6, 3, -6],\n [12, -6, 3, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -1, 0, 3],\n [4, 2, 0, -6],\n [-4, -2, 0, 6],\n [8, 4, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 8, -6, 0],\n [6, 8, -6, 0],\n [16, -6, 4, 0],\n [-17, 14, -11, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 9, 6, 0],\n [0, 0, 0, 0],\n [-6, -6, -4, 0],\n [12, 12, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, 12, -4],\n [4, 21, -3, 0],\n [3, 0, -8, 3],\n [0, -8, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 8, -16],\n [-1, 1, -2, 4],\n [-4, 4, -8, 16],\n [1, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 12, -22, -3],\n [6, -12, -6, -18],\n [6, -12, -6, -18],\n [-2, 12, -2, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -10, -8, -6],\n [-13, 1, -7, 18],\n [4, -5, -3, -7],\n [-14, 8, -1, 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 4x4 matrix:\n[[3, -8, -13, 5],\n [0, 8, 8, -6],\n [9, 8, -7, -9],\n [0, 12, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -10, -16, -10],\n [6, -2, 1, 4],\n [12, 9, 27, 27],\n [-13, 5, -3, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -16, -16, 12],\n [0, 8, 8, -6],\n [0, -4, -4, 3],\n [0, -16, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 8, -16, -8],\n [4, 8, -16, -8],\n [3, 6, -12, -6],\n [4, 8, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 1, 4, 19],\n [-8, 1, -12, -13],\n [6, -1, 10, 9],\n [20, 15, -8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [16, 8, 0, 4],\n [8, 4, 0, 2],\n [-4, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 16, 16, 4],\n [-4, -8, -8, -2],\n [-2, -4, -4, -1],\n [-2, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, 8, 8],\n [3, 3, 2, 2],\n [9, 9, 6, 6],\n [12, 12, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 2, 3, 2],\n [-19, 10, -5, 6],\n [-16, 8, -8, 4],\n [-5, 4, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 3, -9, 7],\n [-6, -12, 9, -2],\n [-7, 14, -2, 19],\n [3, -18, -4, -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[[4, 0, 1, -1],\n [-22, 0, 5, -9],\n [-2, 0, 10, -14],\n [12, 9, -15, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -9, 3, 2],\n [16, -18, 2, 10],\n [-4, 0, -6, 1],\n [16, -6, 12, 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 4x4 matrix:\n[[17, 9, -15, -8],\n [5, -3, -11, 8],\n [2, 0, -3, 1],\n [4, 6, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -5, -6, -8],\n [4, 11, 6, 14],\n [12, 8, 8, 12],\n [0, 10, 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[[24, -12, 16, 4],\n [12, -15, 4, 4],\n [0, 9, 4, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -2, -6, -20],\n [4, 0, 4, 16],\n [17, -18, 25, -4],\n [-13, 14, -27, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 4, -8, -4],\n [8, 2, -4, -2],\n [-12, -3, 6, 3],\n [8, 2, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -6, -7, 26],\n [0, 0, 0, 0],\n [10, -1, 4, -14],\n [2, 10, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -6, 4, -25],\n [-12, -4, -20, 6],\n [4, 4, 4, 10],\n [12, 4, 20, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -2, -3, -4],\n [0, 0, 0, 0],\n [6, -6, -9, -12],\n [-6, 6, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -4, 4, 4],\n [-10, 18, -18, -18],\n [17, -9, -3, 5],\n [-24, 8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -14, -5, -13],\n [-14, 17, 2, 9],\n [-7, -11, 2, 16],\n [10, -16, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 0, -20, 5],\n [5, -1, 9, -1],\n [-31, -31, -12, 8],\n [-10, -24, 16, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 7, -18, -5],\n [-24, 23, 3, 5],\n [-34, 29, -12, 4],\n [0, 1, 6, -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[[16, -15, -14, 5],\n [16, -3, -6, 18],\n [-4, 1, -2, -4],\n [0, 14, 12, 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[[0, 0, 0, 0],\n [3, 1, 4, 0],\n [-3, -1, -4, 0],\n [-6, -2, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -1, -1, 1],\n [-6, 3, 3, -3],\n [-2, 1, 1, -1],\n [-4, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -4, 0, -3],\n [8, -4, 4, -2],\n [-1, 1, 1, 1],\n [4, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, 15, -4, 7],\n [-11, 9, -8, -1],\n [10, -6, 10, 5],\n [-10, -2, -20, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 13, -3, -7],\n [3, -4, 2, 1],\n [-3, 19, 1, -16],\n [6, -13, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -4, -2, -6],\n [-8, -4, -2, -6],\n [-10, 2, 2, 0],\n [-10, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -1, 9, -6],\n [-3, -2, 3, 3],\n [9, 0, 5, -5],\n [-3, 10, -25, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -19, -12, -14],\n [12, -7, -28, -22],\n [12, -13, -20, -18],\n [0, -9, 12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 16, -3, 10],\n [-16, -8, 5, -6],\n [4, -13, -5, -6],\n [8, 10, -1, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, 8, -8, -6],\n [6, -12, 12, 9],\n [2, -4, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, -1, -1, -1],\n [-13, 5, -10, -1],\n [0, -18, 37, 4],\n [-14, 1, -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[[0, -20, -16, -4],\n [0, -15, -14, -6],\n [0, 14, 12, 4],\n [0, 2, 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[[8, -6, -24, 18],\n [-2, -16, 8, 8],\n [0, -6, -25, 22],\n [14, 6, -24, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -37, 20, 27],\n [0, -22, 16, 19],\n [-8, 14, 8, -9],\n [8, 6, -16, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 3, 6, -9],\n [0, 4, 8, -12],\n [0, -1, -2, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 22, 24, 1],\n [4, -1, -10, -7],\n [0, 18, 14, 13],\n [-4, 3, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 20, 4, -28],\n [3, 13, -5, -11],\n [-1, -13, -17, 25],\n [1, -4, -25, 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[[-6, 0, -8, -4],\n [0, 9, -21, -15],\n [0, 0, 0, 0],\n [0, -9, 21, 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 4x4 matrix:\n[[-24, -6, -18, -24],\n [3, -15, -3, 3],\n [8, 14, 10, 8],\n [3, -15, -3, 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[[-21, 0, 3, 12],\n [-8, 20, 4, 1],\n [16, -12, -4, -7],\n [-22, -8, 2, 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[[8, -20, 8, 28],\n [-18, 1, -2, 17],\n [19, -19, 11, 14],\n [-8, 7, -8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 4, -13, -2],\n [-2, 2, -5, -4],\n [20, -6, 22, -2],\n [2, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 20, 8, 30],\n [-20, 10, -13, 10],\n [10, -9, 4, -12],\n [8, -11, 8, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, 8, -8],\n [12, 0, 6, -3],\n [16, -5, 18, -14],\n [0, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 6, -3, 6],\n [8, 4, -2, 4],\n [-12, -6, 3, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 9, -6, 9],\n [0, 12, -8, 12],\n [0, -9, 6, -9],\n [0, -9, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 1, 2, -4],\n [13, -9, 6, -4],\n [-16, 12, 0, -8],\n [-7, 6, 6, -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, -8, 1, 5],\n [6, 18, 6, 8],\n [-1, -10, -1, 1],\n [-2, -14, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -8, -16],\n [0, -8, 8, 16],\n [0, -2, 2, 4],\n [0, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, 12, -17, -9],\n [-8, 6, -4, 0],\n [-6, 9, 3, 9],\n [-4, 0, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -12, 9, 0],\n [8, -16, 12, 0],\n [-2, 4, -3, 0],\n [-8, 16, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -8, 3, 4],\n [-7, 21, 0, -9],\n [-3, 1, -6, 1],\n [-19, 29, 4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 8, 24, 2],\n [0, 0, 8, 2],\n [8, -8, 8, 6],\n [16, -16, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -4, 1, 2],\n [-6, 12, -3, -6],\n [2, -4, 1, 2],\n [2, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 15, 4, -3],\n [-12, 26, 4, -14],\n [10, -7, 1, 5],\n [10, -3, 9, -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[[-4, -4, -8, 12],\n [4, 4, 8, -12],\n [4, 4, 8, -12],\n [-4, -4, -8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 19, -4, 8],\n [-12, 3, 12, -6],\n [4, -1, 0, -6],\n [-4, -5, 0, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -4, 4, 12],\n [0, 0, 0, 0],\n [-6, -2, 2, 6],\n [-3, -1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, 12, -28, -15],\n [10, -6, 12, 7],\n [0, -3, -4, 1],\n [2, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, 6, 9, -11],\n [-11, 2, 3, -5],\n [28, 0, 0, 8],\n [4, -2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 2, 4, 3],\n [-2, 1, 0, 1],\n [3, -1, -4, -2],\n [-10, 3, 16, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 6, 11, 2],\n [10, 6, 7, 4],\n [12, 8, 8, 6],\n [8, 0, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 4, 6, -4],\n [-12, -4, 8, -12],\n [-2, -6, -2, -2],\n [6, 2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -12, 6, -3],\n [17, -15, -1, 8],\n [31, -27, -5, 10],\n [20, -18, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, 0, -2],\n [-6, 0, 0, 2],\n [0, 0, 0, 0],\n [-9, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 8, -9, -17],\n [-10, 8, -6, -22],\n [3, 6, -9, -9],\n [-6, -5, 9, 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[[8, 16, 16, 16],\n [4, 8, 8, 8],\n [0, 0, 0, 0],\n [-6, -12, -12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 8, -10, -9],\n [20, 8, 6, -5],\n [6, 16, -6, -5],\n [14, 16, 0, 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 4x4 matrix:\n[[0, -9, 20, -1],\n [7, -3, 16, 2],\n [7, 6, -4, 3],\n [11, 12, -12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -4, 4, 0],\n [-11, -4, 12, 0],\n [-7, -7, -1, 0],\n [9, 20, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 0, -6, 12],\n [10, -5, 8, -18],\n [6, -5, 4, -8],\n [12, -10, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -4, 4, 0],\n [2, -1, 1, 0],\n [-6, 3, -3, 0],\n [-2, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -16, 4, -12],\n [-20, 20, -8, 8],\n [3, -12, 3, -9],\n [6, 6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 13, -4, -9],\n [2, -18, 3, 15],\n [-2, -17, 2, 15],\n [6, -19, 4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 3, 11, -3],\n [4, 7, -1, 8],\n [-6, -10, 6, -14],\n [-6, -10, -26, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 2, 4],\n [1, 0, -1, 3],\n [0, 0, -4, -8],\n [4, 0, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 8, 6, 8],\n [2, 4, 3, 4],\n [4, 8, 6, 8],\n [-2, -4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 12, -14, -11],\n [-5, 4, 4, -20],\n [-1, 2, -6, 5],\n [0, 12, -8, -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[[12, 10, 4, -8],\n [-2, -1, 4, 4],\n [-16, -10, 18, 24],\n [-10, -6, 13, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 9, -18, 18],\n [8, -6, -2, 0],\n [13, 3, -2, 14],\n [-19, 9, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, -17, -25, 11],\n [9, 10, 8, -2],\n [0, -2, 2, -2],\n [18, 16, 20, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 9, 14, 6],\n [9, -18, -9, -24],\n [14, -6, 10, -20],\n [-12, -3, -8, -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[[-16, 16, -8, 0],\n [-4, 4, -2, 0],\n [16, -16, 8, 0],\n [8, -8, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -10, -9, -2],\n [5, 4, 6, 2],\n [-18, -10, -16, -4],\n [-9, 18, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -4, -4, 16],\n [-8, 4, 4, -16],\n [2, -1, -1, 4],\n [4, -2, -2, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 3, -6, -3],\n [-4, -1, 2, 1],\n [-4, -1, 2, 1],\n [4, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -6, -11, -4],\n [-8, -9, -12, -8],\n [-1, 0, -6, -4],\n [8, 3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 0, 1, -7],\n [11, 1, -7, 2],\n [-10, -13, 0, -5],\n [-3, 3, 1, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -7, 18, 5],\n [-4, 2, -5, -2],\n [-3, -17, -15, -19],\n [-3, 13, 9, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -4, -5, 4],\n [14, -10, -11, 6],\n [-4, 2, 4, -6],\n [16, -12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 12, -12, -12],\n [0, -3, 3, 3],\n [0, -6, 6, 6],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 4, -4, -1],\n [3, 1, -3, 0],\n [25, 15, -13, -4],\n [-16, -7, 13, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 6, -2, -2],\n [-11, -10, 6, 0],\n [3, 24, -14, -8],\n [3, 18, -10, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 18, -13, -15],\n [8, -18, 13, 15],\n [2, -6, 4, 6],\n [-8, 18, -13, -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[[-2, 8, 21, -14],\n [-1, 4, 17, -12],\n [2, -8, 18, -16],\n [-1, 4, -3, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[22, 16, -16, -19],\n [20, 22, -22, -25],\n [-16, -4, 4, 4],\n [25, -9, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, 8, 19, -7],\n [12, 5, -5, 0],\n [3, -14, -10, 6],\n [-16, 8, 15, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -26, 20, 16],\n [4, -2, -8, 9],\n [2, 6, -4, 0],\n [-27, 8, -4, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 16, -16, 10],\n [17, -18, 11, 8],\n [-13, 10, 1, -24],\n [-6, 8, -8, 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[[4, 20, -28, -4],\n [-1, 1, -2, 4],\n [-1, -3, 4, 2],\n [0, -8, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -2, -8, 14],\n [6, 2, -11, 15],\n [16, 20, 13, -3],\n [6, 2, 8, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -2, 4, 16],\n [5, 5, 3, 12],\n [8, 8, 2, 8],\n [-6, -6, -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 4x4 matrix:\n[[4, -4, 0, 3],\n [-16, 16, 0, -12],\n [16, -16, 0, 12],\n [16, -16, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -3, 9, -6],\n [3, -1, 3, -2],\n [-9, 3, -9, 6],\n [9, -3, 9, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 16, -16, -8],\n [-1, -4, 4, 2],\n [2, 8, -8, -4],\n [-2, -8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, 1, -6, -2],\n [-3, 3, -2, -2],\n [0, -15, 6, 9],\n [-6, 11, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -19, 16, -11],\n [14, -20, 22, -16],\n [3, 12, -9, 6],\n [15, 3, 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[[4, -20, 6, 4],\n [-14, 14, -9, -8],\n [5, -2, 13, 26],\n [10, -24, 8, 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[[-1, -16, 0, -20],\n [-4, -13, 17, -12],\n [2, 2, -10, 0],\n [-2, -17, 5, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -4, -8, -6],\n [13, 20, 0, 14],\n [10, 28, 20, 20],\n [-2, 0, 24, -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[[-3, 0, -9, 0],\n [3, -3, 9, -2],\n [-5, -6, -15, -4],\n [7, 12, 21, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, 6, 0],\n [-12, 0, -12, -16],\n [-7, -2, -6, -12],\n [8, 4, 6, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[36, -44, 16, 12],\n [3, -9, -12, 9],\n [-21, 24, 0, -3],\n [0, 1, -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 4x4 matrix:\n[[-6, -13, 0, -4],\n [-2, -10, -2, -2],\n [12, -8, -12, 4],\n [-14, -2, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -2, -11, 12],\n [7, -7, -1, -18],\n [3, -3, -4, -2],\n [4, -4, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, 0, -8, -4],\n [4, 0, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, -3, -3, -3],\n [-6, 15, -20, 2],\n [3, -4, -4, -14],\n [-6, 17, -8, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 1, 14, 20],\n [-14, -6, 16, 20],\n [6, 1, -6, -8],\n [14, -16, -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[[-2, 4, -6, 0],\n [4, -8, 12, 0],\n [4, -8, 12, 0],\n [-3, 6, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 4, 8, -4],\n [1, -2, -4, 2],\n [-4, 8, 16, -8],\n [3, -6, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -6, 0, -6],\n [4, -6, 0, -6],\n [0, 0, 0, 0],\n [-4, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -6, 1, 6],\n [0, 4, -3, 0],\n [-20, -11, 17, -15],\n [12, 1, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[21, 13, 9, 36],\n [-6, 0, -4, -13],\n [14, 6, 6, 28],\n [-9, -17, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -1, 6, -7],\n [21, -6, -10, 4],\n [0, 11, 6, 5],\n [-21, 11, 4, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 0, -6, 4],\n [18, -8, 12, -4],\n [10, 4, 2, -10],\n [-9, 16, -14, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -6, -3, -12],\n [-1, -2, -1, -4],\n [-2, -4, -2, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 0, -10, 7],\n [0, -15, 3, 0],\n [-6, -6, 2, -2],\n [1, -4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 27, -6, 11],\n [-1, -2, -3, 1],\n [16, -2, 16, -16],\n [2, 17, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -1, -4, 20],\n [30, 16, 18, -4],\n [13, 10, 13, -14],\n [26, 14, 16, -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 4x4 matrix:\n[[-4, 8, -8, 16],\n [-2, 4, -4, 8],\n [1, -2, 2, -4],\n [-2, 4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 9, -6, 0],\n [0, -6, 12, -12],\n [2, 6, -4, 0],\n [4, 0, 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[[4, -10, -2, -7],\n [-8, 20, 4, 14],\n [-12, 14, -6, 9],\n [12, -18, 3, -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[[0, 4, -4, 2],\n [0, -8, 8, -4],\n [0, 8, -8, 4],\n [0, -4, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 0, 0, 3],\n [-12, 0, 0, 3],\n [-16, 0, 0, 4],\n [-13, -9, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 2, -3, -8],\n [0, -23, 12, 2],\n [-9, 19, -6, 5],\n [36, -20, -6, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, 12, -4],\n [-6, 2, 12, 2],\n [-6, 0, 18, 0],\n [8, -5, -9, -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 4x4 matrix:\n[[-2, -8, -7, -7],\n [0, -16, -8, -12],\n [-16, -16, -4, 16],\n [-16, -4, -5, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 8, -2, 8],\n [-2, -4, 1, -4],\n [0, 0, 0, 0],\n [8, 16, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 12, 4, 12],\n [9, 9, 3, 9],\n [-12, -12, -4, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 6, -1, 4],\n [0, -6, -3, -3],\n [0, 2, -7, 3],\n [0, 0, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -4, -8, 11],\n [-9, 3, -4, -2],\n [-8, -2, -16, 13],\n [-2, -2, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, -6, 0, -4],\n [17, 16, -4, -4],\n [-2, 0, 0, -2],\n [-29, -36, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 12, 12, -9],\n [-24, 16, 16, -12],\n [2, 0, 2, -1],\n [8, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -4, -4, -12],\n [-1, 2, 0, 2],\n [4, 0, -4, -8],\n [8, -6, -5, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-18, -9, -4, 5],\n [8, -3, 8, 4],\n [-4, -3, 0, 2],\n [12, 9, 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[[-1, 2, 4, 1],\n [1, -2, -4, -1],\n [2, -4, -8, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 9, 12, 12],\n [0, 0, 0, 0],\n [-1, 3, 4, 4],\n [4, -12, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 2, -6, -10],\n [-4, -4, -3, 6],\n [7, -7, 0, 11],\n [-2, -3, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -1, -1, 2],\n [-6, -6, 14, 8],\n [-4, -4, 16, 4],\n [-2, -2, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, -8, -1, -4],\n [6, -15, -3, 6],\n [12, -12, -2, 0],\n [14, 1, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 4, 11, -3],\n [-9, 13, 9, -13],\n [-15, 9, 4, -6],\n [9, -18, -15, 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[[-22, -4, -14, -14],\n [10, 0, 9, 14],\n [7, -16, 4, 9],\n [15, 8, 13, 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, 2, 4, 1],\n [-2, -6, -3, -4],\n [-6, 6, -15, 6],\n [8, 4, 17, 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[[2, -10, 9, -14],\n [-20, 2, -6, 0],\n [4, -6, 6, -8],\n [4, -13, 12, -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[[9, 3, 12, 3],\n [-12, -4, -16, -4],\n [-6, -2, -8, -2],\n [-6, -2, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 7, -3, -12],\n [1, 12, -1, -17],\n [-1, 14, -5, -23],\n [-1, -1, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, 16, 4],\n [0, 4, -16, -4],\n [0, 4, -16, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -18, -16, 4],\n [-14, -6, 18, 4],\n [15, -5, -10, 1],\n [-19, 5, 22, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 9, 12, 9],\n [-8, -6, -8, -6],\n [-16, -12, -16, -12],\n [16, 12, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -8, 0, -2],\n [-10, -15, -1, -3],\n [-12, -4, -4, 2],\n [-20, -25, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -10, -6, -4],\n [-3, 1, 10, 2],\n [13, 11, 1, 4],\n [-3, 2, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -16, -16, 8],\n [-6, -12, -12, 6],\n [-8, -16, -16, 8],\n [-4, -8, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 19, -10, 9],\n [13, -10, -15, 10],\n [-5, -10, 6, 1],\n [-9, -17, 13, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 1, -10, -2],\n [9, 7, -2, 20],\n [9, 5, 2, 16],\n [9, 5, 2, 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 4x4 matrix:\n[[2, 4, -3, -2],\n [-4, -8, 6, 4],\n [-2, -4, 3, 2],\n [-2, -4, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 12, -9, -12],\n [2, -8, 6, 8],\n [-1, 4, -3, -4],\n [3, -12, 9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 13, -20, -4],\n [1, 1, 10, 2],\n [20, -32, 36, -12],\n [0, -8, 12, 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 4x4 matrix:\n[[6, -3, -12, 12],\n [-8, 4, 16, -16],\n [6, -3, -12, 12],\n [2, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 6, 0, 4],\n [-4, -8, -4, -6],\n [-6, -18, 0, -12],\n [-6, -22, 4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -10, -12, 2],\n [-2, -10, -12, 2],\n [2, -8, -6, -2],\n [3, 3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -4, -1, -1],\n [-2, -8, -2, -2],\n [4, 16, 4, 4],\n [-1, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -6, 10, 4],\n [2, 6, -7, -10],\n [-12, 4, -8, 0],\n [-6, 10, -14, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -12, 6, 12],\n [3, -12, 6, 12],\n [3, -12, 6, 12],\n [-2, 8, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 4, -4, 6],\n [8, -8, 8, -12],\n [2, -2, 2, -3],\n [4, -4, 4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[27, 8, 10, 1],\n [9, -15, -2, -11],\n [-8, -2, 0, 6],\n [-2, -5, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 6, -2, 7],\n [-20, -4, 8, -1],\n [-4, 0, 3, -1],\n [0, -6, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 0, 16, 4],\n [6, 0, 12, 3],\n [0, 0, 0, 0],\n [-2, 0, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-1, 2, 2, -4],\n [-3, 6, 6, -12],\n [-3, 6, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -12, 12, 4],\n [18, 15, 3, 16],\n [-2, 0, 6, -12],\n [6, 6, -6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 8, 2, -12],\n [5, 5, 1, -14],\n [-14, 14, -5, -2],\n [0, -15, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 7, 12, -10],\n [0, 9, 5, -26],\n [3, -11, -7, 18],\n [-3, 19, -15, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -3, 2, -3],\n [-8, 12, -8, 12],\n [8, -12, 8, -12],\n [-8, 12, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 4, -3, 10],\n [0, 0, 0, 0],\n [2, -16, 12, -12],\n [0, 1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, -8, 0, -12],\n [-11, -4, 0, -6],\n [-4, 4, 24, -24],\n [16, 9, 14, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -12, -17, -7],\n [5, 1, 1, 1],\n [16, -2, -4, 0],\n [12, 5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 2, -4, 8],\n [0, 2, -4, 8],\n [0, -3, 6, -12],\n [0, 2, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 16, -8, -8],\n [4, 4, -2, -2],\n [-8, -8, 4, 4],\n [16, 16, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 12, -3, -3],\n [-6, -12, 3, 3],\n [-8, -16, 4, 4],\n [8, 16, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 7, -15, 18],\n [-6, 4, -8, 8],\n [15, -5, 21, -22],\n [9, -9, 14, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 17, 2, -34],\n [-14, -10, 6, 12],\n [11, 23, 15, -12],\n [-2, 5, -8, -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[[0, 0, 0, 0],\n [-3, -4, 3, 1],\n [12, 16, -12, -4],\n [-12, -16, 12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, 12, 16],\n [3, 6, 9, 12],\n [1, 2, 3, 4],\n [-4, -8, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 4, -12, 16],\n [-4, -4, 12, -16],\n [0, 0, 0, 0],\n [3, 3, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 2, 1, -17],\n [37, -6, 5, -16],\n [1, 18, -25, 8],\n [4, 2, 0, -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 4x4 matrix:\n[[-10, 14, 10, 4],\n [-3, 3, 3, 2],\n [5, -13, -5, 2],\n [-4, -4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -2, 3, 9],\n [-12, -4, 0, 3],\n [0, -1, 3, -3],\n [19, 9, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -7, -7, 16],\n [7, 4, 2, -8],\n [-2, -2, -1, 4],\n [-7, -4, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -16, -12, -4],\n [-1, 12, -12, 24],\n [2, -8, 6, -14],\n [-8, 0, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 31, 8, -12],\n [12, 16, 6, 12],\n [16, 17, -2, 4],\n [8, 27, 5, -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[[6, 15, 12, 3],\n [6, -3, -12, 13],\n [-1, 11, 16, -8],\n [-8, -20, -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[[4, 4, 8, 8],\n [-4, -4, -8, -8],\n [3, 3, 6, 6],\n [1, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -3, -9, -9],\n [-16, -4, -12, -12],\n [0, 0, 0, 0],\n [-4, -1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 8, -8, -12],\n [2, 4, -4, -6],\n [-1, -2, 2, 3],\n [3, 6, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -8, 6, 0],\n [4, -16, 12, 0],\n [4, -16, 12, 0],\n [4, -16, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -8, -9, 16],\n [-3, -12, -9, -12],\n [-6, -9, -6, -15],\n [-10, 5, 6, -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 4x4 matrix:\n[[3, 12, 6, -9],\n [4, 7, 5, -6],\n [2, 11, 5, -8],\n [-3, -12, -6, 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[[4, -12, -10, -10],\n [-13, 14, 5, 0],\n [-5, 0, -4, -7],\n [-19, 2, -13, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, 3, -3],\n [0, 0, 0, 0],\n [-2, 2, -1, 1],\n [-4, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-6, 3, -3, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [7, -17, -19, -7],\n [-23, 13, 16, -12],\n [-17, 11, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -6, 14, 11],\n [-4, 2, -8, -12],\n [-2, 0, -4, -10],\n [-5, 6, -10, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -1, 4, -2],\n [12, 4, -16, 8],\n [-6, -2, 8, -4],\n [9, 3, -12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -16, 1, 10],\n [20, 18, 7, -6],\n [-5, -2, -12, -16],\n [-10, -6, -5, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 0, 6, -21],\n [10, -4, -8, 18],\n [0, 11, 7, 3],\n [4, -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[[15, 15, 10, 19],\n [12, -6, -4, -4],\n [9, 18, 12, 21],\n [10, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -6, -2, 2],\n [12, -12, -4, 4],\n [6, -6, -2, 2],\n [6, -6, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 16, 4, 16],\n [-6, -12, -3, -12],\n [-4, -8, -2, -8],\n [-8, -16, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 20, 0, 20],\n [8, 36, -4, 28],\n [-6, -3, 21, -3],\n [9, 4, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 0, 3, 3],\n [-4, 0, -4, -4],\n [1, 0, 1, 1],\n [-4, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-31, -22, 2, -32],\n [9, -3, 22, 4],\n [-13, -2, 4, -8],\n [-8, -16, -4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -4, 1, -2],\n [9, 12, -3, 6],\n [3, 4, -1, 2],\n [9, 12, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 0, -4, 12],\n [1, 3, -2, -3],\n [16, -24, 28, -12],\n [4, -6, 7, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 9, -6, -24],\n [-15, 3, 0, -3],\n [-2, 4, -1, -3],\n [15, -3, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 7, -11, -5],\n [-3, -6, 15, 14],\n [-20, -2, 2, -2],\n [-4, -12, 20, 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[[1, -1, 3, -4],\n [2, -2, 6, -8],\n [-4, 4, -12, 16],\n [2, -2, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 14, -5, 11],\n [-5, 5, 1, 2],\n [-5, -5, 12, -11],\n [-16, 8, 12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-6, 2, 2, 4],\n [0, 0, 0, 0],\n [-12, 4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -7, -3, -8],\n [-12, -5, 1, 10],\n [6, 8, -2, -2],\n [21, 14, 2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-3, -9, 0, -6],\n [-2, -6, 0, -4],\n [3, 9, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, 4, -4, -14],\n [21, 7, -3, -24],\n [-1, -15, 2, 8],\n [-3, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -12, 15, 3],\n [0, -2, -2, -4],\n [14, -6, 15, 9],\n [-14, 8, -13, -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 4x4 matrix:\n[[6, 0, 9, -3],\n [-2, 0, -3, 1],\n [24, -8, 12, 4],\n [0, 1, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -3, -9, -2],\n [-6, 0, 9, 4],\n [-12, 10, 13, -2],\n [-9, 13, -2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 7, -23, -8],\n [0, -2, -5, -2],\n [7, 11, -1, 1],\n [-4, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -18, 0, 3],\n [23, 26, -2, -10],\n [-12, 0, 20, -2],\n [-1, 2, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 1, -2, -2],\n [-12, -12, 10, 0],\n [-12, -18, 8, -12],\n [-12, -18, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 6, 2, -10],\n [19, 9, 5, 7],\n [-22, -18, 0, 14],\n [14, 10, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 4, 0, -3],\n [0, 12, 0, -9],\n [0, 12, 0, -9],\n [0, -12, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, -4, -4],\n [8, 0, -8, -8],\n [-16, 0, 16, 16],\n [16, 0, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -2, 3, -3],\n [3, 6, -9, 9],\n [-2, -4, 6, -6],\n [-4, -8, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 10, -7, -6],\n [-10, -9, 8, -8],\n [-13, -9, 7, -2],\n [-1, -1, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, 7, 4, 3],\n [-7, -5, -4, -3],\n [-4, -12, -16, -12],\n [-13, -7, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -8, -31, -17],\n [0, 3, -2, 1],\n [12, -2, 14, 8],\n [-15, 1, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[37, 22, -7, -5],\n [4, -9, -11, 17],\n [-3, 2, 7, 4],\n [-1, 12, 19, 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, -13, 9, -4],\n [6, -8, -8, 24],\n [6, -6, 0, 12],\n [8, 4, -12, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 12, 3, 9],\n [-3, -12, -3, -9],\n [0, 0, 0, 0],\n [-4, -16, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [8, -12, -8, 4],\n [4, -6, -4, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, 12, -8],\n [-3, 0, 3, -2],\n [3, 0, -3, 2],\n [-12, 0, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 8, 4, -4],\n [2, -2, -1, 1],\n [6, -6, -3, 3],\n [6, -6, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, -5, -10],\n [-7, 2, -2, -4],\n [-3, -10, -9, -18],\n [2, 12, 10, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 20, -4, 6],\n [-4, -16, 5, 6],\n [2, -24, 10, 2],\n [18, 24, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -6, 13, 3],\n [1, -6, 5, -3],\n [-3, -2, 15, 9],\n [4, -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[[-9, 12, 6, -6],\n [9, -12, -6, 6],\n [6, -8, -4, 4],\n [9, -12, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 12, -13, 9],\n [-5, 3, -10, 0],\n [3, 0, 9, 3],\n [-12, 15, -11, 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 4x4 matrix:\n[[4, 2, 4, 2],\n [1, -17, 11, 2],\n [-4, -2, -9, -3],\n [-3, 2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[18, -6, 8, 16],\n [-3, -9, -8, -16],\n [3, 3, 4, 8],\n [-21, 12, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, -4, -2],\n [0, 0, -8, -4],\n [0, 0, -12, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, -2, -8],\n [2, -4, 2, 8],\n [-1, 2, -1, -4],\n [4, -8, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -16, 12, 4],\n [-8, -8, 6, 2],\n [0, 0, 0, 0],\n [-16, -16, 12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -6, -6, -8],\n [0, 0, 0, 0],\n [4, -6, -6, -8],\n [-6, 9, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -3, 4, -2],\n [6, -6, 8, -4],\n [3, -3, 4, -2],\n [-9, 9, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -20, 8, 0],\n [9, 9, -3, -3],\n [-7, 1, -1, 3],\n [-7, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 8, 5, -5],\n [15, -21, -15, 0],\n [3, -1, -1, -2],\n [8, 0, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, 8, -2],\n [-10, -10, -24, -10],\n [-10, -10, -6, 3],\n [-2, -2, -4, -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 4x4 matrix:\n[[-19, 8, -26, 8],\n [-4, 16, -16, 0],\n [4, 4, 11, -2],\n [-12, -2, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -4, 0, 8],\n [12, -6, 0, 12],\n [4, -2, 0, 4],\n [21, -18, 9, 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 4x4 matrix:\n[[4, 0, 8, -12],\n [-2, 0, -4, 6],\n [1, 0, 2, -3],\n [4, 0, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 0, -3, -3],\n [12, 0, -12, -12],\n [6, 0, -6, -6],\n [-3, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -6, 9, 9],\n [4, -4, 6, 6],\n [-6, 6, -9, -9],\n [-2, 2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 4, -3, -3],\n [0, 0, 0, 0],\n [-16, 16, -12, -12],\n [-8, 8, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -6, 2, 2],\n [12, -9, -10, 23],\n [8, 0, 0, 16],\n [8, -16, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -4, -4, -8],\n [-6, 3, 3, 6],\n [-6, 3, 3, 6],\n [6, -3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -3, 0, 0],\n [-4, 15, 0, -12],\n [15, 3, -3, 3],\n [8, -6, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 2, 1, 3],\n [-7, 2, -7, -1],\n [-17, 6, -17, -1],\n [-3, -6, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, -10, -30, 12],\n [12, -3, -21, 9],\n [-15, 0, 18, -18],\n [-2, -5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 10, -6, -4],\n [1, -5, -1, 1],\n [8, -16, 0, 4],\n [-1, 5, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, -6, 8, -16],\n [14, -17, 10, -4],\n [-4, -7, -2, 12],\n [-10, 18, -16, -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[[21, 17, 6, 12],\n [9, 3, 2, 3],\n [-13, -21, 0, -16],\n [-8, -16, -1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 2, -10, -3],\n [-7, -10, 14, -5],\n [1, 8, -6, 10],\n [-7, 6, 6, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 6, 8, -4],\n [3, -3, -4, 2],\n [3, -3, -4, 2],\n [-9, 9, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 0, 1, -1],\n [-2, -9, -1, -11],\n [-6, 3, -3, 7],\n [8, 3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 23, 7, -2],\n [17, -7, -15, 2],\n [5, -21, 3, 5],\n [-11, -11, 21, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -14, 20, 4],\n [-1, -6, 8, 1],\n [3, -14, 16, -1],\n [5, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 0, 6, -6],\n [-6, 0, -6, 6],\n [4, 0, 4, -4],\n [8, 0, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -3, 6, 6],\n [5, -10, -13, 5],\n [-16, 2, 2, -10],\n [-19, -4, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 5, 13, 15],\n [0, -2, -22, -6],\n [0, 4, 9, 12],\n [0, -3, -5, -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 4x4 matrix:\n[[2, 0, 4, 3],\n [4, 0, 8, 6],\n [-4, 0, -8, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [16, 4, -8, -16],\n [0, 0, 0, 0],\n [-16, -4, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 12, 12, 8],\n [8, 12, 12, 8],\n [0, 0, 0, 0],\n [6, 9, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -8, -1, 1],\n [-7, -1, -3, 1],\n [-17, 2, -6, 1],\n [-10, -12, -4, 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 4x4 matrix:\n[[12, -2, 0, 18],\n [-16, 24, 10, 8],\n [0, 12, 2, 20],\n [-2, -1, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 8, 4, 5],\n [2, -8, -8, 2],\n [9, 6, 12, -12],\n [4, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -13, -16, 1],\n [18, 9, 0, 18],\n [-24, -3, 9, -30],\n [8, -1, -17, 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, 4, -2],\n [-12, 4, 16, -8],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -1, 4, 4],\n [-4, 2, -8, -8],\n [-8, 4, -16, -16],\n [-8, 4, -16, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -8, -12, -16],\n [-3, -6, -9, -12],\n [0, 0, 0, 0],\n [4, 8, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [4, -8, 6, -6],\n [6, -12, 9, -9],\n [6, -12, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -13, 0, 14],\n [-9, 4, 19, -1],\n [-16, 4, 12, -8],\n [2, -5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 16, 8, -8],\n [-6, -12, -6, 6],\n [6, 12, 6, -6],\n [-2, -4, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, -8, 6],\n [2, -6, 12, -17],\n [3, 8, -16, 0],\n [0, 8, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -4, 6, -8],\n [-8, -4, 6, -8],\n [-8, -4, 6, -8],\n [-4, -2, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -16, 13, 31],\n [-22, 2, 2, -18],\n [-16, 5, -1, -12],\n [8, 16, -15, -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[[-7, -2, -2, 4],\n [6, 20, 4, 8],\n [-5, -6, -2, 0],\n [-12, -8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 16, -8, 12],\n [-16, -16, 8, -12],\n [0, 0, 0, 0],\n [16, 16, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -6, -24, -16],\n [11, -4, -16, -11],\n [3, 0, 0, -3],\n [4, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -12, -2, -22],\n [-4, 4, 7, 13],\n [-1, 0, 7, 6],\n [-7, 3, 4, 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[[-12, -13, 11, 24],\n [8, 0, 2, -2],\n [30, 14, -3, -2],\n [4, 14, -13, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 1, -5, 2],\n [-6, 6, -2, -4],\n [-4, 8, 16, -16],\n [-2, 4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -4, 3, -2],\n [0, 8, -6, 4],\n [0, -8, 6, -4],\n [0, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 6, 6, -8],\n [0, 0, 0, 0],\n [-4, -12, -12, 16],\n [-2, -6, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 4, 3, 1],\n [12, 12, 9, 3],\n [-8, -8, -6, -2],\n [16, 16, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, 2, -2],\n [6, -6, 8, 10],\n [-7, 5, -6, -9],\n [8, -10, 14, 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[[9, -3, 0, 0],\n [-12, 4, 0, 0],\n [0, 0, 0, 0],\n [-9, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[28, 14, -10, -7],\n [16, 22, -14, -5],\n [24, 8, -18, 4],\n [-4, 22, 7, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, 18, -3, -2],\n [15, 2, 1, -2],\n [-2, -20, 2, 4],\n [-6, 20, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 12, 16, -12],\n [0, -9, -15, 21],\n [-4, 9, -2, -9],\n [4, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, -9, 18, -7],\n [-14, -17, 11, 5],\n [-9, -13, 6, 5],\n [10, 0, -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[[-8, -11, 7, -2],\n [7, -4, -3, -10],\n [-11, 6, 6, 20],\n [-13, 11, 7, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 3, -1, -2],\n [2, 6, -5, 5],\n [-6, -18, 10, 0],\n [-2, -6, 3, 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[[-12, -4, -12, -8],\n [12, 4, 12, 8],\n [-6, -2, -6, -4],\n [-6, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [3, 4, 2, 3],\n [9, 12, 6, 9],\n [-6, -8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, 22, 0],\n [-14, -13, 5, 0],\n [2, 1, 4, 0],\n [-14, -11, -6, 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[[7, 9, 5, 8],\n [-3, -1, -9, -8],\n [-9, -9, -3, -12],\n [-15, -15, -13, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -5, 19, 14],\n [3, 2, -7, -2],\n [0, 1, -3, 2],\n [0, 2, -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 4x4 matrix:\n[[4, -8, -4, 2],\n [6, -12, -6, 3],\n [-4, 8, 4, -2],\n [-8, 16, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -3, 9, 3],\n [-2, 6, 4, 8],\n [4, -4, 1, -3],\n [3, 7, 12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 8, -4, 8],\n [3, -12, 6, -12],\n [-2, 8, -4, 8],\n [2, -8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, 8, -8],\n [0, -12, -16, 24],\n [-3, -15, -18, 24],\n [4, 20, 24, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 4, 17, 4],\n [-12, -5, -13, -2],\n [0, 9, -2, -6],\n [-9, 3, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -1, 3, 0],\n [0, 2, -6, 0],\n [0, 1, -3, 0],\n [0, 4, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -12, 9, -3],\n [2, -14, 6, 0],\n [0, 3, 0, -1],\n [-3, 0, -9, 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[[12, 6, -3, -6],\n [20, 14, -1, -10],\n [-16, -12, 0, 8],\n [16, 9, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -9, -6, 13],\n [0, 6, 6, -12],\n [3, -5, 4, -5],\n [2, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 0, -6, -6],\n [1, 4, -17, -25],\n [8, -4, 8, 16],\n [-12, 3, 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, 15, -3, -4],\n [-15, 21, 24, -29],\n [7, -4, -5, 5],\n [16, -8, -31, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -1, 2, 1],\n [4, 2, -4, -2],\n [-2, -1, 2, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 0, 0, -4],\n [-4, 0, 0, 2],\n [-16, 0, 0, 8],\n [4, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 16, -3, 5],\n [-19, -18, 10, 14],\n [-10, -7, 7, 13],\n [-22, -22, 13, 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, 6, 4, -1],\n [-3, 0, -4, -5],\n [-6, -9, -8, -1],\n [-6, -7, -8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, -8, 6],\n [-8, 6, -8, -10],\n [8, -6, 8, 10],\n [-4, 7, -12, -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[[-12, 12, -8, -16],\n [9, -9, 6, 12],\n [12, -12, 8, 16],\n [6, -6, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 2, -4, -6],\n [4, -4, 8, 12],\n [-1, 1, -2, -3],\n [-1, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, 2, 11],\n [-22, 8, 30, 9],\n [12, -2, -16, 0],\n [-34, 13, 16, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 2, 2, -4],\n [0, 0, 0, 0],\n [0, 4, 4, -8],\n [0, 8, 8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -3, 1, -8],\n [2, -1, -1, -4],\n [-6, -3, 13, 4],\n [5, -1, -5, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -6, -12, -12],\n [-9, -6, -12, -12],\n [-3, -2, -4, -4],\n [10, 5, 14, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-6, -4, 4, -4],\n [-3, -2, 2, -2],\n [-9, -6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 1, 3, 9],\n [-4, -8, 12, 6],\n [11, 7, -15, -15],\n [-8, 4, 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[[9, -4, -16, -2],\n [-4, -16, 0, -8],\n [-12, -18, 12, -9],\n [-12, -8, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 6, -4, 5],\n [0, 4, -3, 1],\n [-2, 6, -4, 5],\n [-14, -6, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -11, -5, 22],\n [4, 9, 5, 2],\n [-12, -7, -5, -14],\n [-12, -3, 1, 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 4x4 matrix:\n[[-16, 0, 0, -8],\n [8, 0, 0, 4],\n [12, 0, 0, 6],\n [-12, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -9, -6, 9],\n [0, -3, -2, 3],\n [0, -12, -8, 12],\n [0, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -1, -9, 9],\n [-3, 0, 6, -6],\n [-8, -10, 0, 3],\n [6, -1, -1, 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[[4, 12, -8, 4],\n [0, -10, 2, 0],\n [2, -14, 0, 2],\n [8, -16, -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[[2, 4, 0, 6],\n [-1, -2, 0, -3],\n [-3, -6, 0, -9],\n [-1, -2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[19, -11, 2, -2],\n [-11, -3, -9, -12],\n [4, -6, -3, 18],\n [14, -5, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -16, -8, 12],\n [-2, -9, -8, 4],\n [-4, -18, -16, 8],\n [-8, 8, -10, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, 2, 2, 3],\n [-5, 4, 9, -9],\n [-5, -2, -2, -3],\n [-5, 4, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 8, -10, -2],\n [12, -16, 14, -14],\n [0, 6, -3, 12],\n [4, -2, 3, 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[[-3, -4, -6, -17],\n [4, 8, 6, 11],\n [-22, 4, -18, -24],\n [-2, -12, -6, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [16, -8, 12, -12],\n [8, -4, 6, -6],\n [-8, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -28, -8, 8],\n [13, -7, -1, -13],\n [-7, 13, 3, 7],\n [-3, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, -8, -26, 5],\n [10, -2, -7, -5],\n [12, -8, -12, 0],\n [-2, -2, -11, 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[[-1, -1, -1, 1],\n [1, 1, 1, -1],\n [-3, -3, -3, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, -12, 12],\n [4, 0, 12, -12],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, 11, -16, 6],\n [15, 9, 6, -21],\n [13, 11, -2, -13],\n [12, 4, 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[[3, 0, 9, 0],\n [-5, 0, 0, -9],\n [2, 0, -4, 6],\n [1, 0, -12, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 4, 1, 10],\n [-6, -14, -4, -20],\n [3, 8, -1, 8],\n [-3, -9, -8, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 11, 5, 3],\n [-11, 30, 9, 10],\n [-4, -9, -20, 11],\n [-4, -11, -18, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -14, 0, 1],\n [5, -3, 0, 0],\n [-4, 1, 0, 4],\n [0, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -4, -3, -3],\n [-1, 4, 3, 3],\n [4, -16, -12, -12],\n [-4, 16, 12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -20, 20, 26],\n [16, 4, 6, -6],\n [-11, -18, -8, 13],\n [0, 0, 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[[0, 0, 0, 0],\n [0, -12, 0, -3],\n [0, -16, 0, -4],\n [0, 4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 0, 0, -6],\n [0, 0, 0, 0],\n [-12, 0, 0, 9],\n [-16, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -5, 13, 18],\n [0, 0, 0, 0],\n [4, 12, -20, -4],\n [-28, 4, -12, -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 4x4 matrix:\n[[-4, 6, 7, -3],\n [3, 8, -3, 5],\n [-3, 22, 8, 0],\n [7, -16, -13, 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 4x4 matrix:\n[[-9, 0, 0, 0],\n [-6, 0, 0, 0],\n [0, 0, 0, 0],\n [9, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 4, 2, 0],\n [-12, 8, 4, 0],\n [0, 0, 0, 0],\n [3, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -5, 16, -13],\n [-8, 2, 16, -10],\n [-7, 18, 4, 5],\n [-4, 14, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -8, -13, 9],\n [3, 5, 3, 1],\n [7, -9, 0, 10],\n [18, -26, 1, 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[[-6, 0, -6, 0],\n [-4, -2, 0, -1],\n [-2, 0, -2, 0],\n [14, 8, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 18, 15, 14],\n [-10, -10, -1, 2],\n [4, 6, 3, 2],\n [-12, -18, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, -7, 12, 11],\n [-16, 8, -16, -16],\n [-1, -1, 0, -1],\n [-14, 10, -16, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, 3, 25, 2],\n [3, -1, -7, -1],\n [-12, 8, 20, 3],\n [15, -1, -19, 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[[-34, 0, -8, -6],\n [-8, 18, -10, 18],\n [12, -19, 16, -11],\n [4, -15, 8, -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 4x4 matrix:\n[[0, -3, 3, 4],\n [3, 12, -5, -14],\n [3, -3, 10, 6],\n [12, 9, 19, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 7, 18, -8],\n [-3, -3, 4, -4],\n [-10, -2, -4, 8],\n [-1, -8, -16, 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[[-9, 3, -9, 0],\n [-3, 1, -3, 0],\n [12, 1, 6, 3],\n [6, 13, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 8, -12, -28],\n [7, -4, 6, 11],\n [4, -2, 3, 4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 8, 10, -8],\n [1, 5, 4, 1],\n [13, 17, -12, -3],\n [-4, -2, 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[[3, -3, -15, -5],\n [7, -7, 11, 11],\n [25, -25, -13, 5],\n [11, -11, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -2, 3, 3],\n [2, -4, 6, 6],\n [-3, 6, -9, -9],\n [-2, 4, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -4, 5, 4],\n [-4, -13, -19, 20],\n [-9, -5, -7, 11],\n [12, 0, 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[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, -4, 2, 4],\n [-4, 8, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -6, 0, -2],\n [-3, 12, -21, -3],\n [0, 0, 0, 0],\n [-21, 9, 3, 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[[-9, 9, 9, 0],\n [-6, 6, 12, 9],\n [7, -7, -15, -12],\n [-10, 10, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 8, 8, 2],\n [8, -16, -16, -4],\n [-6, 12, 12, 3],\n [-6, 12, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 0, -4, 12],\n [12, 0, -3, 9],\n [8, 0, -2, 6],\n [-16, 0, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, -2, -4],\n [0, -16, 8, 16],\n [0, -16, 8, 16],\n [0, -12, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -4, -3, -4],\n [4, 4, 3, 4],\n [16, 16, 12, 16],\n [16, 16, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -6, 9, -12],\n [-1, 2, -3, 4],\n [0, 0, 0, 0],\n [-2, 4, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -8, -8, 19],\n [18, -9, 6, -3],\n [-6, 3, -2, 1],\n [0, 9, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 12, -4, 8],\n [-11, -15, -5, -11],\n [-9, -12, -6, -9],\n [-4, -5, -5, -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 4x4 matrix:\n[[-11, -10, -9, 3],\n [5, 0, 19, -19],\n [19, 8, 21, -9],\n [12, 7, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, 6, 0, -7],\n [5, -5, 0, 6],\n [0, 0, 0, 0],\n [0, -15, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -2, 6, 1],\n [-12, -4, -6, -4],\n [0, -6, 9, 0],\n [-15, -4, -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[[-3, 12, 3, -3],\n [-3, 12, 3, -3],\n [12, 0, -20, -12],\n [2, 4, -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[[-13, 0, -2, -6],\n [-11, 2, 0, -11],\n [9, -4, 16, 5],\n [-1, 3, -8, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -8, 3, 10],\n [6, -4, 14, 10],\n [2, 6, 0, 0],\n [-4, 20, -8, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, -14, -2, -12],\n [4, 4, -12, 0],\n [-4, -5, 6, 4],\n [-8, 3, -14, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, 8, -14, -5],\n [20, -8, 24, -4],\n [8, -13, 4, 25],\n [16, -5, 20, -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[[-14, -8, -16, -11],\n [-13, -11, -17, -12],\n [14, 8, 16, 11],\n [16, 12, 20, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -9, 8, -10],\n [-16, 0, 1, -8],\n [-4, -18, 18, -6],\n [-27, -15, 12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, 0, 9],\n [2, -9, 3, 3],\n [-16, -12, 4, 18],\n [16, 6, -2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -7, -2, -7],\n [6, 9, -1, 4],\n [14, 16, 1, 11],\n [-2, -13, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -6, -8, -2],\n [4, 12, 16, 4],\n [-2, -6, -8, -2],\n [-3, -9, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 0, -4, 0],\n [-8, 0, -16, 0],\n [-6, 0, -12, 0],\n [-6, 0, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -2, -1, -8],\n [-3, 6, 12, 6],\n [0, -6, -13, -4],\n [-22, 8, 10, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 6, 12, -1],\n [21, 9, 12, -2],\n [-4, -10, -8, 3],\n [22, -2, 10, 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 4x4 matrix:\n[[2, -2, 2, 0],\n [20, -20, -8, -8],\n [-8, 8, 13, 6],\n [15, -15, -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[[-18, 16, -8, 10],\n [-12, 30, -21, -3],\n [-14, 26, -17, 0],\n [15, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 9, -6, 9],\n [0, 3, -2, 3],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[17, 25, 5, 18],\n [7, -1, -17, -6],\n [-3, -9, -6, -13],\n [3, 7, 3, 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 4x4 matrix:\n[[-3, -3, 9, 6],\n [-2, 4, 2, 2],\n [-3, -6, 11, 7],\n [1, -14, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 0, -16, -12],\n [-4, 1, 14, 6],\n [6, 1, -6, -9],\n [0, -2, -12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -16, 16, 14],\n [-5, -6, 5, -1],\n [-4, -8, 4, 4],\n [8, 15, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 11, -12, -3],\n [6, -8, 0, 6],\n [-1, -2, -8, 5],\n [-7, 11, 4, -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[[23, 17, 28, -15],\n [20, -10, -20, 7],\n [24, 6, 12, -9],\n [12, -12, 0, -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[[8, 0, 6, -8],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-12, 0, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 18, 6, 6],\n [2, -24, 6, -6],\n [13, 8, -9, 1],\n [9, -9, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -6, 3, 12],\n [4, 8, -4, -16],\n [4, 8, -4, -16],\n [-3, -6, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-28, 9, 6, -4],\n [-24, 10, 8, -8],\n [9, -22, -32, 23],\n [-9, 6, 12, 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[[-16, 16, -16, -1],\n [8, -7, 3, -7],\n [-11, 12, -13, -2],\n [2, 14, -16, 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[[4, 3, -1, 4],\n [-8, -8, 0, -4],\n [-16, -20, -4, 0],\n [4, 8, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, 10, -5, -16],\n [-15, 4, -7, 0],\n [14, 18, -8, -16],\n [14, 18, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 9, 22, 12],\n [2, -6, -12, -2],\n [4, -3, 2, 8],\n [2, 1, 14, 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[[-3, -7, 23, -1],\n [7, -8, 10, 1],\n [-4, -7, 5, -4],\n [-7, -4, 26, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 12, -16, 16],\n [-9, -9, 12, -12],\n [0, 0, 0, 0],\n [-3, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 0, -8, 8],\n [0, 0, 0, 0],\n [-16, 0, 16, -16],\n [-4, 0, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 8, -3, 2],\n [-12, 24, 16, 16],\n [0, -12, 2, -4],\n [5, 4, -9, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -1, 4, -4],\n [12, 4, -16, 16],\n [6, 2, -8, 8],\n [-12, -4, 16, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 6, -4, 11],\n [9, -15, 3, -17],\n [12, -6, 4, -11],\n [12, 12, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -3, -9, 9],\n [4, 2, 6, -6],\n [8, 4, 12, -12],\n [6, 3, 9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 6, -15, -16],\n [0, -10, 18, 0],\n [6, 8, 18, 2],\n [9, 8, 9, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 2, -8, -6],\n [-6, 4, 2, -6],\n [7, -3, -9, -3],\n [17, 4, -19, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -5, 6, 0],\n [4, -12, 0, 16],\n [11, 16, -21, 2],\n [2, 15, -9, -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 4x4 matrix:\n[[-1, 0, -2, -2],\n [-3, 0, -6, -6],\n [2, 0, 4, 4],\n [-2, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 8, 16, -4],\n [18, -18, -8, 17],\n [8, 10, 0, -6],\n [-15, 28, 12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -6, 7, 1],\n [3, 21, 2, -1],\n [-1, -24, 10, 4],\n [3, -7, -9, 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[[0, 5, 5, -1],\n [-14, -2, 13, -10],\n [8, 14, -16, 11],\n [-16, -9, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 1, 4, 3],\n [-11, 23, -19, -3],\n [-3, -6, 13, 6],\n [20, -15, -3, -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[[-26, 23, 16, 4],\n [-30, 31, 24, 16],\n [-6, 3, 0, -4],\n [-16, 11, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -14, 11, 15],\n [6, -10, 0, 14],\n [-14, 9, 19, -22],\n [7, -19, 1, 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[[-3, -2, -13, 18],\n [-4, -4, -16, 16],\n [2, 6, 4, 16],\n [-4, -6, -14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 16, 18, 4],\n [10, -2, -2, -5],\n [-24, 4, -8, 6],\n [-15, 0, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 0, 4, -8],\n [4, 4, -8, -24],\n [13, 3, -11, -8],\n [14, 4, -13, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, 16, -12],\n [2, 0, -8, 6],\n [-4, 0, 16, -12],\n [-2, 0, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 2, -6, 8],\n [-3, -1, 3, -4],\n [6, 2, -6, 8],\n [12, 4, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 4, -2, -6],\n [12, 6, -3, -9],\n [12, 6, -3, -9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -3, -8, -11],\n [12, -3, -8, -11],\n [14, 4, 4, -12],\n [-15, 4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -8, 2, -7],\n [22, 28, -7, 24],\n [-16, -24, 6, -22],\n [4, 8, -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[[-2, -6, 9, -3],\n [-9, 4, 7, -15],\n [-5, 6, -6, -4],\n [11, -4, -4, 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[[-3, -12, 3, -3],\n [4, 16, -4, 4],\n [-1, -4, 1, -1],\n [-1, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 2, -6, 0],\n [-4, 4, -12, 0],\n [4, -4, 12, 0],\n [-3, 3, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-3, -4, 4, -3],\n [0, 0, 0, 0],\n [9, 12, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 17, -7, 19],\n [3, 12, -6, 12],\n [-14, -4, 8, 4],\n [10, -12, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, -1, 2],\n [-16, -20, -17, 14],\n [16, 20, 17, -14],\n [-18, -20, -11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -2, -5, 6],\n [4, -4, -16, 12],\n [0, 4, 8, -8],\n [4, 5, 5, -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[[6, -4, 4, 6],\n [12, -8, 8, 12],\n [-6, 4, -4, -6],\n [3, -2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 0, 4, -13],\n [-5, 0, 4, 17],\n [-3, 0, -12, -6],\n [10, 0, 16, -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[[8, 8, 2, -6],\n [9, 8, 12, -15],\n [13, 20, 0, -17],\n [-1, 12, -7, -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[[4, 2, -8, -8],\n [3, 3, 12, -9],\n [3, 0, -24, -3],\n [-1, 0, 8, 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[[-11, -8, -2, 1],\n [-5, -2, -4, -1],\n [9, -9, 11, -7],\n [7, -14, 12, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -28, -20, -10],\n [4, -6, -5, -1],\n [-21, 14, 15, -3],\n [4, 17, 7, 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[[-16, -5, 6, 16],\n [12, 23, 12, -12],\n [-3, 24, 20, 2],\n [7, 21, 16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 12, 18, 7],\n [-15, 7, 12, 9],\n [-16, -3, -4, 9],\n [-6, 7, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 9, 7, -20],\n [-3, 6, -2, -10],\n [9, -12, 0, 22],\n [-12, 0, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -4, -11, -2],\n [0, 2, 7, -2],\n [1, 2, -5, -2],\n [0, -5, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, 16, -12],\n [3, 0, 12, -9],\n [4, 0, 16, -12],\n [4, 0, 16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -3, -6, -9],\n [3, 3, 6, 9],\n [4, 4, 8, 12],\n [-2, -2, -4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -4, 6, -1],\n [0, -8, 8, -12],\n [0, -6, 8, -4],\n [0, 9, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 2, 4, -4],\n [3, 6, 12, -12],\n [-2, -4, -8, 8],\n [3, 6, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 16, 3, -8],\n [-12, -24, -4, 8],\n [6, 12, 4, -20],\n [9, 18, 4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -8, -4, -12],\n [0, 0, 0, 0],\n [0, 8, 4, 12],\n [0, -8, -4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -3, 6, -6],\n [-6, -3, 6, -6],\n [-8, -4, 8, -8],\n [8, 4, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, 9, 1, 6],\n [4, 0, 2, -2],\n [9, 25, -17, -4],\n [2, 4, -13, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 16, -17, -18],\n [9, 9, 1, -2],\n [0, 12, -16, -16],\n [-6, -11, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -12, -13, -13],\n [0, 12, 8, 8],\n [3, -8, -7, -7],\n [-6, 4, 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[[-1, -9, -7, 6],\n [1, 17, 15, -8],\n [1, 9, 7, -6],\n [4, 12, 4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -24, -3, 9],\n [3, -4, -11, -2],\n [-9, 12, 3, -4],\n [18, -24, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -1, 1, 10],\n [15, 5, -5, -18],\n [3, -1, 1, -6],\n [1, 3, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -16, -4, -18],\n [0, 6, 2, 4],\n [-20, 20, -6, 14],\n [-12, 15, -7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -4, -6, 7],\n [-2, 4, 5, -5],\n [-2, 16, 14, -8],\n [-1, 16, 13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 16, 12, -12],\n [-4, 8, 6, -6],\n [-8, 16, 12, -12],\n [6, -12, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [4, 3, -3, -1],\n [16, 12, -12, -4],\n [-16, -12, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-8, 12, 12, -4],\n [-6, 9, 9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[19, 1, 5, -15],\n [9, 3, 3, 3],\n [19, 1, 5, -15],\n [1, 3, 1, 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 4x4 matrix:\n[[-12, -16, 0, -16],\n [1, -4, 3, -1],\n [-7, 12, -12, 0],\n [-16, 0, -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[[4, 2, 3, 2],\n [-16, -8, -12, -8],\n [-16, -8, -12, -8],\n [-12, -6, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 6, 0, 6],\n [2, 4, 0, 4],\n [3, 6, 0, 6],\n [3, 6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 2, 13, -5],\n [8, 11, 16, -5],\n [8, -16, -12, 4],\n [0, -2, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 16, -8, -16],\n [-8, 8, -4, -8],\n [16, -16, 8, 16],\n [-4, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, -12, -16, -10],\n [1, 4, 16, 14],\n [8, -16, -16, -8],\n [-16, 16, -16, -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 4x4 matrix:\n[[20, -4, 16, 32],\n [-15, -10, 12, 20],\n [-12, 2, -15, -12],\n [15, 5, -6, 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, 17, 23, 4],\n [9, -2, -3, -19],\n [-12, -7, -4, -9],\n [3, 12, 13, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, -6, 0, -6],\n [-4, 2, 0, 2],\n [12, -6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 15, -19, -16],\n [-3, 3, 1, -8],\n [0, 4, 5, 5],\n [-4, 4, 20, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 2, 6, -5],\n [-4, -2, -4, 6],\n [9, -3, 6, 0],\n [-2, 6, 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 4x4 matrix:\n[[6, 0, -2, -20],\n [18, 12, -10, -4],\n [0, 6, -2, 28],\n [-3, 3, 0, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -2, -4, -8],\n [-3, -1, -2, -4],\n [0, 0, 0, 0],\n [-12, -4, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -5, 13, 11],\n [-7, 0, 0, 0],\n [9, -1, 3, 1],\n [-17, 7, -16, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, -15, 4, -9],\n [3, 3, -11, 9],\n [2, -1, -6, 10],\n [16, 18, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, 3, -5],\n [5, 2, 13, -6],\n [-2, 4, 0, -9],\n [-11, -4, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 0, 0, 3],\n [12, 0, 0, -12],\n [-12, 0, 0, 12],\n [6, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, -3, 3],\n [0, 0, 0, 0],\n [0, -6, -9, 9],\n [0, 2, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -6, -6, -9],\n [7, -8, -7, -8],\n [3, -12, -9, -6],\n [1, -14, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, -14, -10, 12],\n [-4, 4, 2, 4],\n [14, 4, 6, -14],\n [1, -2, -9, 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, 6, 0, -3],\n [-4, -8, 0, 4],\n [-2, -4, 0, 2],\n [3, 6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 0, 0, 1],\n [-3, 0, 0, -1],\n [12, 0, 0, 4],\n [3, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 16, 10, -18],\n [2, 3, 4, -3],\n [-14, -5, 16, 9],\n [4, 10, 19, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 13, 34, 26],\n [0, 2, -20, -21],\n [26, -5, -14, -3],\n [-24, -5, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 2, -20, 4],\n [12, -8, 8, -22],\n [5, 1, -17, 0],\n [-15, -16, -3, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -5, 26, -11],\n [16, -12, -16, 8],\n [-5, 25, 2, -7],\n [-3, -14, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, -6, 6],\n [0, -18, -12, -12],\n [0, 6, 10, -2],\n [0, 21, 15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 6, 9, 18],\n [-3, -7, 6, -7],\n [-4, 4, 6, 14],\n [13, 17, -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[[3, -6, -9, 9],\n [4, -8, -12, 12],\n [3, -6, -9, 9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -9, -11, 2],\n [-11, 21, 2, 0],\n [0, -12, -7, 2],\n [-18, 6, -22, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 2, -1, -5],\n [4, 14, -16, -8],\n [4, -12, 12, 12],\n [16, 4, -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[[14, -6, -28, 24],\n [6, 21, -2, -4],\n [9, 7, -16, 8],\n [-5, -7, -3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -3, -1, 2],\n [2, 8, 5, -4],\n [10, -5, -11, -2],\n [6, 9, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 0, -3, -12],\n [0, 0, 0, 0],\n [3, 0, -1, -4],\n [-12, 0, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -30, 6, -11],\n [4, -30, 0, -18],\n [-1, 21, 9, 6],\n [-2, 23, 6, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -32, 12, 0],\n [-16, -12, 14, -1],\n [32, -4, -14, 7],\n [16, 32, -24, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -6, 9, -3],\n [14, -10, -11, 1],\n [20, -17, 6, -4],\n [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 4x4 matrix:\n[[7, 17, 15, 14],\n [0, 2, -4, 10],\n [-4, -11, -8, -13],\n [-8, -12, -1, -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 4x4 matrix:\n[[0, -12, -3, 9],\n [-4, 24, 0, -8],\n [-4, -8, -8, 16],\n [4, -8, 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[[-17, -22, -24, -29],\n [-4, -8, 12, -1],\n [19, 18, 32, 31],\n [16, -18, 17, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -12, 4, 8],\n [18, 4, -6, -4],\n [-3, -17, 1, 10],\n [-15, -1, 5, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -10, 2, -13],\n [18, 11, -1, 14],\n [-1, 3, -5, 5],\n [-5, -5, 3, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 2, 0, -3],\n [9, -14, -4, 5],\n [8, -8, -3, 0],\n [11, -10, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 13, -4, 8],\n [-4, 9, -1, 4],\n [-28, 9, -6, 4],\n [-6, 13, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 12, -8, 4],\n [0, -6, 4, -2],\n [0, 6, -4, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [2, -4, -6, -6],\n [4, -8, -12, -12],\n [-4, 8, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 0, -12, 6],\n [-2, 21, 8, 21],\n [5, -24, -6, -24],\n [13, 8, 18, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 4, 2, -6],\n [0, -3, -9, 0],\n [1, -2, -1, 3],\n [4, -10, -10, 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[[0, 10, -8, -5],\n [15, -14, 11, 7],\n [12, -10, 7, 5],\n [-15, 4, -10, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -3, 6, -9],\n [6, -6, 8, -6],\n [8, -7, 10, -9],\n [6, -9, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 2, 12, 0],\n [1, 1, -2, -8],\n [2, 2, 4, -8],\n [-3, -3, -14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -6, -2, -8],\n [-8, 6, 2, 8],\n [8, -6, -2, -8],\n [-16, 12, 4, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 5, 10, 8],\n [10, -3, 0, -3],\n [5, 1, 11, 7],\n [-6, 1, -5, -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[[0, 0, 0, 0],\n [4, -4, 16, -16],\n [1, -1, 4, -4],\n [-2, 2, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 10, -3, 8],\n [0, -4, -2, 0],\n [6, 0, 8, -8],\n [-3, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 6, 0, -3],\n [16, -16, 4, 6],\n [-3, 10, 8, -9],\n [16, -16, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 24, 0, -16],\n [-4, 12, 0, -16],\n [-8, -12, 0, 0],\n [3, -9, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -6, 5, -19],\n [11, 3, 16, 1],\n [-15, -3, -12, 15],\n [-5, 9, 11, 20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -3, 12, 12],\n [22, -2, -18, -10],\n [-1, -4, 3, 7],\n [5, -10, 1, 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 4x4 matrix:\n[[15, -5, 7, 7],\n [-20, 0, 2, 2],\n [10, 0, -1, -1],\n [0, -10, 17, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 16, 3, 20],\n [4, 4, -4, -8],\n [-6, -4, -2, -4],\n [-12, 7, 1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -2, -4, -12],\n [-9, 3, 6, 8],\n [3, 10, 20, -10],\n [-6, -8, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -6, -17, -17],\n [8, -6, -20, -14],\n [0, 8, 12, 16],\n [-8, 8, 23, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[18, -8, -18, -4],\n [-18, 10, 17, 6],\n [1, -8, 2, -6],\n [-1, 1, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -12, -6, -6],\n [0, 20, 8, 11],\n [18, 8, -4, 8],\n [18, 8, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [22, -20, 0, 1],\n [-16, 20, 10, -8],\n [6, 0, 10, -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[[12, 16, 12, 0],\n [-12, -16, -12, 0],\n [6, 8, 6, 0],\n [-4, 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[[-10, 6, -24, -2],\n [-23, -10, -2, 2],\n [24, 1, 10, -7],\n [10, 1, -4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, -12, -8, -8],\n [8, 7, 13, 9],\n [6, -1, 6, -2],\n [1, 14, 17, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -14, 8, -20],\n [12, 12, -6, 17],\n [-4, 7, 2, 9],\n [-4, -8, 2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [1, 1, -1, 0],\n [-4, -4, 4, 0],\n [-3, -3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 6, 6, 12],\n [-16, 8, 8, 16],\n [6, -12, -9, -12],\n [12, -12, -10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -4, 12, 0],\n [-9, -3, 9, 0],\n [0, 0, 0, 0],\n [3, 1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 3, 0, -6],\n [3, 21, 0, 15],\n [9, -5, 6, 7],\n [2, -16, 9, -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[[-15, 25, -9, -20],\n [16, -28, 12, 24],\n [-7, 11, -3, -8],\n [2, 4, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-28, 18, 5, 4],\n [12, -5, 6, 20],\n [20, -14, -7, -12],\n [-16, 12, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -12, 4, -20],\n [-8, 24, -4, 8],\n [-18, 4, 1, -12],\n [2, -6, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -28, -12, 12],\n [-3, 9, 3, -3],\n [13, 0, 2, -2],\n [-10, -22, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 3, 6, -12],\n [-1, 6, 5, -15],\n [-4, 11, -6, -8],\n [-6, 14, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 5, -10, 7],\n [-9, 14, 13, -12],\n [2, -3, -15, 13],\n [-24, 20, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -8, -12, 4],\n [6, 3, -12, 3],\n [5, 1, -2, 4],\n [-14, -10, -20, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 10, 14, 15],\n [-12, 6, -6, 9],\n [-28, 16, 8, 24],\n [21, -12, -6, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -9, 6, 0],\n [-6, 9, -6, 0],\n [8, -12, 8, 0],\n [6, -9, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -16, -16, -4],\n [-2, 4, 4, 1],\n [-6, 12, 12, 3],\n [6, -12, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -1, -2, -9],\n [-6, -8, 2, 18],\n [0, 5, 1, 0],\n [2, 16, 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[[5, 9, 2, 2],\n [-3, 0, -12, -3],\n [6, 12, 0, 2],\n [8, 18, -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 4x4 matrix:\n[[-1, -4, 3, 3],\n [8, 18, -14, -6],\n [-6, -10, 8, 0],\n [-6, -17, 13, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 4, 12, 10],\n [12, 4, -18, 4],\n [-8, -6, -13, 19],\n [12, 4, -18, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -16, -4, 16],\n [-6, -8, -2, 8],\n [12, 16, 4, -16],\n [6, 8, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [4, 2, -2, -4],\n [-12, -6, 6, 12],\n [4, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 3, -3, 9],\n [9, 9, -12, -3],\n [12, -6, 10, 22],\n [-14, 1, -3, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -10, -3, 18],\n [4, -9, 8, 5],\n [-1, -19, -18, 1],\n [-1, 12, 14, 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[[3, 6, 9, 6],\n [-1, -8, -3, 2],\n [0, -12, 0, 8],\n [3, -12, 9, 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[[10, -4, -7, -11],\n [4, -4, 2, -2],\n [8, -4, -4, -8],\n [-4, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -16, -3, -11],\n [-27, -9, 9, -9],\n [-22, -8, 9, -10],\n [1, 8, 18, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 4, 3, 0],\n [-2, -2, 1, -10],\n [-6, -6, -2, -10],\n [10, 10, 4, 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 4x4 matrix:\n[[-2, -5, 0, -11],\n [6, 10, -6, -2],\n [12, 21, -6, 3],\n [-8, -13, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 8, 6, -2],\n [0, 16, 12, -4],\n [0, 12, 9, -3],\n [0, 4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, -15, -8, -8],\n [-14, -10, -8, 4],\n [-19, -4, -14, 5],\n [5, 1, 7, 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[[0, -1, 4, -2],\n [0, 2, -8, 4],\n [0, 3, -12, 6],\n [0, -3, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -4, 8, -8],\n [6, 4, -8, 8],\n [-6, -4, 8, -8],\n [-12, -8, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -12, -9, 0],\n [0, 16, 0, -12],\n [-5, 4, -5, -8],\n [2, -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 4x4 matrix:\n[[-15, -7, -6, 2],\n [-5, -6, -9, 1],\n [4, 8, 10, 6],\n [-12, 3, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 8, 2, -6],\n [-4, 4, 1, -3],\n [-4, 20, 10, -6],\n [-8, 8, 2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -17, -1, -10],\n [11, 20, 14, 3],\n [7, 0, 9, -14],\n [-14, 0, -22, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 0, -4, 16],\n [-6, 0, 3, -12],\n [8, 0, -4, 16],\n [-4, 0, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 7, 4, 7],\n [4, 1, 1, -2],\n [0, 2, 1, 3],\n [-8, 2, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -2, 8, 4],\n [-4, 1, -4, -2],\n [8, -2, 8, 4],\n [12, -3, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 4, 10, 16],\n [16, 4, 16, 16],\n [14, 3, 14, 12],\n [6, 2, 6, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -12, 12, 8],\n [0, 12, -12, -8],\n [0, 12, -12, -8],\n [0, 6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -4, 0, -3],\n [1, 22, 3, 7],\n [1, -7, 0, 0],\n [-16, 3, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 12, 0, 16],\n [3, -9, 0, -12],\n [0, 0, 0, 0],\n [1, -3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -8, -8, -32],\n [0, -6, 18, 0],\n [1, 2, -2, 4],\n [-1, 2, -10, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, 12, -16],\n [-6, 0, 6, -8],\n [0, 0, 0, 0],\n [-3, 0, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 2, 3, -4],\n [16, 4, 17, 16],\n [8, 0, 14, 8],\n [-3, 1, -8, -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[[4, -3, -2, -3],\n [26, 1, -10, 3],\n [-16, 25, 7, 8],\n [-24, 11, 6, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-26, -7, -11, 17],\n [-20, 6, -10, 14],\n [8, 14, 2, -6],\n [-14, 5, -7, 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[[1, 12, 3, -6],\n [-4, 0, 12, 12],\n [3, 16, -1, -13],\n [2, -12, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -17, -24, 2],\n [8, -17, -10, 6],\n [-5, 2, -12, -2],\n [8, 4, 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 4x4 matrix:\n[[-3, -9, 0, -6],\n [0, 0, 0, 0],\n [-2, -6, 0, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -13, -16, -1],\n [-5, 4, 6, 3],\n [-1, 14, 18, 3],\n [-8, -20, -24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 9, 3, -3],\n [-3, -3, -1, 1],\n [6, 6, 2, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 12, -12, -12],\n [-1, -3, 3, 3],\n [3, 9, -9, -9],\n [2, 6, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 6, -2, 4],\n [-3, -3, 1, -2],\n [12, 12, -4, 8],\n [6, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 0, -3, 3],\n [-16, 9, -28, 10],\n [-9, -15, -7, 5],\n [-28, 3, -20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 8, -8, 6],\n [-16, -16, 16, -12],\n [-8, -8, 8, -6],\n [-12, -12, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -2, 0, -3],\n [0, 0, 0, 0],\n [1, -2, 0, -3],\n [-4, 8, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -2, 10, -3],\n [22, 2, 0, -12],\n [-9, -4, 10, 9],\n [-9, 3, -12, 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, 3, 0, 13],\n [18, -10, 11, 8],\n [-12, -5, 1, -17],\n [-4, 10, -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[[-4, 2, -3, 0],\n [0, 24, 0, -12],\n [32, 8, 24, -12],\n [-12, -12, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 10, -7, -7],\n [4, 12, -11, 15],\n [-16, 0, 2, -18],\n [-4, 4, -3, -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 4x4 matrix:\n[[12, 0, 9, -3],\n [-16, 0, -12, 4],\n [0, 0, 0, 0],\n [-12, 0, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -9, -18, 17],\n [11, 2, -2, 8],\n [0, 21, 18, 3],\n [0, -28, -24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, -16, 10, -4],\n [0, 8, -1, 23],\n [8, -7, 5, 4],\n [-3, 5, -1, 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 4x4 matrix:\n[[13, 9, -7, 12],\n [-2, 12, 12, -2],\n [-1, -3, 3, -4],\n [10, 12, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, -21, 0, 21],\n [11, 7, -10, -10],\n [2, 10, 8, -6],\n [-11, -14, -18, 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 4x4 matrix:\n[[7, 4, -17, -12],\n [-10, -3, 20, 10],\n [-5, 28, 25, -12],\n [-15, -18, 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[[4, 4, 4, -6],\n [2, -2, 10, 2],\n [9, 11, 5, -16],\n [-3, -5, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 8, -12, 0],\n [16, -8, 12, 0],\n [4, -2, 3, 0],\n [16, -8, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 15, 1, 1],\n [-9, -3, -5, 13],\n [-15, -6, -3, 16],\n [-2, -4, 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[[4, -8, 0, -4],\n [-8, 16, 0, 8],\n [-8, 16, 0, 8],\n [6, -12, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -4, 4, 8],\n [10, -10, 1, 11],\n [4, -6, 0, 6],\n [-2, -2, -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[[6, -6, -6, -2],\n [6, -6, -6, -2],\n [6, -6, -6, -2],\n [-12, 12, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -8, -4, 14],\n [-9, 12, -3, -12],\n [-10, 16, -2, -18],\n [-1, 4, 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 4x4 matrix:\n[[-16, 16, -2, 4],\n [7, 15, -1, -2],\n [6, -4, 3, 13],\n [8, 28, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, -8, -6],\n [3, -1, 4, -7],\n [-21, -18, 22, 24],\n [3, 3, -4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -14, -4, 2],\n [3, -3, -6, 3],\n [8, 0, -6, 3],\n [12, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -2, 10, 0],\n [6, -13, -7, -18],\n [17, -10, 7, -9],\n [-24, 15, -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[[-9, 5, 17, -17],\n [-3, 1, -9, 11],\n [-2, 5, 6, -1],\n [-3, 5, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 8, 2, 2],\n [4, -8, -2, -2],\n [0, 0, 0, 0],\n [-6, 12, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -2, 8],\n [0, 4, -1, 4],\n [0, 8, -2, 8],\n [0, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 3, -12, 9],\n [1, -1, 4, -3],\n [0, 0, 0, 0],\n [-4, 4, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -2, 2, 0],\n [1, -2, 2, 0],\n [-1, 2, -2, 0],\n [1, -2, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 4, 16, 4],\n [8, 2, 8, 2],\n [0, 0, 0, 0],\n [-16, -4, -16, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -8, -3, -14],\n [-10, -2, -2, -14],\n [21, 9, 15, 15],\n [2, 4, -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[[3, 2, 6, 14],\n [-2, -1, -8, -11],\n [2, -15, -7, -1],\n [-2, 1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -4, -4, -4],\n [-12, 4, 4, 4],\n [-6, 2, 2, 2],\n [-3, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -12, 6, 3],\n [-9, -12, 6, 3],\n [9, 12, -6, -3],\n [6, 8, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -20, 4, -4],\n [-16, 4, -16, 16],\n [2, -5, 1, -1],\n [16, -4, 16, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 16, -12, -12],\n [3, 4, -3, -3],\n [3, 4, -3, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -3, -12, 9],\n [6, 6, -4, -18],\n [-5, -5, 1, 15],\n [-6, -6, -10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, -10, 21, -20],\n [6, -10, -12, 20],\n [-8, 4, 15, -28],\n [4, 16, 0, -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[[-5, 8, -15, -7],\n [9, -6, 12, 6],\n [-5, -6, 10, 4],\n [5, 6, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -4, -20, 12],\n [1, 0, 4, -4],\n [7, -1, 10, -12],\n [1, 0, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -11, 11, -5],\n [9, -17, -2, 12],\n [5, -10, 3, -9],\n [4, -11, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -2, 0, 6],\n [8, -1, -2, 11],\n [7, -5, 2, 7],\n [-2, 14, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [4, -4, -4, 4],\n [-4, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -16, 0, 4],\n [-12, -16, 0, 4],\n [-9, -12, 0, 3],\n [12, 16, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 0, 16, 4],\n [0, 12, -16, 8],\n [-4, -6, 24, 0],\n [-8, 15, 12, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -18, -9, 14],\n [12, -12, -12, 4],\n [13, -5, -8, -1],\n [1, 7, 4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 9, -8, 0],\n [-8, 4, -8, 0],\n [-10, 5, -16, -18],\n [-4, 14, 8, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 7, -10, 1],\n [11, 14, -10, -2],\n [-16, -19, -2, 11],\n [3, -12, 15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 3, 2, -1],\n [8, -6, -8, 22],\n [24, -10, -8, 10],\n [12, -3, 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, -14, 0, 4],\n [1, -2, -3, 4],\n [6, -12, 3, 0],\n [-3, 6, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, 3, 9],\n [-8, 8, -4, -12],\n [-6, 6, -3, -9],\n [2, -2, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 3, 3, 3],\n [-2, -6, -6, -6],\n [1, 3, 3, 3],\n [4, 12, 12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -8, 0, 0],\n [-10, -6, -4, 4],\n [7, 5, 2, -2],\n [9, 7, 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[[2, 8, 0, 4],\n [1, 4, 0, 2],\n [-1, -4, 0, -2],\n [3, 12, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-4, 8, -2, -8],\n [4, -8, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 3, 9, 12],\n [-4, -4, -12, -16],\n [3, 3, 9, 12],\n [-1, -1, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 1, 2, -1],\n [-5, 1, 2, -5],\n [1, -8, -16, -12],\n [8, -4, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 12, -16, -8],\n [2, -6, 8, 4],\n [-2, 6, -8, -4],\n [-2, 6, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, 4, 8],\n [5, -6, -6, -12],\n [5, -4, -4, -8],\n [2, 4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, 0, -2],\n [0, 0, 0, 0],\n [-12, 0, 0, -4],\n [12, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, 9, 12, 0],\n [8, -9, -21, -4],\n [17, -8, -3, 4],\n [-11, 8, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -6, 3, 3],\n [-12, -6, 3, 3],\n [-16, -8, 4, 4],\n [-4, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -6, 15, 6],\n [5, 4, -8, -2],\n [-4, 0, 8, 8],\n [-2, 2, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, -15, 4, -12],\n [6, 10, 23, -2],\n [1, 9, 4, 12],\n [6, 10, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 2, -4, 6],\n [6, -2, 4, -6],\n [-12, 4, -8, 12],\n [-3, 1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -3, -3, 4],\n [-6, 6, -3, 9],\n [-3, 17, 1, -1],\n [-8, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 6, -12, -6],\n [-12, -8, 16, 8],\n [-6, -4, 8, 4],\n [-6, -4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 12, 4, -4],\n [-13, 13, -13, -3],\n [-5, 5, 6, -2],\n [-11, 11, -5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -6, 12, 19],\n [-6, 9, 0, -12],\n [-4, -2, 8, 10],\n [18, -11, -16, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -6, 0, -4],\n [17, -9, 4, -20],\n [-14, -8, -10, 32],\n [15, -10, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -3, -12, 0],\n [-8, -5, -5, -3],\n [-16, -4, 4, -4],\n [12, -3, -17, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 6, -6, 1],\n [-1, -7, 0, 3],\n [9, -6, 7, 4],\n [-6, -9, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -1, 10, -10],\n [-20, 12, 0, -17],\n [8, -12, 0, 14],\n [-16, 12, 12, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -33, -12, -32],\n [-4, -24, -12, -20],\n [-13, -9, -4, -2],\n [15, -12, -13, -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, -16, 16, 4],\n [-6, 16, -20, -5],\n [6, -12, 12, 3],\n [10, -22, 24, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -7, 18, -17],\n [8, -12, 28, -32],\n [5, 6, -6, 3],\n [0, -6, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -2, 8, 6],\n [0, 3, 15, 1],\n [1, -2, -10, 1],\n [13, -14, -4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 0, -16, 8],\n [4, 0, 4, -2],\n [0, 0, 0, 0],\n [4, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 1, 2, -7],\n [12, 4, 5, -19],\n [-8, -6, 18, 8],\n [4, 4, -17, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 12, 15, -8],\n [-11, -12, -19, 4],\n [2, 12, 4, -6],\n [2, -24, -2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 4, 3, -1],\n [-7, 2, -3, -11],\n [-2, 12, 12, 4],\n [6, -4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -1, -4, 1],\n [25, 8, 14, 6],\n [-15, -6, -2, -12],\n [-9, -6, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 2, 1, -4],\n [0, 2, 1, -4],\n [0, -4, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -12, -12, -6],\n [6, -12, -12, -6],\n [-4, 8, 8, 4],\n [2, -4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 4, 12, -12],\n [-2, 4, 4, 0],\n [-6, 6, 8, -3],\n [-2, -8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -10, -2, 7],\n [-6, 1, -8, -14],\n [0, -14, 4, 6],\n [0, 22, 16, -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 4x4 matrix:\n[[-10, 8, -4, 2],\n [-14, 8, -3, 0],\n [-11, 12, -7, 5],\n [16, -16, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, 9, -3],\n [8, 0, 12, -4],\n [0, 0, 0, 0],\n [-6, 0, -9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -2, 4, 4],\n [-9, -3, 6, 6],\n [3, 1, -2, -2],\n [-9, -3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 6, 6, -8],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-12, 12, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -24, -3, -4],\n [8, -13, 15, 1],\n [-6, 24, 3, 4],\n [-6, 9, -12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 10, 10, 18],\n [2, -3, 0, -2],\n [2, -15, -7, -4],\n [-4, -2, 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[[-9, -25, -7, 0],\n [3, -6, 14, 0],\n [0, 11, -3, 0],\n [21, -1, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -12, -8, 17],\n [6, 8, 4, -8],\n [9, 20, 8, -15],\n [-9, -20, -8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -2, -4, 6],\n [-10, 24, 20, -9],\n [-6, -1, -2, 3],\n [24, 4, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 12, 6, -9],\n [-12, -16, -8, 12],\n [0, 0, 0, 0],\n [-9, -12, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -4, 6, 19],\n [24, 4, -6, -19],\n [24, 4, -6, -19],\n [-6, -2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, 0, -6],\n [-8, 0, 0, 4],\n [-4, 0, 0, 2],\n [4, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 18, -9, -3],\n [17, -13, 1, -18],\n [16, 10, 17, -9],\n [8, -13, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 24, 8, 8],\n [-13, 3, -6, 1],\n [-2, -3, -4, -1],\n [-13, 12, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-30, 21, -22, 2],\n [-12, 9, -10, -2],\n [10, -10, 8, 0],\n [10, -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[[-8, 16, -4, 0],\n [-6, 7, -2, -4],\n [0, -5, 1, -4],\n [-2, 19, -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[[3, -9, -9, 0],\n [2, -6, -6, 0],\n [0, 0, 0, 0],\n [2, -6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 8, -2, -8],\n [-4, -16, 8, -16],\n [-4, -16, 8, -16],\n [3, 5, -2, 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 4x4 matrix:\n[[3, -7, -6, -7],\n [-3, 10, 6, 10],\n [-1, 3, 2, 3],\n [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 4x4 matrix:\n[[5, -15, -16, -12],\n [-3, 13, -11, -9],\n [7, 3, -4, 0],\n [17, 17, -7, 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[[4, 0, 8, -4],\n [-2, 0, -4, 2],\n [2, 0, 4, -2],\n [-1, 0, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -1, 7, 4],\n [-2, 4, 11, -16],\n [-8, -2, 8, 8],\n [6, -1, -11, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -2, 2, 0],\n [4, 1, -1, 0],\n [-4, -1, 1, 0],\n [4, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -9, 11, -9],\n [4, -15, 19, -15],\n [-2, 4, -6, 4],\n [3, -6, 9, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, 16, 12],\n [0, 0, 0, 0],\n [0, -1, -4, -3],\n [0, -1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 8, -2, 4],\n [-1, 4, -1, 2],\n [-1, 4, -1, 2],\n [3, -12, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 6, -1, -3],\n [11, -16, 2, 5],\n [13, -20, 4, 13],\n [-12, 18, -3, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 6, 0, 0],\n [-6, -4, 0, 0],\n [9, 6, 0, 0],\n [9, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 0, 0, 6],\n [7, 0, 0, -6],\n [2, -12, -12, 0],\n [-3, 18, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -32, 14, -22],\n [-17, 22, -5, 4],\n [10, -16, 6, -8],\n [11, -26, 15, -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[[-16, -9, 0, -6],\n [-9, -6, 6, 18],\n [20, 11, -2, -12],\n [-1, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 3, 0, 6],\n [8, 2, 0, 4],\n [4, 1, 0, 2],\n [12, 3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, 9, 9],\n [-5, 4, 9, 13],\n [0, -4, 0, 0],\n [-3, 0, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 3, -3, 3],\n [9, -3, 3, -3],\n [6, -2, 2, -2],\n [12, -4, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 10, 2, 0],\n [6, 11, 7, 0],\n [6, 13, 17, 0],\n [-2, -5, -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[[-5, -2, -3, -15],\n [-8, 4, -12, -12],\n [4, 1, 3, 11],\n [0, -3, 3, -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[[-3, 12, 12, 20],\n [-4, -23, -9, 7],\n [0, -10, -6, -6],\n [4, 20, 9, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -2, -1, 3],\n [8, -4, -2, 6],\n [0, 0, 0, 0],\n [8, -4, -2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -6, 18, 9],\n [-9, 6, 17, -2],\n [-6, 4, -7, -5],\n [-15, 11, 10, -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[[12, 2, -3, 5],\n [-9, -9, 9, 9],\n [11, 0, 21, 6],\n [0, -13, 0, 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[[8, -4, 0, 1],\n [-16, 12, 0, 0],\n [-8, 10, 0, 2],\n [4, -5, 0, -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[[-8, -4, 4, 0],\n [2, -8, 6, -4],\n [-2, -10, 8, -4],\n [-12, -6, 6, 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[[-11, 4, -8, 7],\n [12, -8, 16, -12],\n [-11, 4, -8, 7],\n [5, 0, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -5, 16, -12],\n [11, 3, -4, -4],\n [-16, -4, -4, 12],\n [4, -11, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 8, 12, -4],\n [-1, 2, 0, -1],\n [-1, 0, -2, 0],\n [1, 6, 8, -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 4x4 matrix:\n[[-6, -3, 6, 0],\n [-2, -1, 2, 0],\n [-8, -4, 8, 0],\n [2, 1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, -19, -16, 8],\n [-10, 4, 10, -14],\n [4, 1, -1, 3],\n [-9, -25, -24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 12, -3, -3],\n [-8, -16, 4, 4],\n [4, 8, -2, -2],\n [8, 16, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -1, 2, -3],\n [-9, -10, -8, -2],\n [-3, -6, -8, 2],\n [0, -2, -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 4x4 matrix:\n[[20, 8, -10, 12],\n [-4, 16, 4, 8],\n [-8, -28, 5, -8],\n [10, 24, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -15, 4, 16],\n [-1, -8, 16, 12],\n [-4, 7, 12, -4],\n [0, 6, -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[[-7, 4, 4, 3],\n [16, -13, -7, -6],\n [-5, 8, 0, 1],\n [15, -6, -10, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-24, -18, 4, 16],\n [-12, 0, 16, 0],\n [-15, -3, 6, 5],\n [6, 9, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 18, -4, 0],\n [22, 22, -1, 1],\n [12, 10, 10, 6],\n [2, 25, 15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 8, -6, -2],\n [2, 20, -11, -1],\n [2, -8, 10, 6],\n [1, 16, -10, -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 4x4 matrix:\n[[16, 8, 0, 8],\n [-5, -1, 12, -10],\n [0, -2, -16, 10],\n [-7, -5, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, -6, 6],\n [0, 0, -6, 6],\n [0, 0, 9, -9],\n [0, 0, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -12, 18, -2],\n [1, 4, 6, 3],\n [-4, -16, 0, -4],\n [10, -2, -3, 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, -14, 0, -10],\n [-7, 5, 0, 1],\n [4, 4, 0, 8],\n [8, -8, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 4, -12, -8],\n [6, 3, -9, -6],\n [2, 1, -3, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 1, -1, -3],\n [28, -7, 10, 0],\n [10, 1, -5, 1],\n [25, -8, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -10, -1, 8],\n [0, 8, 6, 2],\n [10, -2, -13, -12],\n [2, -4, -5, -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[[-5, 5, 4, 12],\n [7, -1, -5, -12],\n [16, -8, -12, -32],\n [-8, 4, 6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, 2, 0],\n [0, -8, -2, 0],\n [0, 12, 3, 0],\n [0, -12, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -9, -3, -6],\n [-15, -7, 1, -8],\n [-6, 4, 8, -4],\n [28, 4, -12, 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[[-1, 4, 0, -3],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-2, 8, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 3, -6, -3],\n [-6, -3, 6, 3],\n [0, 0, 0, 0],\n [8, 4, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -1, 1, 8],\n [18, 0, -24, -18],\n [-25, -1, -3, 15],\n [-16, -4, -20, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -6, 2, -4],\n [12, -9, 3, -6],\n [-16, 12, -4, 8],\n [-16, 12, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 0, -8, -2],\n [-1, 0, 4, 1],\n [1, 0, -4, -1],\n [2, 0, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -8, 0, -6],\n [-8, -8, 1, -7],\n [-4, -16, -1, -11],\n [10, 4, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -2, 2, -5],\n [0, 8, -15, 13],\n [-7, -6, 13, -8],\n [-13, -2, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 0, 16, 2],\n [3, 16, 0, 6],\n [0, -6, 2, -2],\n [-6, -17, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -1, 8, 14],\n [-9, 4, 12, 15],\n [-9, 0, 10, 19],\n [-6, 7, 10, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 9, -3, 3],\n [12, -9, 3, -3],\n [12, -9, 3, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, 3, 0],\n [-12, -12, 9, 0],\n [-8, -8, 6, 0],\n [16, 16, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 6, 6, 6],\n [-1, -3, -3, -3],\n [4, 12, 12, 12],\n [-2, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -16, -16, -4],\n [-12, -24, 0, 12],\n [7, 8, -4, -7],\n [3, -12, -12, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 6, -3, -6],\n [-12, -6, 3, 6],\n [-12, -6, 3, 6],\n [8, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, 12, -8],\n [-6, 3, 9, -6],\n [2, -1, -3, 2],\n [4, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 3, 0, 3],\n [-3, 1, 3, 1],\n [2, -2, -3, -2],\n [4, -4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, 4, -4],\n [-9, 0, 6, -6],\n [-9, 0, 6, -6],\n [-9, 0, 6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -8, 7, 25],\n [0, 8, 6, -6],\n [-3, -11, -5, 13],\n [-3, -7, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 0, -4, -28],\n [1, 0, -1, -7],\n [7, 0, -13, -16],\n [-6, 0, 12, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -12, -4, -18],\n [6, 14, 2, 23],\n [-4, 0, 0, 12],\n [7, 8, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 0, 14, 0],\n [24, 0, 0, 28],\n [-6, 0, 6, -12],\n [10, 0, 14, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 10, 7, 5],\n [-5, -10, -4, -5],\n [-18, -1, 8, -2],\n [-11, -12, -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 4x4 matrix:\n[[8, -15, 4, 2],\n [0, -12, 6, -15],\n [1, -16, 11, -16],\n [10, -21, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -9, 9, 8],\n [-4, -1, -3, 0],\n [2, -5, 3, 4],\n [9, 5, 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[[-12, 16, -8, 16],\n [-6, 8, -4, 8],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 9, 6, -3],\n [16, -12, -8, 4],\n [8, -6, -4, 2],\n [-4, 3, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-26, -12, 9, -10],\n [-1, -12, -6, 3],\n [-4, 4, -24, 12],\n [12, -4, 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[[-12, 0, 0, 15],\n [11, -7, 7, -12],\n [11, 5, -8, -6],\n [0, 12, -15, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 8, 6, -7],\n [-1, 14, 10, -11],\n [7, -12, -1, -13],\n [2, 1, 6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -9, 13, -12],\n [23, 15, -2, 25],\n [15, 9, 15, 8],\n [7, 9, -13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 10, -1, 3],\n [3, 4, 6, -14],\n [-9, -9, 1, 3],\n [0, -6, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-12, 8, 12, 12],\n [3, -2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -1, 0, 4],\n [8, -16, 4, 12],\n [3, -3, 1, -1],\n [-2, -8, 1, 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[[-2, -5, 0, 0],\n [-8, -20, 0, 0],\n [-4, -13, 1, -1],\n [8, 20, 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[[16, 17, 2, -1],\n [20, 17, 2, 4],\n [-8, -21, -6, 20],\n [-4, 2, -28, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -21, 21, -28],\n [-18, 17, -9, 8],\n [-21, -1, -3, 6],\n [-4, -4, -12, 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[[5, -2, -1, -6],\n [1, -9, 5, -2],\n [9, -9, 7, -10],\n [15, -14, 5, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -18, -10, 6],\n [-4, -11, -10, 7],\n [-15, -25, 2, 4],\n [-15, -25, 2, 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[[-12, 10, 16, 18],\n [-27, -3, 12, 11],\n [-15, -8, 4, 11],\n [-12, 2, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 19, -20, 2],\n [-10, -17, 19, -11],\n [7, 1, -4, 6],\n [-3, 8, -9, -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[[0, -8, -2, -4],\n [6, -12, 9, -3],\n [2, -4, 3, -1],\n [0, 4, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -3, 2, 0],\n [6, -9, 6, 0],\n [2, -3, 2, 0],\n [-4, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-6, 8, -2, 0],\n [12, -16, 4, 0],\n [-6, 8, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -3, 9, 15],\n [2, 25, 1, -1],\n [-6, 5, -1, -8],\n [20, 7, 12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 10, -11, -10],\n [-14, -12, 12, 6],\n [20, 5, -7, 9],\n [4, -1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 7, -9, 9],\n [16, 12, -17, -5],\n [-12, -6, 9, 9],\n [4, 10, -13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -4, 3, -9],\n [6, 8, 0, -6],\n [-10, -8, 4, -10],\n [-15, -16, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -2, 4, -3],\n [14, -8, -14, 8],\n [-16, 6, 5, -17],\n [-2, 2, -20, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 2, 15, -1],\n [-18, -10, 20, -2],\n [-8, -6, 7, 3],\n [2, -1, -7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 8, -6, 0],\n [-14, 8, -9, -4],\n [14, -8, 9, 4],\n [-12, 4, -12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, 0, 2],\n [0, 2, 0, 2],\n [0, 8, 0, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 3, 3, 3],\n [9, 9, 9, 9],\n [-3, -3, -3, -3],\n [6, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-12, 9, 0, 6],\n [12, -9, 0, -6],\n [-4, 3, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -5, -11, 6],\n [-17, 24, 2, -9],\n [-3, 1, -21, 9],\n [-2, 0, -7, 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[[8, 16, 12, -16],\n [0, 0, 0, 0],\n [-6, -12, -9, 12],\n [6, 12, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 8, 2, -6],\n [0, 8, 2, -6],\n [0, 16, 4, -12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -4, -12, -12],\n [-6, -3, -9, -9],\n [0, 0, 0, 0],\n [4, 2, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 3, -6, 12],\n [12, -16, 8, 0],\n [9, -5, -2, 12],\n [1, -6, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -6, 0, -4],\n [9, 9, 0, 6],\n [-12, -12, 0, -8],\n [-6, -6, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 15, -9, 20],\n [3, 1, -3, -4],\n [-24, 12, 0, 32],\n [0, -15, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 9, -4, 7],\n [-6, 6, 2, -2],\n [4, 1, -2, 3],\n [-4, -1, 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[[0, -22, -14, 10],\n [-6, 15, 11, -5],\n [-4, -17, -10, 10],\n [-6, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 12, 20, -16],\n [-12, 9, -3, -21],\n [-3, -4, 6, -5],\n [-3, -26, -16, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, 6, -12],\n [8, 0, 8, -16],\n [-4, 0, -4, 8],\n [-8, 0, -8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[23, 9, -1, -4],\n [-20, 1, -7, 4],\n [-7, 2, -8, 16],\n [-13, -6, 2, 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[[-3, 12, -2, -10],\n [2, 24, 20, -12],\n [22, 0, 14, 2],\n [-5, -16, -7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 5, 5, 7],\n [-9, 18, 17, 25],\n [-12, 14, 16, 20],\n [0, 9, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 21, 22, -6],\n [6, 0, -4, 10],\n [9, 15, 14, 0],\n [-9, -6, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, 6, -1, -8],\n [-17, 11, -5, -17],\n [7, -3, 4, 5],\n [-22, 5, -16, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -8, 2, 2],\n [2, -4, 1, 1],\n [8, -16, 4, 4],\n [-4, 8, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 8, -6, 6],\n [0, 4, -3, 3],\n [0, -16, 12, -12],\n [0, 4, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -6, 6, -3],\n [-16, 8, -8, 4],\n [-8, 4, -4, 2],\n [8, -4, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 6, -6, 0],\n [-2, -2, 2, 0],\n [4, 4, -4, 0],\n [-2, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 12, -16, -12],\n [-1, -1, 0, 0],\n [-11, -25, 28, 21],\n [-9, -19, 20, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 4, 2, 6],\n [-4, -2, -1, -3],\n [-12, -6, -3, -9],\n [8, 4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 11, 4, 6],\n [-14, 5, -16, -6],\n [-28, 28, -20, -12],\n [-10, -6, -18, -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[[1, 4, 4, 2],\n [0, 0, 0, 0],\n [4, 16, 16, 8],\n [3, 12, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 1, 4, 2],\n [-19, -3, -14, 1],\n [1, -3, -4, 1],\n [-9, -4, -10, 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 4x4 matrix:\n[[-6, 2, 0, -2],\n [6, -2, -1, 0],\n [0, 0, -4, -8],\n [-3, 1, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, 4, 2],\n [0, 0, 2, -3],\n [0, 3, -6, 3],\n [0, -3, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 6, -4],\n [0, 0, -9, 6],\n [0, 0, 12, -8],\n [0, 0, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 4, 1, 1],\n [-16, 1, 9, 19],\n [14, 4, -6, -14],\n [13, 0, -7, -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 4x4 matrix:\n[[18, -10, -2, 12],\n [12, -28, 4, 0],\n [-16, 0, 4, -14],\n [-16, 0, 4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -20, 16, 2],\n [16, -16, 16, -8],\n [-6, -12, 9, 3],\n [4, -16, 14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 4, -20, -12],\n [1, -12, 32, 30],\n [-4, 5, 8, 12],\n [5, -30, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 2, -3, 0],\n [6, 4, -6, 0],\n [-9, -6, 9, 0],\n [-12, -8, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 2, 4, -18],\n [-5, -1, -18, 27],\n [-1, -5, 6, -9],\n [-1, 1, -6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -8, 1, -5],\n [-5, -10, 3, -1],\n [5, 10, -3, 1],\n [-4, -8, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-3, -6, -12, 3],\n [-2, -4, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 3, -1, 2],\n [2, 3, -1, 2],\n [2, 3, -1, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -9, -3, -18],\n [-13, -3, 7, -16],\n [14, 3, -10, 4],\n [1, -15, -7, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[23, -2, -24, -25],\n [-11, 17, 18, 26],\n [1, -2, -5, -7],\n [-21, -6, 15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -3, 4, 14],\n [22, 3, 4, 13],\n [-19, -1, 2, -16],\n [-5, -1, 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[[-6, 10, 10, 14],\n [-1, 2, 2, 3],\n [-7, 9, 9, 11],\n [-6, 10, 10, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 12, 12, -15],\n [8, 0, 0, -2],\n [-7, 3, 3, -1],\n [12, 0, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 8, -8, 8],\n [4, 4, -4, 4],\n [-8, -8, 8, -8],\n [4, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 6, -2, -4],\n [4, -3, 1, 2],\n [-2, 6, 4, 14],\n [2, 3, 5, 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[[-12, 8, 14, 28],\n [12, -3, -8, -20],\n [8, 6, 15, 24],\n [-36, 7, 9, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -6, 4, 8],\n [6, -6, 4, 8],\n [-3, 3, -2, -4],\n [9, -9, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 2, 3, 0],\n [-9, 6, 9, 0],\n [-9, 6, 9, 0],\n [12, -8, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 8, 2, 0],\n [-6, 10, 1, 3],\n [-6, 3, 3, -3],\n [0, 2, -1, 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, 9, 3, -12],\n [-13, -6, 5, -14],\n [14, 13, -5, 12],\n [-12, -16, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -32, 0, -4],\n [2, 0, -8, -14],\n [-5, 12, 2, 5],\n [9, -20, -6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -11, 7, -5],\n [-16, 1, 11, -17],\n [-1, -4, -8, 4],\n [-18, 2, 9, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, 2, -1],\n [4, 0, -2, 1],\n [0, 0, 0, 0],\n [16, 0, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 16, 20, -20],\n [18, 8, 2, -2],\n [7, -12, -20, 20],\n [1, -4, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 16, 2, 4],\n [-18, 5, -14, 17],\n [4, -18, 1, -8],\n [-14, 3, -11, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -12, 0, -12],\n [0, -8, 0, -8],\n [0, 16, 0, 16],\n [0, 12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 2, 4, -6],\n [18, -6, -12, 18],\n [0, 13, -2, 10],\n [-3, -2, 4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -16, -10, -10],\n [-23, -36, -11, -4],\n [-31, -20, 8, 9],\n [13, 12, -1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 8, 8, 6],\n [-2, 8, 8, 6],\n [2, -8, -8, -6],\n [-1, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, -7, -17, -16],\n [6, 6, 8, 8],\n [9, -7, -9, 0],\n [-17, -5, -11, -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[[24, -16, 0, 0],\n [-8, 0, 8, 0],\n [-12, 16, -12, 0],\n [12, 0, -12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, 0, 16],\n [0, -1, 0, 4],\n [0, 3, 0, -12],\n [0, -4, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, 0, 4],\n [-12, 12, 0, 8],\n [3, -3, 0, -2],\n [-9, 9, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -16, -12, 16],\n [0, 8, 6, -8],\n [0, 8, 6, -8],\n [0, 8, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 4, 1, -4],\n [3, 2, 2, -4],\n [-15, -2, -8, 12],\n [0, 16, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 4, -18, -12],\n [5, -1, 5, 12],\n [9, -1, 7, -8],\n [23, -5, 20, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 7, 15, 13],\n [11, -3, -5, -2],\n [-21, 3, 3, -3],\n [10, -10, -22, -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[[0, 0, 0, 0],\n [16, 16, 8, -8],\n [4, 4, 2, -2],\n [16, 16, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -5, -18, 11],\n [17, 11, -3, -2],\n [10, 8, 14, -10],\n [19, 24, -3, -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[[15, -5, -4, -9],\n [-3, -9, -9, 0],\n [-12, 6, -3, 9],\n [-3, -3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-16, -4, 0, 0],\n [-16, -4, 0, 0],\n [4, 1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[19, -7, -11, -15],\n [20, -4, -12, -16],\n [-4, 20, 0, 2],\n [-4, -12, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -3, -3, 0],\n [-10, 8, 12, 0],\n [-7, 3, -13, -16],\n [1, 7, 9, 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[[-4, -24, -20, -8],\n [20, 0, -14, -20],\n [4, 24, 20, 8],\n [9, -6, -12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -2, 5, -2],\n [-4, 1, 6, 0],\n [9, -9, -3, -6],\n [-7, -5, 9, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 0, 4, 0],\n [-6, 0, 12, 0],\n [0, 0, 0, 0],\n [-4, 0, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 12, 9, 3],\n [-2, -4, 2, 6],\n [-8, -10, -10, -6],\n [0, 2, -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[[-7, -5, -10, -6],\n [-5, -8, 17, -3],\n [-6, 7, 0, -19],\n [1, -4, 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[[13, 13, -10, -7],\n [-13, 6, 4, 24],\n [0, 7, -12, -1],\n [27, 17, -21, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -12, 10, 14],\n [-17, 4, 1, 4],\n [4, 40, -4, -24],\n [-8, 4, 20, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -16, -8, -4],\n [0, -8, -4, -2],\n [0, 4, 2, 1],\n [0, -8, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -16, 2, 7],\n [13, -14, 1, 7],\n [-1, -10, 3, 1],\n [0, 8, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, 8, 7, 15],\n [3, 29, -1, 8],\n [-15, -7, 5, 8],\n [18, 8, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -1, -4, 9],\n [-16, -3, -4, 13],\n [-12, -1, -4, 9],\n [16, 8, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-23, -13, -8, 6],\n [-14, -4, -8, -6],\n [-24, -19, -10, 3],\n [-3, -3, -9, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 0, -5, 2],\n [-22, 0, 8, -14],\n [16, 0, -9, 0],\n [-2, 0, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -18, 0, 18],\n [-3, -12, -6, 12],\n [7, -14, 2, 14],\n [7, 0, 6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 8, -12, 28],\n [-24, 20, 0, 10],\n [20, -18, 2, -13],\n [8, -2, -7, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 4, -4, 2],\n [16, 16, -16, 8],\n [-8, -8, 8, -4],\n [-12, -12, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 4, 16, 8],\n [4, 1, 4, 2],\n [12, 3, 12, 6],\n [-12, -3, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, 9, -5, 14],\n [-3, 7, -4, 8],\n [-1, 5, -12, 8],\n [14, 14, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 8, -2, -7],\n [6, 8, 12, -8],\n [-20, 6, 16, 4],\n [-12, -8, -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[[32, -29, -19, -4],\n [-3, 0, -2, 6],\n [25, -8, -9, -16],\n [8, 19, 9, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 26, 25, 15],\n [12, 8, 10, 7],\n [16, 16, 24, 20],\n [0, 3, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -6, 5, -21],\n [2, 0, 3, -11],\n [5, -15, -9, 13],\n [0, -24, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 6, -4, -8],\n [8, 6, -4, -8],\n [-8, -6, 4, 8],\n [12, 9, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, -14, 10, 0],\n [3, -3, -3, 12],\n [5, -5, 7, -8],\n [4, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, -8, -32, 2],\n [-10, -9, -12, -5],\n [-14, -14, -16, -10],\n [-4, 20, 0, -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 4x4 matrix:\n[[-15, -5, -2, 5],\n [-1, -11, -2, -5],\n [10, -1, 2, -7],\n [10, -7, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 0, -16, 16],\n [12, 0, -16, 16],\n [-6, 0, 8, -8],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, -31, -20, 19],\n [2, 4, -12, 0],\n [25, -16, -34, 20],\n [-10, -2, 24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [12, 0, -4, 0],\n [12, 0, -4, 0],\n [12, 0, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -7, 0, 1],\n [9, 5, 11, 10],\n [10, 2, -2, -4],\n [5, 5, -11, -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[[-7, 2, 4, 4],\n [-3, 4, 2, -4],\n [0, 11, 1, -20],\n [5, -14, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -12, 10, 16],\n [-10, -8, 1, 0],\n [-14, 6, -9, -12],\n [12, -27, 18, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -8, -13, -23],\n [8, -1, 8, 5],\n [16, 1, 8, 7],\n [-8, -4, 15, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -15, -3, 0],\n [1, 11, 7, 8],\n [0, 0, 0, 0],\n [1, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-27, 16, 20, 4],\n [2, -11, -3, -8],\n [-24, 22, 17, -1],\n [18, 2, -17, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 0, -12, 6],\n [2, 0, 8, -4],\n [-3, 0, -12, 6],\n [-2, 0, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 0, 0, -11],\n [5, 4, 5, 1],\n [-4, 4, 5, 12],\n [5, 5, 7, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -12, -1, -13],\n [-6, 16, 1, 34],\n [5, 0, 4, -13],\n [10, 0, 8, -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[[0, 0, 6, 3],\n [0, 0, 2, 1],\n [0, 0, -2, -1],\n [0, 0, 6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -2, -12, -14],\n [4, -4, 6, -8],\n [-4, -1, 9, 3],\n [-2, 3, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 0, -2, -3],\n [-2, 2, -1, 4],\n [1, -4, -4, -17],\n [-4, 0, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 7, -16, -7],\n [6, -6, 12, 6],\n [9, -7, 16, 7],\n [-9, 15, -24, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 3, 5, 3],\n [22, 4, 8, 6],\n [-3, -3, -15, -18],\n [1, 1, 5, 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, -5, 11, -14],\n [-23, 3, 7, -14],\n [26, 14, -13, 4],\n [-4, 8, -10, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -14, 2, -6],\n [9, 24, -6, 6],\n [6, 8, 16, -4],\n [5, -4, -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[[1, 8, 8, -19],\n [-11, -6, 8, -23],\n [13, 11, -5, 16],\n [-6, -5, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 6, -4, 30],\n [-12, -6, 4, -10],\n [12, 15, 4, 17],\n [-6, 21, 21, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -4, 8, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [6, -4, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -28, -8, 8],\n [-15, 2, 17, -9],\n [-4, -14, -4, 4],\n [8, 18, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -4, 10, 12],\n [12, 2, 0, 9],\n [-12, 6, -12, -9],\n [12, 8, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 12, -12, -4],\n [0, -12, 12, 4],\n [0, -3, 3, 1],\n [0, -12, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 12, 0, 12],\n [3, 12, 0, 12],\n [1, 4, 0, 4],\n [-3, -12, 0, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 0, -2, 2],\n [2, 0, -1, 1],\n [8, 0, -4, 4],\n [-2, 0, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -12, 0, -3],\n [4, -4, 0, -1],\n [8, -8, 0, -2],\n [16, -16, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -6, 3, 3],\n [-4, 2, -1, -1],\n [12, -6, 3, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -10, -6, 4],\n [-4, -6, 9, -13],\n [-4, -4, 3, -5],\n [-16, -11, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -21, 0, -22],\n [-1, 6, 13, 10],\n [12, 9, -12, 6],\n [12, 18, 4, 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[[20, -6, -4, 8],\n [0, -8, 8, -16],\n [6, -5, 2, -4],\n [-8, -4, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -12, 12, -6],\n [-8, -16, 16, -8],\n [-8, -16, 16, -8],\n [-8, -16, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -10, 2, 4],\n [-4, 10, -2, -4],\n [6, -8, 0, 2],\n [-10, 4, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 0, -6, 6],\n [-16, 0, -8, 8],\n [16, 0, 8, -8],\n [-16, 0, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 24, -6, -9],\n [-8, -4, -14, 9],\n [8, -24, 0, 12],\n [12, 0, 18, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -2, 3, 1],\n [12, 6, -9, -3],\n [-8, -4, 6, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 2, -6, -4],\n [-1, 15, 11, -12],\n [-7, 29, 4, -32],\n [2, 0, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 3, 0, -6],\n [12, -4, -5, -2],\n [-8, 4, 2, -4],\n [4, -3, 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, 2, 4, -4],\n [-3, -3, -6, 6],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 6, 8, 4],\n [-8, -16, -22, -4],\n [-8, -4, -6, 4],\n [4, -7, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 8, 0, 8],\n [-6, -8, 0, -8],\n [3, 4, 0, 4],\n [-12, -16, 0, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -6, -4, -8],\n [-3, -9, -6, -12],\n [3, 9, 6, 12],\n [-3, -9, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -3, -9, 9],\n [-10, 0, -6, 20],\n [-10, 0, -6, 20],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -12, -3, 21],\n [7, 0, 3, -5],\n [-18, 10, -2, -10],\n [18, -10, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 3, 12, 10],\n [11, -6, 12, 7],\n [17, -6, 20, 13],\n [-12, 0, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 1, -2, 3],\n [8, -2, 4, -6],\n [16, -4, 8, -12],\n [-12, 3, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -2, -13, 1],\n [-14, -10, 6, -10],\n [1, -2, -5, -1],\n [16, 6, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 12, 0, -12],\n [3, 5, 3, -6],\n [-15, -4, -15, 9],\n [21, 2, 21, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 6, -12, -12],\n [-12, -8, 16, 16],\n [-12, -8, 16, 16],\n [-3, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 10, 7, 12],\n [12, -4, -10, -12],\n [8, 8, 7, 11],\n [-2, -16, -19, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -24, -2, 19],\n [-5, -4, 4, 1],\n [-6, -18, 3, 12],\n [1, 6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -6, 16, 6],\n [9, 7, -17, 0],\n [-1, -4, 14, 10],\n [-7, -2, 22, 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[[3, -6, 6, 3],\n [4, -8, 8, 4],\n [0, 0, 0, 0],\n [4, -8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -13, 16, 13],\n [8, 12, -24, -20],\n [16, 9, -6, -7],\n [-30, 10, -6, -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[[3, -5, 4, 3],\n [-8, -4, 40, 2],\n [10, 16, -36, -5],\n [3, 17, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, -17, 6, -13],\n [0, -20, -8, 4],\n [-6, -11, -17, 1],\n [-11, 1, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 12, 4, 4],\n [0, 0, 0, 0],\n [0, 12, 4, 4],\n [0, 9, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 12, 9, -12],\n [-6, -8, -6, 8],\n [-6, -8, -6, 8],\n [-3, -4, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -6, 23, -8],\n [-3, -5, 24, -15],\n [10, 24, 4, -8],\n [-12, -23, 14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -2, -7, 13],\n [-2, 2, -5, -1],\n [0, 0, 0, 0],\n [0, 0, 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[[-14, 10, 13, -2],\n [18, -10, -14, 2],\n [-6, 0, 12, 2],\n [-12, 0, 3, 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[[-5, 15, 5, -4],\n [3, -9, -3, 0],\n [6, -18, -6, -6],\n [-3, 9, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 14, -15, -7],\n [-8, -7, 17, 4],\n [-4, -5, 8, 3],\n [2, 14, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 6, 8, 4],\n [-8, 12, 16, 8],\n [8, -12, -16, -8],\n [4, -6, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 6, 9, -6],\n [-3, 4, -2, 0],\n [9, -18, 20, -13],\n [17, 0, 24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [3, 3, -2, 1],\n [6, 6, -4, 2],\n [-9, -9, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 8, -11, -11],\n [0, 0, 0, 0],\n [-3, 4, -13, -3],\n [8, -4, -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[[-2, -8, -8, 4],\n [-3, -12, -12, 6],\n [-1, -4, -4, 2],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -12, -10, -14],\n [-8, 4, 6, 2],\n [8, -14, -17, -11],\n [-12, -14, -13, -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[[-3, 12, -9, 12],\n [0, 0, 0, 0],\n [-3, 12, -9, 12],\n [1, -4, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 10, 4, -4],\n [-16, -12, 12, 18],\n [-8, -18, 12, 12],\n [8, 24, -30, -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[[5, -10, 8, -12],\n [16, -5, 16, -18],\n [-11, 4, -10, 8],\n [20, -13, 23, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -10, -14, -6],\n [-3, 17, 23, 5],\n [-6, 5, 1, -6],\n [0, 9, 15, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 3, 1, 3],\n [1, 3, 1, 3],\n [-1, -3, -1, -3],\n [-4, -12, -4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -6, -10, 14],\n [16, 21, -5, -9],\n [-7, -12, 0, 8],\n [13, 12, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -9, 0, 0],\n [-1, 3, 0, 0],\n [-1, 3, 0, 0],\n [-1, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 1, 4, 1],\n [-2, 19, 8, 11],\n [0, 0, 0, 0],\n [-10, 15, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -12, -6, 9],\n [-2, -4, -2, 3],\n [2, 4, 2, -3],\n [-4, -8, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -1, 1, -3],\n [9, 6, 3, 3],\n [10, 3, 3, -1],\n [-10, -3, -3, 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[[12, 7, -13, 15],\n [-14, 22, -6, -6],\n [4, -8, 4, -3],\n [-7, 20, -10, 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 4x4 matrix:\n[[10, -14, 2, -20],\n [-6, -1, 3, 8],\n [3, 13, -12, 4],\n [-7, -2, 13, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 4, -16, -16],\n [0, -3, 12, 12],\n [0, -3, 12, 12],\n [0, 3, -12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -3, -4, 3],\n [-4, -3, -4, 3],\n [-8, -6, -8, 6],\n [12, 9, 12, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -6, -8, -1],\n [-12, -9, -6, -9],\n [10, -12, 18, 8],\n [7, -5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, -1, 3],\n [4, -2, 1, -3],\n [8, -4, 2, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 4, -2, -2],\n [0, 0, 0, 0],\n [8, -8, 4, 4],\n [-12, 12, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 5, 6, -10],\n [8, -5, -2, -10],\n [-4, 3, -2, 3],\n [8, 2, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 4, 1, -2],\n [-1, -13, -23, -4],\n [-9, 8, 3, -6],\n [-14, 8, 14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, -3, 8],\n [-6, -10, 17, -9],\n [-9, -8, 6, -11],\n [0, 8, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 2, 2, 2],\n [-3, 1, 1, 1],\n [6, 10, -11, -8],\n [-15, -3, 11, 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[[-10, 11, -3, -11],\n [7, -9, 6, -3],\n [-14, 7, -3, 17],\n [-1, -1, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -2, 1, -2],\n [13, 1, -5, -2],\n [-2, -2, 1, -2],\n [-11, -7, 5, -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 4x4 matrix:\n[[-2, 5, -4, -6],\n [-16, 1, -14, -5],\n [21, 19, 9, -18],\n [12, -4, 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[[6, 3, -6, -9],\n [-2, -1, 2, 3],\n [-4, -2, 4, 6],\n [8, 4, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 12, 8, 0],\n [-6, 9, 6, 0],\n [-4, 6, 4, 0],\n [-4, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, 5, 7, -10],\n [20, 12, 8, -16],\n [-11, -13, 6, 4],\n [-5, -3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -6, 0, 3],\n [-8, -4, 0, 2],\n [0, 0, 0, 0],\n [16, 8, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -13, 10, -7],\n [1, -14, 14, -5],\n [-7, 8, 10, 17],\n [-4, 11, -2, 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 4x4 matrix:\n[[-4, -2, 12, -8],\n [-8, 2, 8, 4],\n [12, -10, -8, -14],\n [-10, 4, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [2, 4, 4, 0],\n [3, 6, 6, 0],\n [-1, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 7, 0, 0],\n [18, -1, 3, -8],\n [-12, -6, -15, 10],\n [2, -17, -3, 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[[13, 9, 11, -18],\n [21, 3, 9, -9],\n [-21, -9, -11, 6],\n [-20, -15, -11, -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[[-8, 5, -19, -5],\n [-26, 16, -5, 18],\n [8, -6, -6, -10],\n [7, -10, 2, -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[[10, -14, -2, -2],\n [20, -16, 0, 1],\n [3, 13, -1, 15],\n [2, 8, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -7, 12, -15],\n [-2, -7, 15, -17],\n [2, -11, 21, -25],\n [-14, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 12, 9, -5],\n [-25, -7, 24, 3],\n [-17, -9, 8, 12],\n [3, 13, -17, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -12, 3, 3],\n [-1, -4, 1, 1],\n [4, 16, -4, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 4, -6, -8],\n [-3, 2, -3, -4],\n [12, -8, 12, 16],\n [9, -6, 9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -6, 0, -5],\n [1, -3, 9, 8],\n [-2, -4, 2, -1],\n [-1, -3, 3, 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[[0, 0, 0, 0],\n [8, -2, 8, -6],\n [-4, 1, -4, 3],\n [4, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 1, -1, -7],\n [-1, 1, 1, -5],\n [-10, 1, 4, 7],\n [-21, 6, 7, -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[[4, -2, 6, -9],\n [5, 2, 6, -4],\n [9, 4, 3, -4],\n [2, -6, 15, -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[[-6, -20, 9, 3],\n [13, -4, 4, 9],\n [8, 4, -1, 3],\n [-25, -12, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 2, -1, 2],\n [4, -8, 4, -8],\n [-4, 8, -4, 8],\n [-3, 6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -10, 3, 7],\n [-6, 4, -4, 1],\n [2, -2, 3, 9],\n [-5, -14, -1, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 5, 6, -24],\n [-10, -5, -6, 24],\n [0, 0, -1, -11],\n [-8, -4, -7, -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 4x4 matrix:\n[[12, -4, 10, -7],\n [-6, -8, -4, -2],\n [-4, -12, -2, -5],\n [4, 12, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -14, -4, -19],\n [-5, -10, 4, -5],\n [2, 4, 8, 14],\n [4, 8, -16, -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[[-16, 8, -12, 12],\n [-8, 4, -6, 6],\n [-4, 2, -3, 3],\n [-12, 6, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, -8, 0],\n [1, 1, 4, -2],\n [0, 0, 0, 0],\n [3, 3, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 16, 16, -16],\n [3, 4, 4, -4],\n [-3, -4, -4, 4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -4, -4, -9],\n [16, -9, 14, -21],\n [18, -11, 14, -6],\n [16, -12, 8, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 15, -15, 0],\n [8, -4, 8, -4],\n [20, -11, 17, -6],\n [0, -3, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 4, -2, -4],\n [6, -6, -9, 12],\n [-2, -10, 1, 12],\n [6, 6, -7, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, 9, -20],\n [0, -8, -10, 24],\n [2, 2, 3, -8],\n [8, 4, 7, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 3, -4, 1],\n [5, -12, 16, 13],\n [-1, 6, -8, -5],\n [-7, 9, -12, -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[[-11, 17, -30, -15],\n [3, 21, -30, -19],\n [12, 6, 6, 9],\n [-8, 5, -18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 8, -8, 8],\n [-1, 4, -4, 4],\n [-4, 16, -16, 16],\n [4, -16, 16, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -4, 4, -15],\n [3, 4, 20, -3],\n [4, 8, 32, 0],\n [-2, -4, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -16, -9, 4],\n [-6, -12, -12, 3],\n [-6, -12, 3, 3],\n [6, 12, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 12, 12, 6],\n [-3, 12, 12, 6],\n [-2, 8, 8, 4],\n [4, -16, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -6, 8, 0],\n [2, 6, -8, 0],\n [3, 9, -12, 0],\n [-4, -12, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 1, -4, 14],\n [-18, -12, -3, 2],\n [-28, -20, -4, 0],\n [13, 5, 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[[4, -2, -7, 10],\n [2, 2, -2, 2],\n [-9, 3, 15, -21],\n [-12, 4, 20, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -8, 4, -16],\n [-2, 4, -2, 8],\n [-1, 2, -1, 4],\n [-1, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 1, 2, -4],\n [-6, 6, 6, 4],\n [18, -10, -14, 12],\n [-6, -2, 2, -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 4x4 matrix:\n[[-11, -3, -1, -3],\n [-4, -3, -2, -3],\n [6, 15, 12, 15],\n [-6, -15, -12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 7, -21, 9],\n [-3, 12, -9, 0],\n [2, 10, -18, 6],\n [-1, -5, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 7, 2, -7],\n [4, -7, -16, 5],\n [-4, -3, -14, -5],\n [4, -6, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 6, -2, 6],\n [-2, 6, -2, 6],\n [-4, 12, -4, 12],\n [-3, 9, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 4, 4, -18],\n [2, -4, 4, 8],\n [16, -2, 14, 4],\n [-8, 4, -4, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 21, 1, 16],\n [3, -3, 2, -4],\n [5, -12, 3, -12],\n [-8, 15, -5, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -10, 4, 4],\n [-9, 20, -2, -19],\n [5, -6, -8, 21],\n [-7, -4, 12, -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[[-10, 9, -11, 13],\n [-18, 9, -15, 9],\n [-6, 3, -5, 3],\n [4, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, 4, -6, 8],\n [12, -8, 12, -16],\n [-9, 6, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 11, -7, -8],\n [-3, 1, 0, 12],\n [6, -8, 6, 24],\n [-21, 18, -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[[3, -8, 5, 20],\n [-15, -1, 4, 4],\n [12, 3, -11, -40],\n [-3, 15, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [16, 16, -16, -16],\n [-12, -12, 12, 12],\n [16, 16, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, 0, 9],\n [12, 12, 0, 9],\n [4, 4, 0, 3],\n [-16, -16, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -2, 14, 16],\n [9, -12, -12, 6],\n [0, 0, 0, 0],\n [10, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 17, -7, 5],\n [6, -8, 4, -8],\n [8, -10, -5, 4],\n [18, -22, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -16, -8, 4],\n [0, 0, 0, 0],\n [0, 16, 8, -4],\n [0, 16, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 4, 0, -8],\n [6, 4, 0, -8],\n [3, 2, 0, -4],\n [-6, -4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, -4, 4, -7],\n [31, 1, -4, 6],\n [-22, -10, 5, -11],\n [-1, -7, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -2, -2, -11],\n [-11, -1, -1, 2],\n [-8, -5, -5, -7],\n [-13, -2, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, 0, 0],\n [4, -5, 2, 2],\n [4, -4, 0, 0],\n [7, -9, 4, 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[[-4, 0, -3, -1],\n [8, 0, 6, 2],\n [4, 0, 3, 1],\n [16, 0, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -16, 6, -4],\n [-2, 8, 4, 2],\n [-2, 8, 4, 2],\n [-4, 4, 8, 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[[-8, -4, -8, -4],\n [4, 2, 4, 2],\n [8, 4, 8, 4],\n [-2, -1, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 3, 0, 0],\n [-2, -1, 0, 0],\n [0, 0, 0, 0],\n [6, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -6, -12, 12],\n [3, 6, 12, -12],\n [-2, -4, -8, 8],\n [-4, -8, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 14, -2, -12],\n [-3, 17, 3, -8],\n [-9, -11, 3, 8],\n [3, 15, 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[[3, 6, -3, 12],\n [-4, -8, 4, -16],\n [4, 8, -4, 16],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -1, 3, 3],\n [2, -2, 6, 6],\n [-1, 1, -3, -3],\n [-2, 2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -12, -8, -8],\n [0, -3, -2, -2],\n [0, 3, 2, 2],\n [0, -12, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 4, -1, -12],\n [-6, -8, 7, 4],\n [1, 4, -3, -4],\n [-9, -4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 4, 12],\n [0, 0, 0, 0],\n [7, -14, -3, -2],\n [-6, 12, 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[[-18, 4, 2, 18],\n [9, 12, -3, -3],\n [9, 12, -3, -3],\n [6, 1, -1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[28, 4, 14, -18],\n [-12, -12, -6, 6],\n [20, 14, 10, -11],\n [8, -16, 4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 6, -3, -6],\n [-2, -4, 2, 4],\n [4, 8, -4, -8],\n [4, 8, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -7, 28, -28],\n [-4, -4, 4, -4],\n [-5, -5, -16, 16],\n [-10, -10, 24, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 5, -13, 12],\n [-1, -8, 0, 6],\n [-22, -18, 1, 27],\n [-23, -14, -1, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -10, 8, 8],\n [-1, -5, -3, 2],\n [6, -6, 9, 6],\n [-11, 17, -15, -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[[21, -20, -2, 14],\n [11, -11, -2, 9],\n [-29, 22, -2, -16],\n [-2, 2, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 13, 24, -2],\n [0, 1, -4, 2],\n [0, -5, 1, -3],\n [0, 3, 7, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 12, 14, 12],\n [3, -4, -8, -4],\n [-1, -16, 4, -8],\n [6, 0, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 1, -5, -7],\n [-23, 9, 1, 29],\n [-20, 18, -5, 17],\n [-7, -6, 2, 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[[10, -13, 0, 4],\n [12, -15, 3, 6],\n [-6, 5, -14, -8],\n [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[[3, -21, 6, -15],\n [-10, 20, -10, 18],\n [-16, 12, -12, 16],\n [24, 7, 13, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 6, 3, -3],\n [-3, -12, 6, -6],\n [-13, -10, -1, 1],\n [-4, -16, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -3, 11, -7],\n [5, 2, 16, -14],\n [-12, -8, 16, -8],\n [-1, -1, 7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 9, -8, -10],\n [-14, -6, 0, -4],\n [4, -6, 6, 8],\n [1, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 18, -11, 20],\n [-5, 10, -7, 12],\n [-10, 0, -8, 8],\n [13, -22, 17, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 4, 30, -3],\n [13, -5, 11, -19],\n [2, -4, -6, -6],\n [11, 14, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, -3, 3],\n [0, 0, 6, -6],\n [0, 0, -3, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -3, -5, -10],\n [6, 0, -6, -6],\n [5, 6, -17, -7],\n [7, -6, 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[[-4, -4, 2, 0],\n [-4, -4, 2, 0],\n [16, 16, -8, 0],\n [8, 8, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 16, 8, 12],\n [16, 16, 8, 12],\n [4, 4, 2, 3],\n [-16, -16, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 9, 13, -8],\n [15, 29, 1, 0],\n [8, 17, -3, -6],\n [-5, 0, 8, -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[[6, -6, -4, 4],\n [-14, 14, -2, -4],\n [-7, 7, -1, -2],\n [22, -22, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, -17, 11, -24],\n [-6, 3, 15, 0],\n [-16, 5, 19, 0],\n [13, 9, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -16, 8, 8],\n [-2, 12, -9, -8],\n [3, 0, -9, -6],\n [-4, 12, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -1, -28, 7],\n [-32, -4, 0, 12],\n [8, -7, -16, -1],\n [24, 7, 8, -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 4x4 matrix:\n[[2, -10, 9, -9],\n [-12, 4, 2, 14],\n [-8, -16, 20, -4],\n [20, -9, -1, -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[[-3, 0, 12, 9],\n [1, 0, -4, -3],\n [-4, 0, 16, 12],\n [-1, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, 12, -6],\n [3, 0, 2, -9],\n [-1, -9, -26, 30],\n [-2, -1, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, 0, -12],\n [3, -6, 0, 9],\n [-4, 8, 0, -12],\n [1, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[35, -16, -6, -16],\n [4, -4, -12, 20],\n [-36, 14, -2, 30],\n [5, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -2, 1, -2],\n [-8, 8, -4, 8],\n [-8, 8, -4, 8],\n [8, -8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -8, 11, -11],\n [2, -4, -8, 9],\n [8, -12, -3, -2],\n [0, 8, -14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -16, -11, -14],\n [-6, 8, 6, 4],\n [0, 3, 2, 3],\n [-3, -2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 2, -4, -6],\n [-12, 3, -2, -1],\n [4, -1, 0, -1],\n [-8, 2, -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[[4, 8, 0, 8],\n [15, 3, 6, -6],\n [0, -9, 2, -12],\n [16, -4, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -8, 2, -2],\n [1, -4, 1, -1],\n [-4, 16, -4, 4],\n [4, -16, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 4, 4, -4],\n [-1, -1, -1, 1],\n [1, 1, 1, -1],\n [-2, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 12, 0, 9],\n [7, -12, 3, -12],\n [3, -12, 0, -9],\n [4, -16, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 0, 20, -8],\n [2, -2, 13, -18],\n [5, -4, -9, 6],\n [-12, 10, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 2, 6, 5],\n [-13, -2, -18, 10],\n [-10, -12, -16, 11],\n [8, 12, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 0, -12, -12],\n [2, -8, 8, -2],\n [15, -12, 3, -12],\n [-15, -4, 16, 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 4x4 matrix:\n[[-8, 2, -8, -2],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-4, 10, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 4, -6, 8],\n [11, 4, 2, -14],\n [3, 4, -6, 8],\n [7, 16, -22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -3, 5, 8],\n [8, -13, -1, -22],\n [0, -3, 1, -2],\n [-6, 6, 2, 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[[-13, 3, -10, -5],\n [-4, 14, -10, -20],\n [-2, -10, 4, 14],\n [0, -17, 9, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 19, -8, 6],\n [-2, -4, 4, -14],\n [1, 0, -2, 11],\n [4, 12, -8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -4, 2, 2],\n [12, 8, -4, -4],\n [-12, -8, 4, 4],\n [-3, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -2, -2, -16],\n [-5, 5, 8, 19],\n [9, -2, 1, -1],\n [-9, 29, 16, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -4, -3, 1],\n [6, -8, -6, 2],\n [9, -12, -9, 3],\n [6, -8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 4, 15, -18],\n [-10, 2, -14, -2],\n [0, -16, 12, -12],\n [-4, 4, 14, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 7, 9, -8],\n [-4, -6, -2, 4],\n [8, 0, -8, 4],\n [-8, 8, 16, -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, 8, 2, 7],\n [-9, 15, 8, 11],\n [-3, -8, -6, -5],\n [3, -10, -6, -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 4x4 matrix:\n[[0, -6, -16, 0],\n [6, -3, -20, -6],\n [6, 11, 12, -6],\n [0, -5, 24, 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[[-19, -8, -5, 24],\n [2, 4, 7, -9],\n [18, 10, -2, -16],\n [-16, -8, -5, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 19, 4, -1],\n [-3, -1, -4, -1],\n [6, -14, 16, 6],\n [-12, -12, -12, -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 4x4 matrix:\n[[-1, -7, -7, 8],\n [-22, -12, -18, -15],\n [10, 16, 18, -8],\n [-5, -11, -11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -6, 29, -4],\n [-9, 3, -25, 4],\n [16, 5, -12, -7],\n [15, 1, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 13, -14, -9],\n [0, 1, -9, -7],\n [-3, -4, 12, 8],\n [6, -8, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -6, -2, 4],\n [0, 0, 0, 0],\n [-6, -6, -2, 4],\n [-9, -9, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -10, 2, -14],\n [-3, -4, 0, -5],\n [-10, 0, 8, -6],\n [9, 2, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 0, -4, 16],\n [6, 3, 0, 12],\n [-5, -1, 1, -8],\n [3, -3, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -2, 0, -1],\n [-2, -2, 0, -1],\n [-4, -4, 0, -2],\n [-4, -4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 16, -10, -4],\n [-6, -16, 10, 4],\n [18, 12, -12, -12],\n [12, 12, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 1, -4, 9],\n [-3, -3, -4, -3],\n [-6, -5, -6, -6],\n [-6, -6, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 7, 12, 0],\n [7, 6, -3, 2],\n [-7, -10, 12, -9],\n [-16, -7, 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[[-1, -2, -3, 1],\n [-4, -8, -12, 4],\n [-1, -2, -3, 1],\n [-4, -8, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, 18, -3, 14],\n [-8, 4, 12, 1],\n [-17, 18, -3, 14],\n [-18, 20, -6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[21, -4, 1, -17],\n [8, 14, -1, -16],\n [-8, -20, 0, 16],\n [4, -4, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -8, 0, 8],\n [3, 12, 0, -12],\n [-3, -12, 0, 12],\n [4, 16, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 13, 7, 12],\n [3, 5, 3, 8],\n [-3, -5, -3, -8],\n [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 4x4 matrix:\n[[4, 12, 8, 8],\n [-8, 24, -9, -1],\n [11, -15, 11, 7],\n [12, -12, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -8, -8, 4],\n [-8, 8, 8, -4],\n [-8, 8, 8, -4],\n [-12, 12, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -8, -16, 12],\n [0, -16, 0, 16],\n [3, -10, -12, 13],\n [-2, -8, 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, -10, -2, -5],\n [2, 8, 2, 2],\n [2, -7, 0, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 15, 6, -3],\n [-3, 22, 11, -9],\n [-7, 12, 3, -3],\n [11, -15, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -5, 7, -6],\n [-14, -8, -10, -24],\n [-1, 21, -6, 10],\n [9, -21, 18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, 12, 12],\n [-3, 0, 9, 9],\n [1, 0, -3, -3],\n [-2, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, 9, 4, -9],\n [-17, 5, -13, -9],\n [-7, 7, -2, 1],\n [12, 0, 18, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 0, 6, 5],\n [0, 10, 14, 0],\n [-8, -4, 4, 8],\n [28, 24, 0, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -4, 8, -6],\n [-6, -4, 8, -6],\n [-12, -8, 16, -12],\n [-9, -6, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 9, -9, -3],\n [0, 0, 0, 0],\n [8, 6, -6, -2],\n [-12, -9, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -6, 3, -9],\n [6, 6, -3, 9],\n [-8, -8, 4, -12],\n [6, 6, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 3, -8, 8],\n [8, -6, 14, -4],\n [3, 14, 1, -26],\n [5, -6, 9, 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 4x4 matrix:\n[[0, -2, -6, 6],\n [0, 0, 0, 0],\n [0, 3, 9, -9],\n [0, 3, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 7, 15, 11],\n [-2, 11, 15, 8],\n [-7, 10, -6, -14],\n [6, -7, -15, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 4, 32, 4],\n [-6, -2, -8, -8],\n [12, 4, 16, 16],\n [4, 2, 4, 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 4x4 matrix:\n[[4, 2, 2, 1],\n [0, 0, 0, 0],\n [12, 6, 6, 3],\n [-8, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 18, 22, -10],\n [3, -15, -21, 6],\n [6, 3, 3, 4],\n [-2, -11, -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[[2, 6, -2, 4],\n [3, -1, 3, 6],\n [-3, 1, -3, -6],\n [6, 8, 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[[-14, -24, -5, 10],\n [-7, -18, -4, -10],\n [2, 2, -20, -24],\n [-1, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -3, -4, -4],\n [-8, -12, -16, -16],\n [-8, -12, -16, -16],\n [8, 12, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 15, 18, -12],\n [6, -18, -16, 14],\n [2, -7, -8, -7],\n [-1, -19, -24, 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[[-4, -14, 10, -6],\n [0, -16, 4, -12],\n [2, 7, -5, 3],\n [-8, 0, 13, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -4, -2, 0],\n [-2, 4, 2, 0],\n [8, -16, -8, 0],\n [8, -16, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 0, -2, 4],\n [-27, 9, 21, -6],\n [5, 14, 13, 11],\n [-4, 1, 3, -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[[-7, 8, -14, -15],\n [-2, 3, 1, 5],\n [-11, 14, -12, -5],\n [-14, 18, -14, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -8, -1, 5],\n [4, 19, 12, -23],\n [18, 12, 7, -15],\n [12, 20, 12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 16, -16, 4],\n [6, 8, -8, 2],\n [-12, -16, 16, -4],\n [-9, -12, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-3, -3, -9, -6],\n [-3, -3, -9, -6],\n [-2, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, -4, -2],\n [-4, 8, -8, -4],\n [-2, 4, -4, -2],\n [2, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -10, 4, -4],\n [-4, -11, 17, 10],\n [8, 2, 2, 4],\n [4, 1, 1, 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[[28, 24, 16, -8],\n [0, -20, -24, 7],\n [-17, -6, 4, 23],\n [-16, -10, -1, 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 4x4 matrix:\n[[-19, -16, 5, -4],\n [25, 24, -7, 4],\n [5, 9, -2, -1],\n [-21, -21, 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[[8, 8, 2, 2],\n [8, 8, 2, 2],\n [0, 0, 0, 0],\n [16, 16, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -2, -2, -4],\n [-29, -5, -28, -11],\n [-1, -9, 13, 0],\n [8, 2, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 9, 2, -14],\n [-5, -9, -2, 14],\n [8, 10, -10, 4],\n [-6, -9, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, -4, -12, 5],\n [0, 2, 6, -8],\n [1, 1, 3, -5],\n [-3, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -16, 0, 16],\n [3, -12, 0, 12],\n [1, -4, 0, 4],\n [-4, 16, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 0, 0, -8],\n [8, 0, 0, -4],\n [-12, 0, 0, 6],\n [16, 0, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 0, 2, 1],\n [-8, 0, 8, 4],\n [4, 0, -4, -2],\n [6, 0, -6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, -8, -16],\n [0, -12, -4, -20],\n [1, 3, 0, 4],\n [-10, -6, 8, 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[[17, 17, 19, 9],\n [4, 4, 12, 4],\n [10, 10, 6, 4],\n [-5, -5, 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, 0, -6, 0],\n [-2, 0, -6, 0],\n [1, 0, 3, 0],\n [-3, 0, -9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 11, -10, -4],\n [13, 2, 12, -12],\n [-19, -11, 10, 20],\n [11, 9, 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[[11, -6, 13, 1],\n [12, 9, -6, 10],\n [19, 15, -13, 13],\n [14, 3, 4, 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, 12, -6, -6],\n [-9, 11, -18, 2],\n [-27, 1, 2, -2],\n [0, 0, 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[[19, -10, -3, -6],\n [6, 0, -2, 1],\n [-23, 16, 7, 5],\n [21, -12, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -2, -6, 4],\n [3, -1, -3, 2],\n [9, -3, -9, 6],\n [6, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 8, 3, 5],\n [-4, 8, -9, 1],\n [-4, 2, 0, 1],\n [8, 2, -9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -2, -4, 4],\n [-1, -2, -4, 4],\n [-4, -8, -16, 16],\n [3, 6, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -9, -1, 8],\n [0, 2, -2, 1],\n [10, -18, -2, 16],\n [-8, 14, 2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 9, 15, -18],\n [0, -8, -5, -9],\n [-4, -3, -10, 1],\n [-14, 6, -26, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, -12, 4, 5],\n [4, 8, 4, 0],\n [-4, -8, -4, 0],\n [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, 14, -2, 4],\n [7, -10, -4, -3],\n [-2, 12, 0, 9],\n [2, -12, 0, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-18, 2, -6, 6],\n [-4, -12, -12, -12],\n [4, -16, -12, -18],\n [-10, 12, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -8, 8, 2],\n [-12, -12, 12, 3],\n [8, 8, -8, -2],\n [-16, -16, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [2, 0, 4, -1],\n [6, 0, 12, -3],\n [6, 0, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -12, 2, 3],\n [1, 5, -7, 4],\n [1, -16, 7, 4],\n [3, -18, 1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 8, -6, -8],\n [0, 0, 0, 0],\n [0, 8, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 3, -4, 3],\n [-7, 15, -6, 1],\n [4, -6, 3, -1],\n [9, -9, 6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 8, 2, 8],\n [-4, 16, 4, 16],\n [2, -8, -2, -8],\n [-4, 16, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 0, -32, -24],\n [-12, 14, 0, 22],\n [1, -2, 4, -4],\n [-16, 6, 24, 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[[20, 9, -6, 20],\n [12, -15, -7, 12],\n [-20, 9, 9, -20],\n [-4, 15, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, -4, 10],\n [-6, 2, -4, -2],\n [0, 0, -2, 8],\n [8, -6, 10, -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[[-8, 7, 11, -9],\n [8, -4, 4, 12],\n [-6, 7, 17, -5],\n [-6, 6, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -14, -20, 1],\n [-12, 3, -6, 6],\n [11, -17, -24, -4],\n [4, 0, 6, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 2, -1, 1],\n [8, -4, 2, -2],\n [-8, 4, -2, 2],\n [-12, 6, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 3, -8, 19],\n [-9, -13, 8, -15],\n [-6, -7, 6, -12],\n [-12, -21, 6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, -8, -6, 14],\n [2, 0, 1, 1],\n [-4, -4, 0, 10],\n [8, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 2, 2, 6],\n [-5, -4, 14, 12],\n [-28, -10, 16, -2],\n [2, 4, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -3, 13, 11],\n [-3, -9, 9, 3],\n [3, -3, 7, 5],\n [18, 6, 10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, 9, 0, 30],\n [3, -5, 8, 2],\n [3, 3, -4, 0],\n [16, -6, -5, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 0, 6, 10],\n [1, -1, 0, -3],\n [-3, 4, -3, 7],\n [1, 1, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 15, 5, 6],\n [-4, -3, -9, 4],\n [0, -5, 9, 22],\n [-2, 1, -1, 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 4x4 matrix:\n[[3, 4, 1, 2],\n [-6, -8, -2, -4],\n [3, 4, 1, 2],\n [12, 16, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, -16, 28, 14],\n [19, -8, 26, 2],\n [12, -9, 3, -4],\n [9, 13, 5, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -7, -2, -4],\n [-32, -12, -12, -4],\n [16, 1, 11, -3],\n [20, 10, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 3, -3, -12],\n [0, 3, -3, -12],\n [24, -4, -10, -1],\n [-2, 8, 6, 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[[-9, -9, 12, 9],\n [3, 3, -4, -3],\n [0, 0, 0, 0],\n [-3, -3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -4, 4, 8],\n [6, -2, 2, 4],\n [-10, -4, -6, -10],\n [1, 7, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -14, 22, 8],\n [16, 11, -13, 4],\n [-6, -4, 16, 15],\n [-6, -11, -9, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 9, -20, 16],\n [-7, -5, 8, -2],\n [5, 11, -28, 20],\n [2, -10, 20, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -24, -5, 13],\n [2, 0, -4, -9],\n [-4, 0, 2, 1],\n [19, 4, 1, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -12, 12, 9],\n [0, 12, -12, -9],\n [0, 8, -8, -6],\n [0, 8, -8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 8, -8, 12],\n [3, -18, 18, 0],\n [10, 6, -6, -9],\n [0, 22, -22, -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[[-24, -16, 12, -24],\n [-16, -10, 8, -16],\n [10, 4, -5, 10],\n [16, 10, -8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 6, -12, -12],\n [1, -2, 4, 4],\n [1, -2, 4, 4],\n [3, -6, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -3, 4, 1],\n [6, -6, 7, 4],\n [-6, 6, -7, -4],\n [-8, 12, -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[[0, -6, -4, -4],\n [0, 3, 2, 2],\n [0, -3, -2, -2],\n [0, -9, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -6, -4, -8],\n [6, 6, 4, 8],\n [1, -3, -5, -16],\n [-4, -6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -6, 12, -12],\n [8, 8, -16, 16],\n [8, 8, -16, 16],\n [-4, -4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -9, 12, 12],\n [3, 9, -12, -12],\n [4, 12, -16, -16],\n [-2, -6, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [6, -6, 8, 2],\n [-6, 0, 11, -10],\n [-20, 16, -14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, 3, -10],\n [-1, -6, 4, -1],\n [14, -14, 12, -14],\n [-6, -2, 0, -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[[-36, 8, 8, -16],\n [15, 10, -2, 22],\n [-32, 11, 9, -13],\n [12, -26, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -7, 13, 1],\n [-10, 10, -26, 4],\n [2, -4, -16, 14],\n [13, -6, 13, -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[[22, -14, 16, -6],\n [-4, 4, 0, 4],\n [12, -6, 12, 0],\n [-12, 4, -16, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 10, 0, -7],\n [0, -6, 6, 3],\n [4, 10, 10, -9],\n [-4, -14, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -12, -14, 2],\n [5, -13, 6, 4],\n [-2, 9, -7, -11],\n [-2, -3, -1, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -8, -8, -8],\n [1, 6, 14, 14],\n [4, 2, -10, -10],\n [2, 0, -8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -4, -2, 4],\n [-9, 28, 0, -26],\n [-18, -2, -14, -6],\n [3, -9, -8, 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 4x4 matrix:\n[[-8, 0, 6, -6],\n [4, -24, -12, 12],\n [-7, 10, 9, -9],\n [10, -12, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, -16, -16],\n [3, 0, 4, 4],\n [9, 0, 12, 12],\n [-12, 0, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 3, -22, 3],\n [22, -10, -20, 2],\n [9, -11, -12, -14],\n [17, -7, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -21, -9, -3],\n [4, -11, -11, -1],\n [-14, -12, -15, 4],\n [4, -9, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 4, -2, -3],\n [-24, -8, 8, 4],\n [-12, 6, 0, -6],\n [0, -20, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 1, -1, 2],\n [-7, 13, -1, -22],\n [-7, 8, 1, -20],\n [3, 3, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 4, -16, 3],\n [0, -4, 8, -4],\n [4, 8, -8, 9],\n [16, 16, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 3, -30, 11],\n [4, -10, -10, 12],\n [-8, 5, 16, -13],\n [12, -6, 10, 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 4x4 matrix:\n[[-6, -4, 4, 2],\n [3, 2, -2, -1],\n [6, 4, -4, -2],\n [-3, -2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -4, -2, -2],\n [0, 0, 0, 0],\n [3, 12, 6, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 10, -21, -8],\n [-10, 6, -17, -12],\n [12, 0, 22, 12],\n [0, -16, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 1, 1, -2],\n [-16, -4, -4, 8],\n [12, 3, 3, -6],\n [12, 3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 7, -8, -5],\n [3, 3, -5, -2],\n [17, 15, -34, -7],\n [-1, 1, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [3, 6, 6, 9],\n [1, 2, 2, 3],\n [1, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 15, -4, 18],\n [-6, -6, 7, -9],\n [3, 3, -11, 7],\n [15, 15, -1, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 4, -14, 4],\n [-18, 13, 14, -8],\n [-14, 9, 11, -6],\n [-2, 17, 0, -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[[14, -3, 2, -2],\n [-20, 4, -12, -12],\n [9, 3, -9, -13],\n [13, -16, -1, -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[[1, 5, -6, 0],\n [-5, -11, 14, -6],\n [13, -6, -14, 3],\n [-7, -6, 11, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, 4, 6],\n [0, -3, -2, -3],\n [0, -3, -2, -3],\n [0, -12, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 3, -6, 0],\n [-7, 3, -4, -2],\n [13, 3, 1, -7],\n [-12, 0, -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[[0, -6, 0, 0],\n [-2, -2, 4, 1],\n [2, -4, -4, -1],\n [10, -14, -20, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -3, 3, -7],\n [1, 3, 1, 3],\n [-4, -12, -4, 20],\n [-12, -22, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, 0, 2],\n [4, 4, 0, -2],\n [0, 0, 0, 0],\n [4, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 4, 4, -16],\n [-8, 2, 2, -8],\n [-16, 4, 4, -16],\n [16, -4, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -4, 4, 16],\n [13, 15, -2, 24],\n [2, -8, 2, -4],\n [-12, 0, -1, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 12, 12, 4],\n [12, -12, -12, -4],\n [3, -3, -3, -1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -1, 2, -4],\n [12, -3, 6, -12],\n [4, -1, 2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -12, -9, 9],\n [-6, 12, 9, -9],\n [-6, 12, 9, -9],\n [2, -4, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 2, -2, 5],\n [10, -4, 4, 11],\n [-20, 8, -8, -22],\n [24, -8, 8, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 3, 9, 3],\n [12, -3, -9, -3],\n [0, 0, 0, 0],\n [8, -2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 9, 26, -4],\n [5, 18, 6, -17],\n [7, 1, 9, 6],\n [-13, -6, 15, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 8, 6, 4],\n [3, 12, 9, 6],\n [-3, -12, -9, -6],\n [-1, -4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 20, 11, 12],\n [-8, 10, -12, 6],\n [-13, 23, 8, 14],\n [1, -15, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -12, 16, 8],\n [-12, -12, 16, 8],\n [3, 3, -4, -2],\n [6, 6, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 4, 18, 6],\n [-4, 20, 4, -8],\n [-13, 11, 7, 2],\n [9, -9, -9, -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[[-12, 8, 15, -6],\n [8, -9, 1, 4],\n [-8, 4, 14, -4],\n [28, -24, -19, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 4, 0, -16],\n [12, -3, 0, 12],\n [-12, 3, 0, -12],\n [8, -2, 0, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, -15, -8, -2],\n [-20, -9, -10, -4],\n [-16, -6, -11, -5],\n [0, 2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -8, 6, -24],\n [-3, -11, 17, 20],\n [0, 8, -10, 0],\n [-2, 2, 1, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, 16, 12],\n [-16, 12, 7, 6],\n [4, -4, 3, 2],\n [-15, 16, -16, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -4, -3, 1],\n [2, -4, -3, 1],\n [4, -8, -6, 2],\n [4, -8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -16, 20, 0],\n [6, 6, -7, 3],\n [4, -4, 6, 6],\n [-10, -2, 1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 28, 8, -2],\n [2, 14, 6, -8],\n [-3, 9, 6, -18],\n [-2, -15, -8, 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[[16, 24, -8, -6],\n [0, -12, 12, -6],\n [8, -2, 10, -10],\n [16, 20, -4, -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[[10, -25, -2, -34],\n [-3, -17, -7, -22],\n [18, -13, 6, -18],\n [15, -5, 7, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 3, -3, 3],\n [-3, 3, -3, 3],\n [9, -9, 9, -9],\n [-12, 12, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 2, -8, 5],\n [-12, -4, 0, -18],\n [-6, -2, -2, -10],\n [12, 4, 4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, -4, -3],\n [16, -8, 16, 12],\n [4, -2, 4, 3],\n [-8, 4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -4, 4, -6],\n [6, 6, -6, 9],\n [-8, -8, 8, -12],\n [8, 8, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 0, 16, 4],\n [6, 0, 6, -3],\n [7, 0, 4, -3],\n [-1, 0, -1, -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[[-10, -18, -22, 0],\n [21, 13, 8, 8],\n [-14, -2, -7, 8],\n [0, -12, -34, 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, 0, 0, 0],\n [-4, 2, -1, -1],\n [12, -6, 3, 3],\n [-4, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 0, -2, -6],\n [-4, 0, 4, 12],\n [-1, 0, 1, 3],\n [3, 0, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, -8, -6],\n [8, 8, 16, 12],\n [2, 2, 4, 3],\n [-8, -8, -16, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 0, -18, 2],\n [-20, -14, -10, 28],\n [-13, -9, 2, 24],\n [9, -1, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 8, -4, 4],\n [-12, 8, -4, 4],\n [-9, 6, -3, 3],\n [-6, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -6, 6, 6],\n [8, 4, -4, -4],\n [-16, -8, 8, 8],\n [16, 8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, 4, -6],\n [10, -24, -18, 7],\n [4, -14, 10, 4],\n [-12, 26, 14, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, 4, -1],\n [8, -8, -8, 2],\n [8, -8, -8, 2],\n [16, -16, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 12, 16, 12],\n [4, -12, -16, -12],\n [2, -6, -8, -6],\n [-1, 3, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[29, 9, -5, -26],\n [-3, 3, 3, 4],\n [-18, -15, -2, 13],\n [-12, -24, -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[[8, 0, -12, 12],\n [0, 0, 0, 0],\n [8, 0, -12, 12],\n [6, 0, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 0, -12, -3],\n [9, 0, -12, -3],\n [0, 0, 0, 0],\n [-12, 0, 16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 12, -6, 4],\n [7, -16, 10, 8],\n [0, 12, -9, -7],\n [-9, 12, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -2, -12, 8],\n [-1, -4, -19, 1],\n [-3, 1, 8, -10],\n [-6, -2, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -3, -4, 2],\n [12, -9, -12, 6],\n [12, -9, -12, 6],\n [16, -12, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 8, 8, 18],\n [-5, 5, -11, -9],\n [-3, 1, -5, -7],\n [0, 2, 16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[21, 18, -16, -24],\n [6, 2, 8, -10],\n [9, 7, -4, -11],\n [-12, -8, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 1, -12, -4],\n [-8, 0, 9, 4],\n [-8, 12, 0, 16],\n [2, -7, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, 0, 6],\n [-1, 1, 0, -3],\n [-1, 1, 0, -3],\n [-4, 4, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -2, -11, -6],\n [-15, 9, 17, 16],\n [32, -6, -20, -30],\n [18, -8, -12, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 15, 20, -4],\n [-4, -24, -32, 0],\n [17, -3, -4, -20],\n [8, 6, 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[[-15, -1, 10, -2],\n [6, -2, 2, -4],\n [-8, 4, -6, 8],\n [13, 3, -14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, 10, 2],\n [-8, 2, -1, 4],\n [0, 2, 3, 0],\n [-2, -4, -7, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [-6, 3, 0, 3],\n [4, -2, 0, -2],\n [4, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 3, -3, 0],\n [-4, -17, -7, 8],\n [-28, 4, 8, -4],\n [10, 15, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 23, 1, -5],\n [14, -26, 20, 14],\n [2, -14, 4, 18],\n [10, -19, 21, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 1, -3, -1],\n [2, -1, 3, 1],\n [-6, 3, -9, -3],\n [4, -2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, 6, 8],\n [-2, 1, 3, 4],\n [-6, 3, 9, 12],\n [2, -1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 6, 5, 5],\n [-13, 14, 33, -3],\n [3, -8, -18, 3],\n [6, -12, -22, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -12, 0, -16],\n [8, -12, 0, -16],\n [-2, 3, 0, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 6, 8, 10],\n [-12, 22, -14, 10],\n [-7, 11, -2, 14],\n [8, -9, 13, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 15, -24, -14],\n [4, 16, -13, -1],\n [24, -12, -2, -18],\n [16, 12, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -8, 0, -5],\n [-7, -20, 4, -12],\n [-2, -8, 8, -4],\n [-3, -4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -11, -7, -1],\n [4, -8, -4, 8],\n [-3, 1, 1, 3],\n [6, -7, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -8, 4, -2],\n [-4, 4, -2, 1],\n [4, -4, 2, -1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, 2, 2],\n [-6, 5, 3, 2],\n [4, -22, -2, -4],\n [4, -8, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -8, 4, 8],\n [-1, 2, -1, -2],\n [0, 0, 0, 0],\n [-1, 2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 8, -1, 6],\n [6, 17, 5, 6],\n [-8, -16, -16, -12],\n [-8, -16, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, -12, 4, 0],\n [-6, 6, -2, 0],\n [12, -12, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -17, -3, 7],\n [-7, 11, 1, -5],\n [-9, 21, 3, -9],\n [8, -8, 0, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [-4, -16, 4, 4],\n [4, 16, -4, -4],\n [2, 8, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 4, -8, 1],\n [12, -16, 4, 17],\n [-4, 16, -12, -11],\n [-8, 8, 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[[16, 4, 12, -8],\n [-4, 2, -3, 1],\n [-16, -10, -12, 10],\n [-16, -16, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -6, 4, 8],\n [-15, -14, 13, 22],\n [-12, -7, 6, 16],\n [6, 5, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -1, -13, -16],\n [7, 3, -3, -6],\n [-7, -6, -8, -10],\n [6, 1, 21, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -7, 10, -12],\n [12, 15, -17, 14],\n [-4, 8, -8, 0],\n [-10, -13, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, 14, -16, 13],\n [8, 4, -5, 4],\n [-16, -8, 7, -6],\n [8, 7, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 5, -4, 8],\n [0, -1, 0, -4],\n [-2, 2, -2, 2],\n [2, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -16, 2, 24],\n [-9, -14, 3, 20],\n [-14, 31, 19, 12],\n [6, 10, 0, -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[[-11, -4, -7, 3],\n [-5, 0, -1, -1],\n [-13, -2, -5, 0],\n [-2, 12, 14, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 3, -2, -1],\n [-6, -9, 6, 3],\n [4, 6, -4, -2],\n [2, 3, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 4, 3, 2],\n [0, 0, 0, 0],\n [0, -12, -9, -6],\n [0, -12, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -3, -10, 9],\n [-13, 4, 11, -7],\n [-17, 7, 4, 10],\n [1, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -2, 2, 0],\n [4, 2, -2, 0],\n [-8, -4, 4, 0],\n [12, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -2, 4, 0],\n [-9, 6, -12, 0],\n [-9, 6, -12, 0],\n [9, -6, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, -15, -18, 12],\n [-7, 12, 14, -10],\n [-2, 12, 12, -12],\n [-8, 3, 6, 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, -23, 5, -5],\n [-7, 7, 8, -8],\n [-27, -3, 1, -1],\n [-19, 0, -7, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-8, -6, 2, 6],\n [-16, -12, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 11, 29, 16],\n [-14, 14, -4, 1],\n [-3, 11, 24, 12],\n [1, 11, 29, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -16, -4, 32],\n [27, -18, -7, 37],\n [10, -4, -2, 14],\n [11, -5, -5, 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 4x4 matrix:\n[[-6, 8, 6, 2],\n [3, -4, -3, -1],\n [12, -16, -12, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -12, 12, -6],\n [10, -4, -8, 4],\n [-4, -2, 8, -4],\n [3, -12, 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 4x4 matrix:\n[[-22, -8, -10, 2],\n [5, -8, 3, 21],\n [1, -2, 1, 9],\n [8, 8, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -9, 6, -9],\n [-6, 9, -6, 9],\n [-4, 6, -4, 6],\n [8, -12, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, -9, -3, -6],\n [0, 0, 0, 0],\n [2, 3, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -4, -6, -28],\n [24, 8, 12, 40],\n [18, 4, -2, 12],\n [8, -12, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -11, 18, -9],\n [11, -16, 3, -9],\n [-2, -4, -8, -3],\n [5, -6, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -1, 8, -5],\n [23, -13, -10, 16],\n [-14, 12, 6, -15],\n [19, -16, -4, 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[[11, -4, -2, -15],\n [-5, 4, 2, -3],\n [6, -2, -1, -9],\n [-9, 4, 2, 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, 0, 0, 0],\n [0, 0, 0, 0],\n [-3, -3, -12, -6],\n [-4, -4, -16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -3, -1, -2],\n [4, 6, 2, 4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 16, 4, -4],\n [-4, 16, 4, -4],\n [0, 0, 0, 0],\n [-4, 16, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, 6, 12],\n [0, -8, -8, -16],\n [0, -4, -4, -8],\n [0, -8, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -4, -2, 4],\n [-1, -2, 2, 8],\n [-10, -8, -4, 8],\n [13, 6, 14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -12, -4, 16],\n [-6, 9, 3, -12],\n [-8, 12, 4, -16],\n [2, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -16, 11, 17],\n [-7, 5, -10, -11],\n [-5, -9, -6, -1],\n [6, -20, 10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 0, -4, -1],\n [-9, 0, 12, 3],\n [6, 0, -8, -2],\n [-9, 0, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 24, -4, 12],\n [-10, 2, -7, 2],\n [-3, -3, 0, -1],\n [6, -3, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -6, -11, 0],\n [-5, -18, -13, -2],\n [-19, 5, 24, 4],\n [-6, -21, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 14, -8, 0],\n [11, -10, 16, -8],\n [0, -16, -14, 18],\n [-5, 22, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 2, 4, 0],\n [-3, 9, -4, 19],\n [-11, -4, 6, 7],\n [-20, 1, -8, 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 4x4 matrix:\n[[24, -6, 18, 15],\n [12, -18, 4, 0],\n [-12, 6, -8, -6],\n [24, -6, 18, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 6, -12, -8],\n [3, -3, -6, -8],\n [3, -12, 12, 4],\n [-5, 6, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 7, 4, -1],\n [-4, -4, -1, 15],\n [8, 12, 4, 8],\n [16, 8, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -2, 12, 2],\n [-18, -4, 4, 26],\n [24, 6, -10, -34],\n [-13, -4, 4, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -12, 14],\n [-4, -8, 8, -16],\n [-2, 12, -20, 20],\n [3, -10, 18, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 26, 19, 13],\n [-8, -20, -22, -22],\n [0, -6, 5, 13],\n [-12, -12, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 25, 10, 13],\n [-1, -4, -1, -4],\n [10, 1, 4, -11],\n [-14, -17, -8, -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, -2, -4, -4],\n [15, -5, 2, 0],\n [-6, -1, 1, 6],\n [24, 6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -4, -3, 5],\n [4, 16, -12, 4],\n [7, 12, -12, 6],\n [2, 8, -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[[3, 2, -3, 3],\n [-12, -8, 12, -12],\n [9, 6, -9, 9],\n [-12, -8, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -6, 5, 8],\n [-5, 1, -5, -7],\n [-7, 5, -7, -12],\n [-1, -7, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 4, -6, 4],\n [9, -12, 12, -12],\n [-24, 16, 3, 25],\n [-5, 12, 7, 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[[0, 0, 0, 0],\n [-2, -3, 4, -3],\n [-4, -6, 8, -6],\n [8, 12, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[21, -12, 3, -6],\n [15, -8, 7, 0],\n [-1, 2, 12, 11],\n [2, 0, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -16, 4, 16],\n [0, 4, -1, -4],\n [0, -16, 4, 16],\n [0, 8, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, -1, 2],\n [12, 24, -14, -20],\n [6, 12, -6, -12],\n [-4, -8, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -10, 4, 4],\n [-5, -3, -6, -2],\n [-4, -4, -2, 0],\n [8, 0, 18, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -3, 4, 19],\n [-14, 11, 9, -17],\n [-5, 12, 13, -16],\n [1, -7, -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[[3, 3, -1, 0],\n [3, 3, -1, 0],\n [9, 9, -3, 0],\n [9, 9, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 12, 6, -3],\n [3, 4, 2, -1],\n [9, 12, 6, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -10, -15, -8],\n [-15, 2, -4, 19],\n [17, 6, 8, -21],\n [24, 20, -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 4x4 matrix:\n[[7, -17, -2, -22],\n [1, -2, 1, -4],\n [-4, 11, 5, 10],\n [-1, -6, -10, -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[[24, -19, -10, 10],\n [6, 9, 0, 20],\n [9, 2, 20, -1],\n [-16, 16, 4, 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[[-9, -12, -12, -6],\n [18, 6, 18, 3],\n [-3, -22, -10, -11],\n [-18, 0, -16, 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 4x4 matrix:\n[[4, -2, -4, -2],\n [-12, 6, 0, 14],\n [-6, 3, 0, 7],\n [-2, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 13, -6, -4],\n [-16, 4, 10, 16],\n [8, -2, -5, -8],\n [-9, -3, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 6, 6, 6],\n [4, 4, 4, 4],\n [-8, -8, -8, -8],\n [6, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, 4, 0],\n [0, 0, 0, 0],\n [-2, 0, 4, 0],\n [-3, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -16, 12, 16],\n [-8, 8, -6, -8],\n [-8, 8, -6, -8],\n [16, -16, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -8, -4, -8],\n [-6, -4, 10, -4],\n [-10, 12, 12, 12],\n [4, 16, -10, 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 4x4 matrix:\n[[-3, 3, 12, 3],\n [-1, 1, 4, 1],\n [-3, 3, 12, 3],\n [1, -1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 2, 2, -2],\n [12, -4, -4, 4],\n [12, -14, 16, 19],\n [-3, 5, -7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 8, -12, -4],\n [-2, 4, -20, 0],\n [-12, 10, -1, -7],\n [-5, 2, 18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 0, 6, -1],\n [3, -1, 8, 1],\n [6, 0, 12, -2],\n [-12, -5, -14, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 9, -2, -9],\n [6, 4, 3, 9],\n [10, -20, -3, -5],\n [4, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -12, 8, 14],\n [-2, 2, -3, -4],\n [2, 4, -4, -6],\n [-11, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -1, -1, -3],\n [32, -8, 4, -16],\n [-24, 6, -3, 12],\n [-12, 3, -9, 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, -8, -16, -12],\n [-4, -12, -20, -9],\n [2, 7, 12, 6],\n [-2, -5, -8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -16, -10, -6],\n [-10, -8, 1, -10],\n [-5, -1, -4, -3],\n [11, 25, 13, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -16, -2, 0],\n [10, 10, 15, -22],\n [2, 2, 9, -14],\n [4, 4, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 12, -12, -2],\n [6, 21, -22, -7],\n [4, -6, 4, -6],\n [-8, 12, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, 12, 12],\n [0, 0, 0, 0],\n [0, 3, -9, -9],\n [0, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-25, 18, -16, -23],\n [-5, 14, -16, -11],\n [-4, -16, 20, 8],\n [-17, -8, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -2, 0, -3],\n [-1, -2, 0, -3],\n [3, 6, 0, 9],\n [-2, -4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -9, -2, -20],\n [-1, 4, 3, 4],\n [7, 11, 7, 21],\n [-13, 6, 17, -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[[24, 4, 4, 8],\n [2, -1, -3, 4],\n [14, 2, 9, 13],\n [-8, 0, 5, -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 4x4 matrix:\n[[-5, 9, -18, 5],\n [-6, -9, 9, 6],\n [-4, -6, 6, 4],\n [-5, -2, -1, 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[[34, 13, -4, -11],\n [4, 16, 17, -8],\n [-8, -24, -14, 11],\n [2, 11, 1, -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 4x4 matrix:\n[[3, 5, 12, 4],\n [0, -6, -12, -3],\n [-6, 14, 24, 4],\n [-6, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, -16, 3, 7],\n [10, 4, -4, -4],\n [-9, -3, 5, 6],\n [4, 3, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 0, -6, 0],\n [-4, 4, -8, 4],\n [-16, -14, 22, -23],\n [13, 15, -10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 4, -14, 18],\n [-8, -8, 8, 4],\n [-6, 0, 6, -12],\n [-5, -2, 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[[9, -6, -6, -12],\n [3, -2, -2, -4],\n [3, -2, -2, -4],\n [9, -6, -6, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 8, -8, -8],\n [16, 8, -8, -8],\n [16, 8, -8, -8],\n [16, 8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 8, -12, -16],\n [-3, -6, 9, 12],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -1, 3, 0],\n [0, 4, -2, 10],\n [-2, 1, -1, 2],\n [6, -3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -16, -20, 10],\n [3, 8, 6, 1],\n [6, 12, 10, 0],\n [0, 16, 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[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [12, 3, -12, -3],\n [-16, -4, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 0, 1, -16],\n [-9, -12, -12, -9],\n [13, 1, 0, 13],\n [-30, -2, -11, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -30, 9, 0],\n [4, 12, -5, -10],\n [7, 11, 6, 13],\n [8, 14, 1, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -3, 10, 6],\n [14, 17, -8, -9],\n [19, 10, -25, -15],\n [9, -1, -17, -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[[6, 1, 5, -2],\n [-4, -2, -6, 0],\n [-4, -2, -6, 0],\n [0, -6, -12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 3, 12, 6],\n [-3, 1, 4, 2],\n [12, -4, -16, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -4, -10, -6],\n [-4, -16, 12, -20],\n [-6, -7, 22, 11],\n [6, 0, -25, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -7, -6, 16],\n [18, -15, 2, 25],\n [13, -11, 2, 18],\n [1, -2, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 1, -7, 1],\n [-10, -14, 8, 16],\n [14, 4, -10, -2],\n [16, 12, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -12, 3, -6],\n [1, -4, 1, -2],\n [0, 0, 0, 0],\n [1, -4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 4, 2, 0],\n [-1, -2, -3, 7],\n [0, -12, -8, 20],\n [3, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -12, -9, -3],\n [-1, 1, 2, 9],\n [4, -16, -8, -9],\n [2, 8, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, -16, -28],\n [-7, -1, 8, -34],\n [10, 1, -22, -4],\n [-14, 1, 8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 12, 6, 4],\n [24, -20, 8, -10],\n [16, -4, -9, -3],\n [6, 4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 3, 1, 0],\n [-12, 9, 3, 0],\n [4, -3, -1, 0],\n [8, -6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -8, -8, -4],\n [-6, 4, 7, 2],\n [3, -2, -2, -1],\n [-6, 4, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [4, 8, 6, 4],\n [-6, -12, -9, -6],\n [-6, -12, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 5, 7, -8],\n [3, 1, -3, 2],\n [0, 8, 9, -11],\n [12, 4, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 6, 22, -6],\n [-24, -15, -6, -20],\n [3, -3, -10, 3],\n [21, 12, 4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -1, -3, 2],\n [0, 3, 9, -6],\n [0, -2, -6, 4],\n [0, 4, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -10, -11, -3],\n [-4, 16, 12, 12],\n [9, -6, -1, -9],\n [13, -7, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -3, 6, 3],\n [-10, 18, -36, -20],\n [-6, 0, -19, 4],\n [-13, 21, -36, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -8, 3, 6],\n [4, -1, 6, 12],\n [20, -15, -27, -5],\n [8, -24, 0, 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[[4, -16, 0, 0],\n [2, 2, 8, 6],\n [10, -20, 16, 12],\n [5, -15, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -2, 7, -3],\n [12, 16, 16, -18],\n [-16, -5, -12, 10],\n [8, -17, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 4, 10, 7],\n [3, 6, 30, -3],\n [4, 8, 20, 6],\n [16, 4, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, 13, -11, -6],\n [-15, 11, -2, -2],\n [-8, 6, -7, -2],\n [-21, 15, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 2, 6, -1],\n [5, 2, 12, -11],\n [-1, -8, -16, 8],\n [-5, -6, -22, 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, 12, 10],\n [24, -11, -11, 7],\n [16, 9, 9, 7],\n [12, 11, 10, 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[[-1, -4, -5, 16],\n [-9, 16, -19, -12],\n [-1, 0, -3, 4],\n [11, -16, 25, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -3, -1, 2],\n [9, -9, -3, 6],\n [-9, 9, 3, -6],\n [3, -3, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 6, -8, -8],\n [18, 8, -14, -25],\n [2, 4, -6, -10],\n [-3, 8, -11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 8, -11, -15],\n [5, 17, 7, -15],\n [-3, -12, -8, 4],\n [-1, 3, 8, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -6, -12, 6],\n [0, 0, 0, 0],\n [-4, 8, 16, -8],\n [-1, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[34, -2, 19, -11],\n [26, 2, 17, -7],\n [14, -2, 4, -8],\n [16, 12, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -1, 8, -18],\n [6, 6, -7, 13],\n [20, 9, 5, 7],\n [-15, -7, -5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 7, 5, -6],\n [11, -6, 1, 2],\n [9, 0, -1, -4],\n [0, 12, -2, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -4, -4, 0],\n [-1, 0, 0, 4],\n [-2, 4, 4, 16],\n [-2, -10, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 3, 0, 10],\n [17, -9, 8, -16],\n [11, -12, -6, -8],\n [27, 0, 12, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -10, 2, -3],\n [4, -4, 18, -12],\n [-3, 12, 0, 9],\n [3, -10, -10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, 4, 12],\n [0, 2, 2, 6],\n [0, 1, 1, 3],\n [0, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 12, -4, -8],\n [-10, -6, 14, 20],\n [-6, 0, 6, 8],\n [-12, 0, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 10, 8, -13],\n [20, 12, 0, 2],\n [0, -14, -10, 16],\n [-8, 12, 12, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, -10, -15],\n [11, 16, -19, 4],\n [6, -8, 10, 0],\n [2, -4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 4, -4, -4],\n [1, 1, -1, -1],\n [3, 3, -3, -3],\n [4, 4, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -2, -6, -4],\n [6, 2, 6, 4],\n [-3, -1, -3, -2],\n [-12, -4, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -3, 3, -6],\n [-8, 4, -4, 8],\n [6, -3, 3, -6],\n [4, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, -1, -3, -2],\n [3, 9, 12, -12],\n [-24, -2, -5, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -1, -3, -4],\n [17, -7, 9, -28],\n [-5, 3, 3, 12],\n [11, -4, 9, -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[[16, -3, 3, 12],\n [-12, 6, -1, -4],\n [-8, -6, -4, -16],\n [-8, 15, 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[[-2, -6, 3, 8],\n [-12, -11, 10, 13],\n [4, 7, -4, -11],\n [-20, -14, 13, 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[[-1, 17, 2, 22],\n [0, -18, 0, -21],\n [9, -11, 2, -9],\n [4, 10, 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[[-2, 8, 8, 2],\n [-3, 12, 12, 3],\n [0, 0, 0, 0],\n [-1, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -6, -3, 12],\n [-8, -10, 1, 2],\n [8, 12, 2, -12],\n [1, 8, 17, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [12, 8, 8, 12],\n [-3, -2, -2, -3],\n [3, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -27, 30, -8],\n [20, -1, 5, -19],\n [28, 9, -6, -14],\n [-48, -20, 16, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -1, 3, -2],\n [-8, 4, -12, 8],\n [-8, 4, -12, 8],\n [4, -2, 6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -15, -2, -16],\n [-4, 28, -8, 32],\n [2, -6, 8, -8],\n [-4, 12, -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[[-16, -8, 12, 12],\n [8, 4, -6, -6],\n [8, 4, -6, -6],\n [-8, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 2, 8, 6],\n [4, 2, 8, 6],\n [4, 2, 8, 6],\n [4, 2, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -10, -10, 0],\n [8, -6, 12, 1],\n [12, 0, 10, -11],\n [16, 8, -16, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 7, 0, 9],\n [32, 24, 6, 16],\n [2, 2, -5, 5],\n [12, 19, 6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 24, 4, -16],\n [16, 20, -6, -11],\n [20, 24, -4, -14],\n [6, 4, 10, -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 4x4 matrix:\n[[-3, 8, 5, -6],\n [-3, -16, 17, -6],\n [-2, -16, 14, -4],\n [2, 12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 18, 2, -6],\n [-4, -6, -2, 2],\n [4, -4, -1, 0],\n [4, 12, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 4, -18, 12],\n [-4, 0, -12, 4],\n [2, 2, 8, -8],\n [1, 11, 10, -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[[-3, 13, -15, -8],\n [1, -4, 4, 2],\n [-3, 9, -3, 0],\n [-4, 16, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 16, -16, -24],\n [11, -1, -8, 16],\n [9, 1, 20, -24],\n [-13, 5, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 2, -18, -9],\n [8, 3, 22, -4],\n [-6, -11, 16, 13],\n [4, 6, 10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, -2, 0, 3],\n [19, -8, 4, 7],\n [-3, -4, 4, 1],\n [28, 4, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -12, 10, 4],\n [-8, 8, -16, -4],\n [4, -4, 8, 2],\n [0, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 0, 12, 12],\n [0, 0, 0, 0],\n [8, 0, -12, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, -6, 6],\n [6, 6, -6, 6],\n [0, 6, 2, 6],\n [12, 0, -16, 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[[-20, -4, 6, 12],\n [-25, 2, 2, 4],\n [1, -4, 3, 6],\n [12, 8, -8, -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 4x4 matrix:\n[[9, 0, -12, -12],\n [-3, 0, 4, 4],\n [9, 0, -12, -12],\n [-3, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -22, 14, -3],\n [9, 4, 4, 3],\n [12, -12, 8, -2],\n [0, 14, -8, 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 4x4 matrix:\n[[4, -4, -12, 28],\n [-4, 0, 6, -18],\n [2, -6, -12, 24],\n [10, 18, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 0, 2, -4],\n [-3, 0, 3, -6],\n [-4, 0, 4, -8],\n [-1, 0, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 2, -4, 3],\n [-3, -6, 12, -9],\n [3, 6, -12, 9],\n [-2, -4, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 9, 3, 3],\n [1, -3, -1, -1],\n [-1, 3, 1, 1],\n [3, -9, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -8, -16, -8],\n [12, 8, 16, 8],\n [-9, -6, -12, -6],\n [3, 2, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -10, 4, -9],\n [-4, -10, 1, -6],\n [25, 10, 14, -9],\n [18, 4, 11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -1, -15, -1],\n [-10, 0, -1, 0],\n [-12, -5, 13, -5],\n [-17, 8, 14, 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[[14, 13, 18, -20],\n [4, 8, 8, 0],\n [10, 8, 12, -16],\n [8, 10, 12, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 12, -12],\n [0, 0, 12, -12],\n [0, 0, 4, -4],\n [0, 0, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 6, -12, 3],\n [0, 0, 0, 0],\n [6, 6, -6, -4],\n [9, 7, -11, 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[[-4, -2, -2, -4],\n [-13, -11, -11, -4],\n [1, -1, -1, 4],\n [16, 14, 14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 6, -16, 14],\n [-9, -8, -9, 3],\n [-3, 6, -16, 14],\n [-9, 0, -21, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, -8, 6],\n [0, 1, -4, 3],\n [0, 4, -16, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 11, 0, -4],\n [1, -12, -4, 7],\n [-6, 0, 0, -10],\n [2, 22, 8, -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[[-4, -4, -1, 0],\n [14, 15, 2, -3],\n [4, 4, 1, 0],\n [0, 2, -3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 16, -12, 8],\n [0, 18, -19, 15],\n [-12, 8, -8, 10],\n [-12, 13, -18, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -9, -9, 6],\n [-8, 6, 6, -4],\n [-4, 3, 3, -2],\n [12, -9, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -3, 6, 0],\n [1, -14, 6, -2],\n [8, 9, 8, 10],\n [-10, -14, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 24, 18, -16],\n [20, 7, -1, 12],\n [-12, 9, 9, -12],\n [-16, 12, 12, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 22, -28, -13],\n [21, 4, -13, 0],\n [2, 26, -23, -20],\n [-7, -16, 25, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -22, 17, -9],\n [-24, 22, -16, 5],\n [-12, 14, -13, 21],\n [2, 0, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -2, -4, -4],\n [4, -2, -4, -4],\n [0, 0, 0, 0],\n [6, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 0, -3, 15],\n [6, 5, 4, -10],\n [-4, 0, 4, -20],\n [2, 0, -2, 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, -3, 5, 0],\n [-16, -7, 14, 0],\n [-16, -10, 12, 0],\n [-12, 0, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -6, -31, 12],\n [15, -18, -15, -4],\n [4, -7, 4, -6],\n [-1, -3, -7, 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 4x4 matrix:\n[[-7, 3, -6, -3],\n [7, -2, -3, 2],\n [8, -3, 3, 3],\n [10, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, -2, 8],\n [6, -6, 9, -21],\n [6, 14, -2, 8],\n [12, 18, 2, 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 4x4 matrix:\n[[-8, 2, -4, 2],\n [3, 6, -3, 6],\n [-4, -2, 0, -2],\n [-6, 0, -2, 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 4x4 matrix:\n[[12, -24, -32, -16],\n [3, -15, -11, -10],\n [-8, 24, 26, 14],\n [0, -6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [28, 13, 9, -28],\n [12, 7, 3, -12],\n [4, 14, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -5, -3, -23],\n [-4, 4, 16, -12],\n [4, -7, -10, -21],\n [11, -4, -3, -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 4x4 matrix:\n[[-8, 2, 2, -8],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-12, 3, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 6, 12, 11],\n [-10, 21, 17, 10],\n [7, -9, -3, -27],\n [4, 0, 0, -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[[-4, 8, -8, -4],\n [9, -3, -12, 9],\n [-10, 0, 20, -10],\n [-4, 3, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -6, -6, 4],\n [-3, 3, 3, -2],\n [9, -9, -9, 6],\n [-6, 6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 6, 7, 2],\n [2, -6, 4, -10],\n [13, -7, -10, -1],\n [-18, 14, 9, 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[[16, -8, -8, 12],\n [-2, -10, -7, 8],\n [-5, 6, 6, -2],\n [6, 6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -16, -4, -8],\n [0, 0, 0, 0],\n [-2, -8, -2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, -4, 4],\n [0, -4, 2, -2],\n [0, -8, 4, -4],\n [0, -12, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 1, -6, 3],\n [-7, 11, 14, 1],\n [-8, 10, 10, 2],\n [4, -5, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 33, -13, -25],\n [-10, -6, -2, -2],\n [-14, -28, -4, 20],\n [-4, -12, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 9, 5, 1],\n [1, 16, 0, -1],\n [2, -18, -10, -2],\n [0, -15, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -18, 0, -10],\n [20, -18, 0, -10],\n [12, -12, 0, -6],\n [12, -8, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -8, 15, 0],\n [-4, -3, -3, 3],\n [2, -3, 8, -11],\n [-6, -10, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 16, 16, -12],\n [-9, 12, 12, -9],\n [-6, 8, 8, -6],\n [9, -12, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 4, 24, -4],\n [-12, 12, 32, 4],\n [-9, 12, 12, 12],\n [-6, 7, 12, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 2, -12, 3],\n [-8, 18, 4, -1],\n [0, 0, 0, 0],\n [-4, 15, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -4, -6, 6],\n [-4, -2, -3, 3],\n [4, 2, 3, -3],\n [4, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -2, -6, 2],\n [0, 2, 6, -2],\n [0, -2, -6, 2],\n [0, 2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 6, -6, 3],\n [4, -8, 8, -4],\n [1, -2, 2, -1],\n [-2, 4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -7, 12, -15],\n [-9, 2, 13, -3],\n [-6, -10, 10, -12],\n [-9, -1, 1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -4, 28, 16],\n [10, -7, 13, 6],\n [8, 4, 8, 6],\n [-22, 1, -25, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -12, 0, 16],\n [-3, -3, 0, 4],\n [12, 12, 0, -16],\n [12, 12, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -4, 4, -8],\n [0, 8, -8, 16],\n [0, -4, 4, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 0, 16, 16],\n [-16, 4, -8, -8],\n [20, -2, 16, 16],\n [-20, 2, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 15, -2, 5],\n [-16, -12, 0, 4],\n [-16, -12, 3, -11],\n [-12, -9, -1, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 16, 20, 8],\n [9, -8, -2, -12],\n [0, -12, -21, 0],\n [9, -16, -16, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[21, 4, 6, -7],\n [15, 4, 4, -5],\n [-12, -16, 0, 4],\n [-6, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -3, 2, 7],\n [-6, -14, 16, 6],\n [-1, 11, -14, 1],\n [10, 2, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 8, 24, 4],\n [-10, 6, 1, 14],\n [5, -8, -7, -15],\n [7, 7, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, 3, 15],\n [0, -2, -1, -3],\n [0, -4, -2, -6],\n [-4, 10, 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[[4, -8, 1, 6],\n [-4, 5, 0, -5],\n [-8, -14, 8, -2],\n [8, 2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 16, -16, 4],\n [16, 16, -16, 4],\n [4, 4, -4, 1],\n [12, 12, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -6, -1, 6],\n [-4, 6, 1, -6],\n [12, -12, 0, 12],\n [6, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 4, -8, 0],\n [0, 0, 0, 0],\n [8, 4, -8, 0],\n [12, 6, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 4, -4, -3],\n [16, -16, 16, 12],\n [0, 0, 0, 0],\n [8, -8, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 8, -6, 6],\n [-7, -12, 10, -11],\n [-6, -8, 6, -6],\n [-2, -10, 2, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 13, 4, 11],\n [4, 13, 16, 18],\n [4, 3, 0, 2],\n [-18, -6, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 8, -16, 16],\n [6, 6, -12, 12],\n [2, 2, -4, 4],\n [2, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -9, -8, 3],\n [0, 9, 12, 9],\n [16, 9, 4, -15],\n [0, 3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 4, -4, 16],\n [0, -4, 22, 8],\n [5, 3, -24, -16],\n [3, 1, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -11, -21, -3],\n [-6, 16, 12, 3],\n [3, 2, 0, 0],\n [-1, 3, -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 4x4 matrix:\n[[-2, -2, -12, -8],\n [-6, 2, -20, -16],\n [6, -8, 8, 10],\n [-6, 9, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -1, 2],\n [12, -12, -3, 6],\n [-4, 4, 1, -2],\n [-12, 12, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -4, -16, -16],\n [-3, -1, -4, -4],\n [-6, -2, -8, -8],\n [6, 2, 8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 2, 24, -1],\n [9, -1, 16, -4],\n [-5, 3, -4, 6],\n [-15, 2, -16, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 4, 0, -2],\n [-9, -6, 0, 3],\n [-9, -6, 0, 3],\n [-9, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -7, -4, 18],\n [19, -2, -7, -6],\n [3, 4, -10, 1],\n [-9, -7, -4, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 6, 6],\n [0, 0, -6, -6],\n [0, 0, 3, 3],\n [0, 0, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, -6, -6],\n [0, 0, 0, 0],\n [12, 0, 9, -9],\n [4, 6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -3, 0, 3],\n [-12, -16, -4, 4],\n [0, -6, 0, 6],\n [3, -8, 1, 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 4x4 matrix:\n[[-8, 10, 2, -15],\n [-2, 22, -4, -9],\n [1, -18, 7, 9],\n [7, -14, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -6, -4, 2],\n [-4, 12, 8, -4],\n [-2, 6, 4, -2],\n [-1, 3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 20, -5, 3],\n [-7, -4, 1, -12],\n [-10, 22, -8, 32],\n [-8, -14, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -8, -6, 2],\n [6, -8, -6, 2],\n [3, -4, -3, 1],\n [-9, 12, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, -4, 1],\n [-12, 0, -12, 3],\n [8, 0, 8, -2],\n [12, 0, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 15, -13, -6],\n [-1, 2, 0, -4],\n [-2, 18, -18, -2],\n [-9, 1, 7, -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 4x4 matrix:\n[[-1, 4, 0, 1],\n [1, -4, 0, -1],\n [-2, 8, 0, 2],\n [1, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 12, 12, 4],\n [11, 3, -6, 7],\n [10, 2, 15, 2],\n [18, 2, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 12, 16, 0],\n [12, 12, 16, 0],\n [9, 9, 12, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -6, -5, -9],\n [1, 7, 7, 12],\n [-2, 10, 6, 12],\n [1, 1, 2, 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[[-20, 2, -24, -13],\n [4, -10, 0, 5],\n [8, 4, 12, 4],\n [10, 1, 13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -2, 2, -7],\n [-2, 5, -3, -9],\n [-28, 28, 12, 8],\n [-3, 10, -2, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -8, 8, -18],\n [-8, -4, 4, -9],\n [-4, 4, -4, -6],\n [12, 0, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [3, -12, 0, 6],\n [-4, 16, 0, -8],\n [-3, 12, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -3, -9, 1],\n [-5, 1, -1, -3],\n [-15, 17, 3, -15],\n [8, 8, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 3, -3, 0],\n [-3, -3, 3, 0],\n [9, 9, -9, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 0, 6, 6],\n [-6, 0, 6, 6],\n [6, 0, -6, -6],\n [-6, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -16, 4, -12],\n [-17, 16, -3, 17],\n [-1, 3, -1, 1],\n [-6, 13, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -9, 0, -3],\n [6, 9, 0, 3],\n [-8, -12, 0, -4],\n [-8, -12, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, -9, -14],\n [0, 8, 3, -3],\n [0, 6, -19, -4],\n [0, -13, 1, -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 4x4 matrix:\n[[0, -8, 0, 4],\n [0, 4, 0, -2],\n [0, 16, 0, -8],\n [0, -8, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 6, 6, -2],\n [20, 4, 8, -4],\n [10, 2, 4, -2],\n [13, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -2, 18, 14],\n [-20, 16, 2, 6],\n [-20, 18, -4, 4],\n [-24, 14, 6, 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[[0, -16, 0, 4],\n [0, -4, 0, 1],\n [0, 8, 0, -2],\n [0, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, 2, -8],\n [-6, -6, -2, 8],\n [-12, -12, -4, 16],\n [-3, -3, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 20, 20, 20],\n [12, 0, 0, 0],\n [-16, 0, 0, 0],\n [7, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 22, -8, 4],\n [10, 4, -16, -22],\n [4, 3, -4, -4],\n [11, 10, -8, -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, -4, -2, -6],\n [9, -6, -3, -9],\n [9, -6, -3, -9],\n [6, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -3, 0, 2],\n [0, 3, -9, -5],\n [0, 0, -12, -4],\n [0, 9, 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 4x4 matrix:\n[[-27, -9, -2, 15],\n [23, 10, -2, -12],\n [-21, -9, -10, 15],\n [2, 18, -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[[24, -6, -6, 19],\n [12, -5, -8, -2],\n [-8, -3, 0, -10],\n [-10, 2, 2, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [4, -4, -2, -4],\n [2, -2, -1, -2],\n [4, -4, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -2, -8, 4],\n [12, 3, 12, -6],\n [-8, -2, -8, 4],\n [-4, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-24, -4, 7, -5],\n [24, -16, -20, 10],\n [20, -12, -17, 14],\n [-8, 16, 14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 11, -6, 5],\n [-8, 1, -19, -9],\n [8, 6, -9, 3],\n [0, -8, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -6, 18, 0],\n [-4, 0, 10, -3],\n [-8, -10, 0, 9],\n [12, 16, 2, -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, 13, 14, -3],\n [0, -6, -8, 6],\n [0, -1, 2, -9],\n [0, -4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-3, -9, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-19, 9, 8, -5],\n [-10, 12, 7, 0],\n [18, -12, -15, 12],\n [0, 0, 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[[1, 11, 28, 2],\n [6, -3, -8, -5],\n [8, -2, -12, -11],\n [11, -2, -8, -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 4x4 matrix:\n[[0, -10, 16, -2],\n [0, -12, 24, -6],\n [0, 8, -20, 7],\n [0, 1, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 2, 1, 2],\n [4, 4, 2, 4],\n [8, 8, 4, 8],\n [-6, -6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -1, -7],\n [-6, 8, 19, 7],\n [-18, 0, 7, -1],\n [15, 6, 0, 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[[-10, 8, -6, 16],\n [0, -12, -1, -4],\n [14, 5, -4, -6],\n [-7, -18, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 10, 7, -5],\n [-3, 10, 7, -5],\n [-1, 7, 3, -4],\n [0, 22, 4, -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 4x4 matrix:\n[[15, -6, 0, 12],\n [1, 13, 7, 13],\n [4, 0, -11, 0],\n [4, -2, 18, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -4, -16, -8],\n [0, 0, 0, 0],\n [9, -3, -12, -6],\n [-9, 3, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 6, 17, 20],\n [11, 0, 12, 4],\n [7, -3, -10, -12],\n [17, -9, 0, -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 4x4 matrix:\n[[-14, 20, -2, 4],\n [19, -8, -10, 4],\n [-25, 12, 5, 4],\n [14, 8, -5, -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[[-3, -20, -14, -4],\n [-10, -10, 5, 19],\n [13, 22, 7, -13],\n [-8, -10, 11, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 0, -2, 2],\n [-9, 0, -6, -6],\n [0, 0, 11, 5],\n [9, 0, -5, 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 4x4 matrix:\n[[-4, -3, -15, -4],\n [4, 1, 21, 4],\n [-4, -4, -12, -4],\n [-3, -2, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, -10, 4, -7],\n [-10, 12, -4, 10],\n [-14, 20, -6, 18],\n [6, -12, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 0, 3, -12],\n [10, 0, -12, 6],\n [12, 0, -12, 0],\n [-10, 0, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 0, -1, 1],\n [8, 0, -4, 4],\n [-6, 0, 3, -3],\n [2, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -14, 12, -2],\n [-4, 16, -8, 4],\n [4, 2, 4, 2],\n [-7, 10, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 0, 10, -3],\n [15, 1, -7, 12],\n [5, -1, 8, 15],\n [1, 3, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -3, -9, -7],\n [-16, -1, -11, -5],\n [-20, 0, -12, -4],\n [18, -2, 8, 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[[4, -16, -8, -16],\n [0, 0, 0, 0],\n [-4, 16, 8, 16],\n [3, -12, -6, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 6, -3, -12],\n [9, 0, 1, 12],\n [24, -4, 4, 32],\n [-36, -5, -10, -38]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, -14, -14],\n [-24, -20, -1, -1],\n [8, 8, 6, 6],\n [4, 8, 20, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-4, -4, -2, -2],\n [-12, -12, -6, -6],\n [12, 12, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, 24, 16],\n [-10, -1, -2, -3],\n [6, -13, 14, 1],\n [12, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -12, -10, -7],\n [5, -16, -14, -7],\n [11, -20, -8, -10],\n [-5, 16, 14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -1, -2, -11],\n [3, -3, -6, -6],\n [6, -8, -16, -2],\n [4, 2, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-9, 0, -12, -3],\n [6, 0, 8, 2],\n [-9, 0, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -9, -9, 9],\n [-16, 12, 12, -12],\n [4, -3, -3, 3],\n [-8, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 2, 4, -25],\n [6, 2, -6, 10],\n [-9, -5, -3, -10],\n [-24, -8, 24, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-8, 14, -1, -22],\n [12, 9, 4, -2],\n [13, 11, 8, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -1, 9, 4],\n [-7, 10, 16, 9],\n [-9, -3, 9, -9],\n [10, -16, -14, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 22, 9, 12],\n [-12, 16, 0, 12],\n [-9, 18, 9, 9],\n [9, -16, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 8, 7, 22],\n [2, -6, 12, 16],\n [-2, -5, 7, -6],\n [1, 15, 0, -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[[-19, 3, 24, 30],\n [-14, -2, 24, 15],\n [-1, 0, 3, -3],\n [3, 2, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 16, -8, -20],\n [-19, -3, -12, 10],\n [9, -13, 12, 14],\n [23, -9, 28, -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[[-16, -16, 4, -4],\n [4, 4, -1, 1],\n [-16, -16, 4, -4],\n [-16, -16, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, 0, 6],\n [-8, 0, 0, 12],\n [6, 0, 0, -9],\n [4, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -16, -12, -8],\n [0, 10, 1, -8],\n [-8, 2, -5, -12],\n [-4, -8, 17, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -1, -2, 3],\n [20, 6, -16, 10],\n [12, -3, -6, 9],\n [5, 7, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -12, 9, 9],\n [-6, 12, -9, -9],\n [-2, 4, -3, -3],\n [-4, 8, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -11, -4, -5],\n [-9, -2, 6, -1],\n [8, -7, 16, 5],\n [-5, -4, 8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 1, -4, 1],\n [12, -4, 16, -4],\n [3, -1, 4, -1],\n [3, -1, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 15, -19, -7],\n [-3, 19, -15, -7],\n [-2, -7, 8, 0],\n [7, 10, -11, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 16, -28, -12],\n [2, -4, 15, 5],\n [-20, -12, -7, 2],\n [8, 12, -17, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -13, -20, 0],\n [-12, 0, 8, -2],\n [6, -7, -14, 6],\n [18, -4, -18, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 16, 12, -8],\n [-8, -4, 12, -8],\n [-8, 4, 18, -12],\n [0, 16, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -6, 9, 12],\n [-10, -4, -6, 0],\n [-4, -16, 12, 24],\n [-3, 6, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 10, -6, 2],\n [0, 8, 30, -14],\n [-18, 8, -14, 10],\n [-6, 2, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -1, -7, -14],\n [4, 2, 2, -8],\n [-2, 8, 20, -12],\n [2, 6, 19, 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[[3, 3, 1, 0],\n [-12, -12, -4, 0],\n [12, 12, 4, 0],\n [-9, -9, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 3, -4, 1],\n [-1, 3, -4, 1],\n [1, -3, 4, -1],\n [-1, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -14, 1, 12],\n [-10, -12, 6, 12],\n [-4, -6, -6, 3],\n [3, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 4, -4, 24],\n [-4, 0, -2, 20],\n [0, -4, 2, -4],\n [-1, -13, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 12, -12, 13],\n [4, 8, 26, 8],\n [26, -14, -8, -19],\n [-30, 0, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 0, 4, 0],\n [1, 0, 4, 0],\n [-4, 0, -16, 0],\n [2, 0, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -1, -7, -2],\n [10, 8, 6, -4],\n [-1, -5, 5, 6],\n [5, 7, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -14, -11, 15],\n [-6, 0, -5, -11],\n [12, -4, 4, 20],\n [9, -13, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -18, 17, 9],\n [-16, -20, 20, 12],\n [6, 6, -9, -9],\n [-2, 0, 5, 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 4x4 matrix:\n[[-2, -19, 9, -22],\n [14, 8, 12, 4],\n [0, -5, 3, -6],\n [-2, -4, 0, -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 4x4 matrix:\n[[12, -6, 3, 9],\n [8, -4, 2, 6],\n [12, -6, 3, 9],\n [8, -4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-12, -16, 16, 12],\n [3, 4, -4, -3],\n [-6, -8, 8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [4, 0, -4, -1],\n [-12, 0, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -4, -2, 1],\n [0, -8, -4, 2],\n [0, -12, -6, 3],\n [0, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 4, -6, -4],\n [-1, -2, 3, 2],\n [-1, -2, 3, 2],\n [1, 2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -3, -3, 3],\n [6, 6, 6, -6],\n [-9, -9, -9, 9],\n [-6, -6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -15, -22, -26],\n [9, -12, -9, -12],\n [-14, 10, -16, -16],\n [-20, -8, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 1, -4, -5],\n [8, 2, -8, -2],\n [10, 1, 11, 1],\n [-24, -3, -9, 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 4x4 matrix:\n[[2, 3, -2, -4],\n [-4, -6, 4, 8],\n [0, 0, 0, 0],\n [-4, -6, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -3, 9, 6],\n [-12, 3, -9, -6],\n [12, -3, 9, 6],\n [-16, 4, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 16, 11, 25],\n [-8, -18, -4, 0],\n [8, -12, -9, -17],\n [8, -2, -6, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -8, -8, -16],\n [6, -4, -4, -8],\n [6, -4, -4, -8],\n [12, -8, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, 6, -12],\n [0, 0, 0, 0],\n [-2, 0, 2, -4],\n [-6, 0, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [6, -4, 4, 2],\n [-12, 8, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 14, 13, 4],\n [-1, -2, 1, -12],\n [13, -14, -13, -4],\n [12, -12, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -14, -9, -7],\n [-19, -8, -9, -31],\n [11, 12, -3, 11],\n [0, 6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 0, 4, -4],\n [-3, -4, -8, 6],\n [0, 6, 9, -6],\n [0, -8, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -18, 4, -8],\n [9, 0, 20, -10],\n [-1, 14, 4, -9],\n [-16, 8, -20, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 7, 24, -29],\n [0, 26, 15, -16],\n [-4, 19, -9, 13],\n [-22, 20, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 3, 1, 1],\n [6, -3, -1, -1],\n [0, 12, 10, -2],\n [4, -6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -18, 9, -10],\n [28, 6, -15, -2],\n [12, 4, -7, 0],\n [-16, -12, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 0, -4, 1],\n [9, 0, 12, -3],\n [9, 0, 12, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 12, -8, 12],\n [-8, 12, -8, 12],\n [6, -9, 6, -9],\n [-8, 12, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-16, 12, -4, -4],\n [-12, 9, -3, -3],\n [-4, 3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -12, -12, 26],\n [-8, 10, 21, -31],\n [13, -5, 17, -10],\n [-15, 3, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, -1, 4],\n [-2, -2, -6, -12],\n [-5, -6, -4, 6],\n [0, 2, 5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 10, 4, -2],\n [0, -20, -32, -2],\n [-10, 0, 12, 6],\n [-5, 0, -12, -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 4x4 matrix:\n[[8, 24, 8, 16],\n [14, -26, 9, 0],\n [0, -5, -2, 11],\n [-6, 8, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 2, -4, 2],\n [0, 0, 0, 0],\n [-8, 2, -4, 2],\n [-16, 4, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -13, -4, -2],\n [-4, -17, -16, -8],\n [4, 28, 24, 12],\n [-7, 6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 1, 2, -2],\n [10, 14, 12, 2],\n [-9, 25, 16, 13],\n [-20, -8, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -8, -2, 4],\n [0, 4, 1, -2],\n [0, 8, 2, -4],\n [0, -12, -3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 31, 38, -26],\n [9, -21, -24, 15],\n [-14, 14, 14, -7],\n [4, 11, 14, -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[[2, 2, -7, -7],\n [6, -6, 12, 12],\n [12, 4, -20, -20],\n [-12, 8, -13, -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[[-4, -5, -5, -6],\n [-16, -10, -10, -4],\n [12, 3, 3, -6],\n [0, -8, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 4, 0, -4],\n [0, 0, 0, 0],\n [4, -4, 0, 4],\n [4, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 2, -1, -2],\n [3, 6, -3, -6],\n [-2, -4, 2, 4],\n [-3, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -8, 8, -6],\n [-1, -4, 4, -3],\n [0, 0, 0, 0],\n [1, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -8, -16, 12],\n [-8, -4, -8, 6],\n [-8, -4, -8, 6],\n [-16, -8, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 4, 2, 4],\n [-3, 4, 2, 4],\n [9, -12, -6, -12],\n [9, -12, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 4, -6, -2],\n [0, 0, 0, 0],\n [2, -2, 3, 1],\n [-6, 6, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 2, -4, 2],\n [12, -3, 6, -3],\n [-12, 3, -6, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -2, 1, 4],\n [0, 0, 0, 0],\n [6, -6, 3, 12],\n [-4, 4, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[17, -3, 4, -15],\n [25, -15, -13, -30],\n [-10, -2, -4, 6],\n [2, -2, 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 4x4 matrix:\n[[3, -9, 20, -11],\n [6, -18, 0, -12],\n [6, -18, 8, -14],\n [-2, 6, 8, 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 4x4 matrix:\n[[12, -15, 8, 8],\n [-8, 5, -4, -9],\n [-1, -19, 6, 0],\n [0, -11, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -2, 8, 4],\n [1, 1, -4, -2],\n [1, 1, -4, -2],\n [-4, -4, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 8, -8, 0],\n [2, 4, -4, 0],\n [2, 4, -4, 0],\n [4, 8, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 4, 1, -4],\n [0, 0, -12, 12],\n [12, -16, 8, 4],\n [12, -16, 0, 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 4x4 matrix:\n[[8, 8, 8, 8],\n [0, 0, 0, 0],\n [-2, -2, -2, -2],\n [8, 8, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, -6, 8, -2],\n [0, -3, 4, -1],\n [0, 6, -8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 0, 12, -4],\n [6, 0, -9, 3],\n [8, 0, -12, 4],\n [2, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -8, -6, 2],\n [0, 0, 0, 0],\n [16, -16, -12, 4],\n [8, -8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -8, 8, 8],\n [0, 4, -4, -4],\n [0, 0, 0, 0],\n [0, -8, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, -8, 6],\n [-6, 6, -8, 6],\n [3, -3, 4, -3],\n [6, -6, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -12, 8, 8],\n [16, -16, 12, 6],\n [-10, 10, -12, 12],\n [19, -19, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 6, -15, -4],\n [-2, 5, -2, -1],\n [0, -3, 3, 5],\n [16, -7, 19, -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[[-15, -14, -18, -2],\n [-3, 6, 6, 12],\n [-9, -6, -12, -6],\n [11, 0, 2, -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[[-4, 3, 1, -4],\n [-28, 21, 10, -7],\n [-24, 18, 9, -3],\n [-24, 18, 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 4x4 matrix:\n[[10, -6, 25, 18],\n [8, -1, 20, 16],\n [12, 15, 9, 0],\n [2, 2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -12, 12, 10],\n [6, -6, 0, -2],\n [18, 2, -16, -18],\n [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 4x4 matrix:\n[[0, 0, 0, 0],\n [9, -12, -6, -9],\n [-6, 8, 4, 6],\n [3, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 4, 4, 2],\n [-7, 7, 8, -1],\n [0, 0, -4, -10],\n [2, 0, -4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -6, -8, -4],\n [-12, -13, -13, -3],\n [4, -1, 3, 5],\n [-8, -6, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -3, 1, -4],\n [9, 9, -3, 12],\n [-12, -12, 4, -16],\n [12, 12, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 1, -5, -13],\n [22, -6, 4, 2],\n [-17, 7, 11, 13],\n [-4, 0, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 19, -14, 5],\n [-10, 4, -20, -19],\n [20, 28, 16, 26],\n [4, -10, 22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -5, 16, 20],\n [10, 10, 2, -24],\n [10, 0, 13, 9],\n [6, -12, -4, -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[[-1, -14, 6, -5],\n [-15, 6, 6, 7],\n [-8, 8, -8, 4],\n [-6, 12, 2, 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 4x4 matrix:\n[[6, -21, 10, 9],\n [2, 29, -8, -7],\n [8, -16, 1, -3],\n [-12, -15, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -1, 1, 2],\n [-6, 3, -3, -6],\n [-6, 3, -3, -6],\n [-4, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 20, -20, 20],\n [16, 10, -15, 15],\n [-13, -7, 11, -11],\n [13, 7, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 2, 4, 3],\n [-8, 8, 16, 12],\n [-6, 6, 12, 9],\n [4, -4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 0, -4, -4],\n [0, -16, -4, 20],\n [-14, 12, 17, -1],\n [-2, -8, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 4, -2, -6],\n [12, 20, 8, 4],\n [0, -14, -11, -13],\n [-6, 4, 7, 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 4x4 matrix:\n[[3, -6, 3, -6],\n [2, -4, 2, -4],\n [1, -2, 1, -2],\n [-4, 8, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 12, 9, 7],\n [3, -3, 0, -13],\n [0, 3, 3, -2],\n [-1, 6, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -2, -9, 26],\n [-2, 2, -3, 6],\n [-2, -4, -6, 36],\n [8, -2, 7, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -4, -16, 12],\n [-6, 2, 8, -6],\n [-3, 1, 4, -3],\n [-12, 4, 16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, -9, -6, 2],\n [20, -16, 8, -12],\n [-19, 15, -6, 10],\n [14, -11, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 4, -3, -11],\n [-12, 8, -12, 8],\n [8, -16, 0, 8],\n [-20, 16, -12, 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[[-28, 8, -12, 4],\n [12, 4, 4, -16],\n [-8, -7, -2, 19],\n [-3, -1, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 1, 13, 2],\n [16, 5, 5, 10],\n [-8, -5, 15, -10],\n [-28, -10, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 3, 3, -6],\n [-2, 3, 0, -2],\n [-10, -9, -12, 22],\n [0, 12, 6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 3, -4, 2],\n [2, 3, -4, 2],\n [6, 9, -12, 6],\n [-2, -21, 4, -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 4x4 matrix:\n[[2, 1, -2, -7],\n [-3, -4, 18, 8],\n [-2, 2, -16, 10],\n [-1, -2, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 16, -12, -12],\n [8, -16, 12, 12],\n [8, -16, 12, 12],\n [-6, 12, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 1, 0, -1],\n [-5, -2, 3, -3],\n [-9, -12, 9, -3],\n [-1, -6, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 0, 0, -6],\n [9, 0, 0, 9],\n [12, 0, 0, 12],\n [-9, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, -1, 2],\n [0, 4, 1, -2],\n [0, -8, -2, 4],\n [0, 12, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 0, -8, -3],\n [-6, -3, -9, -9],\n [24, -4, 20, 0],\n [16, -4, 12, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -1, 4, 1],\n [-15, 7, -28, 9],\n [7, -14, 4, 2],\n [0, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -4, 8, 4],\n [-8, -4, 8, 4],\n [-6, -3, 6, 3],\n [-8, -4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, -4, 12],\n [-2, -11, -9, -8],\n [-17, 1, -8, 24],\n [-6, -6, -10, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 1, -10, -7],\n [-10, -5, -4, -10],\n [10, 5, -2, 5],\n [12, 6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -9, 3, 3],\n [0, -9, 3, 3],\n [0, 9, -3, -3],\n [0, -9, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -20, -17, -11],\n [5, -8, -9, -11],\n [-2, 20, 19, 17],\n [-9, -12, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -21, -28, -8],\n [-17, 3, -6, -7],\n [2, 2, -4, -10],\n [0, 27, 26, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -16, 15, -9],\n [1, 3, -4, 2],\n [-10, -20, 14, -10],\n [-13, -19, 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[[-6, 7, -8, 3],\n [2, 3, -2, 3],\n [8, 12, -8, 12],\n [-14, 3, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -9, 3, -6],\n [0, 6, -2, 4],\n [0, -3, 1, -2],\n [0, -12, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 3, 9, -12],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [3, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -4, 3, 0],\n [-2, 8, -6, 0],\n [3, -12, 9, 0],\n [-1, 4, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -5, 2, -6],\n [4, -16, -22, 10],\n [-1, -2, 5, 6],\n [-8, 17, 19, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 6, -3, 0],\n [-8, 8, -4, 0],\n [-8, 8, -4, 0],\n [6, -6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-4, 0, 1, 4],\n [8, 0, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -9, -2, -9],\n [-6, -18, 16, -18],\n [8, -7, -2, 9],\n [-6, -1, 8, 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, -9, -2, -3],\n [-14, 6, 27, 21],\n [-24, 21, 40, 33],\n [-12, -2, 15, 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[[12, 9, 3, -12],\n [-8, -6, -2, 8],\n [16, 12, 4, -16],\n [-16, -12, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [3, 9, 12, 3],\n [-1, -3, -4, -1],\n [-3, -9, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 4, 4, -2],\n [0, 4, 4, -2],\n [0, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -16, -8, -4],\n [9, -12, -6, -3],\n [0, 0, 0, 0],\n [9, -12, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -1, 1, 0],\n [16, 4, -4, 0],\n [16, 4, -4, 0],\n [-16, -4, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -12, -27, 2],\n [-6, -9, -9, 6],\n [-6, -11, -1, -10],\n [-8, -14, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 6, 12, 6],\n [16, 8, 16, 8],\n [-8, -4, -8, -4],\n [8, 4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 2, -6, -4],\n [11, 1, -3, 6],\n [15, 1, -3, 8],\n [-2, -2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -9, 12, -9],\n [16, 12, 6, 2],\n [8, 15, -2, 8],\n [-8, -18, 16, -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 4x4 matrix:\n[[0, 16, -16, -16],\n [0, 0, 0, 0],\n [0, 16, -16, -16],\n [0, 8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 4, 4, 4],\n [0, 0, 0, 0],\n [-2, 1, 1, 1],\n [-6, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -12, -12, -6],\n [6, 12, 12, 6],\n [-6, -12, -12, -6],\n [4, 8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -4, -3, -1],\n [-6, -8, -6, -2],\n [0, 0, 0, 0],\n [3, 4, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -4, 2, -2],\n [3, -2, 2, 0],\n [9, -12, 18, 6],\n [-9, 4, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-6, 6, 0, -2],\n [-6, 6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 6, 3, 12],\n [-6, 4, 2, 8],\n [-9, 6, 3, 12],\n [9, -6, -3, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 7, 3, 3],\n [3, -7, -3, -3],\n [0, 8, 0, 0],\n [-6, 0, 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[[-20, -16, -20, 20],\n [-5, -7, -5, 5],\n [-17, -13, -17, 17],\n [8, 10, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 4, -8, -6],\n [-3, 6, -12, -9],\n [4, -8, 16, 12],\n [4, -8, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, 22, 2, 15],\n [36, 16, -2, -8],\n [-9, 7, 4, 2],\n [-5, -8, -4, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 20, 8, 2],\n [6, 17, 9, 0],\n [-4, 26, 10, 0],\n [24, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 6, -4, 8],\n [12, -9, 6, -12],\n [0, 0, 0, 0],\n [12, -9, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 21, 1, 20],\n [6, -7, -5, -10],\n [16, -4, -23, -14],\n [-4, 14, -7, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, 0, 4],\n [-29, -19, -11, 4],\n [-6, -2, -7, 9],\n [-9, -3, -8, 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 4x4 matrix:\n[[-3, 0, 12, -9],\n [4, 0, -16, 12],\n [4, 0, -16, 12],\n [-3, 0, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-8, 0, -2, 6],\n [0, 0, 0, 0],\n [-4, 0, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 12, 4, 16],\n [0, 0, 0, 0],\n [-2, 3, 1, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [12, -6, 3, 12],\n [8, -4, 2, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 10, -1, -7],\n [0, 2, 6, -18],\n [-10, -6, 0, 0],\n [7, 6, 1, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -16, 16, 4],\n [-1, -14, 23, 8],\n [-15, -3, 3, 3],\n [-8, 20, -20, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 8, -8, -2],\n [4, 16, -16, -4],\n [-1, -4, 4, 1],\n [3, 12, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -8, 12, 12],\n [0, 0, 0, 0],\n [-4, 4, -6, -6],\n [-2, 2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -8, -11, 8],\n [-3, 2, 2, 0],\n [6, -4, 0, 16],\n [12, -16, -27, 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 4x4 matrix:\n[[-16, 8, 0, 12],\n [16, -8, 0, -12],\n [16, -8, 0, -12],\n [4, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -10, 8, 14],\n [-6, 8, 2, 0],\n [10, -16, 2, 8],\n [-4, 6, 0, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [4, -4, -12, 16],\n [-1, 1, 3, -4],\n [4, -4, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -16, 22, -14],\n [-2, -6, 6, -2],\n [-28, 28, -40, 28],\n [-31, 3, -15, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 3, -9, 6],\n [8, -6, 12, -8],\n [-13, 12, -15, 10],\n [4, -3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 6, 1, 1],\n [-25, -1, -18, -15],\n [-8, -2, -1, -2],\n [-6, -4, 0, 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[[11, 9, 17, -11],\n [-7, 12, -4, 2],\n [-6, -10, -18, 14],\n [3, 10, -6, 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[[-14, -1, 11, -5],\n [20, -19, -24, 14],\n [8, 9, 2, -2],\n [12, 0, -6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, -4, 0],\n [-7, 20, -8, 4],\n [7, -20, 8, -4],\n [5, -4, 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[[8, -24, -12, -8],\n [22, -3, 16, 6],\n [6, 0, 5, 2],\n [-6, 9, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -4, 6, -8],\n [2, 2, -3, 4],\n [-4, -4, 6, -8],\n [-6, -6, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 23, 34, -1],\n [-2, 14, 14, 0],\n [-8, -2, 8, 1],\n [6, 0, -6, 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[[-4, -8, -16, 16],\n [0, 0, 0, 0],\n [3, 6, 12, -12],\n [1, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -3, -1, -4],\n [-4, 12, 4, 16],\n [0, 0, 0, 0],\n [-4, 12, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 3, -9, 7],\n [9, 5, -6, -15],\n [-17, -21, 6, 11],\n [-19, -19, 18, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -2, -8, -5],\n [24, 8, -10, 0],\n [24, 20, -6, 8],\n [-8, 7, -16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -4, 8, -4],\n [-6, 4, -8, 4],\n [12, -8, 16, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -8, -4, 8],\n [-3, 6, -6, 9],\n [3, 2, 4, -7],\n [-1, -18, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -9, 0, 0],\n [-2, 1, -2, -3],\n [-13, -7, -4, -6],\n [20, 8, 8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 13, -5, 8],\n [-8, -6, -9, 4],\n [5, 12, 12, -1],\n [-5, 14, -6, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 0, 0, 4],\n [-3, 0, 0, -1],\n [-9, 0, 0, -3],\n [6, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -6, -12, 0],\n [3, 3, 0, 6],\n [4, 5, 3, 7],\n [2, 3, 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[[-21, 0, 3, -6],\n [16, -9, 5, -1],\n [1, -15, 12, -9],\n [16, -9, 5, -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 4x4 matrix:\n[[0, -16, 8, 16],\n [0, -16, 8, 16],\n [0, 16, -8, -16],\n [0, 12, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 3, -1, -3],\n [4, 6, -2, -6],\n [-4, -6, 2, 6],\n [-8, -12, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -4, 16, 8],\n [-12, -4, 16, 8],\n [-9, -3, 12, 6],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -4, 4, -12],\n [6, 2, -2, 6],\n [-9, -3, 3, -9],\n [-9, -3, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -4, 4, 4],\n [-1, -2, 2, 2],\n [0, 0, 0, 0],\n [1, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 11, 6, -11],\n [11, 12, -3, -18],\n [-2, 10, 2, 16],\n [-20, -22, -10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -3, -12, -9],\n [1, -1, -4, -3],\n [-1, 1, 4, 3],\n [-3, 3, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -10, 9, 16],\n [24, 0, 8, -8],\n [8, -2, 5, 0],\n [4, 14, -15, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, -11, -4, -11],\n [-15, 10, -16, 15],\n [8, -13, -2, -13],\n [-4, 16, -28, 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[[-7, 20, 4, 1],\n [3, -22, -15, -9],\n [0, 6, 9, 12],\n [-2, 16, 14, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -2, 9, -1],\n [-18, 4, 18, -10],\n [6, 0, -6, 2],\n [0, 16, 0, -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[[1, -16, -9, -2],\n [5, -20, -12, 2],\n [-2, -8, -4, -4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, -4, 3],\n [3, -9, 2, 1],\n [3, -9, -9, 3],\n [16, 12, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -2, -1, -16],\n [-20, -1, 0, 14],\n [-24, -3, -3, 10],\n [24, 10, 17, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -13, 3, -10],\n [9, -26, 7, -6],\n [-3, -14, 4, 0],\n [-14, 13, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 3, -1, 1],\n [4, 12, -4, 4],\n [4, 12, -4, 4],\n [4, 12, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, -1, -11],\n [-13, 2, -8, -13],\n [-4, -8, -10, 10],\n [6, -4, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 1, 6, 4],\n [-5, 2, -8, 3],\n [19, -4, -20, -15],\n [8, -1, -18, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -6, 12, -10],\n [-8, 9, -14, 14],\n [-5, 3, -14, 7],\n [2, -3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 8, 6, 16],\n [11, 4, -7, 8],\n [15, -6, -7, -12],\n [-1, 7, -1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 10, -3, -13],\n [-3, -3, -4, 21],\n [-13, -14, 5, -13],\n [-6, 6, -16, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, -1, 4],\n [-4, -4, -1, 4],\n [8, 8, 2, -8],\n [-16, -16, -4, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 9, -12, 20],\n [-14, -11, 20, 0],\n [-18, 10, 8, -8],\n [-14, 3, 12, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 4, 4, -4],\n [2, -4, -4, 4],\n [8, -16, -16, 16],\n [2, -4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -13, 13, -17],\n [14, -7, -11, -5],\n [-4, -4, 16, -8],\n [12, -2, -18, 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 4x4 matrix:\n[[-11, -16, 6, 19],\n [-14, -8, -20, 6],\n [-1, -4, 20, 15],\n [-2, -16, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -12, 12, 3],\n [-2, 4, -4, -1],\n [0, 0, 0, 0],\n [-6, 12, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 4, -4, -6],\n [-9, -4, 7, 6],\n [3, 6, -7, -9],\n [-15, -8, 13, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -14, -2, -3],\n [-5, -11, -5, 9],\n [5, 5, -5, -6],\n [3, 11, 14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -12, -3, 12],\n [0, -8, -2, 8],\n [0, 12, 3, -12],\n [0, -16, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -8, -8, -4],\n [0, 0, 0, 0],\n [-12, 8, 8, 4],\n [-9, 6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -8, -4, 16],\n [-9, 2, -1, -2],\n [21, 2, 4, -7],\n [0, 4, 1, -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[[0, 6, 0, -2],\n [0, -3, 0, 1],\n [0, -9, 0, 3],\n [0, -3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -10, 0, -5],\n [4, 10, -10, 10],\n [2, 2, -4, 3],\n [-8, -8, 16, -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[[28, -11, -28, 4],\n [-4, 2, 4, -20],\n [-22, 6, 22, 14],\n [-6, 9, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-16, 0, -8, -12],\n [12, 0, 6, 9],\n [-8, 0, -4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 9, 6, -6],\n [2, 6, 4, -4],\n [1, 3, 2, -2],\n [-1, -3, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 2, 0, -3],\n [0, 0, 0, 0],\n [-4, 8, 0, -12],\n [-2, 4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 10, -19, 6],\n [0, -8, 20, -8],\n [-2, 2, 1, -2],\n [16, -24, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 2, -9, 6],\n [-7, -1, 1, 10],\n [-2, -6, 18, 4],\n [-3, 3, -11, 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[[18, 11, 2, -3],\n [-16, -5, 8, 11],\n [34, 17, 4, -5],\n [-4, 5, -21, -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 4x4 matrix:\n[[5, 4, 6, 25],\n [-2, 8, 12, 14],\n [5, 4, 6, 25],\n [6, -8, -12, -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 4x4 matrix:\n[[-4, -12, -6, -14],\n [-8, -12, -6, 2],\n [0, -6, -3, -15],\n [-12, -18, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -6, -6, 0],\n [2, -8, -2, -10],\n [4, 8, 2, 6],\n [7, 2, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 9, 7, -8],\n [3, -5, -10, -9],\n [-12, -1, 7, 18],\n [0, -7, -11, -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[[-8, -3, 28, 19],\n [-9, 31, 6, 4],\n [9, -15, -18, -12],\n [6, -27, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -1, 1, -1],\n [0, 2, -2, 2],\n [0, -3, 3, -3],\n [0, 3, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-2, -4, 4, 0],\n [-4, -8, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -19, 11, -32],\n [-4, -5, 7, 0],\n [11, -17, 13, -16],\n [-30, -3, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 14, -4, -6],\n [-2, -3, 4, 2],\n [7, 8, -18, -7],\n [3, 2, -10, -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[[-23, -9, 5, -4],\n [-9, -6, 4, 5],\n [-2, 0, -4, -1],\n [1, -12, 10, 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[[-2, 1, -8, -2],\n [18, 2, 3, -13],\n [17, 2, 5, -11],\n [-11, -4, -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[[9, 3, -9, 10],\n [9, -5, -11, 10],\n [8, 5, -2, 10],\n [4, -10, -9, 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[[-12, 12, -6, -3],\n [12, -12, 6, 3],\n [-4, 4, -2, -1],\n [12, -12, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -20, -8, -8],\n [8, -13, -11, -17],\n [5, -10, 1, 7],\n [-18, 8, 6, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 8, -4, -18],\n [9, 4, -2, 27],\n [3, 12, -6, 9],\n [-14, -24, 4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -9, -12, 0],\n [-8, -6, -8, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -4, 12, 4],\n [-4, 20, 4, 0],\n [12, -12, 4, 4],\n [-4, -12, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -12, -4, -10],\n [16, -12, -4, -4],\n [0, 0, 0, 0],\n [22, -12, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -20, 3, 1],\n [0, -18, -3, 7],\n [13, 10, 7, -15],\n [-3, 7, 8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 9, -16, 8],\n [19, 5, -2, -8],\n [14, 2, 8, -24],\n [-4, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 12, 12, -9],\n [6, 12, 12, -9],\n [0, 0, 0, 0],\n [4, 8, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, 9, -9],\n [4, 0, 6, -6],\n [6, 0, 9, -9],\n [-6, 0, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -2, 11, 8],\n [-4, 20, -12, -40],\n [-19, 0, -17, -10],\n [16, -3, 20, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -6, 3, -5],\n [17, 2, 17, 5],\n [20, 0, 16, 18],\n [10, 10, 12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -5, -6, 12],\n [3, -2, 3, 12],\n [-12, -7, -12, 12],\n [3, -2, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 8, -8, 0],\n [-8, 16, -16, 0],\n [-6, 12, -12, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 4, 0, -8],\n [6, -6, 0, 12],\n [8, -8, 0, 16],\n [-6, 6, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -3, -6, 7],\n [12, 12, 8, -12],\n [-7, 9, -10, 7],\n [2, -6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -8, -12, 16],\n [10, -20, -24, 16],\n [2, -1, 0, -4],\n [8, -14, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 19, 20, -19],\n [-2, 8, -23, 1],\n [24, 12, 14, -24],\n [22, 11, 6, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 8, 16, -4],\n [6, 4, 8, -2],\n [-6, -4, -8, 2],\n [12, 8, 16, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 16, 8, -8],\n [0, 16, 8, -8],\n [8, -8, 0, -12],\n [4, -12, -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[[24, 13, -24, -11],\n [20, -2, -15, -10],\n [4, 1, -6, 3],\n [-18, -1, 16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 2, 20, -10],\n [-18, 23, -6, 12],\n [-9, -8, -12, 4],\n [5, 11, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -8, 16, 8],\n [11, 4, 16, 8],\n [4, 8, -4, -2],\n [-2, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, 12, -16],\n [0, -3, 9, -12],\n [0, -1, 3, -4],\n [0, 1, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, 2, 1],\n [8, -4, 4, 2],\n [0, 0, 0, 0],\n [12, -6, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 2, 16, -4],\n [-3, 1, 4, 1],\n [-3, -6, -12, -15],\n [-5, -3, -4, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -2, 4, -8],\n [-12, 3, -6, 12],\n [-16, 4, -8, 16],\n [8, -2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 4, 9, 7],\n [-2, -2, -2, 4],\n [-10, 2, 8, 14],\n [8, -8, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -2, 8, 8],\n [3, -1, 4, 4],\n [0, 0, 0, 0],\n [-12, 4, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 6, -12, -12],\n [2, -4, 8, 8],\n [-4, 8, -16, -16],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, 4, -4],\n [4, 4, -4, 4],\n [-12, -12, 12, -12],\n [-4, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 4, -6, 8],\n [-6, 4, -6, 8],\n [9, -6, 9, -12],\n [-3, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-22, 16, 10, -4],\n [21, -12, -3, 6],\n [9, -12, -15, -2],\n [-12, 12, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, 9, 6],\n [-4, -4, -6, -4],\n [8, 8, 12, 8],\n [2, 2, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 6, -4, -2],\n [12, 0, -11, -7],\n [4, -8, -13, -7],\n [16, 7, -32, -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[[-12, -6, -3, -3],\n [-12, -6, -3, -3],\n [12, 6, 3, 3],\n [12, 6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -10, 8, -10],\n [0, 0, -3, 0],\n [12, -6, 3, -6],\n [-4, 2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, 15, 18],\n [25, -35, -19, 0],\n [-8, 16, 14, 6],\n [-24, 20, 3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 0, -2, -8],\n [3, -14, -11, 12],\n [1, -15, -16, 16],\n [-8, 7, -7, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -8, -12, 0],\n [-3, -2, -10, -15],\n [-2, 2, 1, -5],\n [0, -10, -9, 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[[-2, -2, -2, -4],\n [-2, -2, -2, -4],\n [6, 6, 6, 12],\n [-8, -8, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 0, 0, 4],\n [3, 0, 0, 6],\n [-4, 0, 0, -8],\n [-2, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-22, 2, 0, -4],\n [-21, -3, 6, -9],\n [0, -18, 22, -19],\n [16, -8, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 12, -12, -12],\n [6, -6, 6, 6],\n [0, 0, 0, 0],\n [-12, 12, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 19, -1, 2],\n [0, -6, 2, 4],\n [-2, 7, -1, -1],\n [-6, 24, -4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 1, 2, -2],\n [3, 1, 2, -2],\n [-12, -4, -8, 8],\n [12, 4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -8, -2, 8],\n [4, -16, -4, 16],\n [-2, 8, 2, -8],\n [1, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 3, 0, -4],\n [3, -9, 9, 8],\n [-9, 7, -12, -4],\n [0, 16, -12, -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[[-22, -8, -4, -12],\n [4, 3, 2, 1],\n [-13, 3, 4, -13],\n [-13, 3, 4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -14, -15, 9],\n [6, 15, 9, -11],\n [-5, -11, -4, 8],\n [12, 20, 6, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, 11, -6, -13],\n [7, -11, 6, 13],\n [-5, 19, -12, -17],\n [2, 8, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -12, -4, 12],\n [-2, 6, 2, -6],\n [3, -9, -3, 9],\n [-2, 6, 2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 12, 0, -16],\n [4, 12, 0, -16],\n [-3, -9, 0, 12],\n [-2, -6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 11, 23, -18],\n [10, 1, -2, -11],\n [2, -2, 10, 20],\n [19, -3, -12, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 12, 15, 7],\n [4, -16, -3, -15],\n [-8, -16, -12, -12],\n [-14, 4, -9, 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[[4, -12, 4, 12],\n [4, -12, 4, 12],\n [2, -6, 2, 6],\n [-3, 9, -3, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, -8, -2],\n [-9, -8, 0, 19],\n [-13, 16, 28, 7],\n [8, -12, -17, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 11, -8, -1],\n [-3, -12, 9, 3],\n [-5, -6, 5, 5],\n [1, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 7, 2, -2],\n [-1, 2, 3, 1],\n [11, -12, -1, 5],\n [11, -7, 15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, -2, 5, 2],\n [3, -10, 12, -2],\n [-7, 0, 1, 2],\n [14, 4, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, -5, -23, 7],\n [-25, -13, -18, 14],\n [0, -19, 5, -21],\n [-4, -5, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -10, 18, 7],\n [-3, 1, -14, -11],\n [-11, 1, -20, -15],\n [-9, 1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 6, 4, -5],\n [21, -18, -20, 20],\n [-8, 11, 18, -11],\n [-6, 8, 16, -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[[-8, -5, -13, -2],\n [18, 2, -19, -8],\n [-16, 6, 6, 4],\n [-10, -24, -5, 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 4x4 matrix:\n[[-8, 12, 8, -12],\n [-2, 14, 0, -10],\n [-1, 7, 0, -5],\n [-2, 14, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -6, 4, 8],\n [-11, 7, -10, -2],\n [-14, 9, -9, 4],\n [3, -6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -12, -6, -3],\n [6, 12, 6, 3],\n [-6, -12, -6, -3],\n [-2, -4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 0, 5, -9],\n [2, 7, -4, 3],\n [11, 1, 3, -6],\n [1, -4, 3, -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 4x4 matrix:\n[[13, 14, -11, -13],\n [-6, -8, 6, 6],\n [-6, -8, 6, 6],\n [8, 9, -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[[-8, -26, -8, -7],\n [-3, 26, 5, 5],\n [-11, -28, -9, -8],\n [16, 16, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -1, 10, 9],\n [-9, -3, -4, 11],\n [-4, 0, -10, -6],\n [15, 7, 12, -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[[8, -6, 12, -8],\n [12, -4, 12, -16],\n [5, -5, 9, -4],\n [-1, 2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 16, 0, 0],\n [-16, 16, 0, 0],\n [4, -4, 0, 0],\n [-16, 16, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 4, -22, -9],\n [12, 32, -8, -12],\n [14, 4, -14, -3],\n [1, -12, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 2, 8, -2],\n [7, 9, 11, -2],\n [-12, -21, -24, 3],\n [-11, 10, 5, 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 4x4 matrix:\n[[-8, -13, 11, -10],\n [-6, -8, 6, -7],\n [-16, -12, 4, -16],\n [8, -1, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, -2, 1],\n [12, -6, -6, 3],\n [0, 0, 0, 0],\n [8, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 0, 9, 3],\n [-3, -10, -3, 7],\n [-1, -16, 6, 1],\n [-21, -6, 21, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 20, -18, 3],\n [3, 12, -18, -9],\n [-14, -4, 2, -13],\n [17, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -3, 8, -13],\n [-5, -9, -15, 13],\n [-4, -3, 2, -5],\n [1, -3, -13, 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[[2, 4, 2, 4],\n [4, 8, 4, 8],\n [-4, -8, -4, -8],\n [6, 12, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 10, 3, 3],\n [-9, -18, 0, 0],\n [3, 1, 10, 15],\n [-9, -28, -7, 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[[4, 2, 10, 10],\n [6, 12, 12, 12],\n [24, -18, 14, 14],\n [-4, -8, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 12, -12, 0],\n [9, -9, 9, 0],\n [-12, 12, -12, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -4, -4, -4],\n [3, -12, -12, -12],\n [0, 0, 0, 0],\n [-2, 8, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 11, 26, 3],\n [-2, 7, 19, 2],\n [-20, -14, 5, 9],\n [-10, 11, 15, 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[[4, -3, -5, -23],\n [-8, 0, 6, -3],\n [-5, 3, 5, -4],\n [1, -16, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 0, 6, 0],\n [9, 0, 6, 0],\n [-9, 0, -6, 0],\n [3, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 4, 12, -4],\n [4, -2, -6, 2],\n [4, -2, -6, 2],\n [6, -3, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -2, 1, -1],\n [12, 6, -3, 3],\n [-12, -6, 3, -3],\n [16, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -12, -1, 6],\n [17, -8, 24, 25],\n [12, -8, 17, 16],\n [-13, -14, -16, -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 4x4 matrix:\n[[-3, -1, 6, 5],\n [-14, -2, 16, 16],\n [-1, 1, -4, -2],\n [3, 1, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, 6, -9],\n [10, -6, 8, -4],\n [-10, -18, 4, 18],\n [-4, 0, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, 4, 2, -2],\n [1, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 2, -7, -6],\n [10, 17, -8, -16],\n [18, -3, 8, 8],\n [14, 14, 7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -9, 1, -16],\n [12, -12, 8, -8],\n [4, -2, -2, -8],\n [-1, -1, 4, 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, -1, -4, 3],\n [-1, -1, -4, 3],\n [4, 4, 16, -12],\n [2, 2, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -3, -9, 6],\n [0, 0, 0, 0],\n [2, -2, -6, 4],\n [-3, 3, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 16, 12, 0],\n [0, 0, 0, 0],\n [-4, 16, 12, 0],\n [1, -4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 0, 10, 2],\n [-20, -17, -2, 20],\n [-12, -11, -6, 12],\n [-14, -12, -2, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 12, 2, -5],\n [8, 20, 22, 9],\n [-8, -18, -16, -11],\n [4, 14, 12, 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 4x4 matrix:\n[[-10, 1, 9, 6],\n [10, 12, -22, -18],\n [-7, -11, 18, 15],\n [1, 9, -10, -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 4x4 matrix:\n[[15, 15, -4, -9],\n [-12, 6, 2, 18],\n [1, 12, -1, 6],\n [4, 18, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 16, 6, 4],\n [-1, -16, -7, -8],\n [0, -12, -6, -9],\n [-2, 4, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 6, -2, 8],\n [-16, -12, 4, -16],\n [4, 3, -1, 4],\n [-12, -9, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -3, -4, -4],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-8, 12, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 0, -2, -4],\n [16, 0, 8, 16],\n [12, 0, 6, 12],\n [8, 0, 4, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 3, 16, 18],\n [-20, 24, -12, 4],\n [7, -9, 7, 1],\n [-14, 18, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 9, -12, -3],\n [-8, 12, -16, -4],\n [0, 0, 0, 0],\n [8, -12, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, 4, 12],\n [0, -3, -6, -18],\n [-3, 1, 1, 8],\n [15, 3, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 4, -18, -2],\n [-23, -9, 4, 23],\n [20, 7, -28, -11],\n [-14, 4, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -18, 0, 9],\n [6, 8, -6, 9],\n [-5, -10, -9, 12],\n [-5, 10, 3, -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 4x4 matrix:\n[[2, -6, -6, 6],\n [3, -9, -9, 9],\n [-3, 9, 9, -9],\n [2, -6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -6, -16, 8],\n [-3, -4, 7, -10],\n [4, 5, -7, 12],\n [-9, 4, -1, -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[[6, -9, -6, -9],\n [-2, 3, 2, 3],\n [4, -6, -4, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 8, -2],\n [0, 0, -4, 1],\n [0, 0, 8, -2],\n [0, 0, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 18, -9, 5],\n [-8, -19, 8, 9],\n [9, 14, 5, -13],\n [-25, -15, 4, -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[[3, -12, -3, 3],\n [3, -12, -3, 3],\n [-1, 4, 1, -1],\n [-3, 12, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 1, 2, 1],\n [1, 1, 2, 1],\n [-2, -2, -4, -2],\n [-4, -4, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 3, -19, 17],\n [16, -5, -23, 15],\n [8, 9, -17, 11],\n [8, -4, -28, 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[[-14, -24, 4, 9],\n [0, -3, -24, -12],\n [4, 4, -24, -14],\n [6, 10, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 12, 6, -9],\n [4, 8, 4, -6],\n [-6, -12, -6, 9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 0, -20, -4],\n [15, -21, 1, -11],\n [-13, 21, -6, 10],\n [-11, 15, 0, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 6, 9, 12],\n [4, -8, -12, -16],\n [3, -6, -9, -12],\n [-1, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -8, 0, -4],\n [-16, 8, 0, 4],\n [16, -8, 0, -4],\n [-16, 8, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -8, 6, 6],\n [3, -12, 9, 9],\n [-1, 4, -3, -3],\n [-3, 12, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 0, -10, 4],\n [24, 15, 14, 1],\n [4, 4, 1, 15],\n [16, 9, 11, -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 4x4 matrix:\n[[-12, 4, -8, -16],\n [-3, 1, -2, -6],\n [0, 0, 0, 0],\n [-9, 3, -6, -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[[-16, 16, 8, -3],\n [-1, -17, -16, -3],\n [0, 11, 9, 7],\n [-12, 4, 0, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 5, -14, 4],\n [10, -3, -7, 6],\n [-4, 10, -6, -4],\n [9, 5, -14, 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[[0, -24, 0, 8],\n [-8, -16, 8, 0],\n [2, -8, -2, 4],\n [6, 24, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 2, -5, -14],\n [0, 18, -24, -6],\n [-32, 32, -20, -8],\n [8, -8, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 4, 14, 15],\n [21, -1, 1, -18],\n [-16, 3, 11, 9],\n [-15, 1, 2, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -10, 0, 4],\n [12, -6, 3, -3],\n [-2, 6, 2, -6],\n [25, 8, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 6, -16, 1],\n [-2, 8, 2, 28],\n [1, 0, 2, 25],\n [-3, 2, 12, 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[[0, -8, 6, 2],\n [0, 8, -6, -2],\n [0, 0, 0, 0],\n [0, 8, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 8, 3, -10],\n [-24, 10, 15, -12],\n [-8, -13, 6, 13],\n [-20, 6, 15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -4, -13, 0],\n [-1, 11, -2, 4],\n [2, 1, -10, -3],\n [-1, 5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, 2, -8],\n [-10, 6, -6, -6],\n [-6, 0, 2, -8],\n [-11, 12, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -2, 3, 3],\n [-9, -7, 6, 8],\n [-4, -2, 3, 3],\n [18, 14, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -12, -12, 12],\n [21, -16, -4, 14],\n [14, -12, -2, 10],\n [4, 2, -21, 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[[0, 9, -8, 3],\n [6, -9, 3, -9],\n [6, -12, 7, 0],\n [-8, 14, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -9, -6, 0],\n [-4, -17, 24, 2],\n [-7, 8, 19, -22],\n [0, 36, -10, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -4, -7, 0],\n [2, -10, -14, -14],\n [4, 0, -10, 8],\n [-4, -4, -17, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 12, -8, -8],\n [0, -6, 4, 4],\n [0, 3, -2, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -16, -4, 12],\n [-2, -8, -2, 6],\n [-4, -16, -4, 12],\n [-4, -16, -4, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 0, 9, -6],\n [-9, 0, -9, 6],\n [3, 0, 3, -2],\n [3, 0, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, 0, 6],\n [-8, 16, 8, -8],\n [5, -12, -6, 9],\n [5, -16, -8, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -16, 0],\n [0, -2, 4, 0],\n [16, 0, -8, 8],\n [6, 3, -9, 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 4x4 matrix:\n[[3, 7, -5, -12],\n [3, 1, -20, -21],\n [12, 12, -4, -24],\n [1, -1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, -12, 0],\n [2, 0, 6, 0],\n [0, 0, 0, 0],\n [-3, 0, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -4, -1, 6],\n [12, 9, -24, -22],\n [-26, 14, -4, 12],\n [-16, 4, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 4, -2, 1],\n [8, 16, -8, 4],\n [-4, -8, 4, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 6, 3, 12],\n [16, -8, -4, -16],\n [16, -8, -4, -16],\n [8, -4, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 8, -12, -12],\n [4, 10, -15, -21],\n [-9, -12, 20, 32],\n [-4, 32, -32, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, -1, -9, 5],\n [-19, -13, 18, -4],\n [-8, -11, -1, -1],\n [-15, -23, 1, 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 4x4 matrix:\n[[18, -12, -2, -18],\n [3, 8, 3, 2],\n [15, -8, -1, -14],\n [15, 4, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 2, -1, 3],\n [-4, -8, 4, -12],\n [0, 0, 0, 0],\n [-4, -8, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 8, 6, 4],\n [-6, 8, 6, 4],\n [-9, 12, 9, 6],\n [9, -12, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 6, -6, -6],\n [6, 0, 0, 8],\n [-9, -16, 16, 4],\n [6, 6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 6, 4, 6],\n [9, 9, 6, 9],\n [12, 12, 8, 12],\n [-6, -6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 2, 0, 2],\n [17, -4, -3, -1],\n [16, 10, 1, 9],\n [7, 10, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, 0, 16],\n [-3, 0, 0, 4],\n [6, 0, 0, -8],\n [-9, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 10, -6, -2],\n [5, -5, 6, 7],\n [10, 3, 1, 7],\n [3, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 3, 1, -4],\n [0, 0, 0, 0],\n [2, 3, 1, -4],\n [6, 9, 3, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -1, 8, 5],\n [-8, 2, -6, 0],\n [-24, 8, -8, 16],\n [7, -3, 4, -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[[0, 0, 0, 0],\n [-2, -2, -6, 0],\n [1, 1, 3, 0],\n [3, 3, 9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-23, 15, -9, 1],\n [10, -15, -12, 4],\n [15, -7, 21, -9],\n [11, -17, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 12, -12, -12],\n [28, 7, -10, -15],\n [-16, 19, 6, 1],\n [-3, -19, 0, 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[[5, 5, -4, 12],\n [-8, -6, 5, -17],\n [-12, 16, -10, 2],\n [-9, -3, 3, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [8, -4, -4, -4],\n [-6, 3, 3, 3],\n [-6, 3, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -14, 10, -1],\n [21, -12, -9, -19],\n [-8, 0, 8, 9],\n [8, -16, 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[[-8, 18, 8, 18],\n [-11, 7, 4, 9],\n [-12, 0, 6, 8],\n [1, 0, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 4, 2, 2],\n [3, 6, 3, 3],\n [-3, -6, -3, -3],\n [2, 4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 8, -6, 8],\n [-4, -4, 3, -4],\n [0, 0, 0, 0],\n [8, 8, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, 10, 16, -9],\n [8, 8, -14, 7],\n [-10, 8, 6, -14],\n [22, -2, -24, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 16, 0, -10],\n [28, -16, 28, 0],\n [-8, 16, -8, -7],\n [12, -28, 12, 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, 10, 5, 7],\n [6, -18, -21, -3],\n [2, -6, -7, -1],\n [-8, 22, 24, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -2, -3, -4],\n [-3, -2, 1, 10],\n [4, -12, -16, -17],\n [-4, 12, 16, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -27, 13, 17],\n [4, -9, -1, 4],\n [11, 11, -9, -9],\n [7, -33, 11, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -20, 20, -8],\n [4, 7, -11, 0],\n [-12, -10, 0, -11],\n [-16, -14, 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[[-1, -1, -3, 5],\n [2, 2, 0, 2],\n [2, 2, 6, -10],\n [-12, -12, -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 4x4 matrix:\n[[-12, -16, -12, -4],\n [9, 12, 9, 3],\n [9, 12, 9, 3],\n [6, 8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -4, 12, 8],\n [-4, 0, -2, -5],\n [4, -2, 8, 12],\n [-12, -3, 12, 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[[-1, 3, -2, -1],\n [-4, 12, -8, -4],\n [1, -3, 2, 1],\n [1, -3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -16, 14, 3],\n [8, -4, 6, 7],\n [-1, -6, -2, -17],\n [-8, 13, -2, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 11, -4, 14],\n [7, -1, 18, -18],\n [-15, 2, -15, 23],\n [4, -8, 18, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-32, -9, -3, 6],\n [-14, -1, 6, -9],\n [0, 9, -12, 4],\n [16, -4, 0, 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[[8, -12, -2, 14],\n [-20, 9, 5, -7],\n [12, -9, -3, 9],\n [-4, 0, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, -16, -4],\n [0, 0, 0, 0],\n [0, 1, 4, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -6, -14, 0],\n [3, 8, 18, 3],\n [0, 0, 0, 0],\n [8, 12, 28, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 0, -9, -9],\n [16, 0, 12, 12],\n [-16, 0, -12, -12],\n [12, 0, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -9, -17, 15],\n [3, 1, -4, -1],\n [15, 2, -20, 0],\n [-24, 4, 32, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-16, 8, -16, 0],\n [-12, -18, 12, 0],\n [-20, -14, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 6, 6, 0],\n [0, 12, 12, 0],\n [0, -12, -12, 0],\n [0, 12, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 8, -2, 2],\n [3, -4, 1, -1],\n [12, -16, 4, -4],\n [-6, 8, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -7, -16, 9],\n [-6, 5, 12, -12],\n [-3, -4, 0, -3],\n [-1, -7, -8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 4, -5, 23],\n [-4, 0, -16, 8],\n [6, -8, -26, -10],\n [3, -8, -17, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -3, 3, 9],\n [-8, 16, 12, -12],\n [0, -7, -7, 3],\n [10, -13, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -13, -4, -6],\n [-14, 16, 8, 8],\n [8, -6, -8, -4],\n [-6, -1, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 12, -3, 3],\n [6, -12, 3, -3],\n [-4, 8, -2, 2],\n [-2, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 9, 12, 19],\n [5, 5, 28, 7],\n [6, 6, -12, 16],\n [4, 4, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -11, 4, 6],\n [0, -15, -12, 12],\n [1, -8, -2, 3],\n [11, 11, 20, -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[[1, 14, 1, -3],\n [-7, 12, 5, 3],\n [-13, 10, 11, 9],\n [-6, -12, 10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 1, 1, 12],\n [3, 11, -5, 4],\n [-3, 24, -10, 16],\n [-12, -9, 5, 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 4x4 matrix:\n[[12, 8, 12, -4],\n [4, 0, 4, 12],\n [5, 4, 5, -5],\n [-6, -4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, -1, -5],\n [16, 16, 14, -7],\n [-4, -8, -15, 0],\n [-8, -10, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -6, 5, -1],\n [-3, -12, 9, -12],\n [0, -10, 8, -5],\n [-5, 10, -9, -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 4x4 matrix:\n[[4, -12, -16, -16],\n [12, 26, 13, 18],\n [14, -3, -5, -7],\n [20, 26, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 0, -3, 1],\n [-2, 12, 3, 11],\n [11, -2, -15, 1],\n [14, 4, -15, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -6, -5, 8],\n [-6, 6, 7, -4],\n [-10, 10, 13, -4],\n [-10, 10, 7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 5, 3, 2],\n [2, -19, -13, -8],\n [-14, 13, 19, 8],\n [2, -4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -3, -9, 3],\n [-6, -3, -9, 3],\n [1, 3, 4, -3],\n [-8, 1, -7, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 1, -4, 3],\n [0, 0, 0, 0],\n [1, 1, -4, 3],\n [1, 1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 0, 10, 12],\n [4, 14, -2, -20],\n [-3, 0, 3, 18],\n [-4, 2, -5, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 2, 0, 6],\n [-6, 2, 0, 6],\n [-3, 1, 0, 3],\n [-3, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, -4, 10, -9],\n [-8, -4, -8, 0],\n [-6, -2, 8, -6],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 1, -4, 2],\n [4, 1, -4, 2],\n [-12, -3, 12, -6],\n [-16, -4, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 2, -4, 0],\n [2, 2, -4, 0],\n [-2, -2, 4, 0],\n [4, 4, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 3, -12, -9],\n [2, -2, 8, 6],\n [-1, 1, -4, -3],\n [-1, 1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, -1, -1],\n [0, -4, 1, 1],\n [0, 0, 0, 0],\n [0, 16, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -10, -12, 14],\n [-21, 19, 26, -25],\n [20, 5, -18, 21],\n [0, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -4, -16, -4],\n [6, -2, -8, -2],\n [-12, 4, 16, 4],\n [3, -1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 18, -21, 9],\n [1, -8, 10, -5],\n [-2, -12, 14, -6],\n [1, 20, -24, 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[[-4, 2, 8, -8],\n [-4, 2, 8, -8],\n [2, -1, -4, 4],\n [6, -3, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -2, -1, -2],\n [7, -1, -1, -2],\n [6, -4, -2, -4],\n [17, -4, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 1, -15, 9],\n [-14, 6, -13, 5],\n [16, -14, 12, 0],\n [-18, 12, -15, 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[[0, 0, 0, 0],\n [12, -16, -16, -12],\n [12, -16, -16, -12],\n [9, -12, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 0, 6, 12],\n [-15, -3, 10, 5],\n [6, -1, -4, -13],\n [-12, 0, 8, 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 4x4 matrix:\n[[4, 6, 4, 4],\n [8, 12, 8, 8],\n [2, 3, 2, 2],\n [8, 12, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 4, -1, -4],\n [11, 9, -3, -9],\n [2, 22, 20, -22],\n [-4, -6, -5, 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, -7, -1, 6],\n [0, 0, 0, 0],\n [10, 19, 7, -22],\n [-10, -7, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 5, -8, -5],\n [-19, -7, -8, 4],\n [-16, -7, 1, 4],\n [-17, -7, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-4, -8, -8, 4],\n [-8, -16, -16, 8],\n [-6, -12, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 0, -16, -16],\n [12, 3, 13, 9],\n [6, -3, 11, 15],\n [21, 12, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 4, 4, 1],\n [-4, 4, 4, 1],\n [-16, 16, 16, 4],\n [-16, 16, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 10, -4, 6],\n [-4, 8, 0, 16],\n [-2, 5, 2, 17],\n [12, -20, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -6, -30, 24],\n [1, 6, 19, -17],\n [-5, -2, 1, -2],\n [-2, -4, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 15, -5, -12],\n [-4, -3, 1, 4],\n [-4, -3, 1, 4],\n [8, -12, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 12, 6, -5],\n [21, 5, -10, 7],\n [-29, 7, 12, -11],\n [-12, 6, 6, -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[[-5, -13, 0, -3],\n [-9, -26, -3, -10],\n [3, 9, 3, 12],\n [-7, -18, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 3],\n [8, 4, -2, -3],\n [-12, -6, 3, 4],\n [16, 8, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 0, -1, 1],\n [0, 0, 0, 0],\n [-12, 0, 4, -4],\n [9, 0, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 2, 8, 6],\n [14, -2, 8, 12],\n [10, -3, 4, 9],\n [-8, 9, 4, -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 4x4 matrix:\n[[4, 5, -9, -6],\n [4, 7, -15, -10],\n [12, 7, -3, -2],\n [-16, -12, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -7, 9, -5],\n [-8, -10, 6, 2],\n [0, 6, 0, -6],\n [0, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -8, 8, -6],\n [18, -1, -17, 12],\n [-10, 20, 4, -2],\n [-3, -4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 12, 8, 4],\n [0, -12, -8, -4],\n [0, -9, -6, -3],\n [0, 12, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 9, 0, 3],\n [-9, 9, 0, 3],\n [3, -3, 0, -1],\n [9, -9, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, 4, -19, 26],\n [8, 4, -8, 6],\n [4, 2, -2, 3],\n [11, 4, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -9, -9, -9],\n [-16, -15, 13, -7],\n [12, 12, -9, 6],\n [4, 9, 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[[-2, 10, -2, 8],\n [28, 12, 12, 8],\n [-24, -13, -20, -14],\n [-8, 2, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -3, 1, 1],\n [0, 0, 0, 0],\n [-3, -9, 3, 3],\n [-2, -6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -14, -28, -9],\n [3, 0, 0, 4],\n [9, 10, 20, 7],\n [6, -4, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -1, 3, -1],\n [-3, 3, -9, 3],\n [-1, -4, 11, -1],\n [6, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 1, -2, -1],\n [-4, -1, 2, 1],\n [-12, -3, 6, 3],\n [-16, -4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 19, 15, -13],\n [3, -21, -18, 12],\n [-1, 7, 6, -4],\n [-17, -6, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, -4, 4, -2],\n [7, 7, -14, 7],\n [2, -1, -2, 1],\n [-11, 17, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -8, -10, -16],\n [5, -12, -10, -4],\n [6, 0, -3, -12],\n [-6, 0, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 6, -3, 12],\n [-4, 2, -1, 4],\n [9, -3, 3, -5],\n [8, 2, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 19, 0, 5],\n [14, -12, 9, 4],\n [-25, 15, 3, -11],\n [10, -8, 6, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[33, 18, -25, -9],\n [-15, -14, 7, 5],\n [-8, -6, 4, 4],\n [17, 6, -17, -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, -9, 6, 3],\n [-12, -12, 8, 4],\n [-9, -9, 6, 3],\n [3, 3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 10, 5, -21],\n [-15, -2, -7, -9],\n [-3, 0, 3, -3],\n [-16, -8, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -9, -12, -9],\n [4, -6, -8, -6],\n [4, -6, -8, -6],\n [8, -12, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -2, 0, -15],\n [-13, -17, -12, 0],\n [2, 4, 4, 4],\n [-7, 22, -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 4x4 matrix:\n[[13, 15, 12, 16],\n [13, 15, 12, 16],\n [6, 2, 0, 8],\n [-10, -6, -3, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 30, 11, -17],\n [20, 41, 16, -22],\n [0, -2, -8, 14],\n [-4, 23, -8, -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[[3, 13, 15, 2],\n [9, 6, 9, -6],\n [-1, -8, -9, -2],\n [2, 16, 18, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 4, 0, 1],\n [1, -4, 0, -1],\n [2, -8, 0, -2],\n [-3, 12, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-1, 2, 4, 2],\n [-4, 8, 16, 8],\n [-2, 4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 8, 2, 12],\n [-1, -16, -1, -6],\n [17, 15, -9, -2],\n [6, 20, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 24, -20, -2],\n [-6, -13, 10, -1],\n [-8, -16, 12, -2],\n [-4, -6, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 0, 1, 3],\n [-3, 3, 0, 3],\n [4, -4, 0, -4],\n [4, -1, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 16, 4, -4],\n [3, 3, 6, 1],\n [-3, -9, -6, 1],\n [-1, -8, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -12, 4, -12],\n [1, 3, -1, 3],\n [-2, -6, 2, -6],\n [3, 9, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -4, 3, 2],\n [0, 16, -12, -8],\n [0, 12, -9, -6],\n [0, -8, 6, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -2, -4, 10],\n [15, -18, 20, -8],\n [-11, 14, -16, 7],\n [15, -6, 0, 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[[12, 14, 8, -13],\n [4, 6, 8, -1],\n [5, 4, -4, -10],\n [-13, -16, -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[[0, 0, 0, 0],\n [-4, 0, 0, -3],\n [12, 0, 0, 9],\n [-12, 0, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 5, 13, -3],\n [7, -13, -12, 0],\n [-31, 14, 6, 5],\n [-5, 2, -28, 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[[2, 7, -15, 33],\n [-6, -7, 5, -11],\n [6, 1, 7, -19],\n [6, 7, -9, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 16, -18, 8],\n [-6, 0, 6, 4],\n [-5, 8, -9, 4],\n [2, -8, 12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -3, 4, 3],\n [-3, 9, -12, -9],\n [2, -6, 8, 6],\n [2, -6, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 4, -5, -6],\n [13, -17, 24, 9],\n [-16, -6, 7, 12],\n [-5, 13, -18, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -6, 3, 6],\n [12, 6, -3, -6],\n [-12, -6, 3, 6],\n [-16, -8, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -20, -12, -24],\n [0, -15, -9, -18],\n [24, -8, 6, -12],\n [-12, -11, -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[[-14, -10, -20, 4],\n [-7, -4, -8, -4],\n [6, 6, 12, -12],\n [-15, -12, -24, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -24, -4, 0],\n [12, -3, 3, 0],\n [-12, -6, -3, 0],\n [-16, -6, -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[[-12, -13, 0, -1],\n [8, -12, -16, 20],\n [-1, -3, -1, -7],\n [-8, 8, 13, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -6, 4, 8],\n [-2, -6, 4, 8],\n [3, 9, -6, -12],\n [2, 6, -4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -3, -3, -12],\n [4, -4, -4, -16],\n [4, -4, -4, -16],\n [3, -3, -3, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -8, 6, 12],\n [-8, -6, 6, -6],\n [13, 5, -5, 19],\n [11, 8, -11, 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[[1, 11, 14, -3],\n [2, -18, 14, -10],\n [5, -5, 4, -11],\n [-6, 14, -29, 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, 32, -4, 23],\n [13, -8, 4, -23],\n [-8, -8, -14, 8],\n [0, -20, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -2, 11, 0],\n [11, 3, 6, 3],\n [19, 4, 14, 9],\n [-12, 0, -8, 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 4x4 matrix:\n[[-12, 2, -2, -14],\n [0, 6, 18, -16],\n [3, 7, 23, -13],\n [-3, -4, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -1, 14, -14],\n [0, 0, 0, 0],\n [-8, -2, 10, -10],\n [-3, -2, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 4, 1, 1],\n [-16, -16, -4, -4],\n [12, 12, 3, 3],\n [4, 4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, 15, 13, 13],\n [8, 24, 12, 18],\n [15, 2, 12, 4],\n [-3, 4, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -10, 7, -2],\n [5, 14, -13, 4],\n [7, -14, 7, -4],\n [19, -14, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 0, 6, 12],\n [16, 0, -8, -16],\n [-8, 0, 4, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -9, -3, 0],\n [-8, 12, 4, 0],\n [0, 0, 0, 0],\n [-6, 9, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -2, 0, -4],\n [-3, -6, 0, -12],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -32, 12, -24],\n [-10, 8, -3, 4],\n [11, -14, 9, -8],\n [-13, 14, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -12, 16, 4],\n [0, 3, -4, -1],\n [0, -12, 16, 4],\n [0, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 8, -6, 1],\n [-20, 2, -28, -2],\n [-15, 18, -6, 0],\n [19, -2, 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[[-7, 21, -4, -12],\n [-1, -21, 14, 12],\n [5, 11, -11, -14],\n [10, 1, -16, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 1, -1, -1],\n [0, 10, -2, 2],\n [-6, -9, 1, -3],\n [24, -4, 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[[12, 8, -8, 8],\n [9, 6, -6, 6],\n [-9, -6, 6, -6],\n [-6, -4, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, 8, -6],\n [-2, 0, 4, -3],\n [-4, 0, 8, -6],\n [4, 0, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-18, 5, -12, 8],\n [16, -1, 26, 2],\n [-8, -3, 8, 15],\n [4, 5, -4, -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[[-4, -24, -28, -16],\n [-20, 6, 10, -8],\n [-12, 12, 16, 0],\n [-3, 3, 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[[4, -9, -2, -7],\n [-2, 15, -9, -5],\n [-20, 2, -5, -13],\n [-10, -4, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-4, 4, 2, 0],\n [-6, 6, 3, 0],\n [6, -6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -4, 8, 6],\n [12, 12, 0, -8],\n [4, -4, -16, -4],\n [-6, -6, 0, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [1, -3, 4, -3],\n [2, -6, 8, -6],\n [2, -6, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -3, -3, 0],\n [-9, -9, -9, 0],\n [-9, -9, -9, 0],\n [-6, -6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 12, 12, 16],\n [-1, 3, 3, 4],\n [3, -9, -9, -12],\n [-4, 12, 12, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -8, -10, -6],\n [-14, -17, -18, -13],\n [-7, -5, -8, -4],\n [-9, 5, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 2, 11, -8],\n [-20, -4, 10, -8],\n [17, 4, -6, 5],\n [-10, -2, 5, -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 4x4 matrix:\n[[21, 7, 7, 6],\n [-18, -16, -6, 0],\n [3, 20, 1, -10],\n [-18, -1, -6, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 5, 12, 3],\n [5, 2, 10, -19],\n [2, -2, 0, 14],\n [9, 2, 20, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -12, 8, -12],\n [3, -3, -9, 3],\n [8, 6, -4, 6],\n [-7, -7, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 3, -1, -4],\n [9, 9, -3, -12],\n [3, 3, -1, -4],\n [-9, -9, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 14, -12, 19],\n [2, -14, -14, 6],\n [1, -11, -11, 4],\n [3, -6, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 4, -4, -4],\n [4, 8, -8, -8],\n [-2, -4, 4, 4],\n [-1, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -4, 8, 0],\n [-4, 1, -2, 0],\n [8, -2, 4, 0],\n [-12, 3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, -16, 1],\n [0, -1, 3, 0],\n [0, -4, 12, 0],\n [12, 7, -15, 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, -16, -40, 0],\n [-18, 10, -8, 12],\n [-8, 12, -12, 14],\n [4, -20, 0, -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[[-25, -26, 6, 24],\n [-13, -10, -5, 16],\n [-17, -3, -17, 6],\n [6, 15, -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 4x4 matrix:\n[[8, 17, -8, -18],\n [-25, -8, -13, 4],\n [-10, -7, -2, 6],\n [-10, -7, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -4, 0, 1],\n [-3, 12, 0, -3],\n [-3, 12, 0, -3],\n [-4, 16, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -14, 13, -24],\n [-3, 5, 9, -12],\n [1, 9, -13, 28],\n [12, 3, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -10, 4, -8],\n [7, -11, 0, -1],\n [2, 14, -3, 10],\n [3, -7, -2, -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[[-2, 3, 6, 5],\n [10, 1, -6, -7],\n [12, -10, -20, -2],\n [0, 3, 4, 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 4x4 matrix:\n[[-24, -20, 8, -8],\n [-2, 3, -4, 6],\n [8, 16, -12, 16],\n [12, -4, 10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 4, -14, 19],\n [20, 8, 2, 13],\n [20, -4, 8, 16],\n [-2, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -9, -12, 3],\n [-12, 12, 16, -4],\n [9, -9, -12, 3],\n [-3, 3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -6, 0, -22],\n [11, 5, -10, -25],\n [4, 5, -6, 5],\n [-6, 0, 5, 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[[13, -7, 2, -2],\n [-5, 13, 6, -10],\n [3, -9, -7, 8],\n [8, -12, -8, 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[[0, -16, -8, 16],\n [-2, 5, 14, -2],\n [10, 15, -2, -6],\n [-16, -2, 9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 3, -1, 6],\n [5, 6, -9, -2],\n [2, 6, -6, 4],\n [-9, -12, 17, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -3, 6, -12],\n [-9, 3, -6, 12],\n [-6, 2, -4, 8],\n [-6, 2, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -8, 1, -12],\n [-3, 15, -15, -9],\n [8, -4, -2, -12],\n [-11, 13, -6, 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[[-11, -10, 3, 25],\n [-27, 10, 9, 17],\n [8, 1, 5, 3],\n [18, -8, -4, -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[[4, 2, -8, 2],\n [0, 0, 0, 0],\n [4, 2, -8, 2],\n [-6, -3, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-3, 0, 15, 12],\n [0, -4, 2, 4],\n [2, 0, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 6, 9, 6],\n [4, -2, -3, -2],\n [4, -2, -3, -2],\n [8, -4, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -6, 4, 0],\n [-12, -9, 6, 0],\n [16, 12, -8, 0],\n [8, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, 24, 14, 6],\n [5, 1, -11, 16],\n [-30, 1, -6, 1],\n [-17, -19, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, -12, -14, 8],\n [-1, -6, -2, -4],\n [-4, 8, -4, 16],\n [-2, 4, -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[[6, 6, 12, -3],\n [1, 3, 4, -4],\n [1, -5, -4, 10],\n [-16, 0, -16, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -9, -5, 19],\n [1, 5, 4, -13],\n [7, -7, 2, 11],\n [-20, 29, -5, -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 4x4 matrix:\n[[3, -1, 4, -3],\n [12, -4, 16, -12],\n [12, -4, 16, -12],\n [3, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, 18, -11, -18],\n [-28, 28, -20, -28],\n [-6, 1, -10, -1],\n [-12, 9, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 3, -12, -6],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-2, -1, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 8, 2, -8],\n [-3, 12, 3, -12],\n [-4, 16, 4, -16],\n [-4, 16, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 12, 0, -6],\n [6, -8, 0, 4],\n [6, -8, 0, 4],\n [-3, 4, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[19, -1, 12, 26],\n [-1, 16, -16, -1],\n [-9, -3, 4, -12],\n [-4, 4, -16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, -9, -18, -12],\n [-14, -6, -12, -8],\n [-3, -3, -4, -2],\n [-3, 9, 6, 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[[-9, -12, 12, 12],\n [4, 5, -2, 0],\n [-10, -3, -13, -12],\n [21, 26, -30, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 2, -1, 2],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 6, 0, -2],\n [-9, -8, 2, 0],\n [-12, -9, 0, 3],\n [0, 5, -8, 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 4x4 matrix:\n[[-6, -6, -3, -3],\n [4, 9, 6, 1],\n [-2, 3, 3, -2],\n [-6, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 4, -20, 12],\n [16, -6, 10, -6],\n [6, -6, -1, 3],\n [8, 6, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 9, -3, 3],\n [-8, 12, -4, 4],\n [2, -3, 1, -1],\n [8, -12, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -2, 8, 8],\n [0, 2, -8, -8],\n [0, 0, 0, 0],\n [0, -1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -8, -16, -28],\n [8, 0, 10, 20],\n [2, 14, 13, 19],\n [-2, 2, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 6, -8, 2],\n [0, 12, -16, 4],\n [0, 3, -4, 1],\n [0, 12, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -8, -5, 1],\n [6, 0, -4, 2],\n [-8, -17, -6, -2],\n [14, -14, -23, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 16, 8, -4],\n [4, -8, -4, 2],\n [-2, 4, 2, -1],\n [-4, 8, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 8, 12, 16],\n [3, 2, 3, 4],\n [-9, -6, -9, -12],\n [-12, -8, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 12, 8, -8],\n [-1, -12, 7, 9],\n [-18, -5, -15, 4],\n [-6, 1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 0, -12, -18],\n [-13, 9, -4, 10],\n [-3, -12, -5, -2],\n [-11, 3, 0, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -2, 4, -2],\n [8, -2, 4, -2],\n [0, 0, 0, 0],\n [-4, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 4, -6, 8],\n [4, -2, 3, -4],\n [12, -6, 9, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, -4, -20, -4],\n [19, -8, 14, 1],\n [-6, 17, -5, 2],\n [-14, -2, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 8, -20, -5],\n [24, -10, 6, -10],\n [5, 8, -7, -3],\n [-24, 16, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, -8, -8, 2],\n [12, -16, -12, 8],\n [24, -16, -15, 5],\n [-9, 12, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -9, -5, -6],\n [-8, -1, -10, -9],\n [-1, -5, 1, 0],\n [20, -4, 28, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 12, 0, -12],\n [6, -6, 0, 6],\n [3, -3, 0, 3],\n [12, -12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -7, 5, 1],\n [-8, -7, -7, -19],\n [3, 8, 11, 13],\n [18, -1, 9, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -4, 1, -2],\n [-4, 16, -4, 8],\n [-1, 4, -1, 2],\n [-2, 8, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 5, -3, 1],\n [-15, 7, 3, -7],\n [-4, 4, -12, 12],\n [-2, 0, 6, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 9, -10, 9],\n [2, -26, 10, -18],\n [12, -11, 20, -3],\n [0, 26, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, -26, 16, -2],\n [9, -24, 10, 0],\n [0, 12, -7, 9],\n [-11, 18, -13, -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[[0, -8, 8, -12],\n [0, -2, 2, -3],\n [0, -8, 8, -12],\n [0, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 16, -4, 0],\n [-3, -12, 3, 0],\n [1, 4, -1, 0],\n [-4, -16, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 6, -8, 8],\n [4, 6, -8, 2],\n [-10, -3, 4, 11],\n [-16, -6, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -7, -9, 5],\n [-5, -2, 1, 0],\n [-8, -12, -4, 4],\n [3, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 13, -7, -4],\n [-12, -10, -18, -6],\n [8, -12, 17, 5],\n [-12, -3, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -3, 4, 0],\n [9, -9, 12, 0],\n [0, 0, 0, 0],\n [-3, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 16, 12, 16],\n [-8, -1, 15, 14],\n [-20, -25, -3, -10],\n [6, 2, -9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-1, 4, 0, 0],\n [-4, 16, 0, 0],\n [-1, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 1, -3, -1],\n [-8, 4, -12, -4],\n [0, 0, 0, 0],\n [8, -4, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 3, -2, -3],\n [-12, -12, 8, 12],\n [12, 12, -8, -12],\n [-3, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 2, -2, -4],\n [8, -4, 4, 8],\n [12, -6, 6, 12],\n [8, -4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 17, 9, 11],\n [3, -11, 3, 9],\n [-30, -14, 20, 22],\n [11, 12, -13, -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 4x4 matrix:\n[[13, -1, 12, 9],\n [-10, 18, -32, 4],\n [-8, 8, -8, 6],\n [1, -5, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 2, 0, -9],\n [-7, 7, 5, 1],\n [6, 10, 6, -10],\n [4, 5, 1, -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 4x4 matrix:\n[[9, -7, 7, -21],\n [-3, 3, -6, 15],\n [-12, 13, -12, 30],\n [3, -4, 4, -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[[-11, -8, -3, -1],\n [24, 22, 12, 9],\n [0, -10, -12, -15],\n [17, 16, 9, 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[[8, -2, 14, 10],\n [-4, 8, 0, -10],\n [-10, 8, 8, 20],\n [-2, 10, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 20, 28, -8],\n [1, -3, -4, 0],\n [-1, 10, 13, 2],\n [9, 1, 0, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -3, 4, 6],\n [-15, -9, -4, -8],\n [-1, -13, -10, -12],\n [-18, -30, -16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -31, 0, -31],\n [2, 12, 7, 11],\n [2, 7, -1, 8],\n [-2, -16, -5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, -8, 0],\n [0, 8, 4, 8],\n [25, 6, -11, -4],\n [3, 5, -8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 2, 4, -3],\n [-4, -4, -8, 6],\n [-4, -4, -8, 6],\n [2, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -10, 22, -5],\n [8, 0, 17, -2],\n [14, 10, 21, -1],\n [-22, 8, -11, -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[[-2, 20, -16, -4],\n [8, -2, 8, 15],\n [-2, 2, -8, -1],\n [-7, 1, -12, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, -2, -4],\n [0, 0, 4, 8],\n [0, 0, -6, -12],\n [0, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 6, -8, 6],\n [4, 0, 1, 0],\n [-12, 2, -6, 2],\n [8, -10, 17, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, -3, -1],\n [-4, 4, 6, 2],\n [6, -6, -9, -3],\n [4, -4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 2, -8, 12],\n [2, -1, 1, -2],\n [-10, 8, 4, 0],\n [11, -10, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -16, -4, 9],\n [12, -8, -2, 6],\n [24, -16, -4, 12],\n [-18, 12, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -4, -2, 4],\n [4, 6, 6, -2],\n [4, -18, -24, -2],\n [6, -7, -11, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -6, -3, 3],\n [20, 3, 0, -19],\n [2, 2, 1, -1],\n [-4, 8, -18, 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 4x4 matrix:\n[[4, 0, 12, 8],\n [1, 0, 3, 2],\n [0, 0, 0, 0],\n [-2, 0, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -9, 16, 14],\n [1, -2, -4, -6],\n [1, 2, 11, 15],\n [2, -1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -11, -7, 17],\n [-6, -12, -4, 12],\n [-1, 4, 0, 2],\n [-12, -21, 3, -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[[-29, -5, -34, -25],\n [10, 9, 11, 7],\n [5, -4, -7, 6],\n [9, 3, 20, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 7, 0, 13],\n [-11, 17, -6, 14],\n [5, -5, 4, -10],\n [-5, -2, -1, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 12, -12, 9],\n [-8, 16, -16, 12],\n [-5, 8, -10, 3],\n [0, -4, 0, -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 4x4 matrix:\n[[4, -18, 8, -16],\n [1, 4, 12, -22],\n [-1, 12, -12, 14],\n [-4, 2, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -1, -3, 5],\n [-4, 3, -12, -14],\n [4, 2, 1, -25],\n [-20, 3, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 5, 8, -9],\n [-13, 18, -4, -11],\n [26, -10, 0, 7],\n [-33, 9, 0, -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[[-4, 4, -4, -3],\n [-16, 16, -16, -12],\n [0, 0, 0, 0],\n [-8, 8, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 24, -32, 9],\n [-12, 1, 0, 6],\n [-17, 0, 2, 8],\n [-8, 18, -16, 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[[-8, -9, -4, 13],\n [16, 4, -16, -4],\n [-6, -5, 0, 7],\n [0, 7, 12, -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[[-7, -9, -14, -2],\n [17, 7, 31, 18],\n [7, 8, 26, 6],\n [-18, 9, 8, -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[[-13, 16, 7, 27],\n [-18, 19, 8, 7],\n [-10, 7, 6, 6],\n [-25, 26, 11, 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 4x4 matrix:\n[[4, 4, 8, 4],\n [3, 2, 2, -3],\n [2, 6, 20, 6],\n [6, 2, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 4, -4, 8],\n [-9, 6, -6, 12],\n [3, -2, 2, -4],\n [-3, 2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 4, 0, 0],\n [-8, 10, 24, -18],\n [7, 0, 4, -3],\n [-10, 9, 20, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 7, 17, 4],\n [9, 3, 15, -6],\n [4, -2, 2, -8],\n [3, -4, -2, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 13, 8, 5],\n [-2, 6, -12, 16],\n [-1, -1, 10, -9],\n [-3, 5, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 3, 15, -15],\n [-12, 3, 15, -15],\n [-15, 2, 18, -18],\n [-14, 0, 16, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-1, 4, 0, -4],\n [3, -12, 0, 12],\n [-3, 12, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 2, 2, -2],\n [-12, 6, 6, -6],\n [-8, 4, 4, -4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -8, 0, -6],\n [-8, 4, -8, 6],\n [4, -1, 6, -3],\n [-16, 13, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -4, 4, 10],\n [-16, 8, 16, 16],\n [-14, -4, 4, 10],\n [0, -22, -20, -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, -10, 20, 4],\n [-2, 15, -10, 12],\n [-28, 18, -8, 32],\n [14, -23, -2, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 2, 3, 2],\n [-6, 6, 9, 6],\n [-8, 8, 12, 8],\n [-4, 4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, -2, 0],\n [-4, 6, -10, 6],\n [6, -2, 1, -2],\n [2, -4, 7, -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[[-3, -3, -11, -8],\n [3, 3, 11, 8],\n [6, -12, -8, -14],\n [3, 3, 11, 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 4x4 matrix:\n[[-4, -10, 8, -6],\n [-4, -10, 8, -6],\n [2, 5, -4, 3],\n [1, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -1, -1, 3],\n [12, -4, -4, 12],\n [3, -1, -1, 3],\n [9, -3, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[22, -16, 8, 18],\n [-9, 8, 31, 3],\n [15, -14, 17, -3],\n [22, -19, 17, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 9, 11, 2],\n [10, -1, 4, 15],\n [7, -4, 0, 13],\n [-1, 4, -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[[0, 0, -8, -12],\n [-12, -24, 4, -12],\n [-5, 4, -15, -23],\n [9, 12, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -16, 12, -8],\n [8, -16, 12, -8],\n [2, -4, 3, -2],\n [4, -8, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -32, -22, -12],\n [-7, 7, 14, 1],\n [-5, -25, -14, -8],\n [-1, 11, 10, -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 4x4 matrix:\n[[6, 1, 1, 0],\n [-27, 5, -2, -2],\n [0, 7, 9, -8],\n [-23, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -4, 12],\n [-1, 1, 1, -3],\n [-2, 2, 2, -6],\n [-2, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 6, 9, -12],\n [-2, 2, 3, -4],\n [0, 0, 0, 0],\n [4, -4, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -9, -6, 6],\n [8, -20, -12, 2],\n [1, -19, -6, -2],\n [-7, 16, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 6, 10, 2],\n [-9, 23, 8, 5],\n [3, -11, -5, -2],\n [1, -17, -11, -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[[8, 1, 9, -5],\n [6, 1, 6, -2],\n [6, 1, 6, -2],\n [-4, -2, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 0, 5, -2],\n [-17, 0, -24, 25],\n [17, 0, 24, -25],\n [-13, 0, -18, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 18, -3, 21],\n [-22, -12, 8, -21],\n [0, -9, 9, -8],\n [-24, -9, 3, -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[[4, 4, 8, 4],\n [-12, 2, -2, -13],\n [10, -11, -15, 12],\n [11, 4, 1, 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[[-9, -9, 0, -3],\n [-3, -3, 0, -1],\n [-6, -6, 0, -2],\n [-9, -9, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 2, 9, -1],\n [3, -5, 0, -5],\n [5, 8, 21, 1],\n [7, 0, 15, -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[[0, -2, -20, -14],\n [0, 0, 0, 0],\n [-14, -5, -1, -7],\n [-2, 1, 17, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 24, 12, -12],\n [6, 16, 8, -10],\n [-6, -16, -8, 10],\n [0, -4, -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[[15, 16, -2, -16],\n [-3, -6, 4, -6],\n [-15, -17, 2, 14],\n [12, 15, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, 8, 8, 2],\n [-3, 4, 4, 1],\n [6, -8, -8, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -8, -8, 0],\n [1, 2, 2, 0],\n [-4, -8, -8, 0],\n [-1, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 3, 0, 2],\n [-4, -4, -12, 10],\n [-2, 8, 2, -4],\n [-3, 17, 5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -1, -4, -4],\n [-12, 0, -3, 0],\n [28, 4, 8, 16],\n [-12, 0, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 12, -12, -6],\n [8, -8, 8, 4],\n [-4, 4, -4, -2],\n [-16, 16, -16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 9, 0, -6],\n [-12, -9, -9, 3],\n [-4, -3, 9, 5],\n [0, 0, 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[[-29, -7, 16, 7],\n [-20, -6, 11, 7],\n [2, 10, -4, 2],\n [0, -2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 1, 3, -4],\n [-4, 4, 12, -16],\n [0, 0, 0, 0],\n [-1, 1, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -15, -10, 7],\n [8, 11, 10, -9],\n [0, 10, -8, 15],\n [12, 14, 20, -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[[10, 0, 12, 21],\n [-4, 2, -8, -12],\n [-12, -19, 16, 9],\n [4, 13, -16, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 4, 12, -3],\n [-5, 4, -12, 5],\n [7, 0, 0, -16],\n [0, -20, 22, 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, -24, -12, -12],\n [0, -3, -1, -3],\n [6, -6, -4, 0],\n [-9, 3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, -12, -30, -6],\n [10, 8, -15, -11],\n [-3, -6, 6, 6],\n [22, -7, -24, -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 4x4 matrix:\n[[-9, -10, 11, 4],\n [11, -2, -1, -4],\n [-3, -14, 13, 2],\n [-10, 12, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -2, -2, -20],\n [-11, -2, 3, -5],\n [1, -2, -1, -17],\n [-2, -2, 0, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 4, 27, -26],\n [0, -1, -24, 24],\n [-18, 13, 6, 0],\n [-12, 3, 24, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-17, 1, 10, -6],\n [-13, -5, -8, -12],\n [15, 3, -5, 9],\n [21, -4, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -8, 16, -16],\n [-3, 2, -4, 4],\n [6, -4, 8, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -2, 2, -2],\n [-28, -9, 5, -6],\n [-12, -1, 5, -4],\n [-12, -13, -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[[-1, 0, 4, 1],\n [2, 0, -8, -2],\n [-2, 0, 8, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 12, -8, -4],\n [12, -9, 6, 3],\n [-4, 3, -2, -1],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 9, -4, 0],\n [0, 0, 0, 0],\n [0, 2, -8, 8],\n [-12, 5, 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[[2, 2, -8, 4],\n [-4, -4, 16, -8],\n [-4, -4, 16, -8],\n [4, 4, -16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, 4, -8],\n [0, 12, 6, -12],\n [0, 16, 8, -16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 8, 6, 2],\n [4, 8, 6, 2],\n [6, 12, 9, 3],\n [-8, -16, -12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 18, -2, -4],\n [-6, 4, -16, -22],\n [8, 1, 4, 9],\n [3, -21, -2, 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[[-3, 13, -8, -5],\n [3, 8, 8, -7],\n [0, 4, 24, -16],\n [-4, 1, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 27, 26, 7],\n [4, -12, -4, 4],\n [23, -7, 2, 8],\n [20, -24, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-26, -7, -7, 18],\n [-15, -4, -7, 12],\n [6, 1, -9, -1],\n [4, 1, 3, -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 4x4 matrix:\n[[-12, 10, -4, 4],\n [-4, -13, 1, 6],\n [4, 6, 0, -4],\n [12, -17, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -2, 4, 4],\n [0, 0, 0, 0],\n [-3, -3, 6, 6],\n [-4, -4, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 4, -4, -3],\n [9, -12, 12, 9],\n [6, -8, 8, 6],\n [9, -12, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -14, 14, 2],\n [-25, -20, 3, -5],\n [-16, -12, -12, 0],\n [12, 8, -11, 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[[-8, 0, -10, 22],\n [-2, -9, 20, -8],\n [-6, 2, 6, -4],\n [-5, -9, 7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, -8, 4],\n [0, 0, 0, 0],\n [-4, 4, 16, -8],\n [-4, 4, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -1, 14, -3],\n [11, -15, 12, 10],\n [8, 12, 12, -14],\n [-12, 10, -14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -2, 2, -8],\n [2, 0, -2, -4],\n [-1, -1, -2, -10],\n [2, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -1, -2, 1],\n [8, -4, -8, 4],\n [-4, 2, 4, -2],\n [-4, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -6, -12, -12],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-2, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 3, 0, 6],\n [6, -3, 1, -8],\n [-12, 4, 0, 8],\n [-6, -3, 5, -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, 6, 11, 11],\n [2, -24, 19, 19],\n [-10, 0, -5, -5],\n [12, 12, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 16, -8, -8],\n [0, 8, -4, -4],\n [0, -16, 8, 8],\n [0, 12, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 4, 8, 0],\n [3, -2, -4, 0],\n [6, -4, -8, 0],\n [-9, 6, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 13, 14, -14],\n [-22, 4, 0, 0],\n [-13, -8, -12, 12],\n [-16, -4, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, 10, -17, -4],\n [-10, -14, 10, -6],\n [3, -8, -5, -16],\n [-16, -24, 24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -12, -9, -9],\n [-3, 4, 3, 3],\n [-3, 4, 3, 3],\n [9, -12, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -1, 0, 13],\n [2, 5, 3, 4],\n [-3, -16, -5, -15],\n [-17, 0, -23, 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 4x4 matrix:\n[[23, -19, 0, -2],\n [2, -9, 17, 5],\n [-12, -1, 19, 14],\n [-25, 11, 14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 7, -2, 9],\n [16, -3, 10, 3],\n [17, -1, 10, 6],\n [-5, -3, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -4, 8, 0],\n [7, -8, 18, 0],\n [-12, 8, -16, 0],\n [0, 5, -13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, -5, 7, -5],\n [12, 16, -16, 16],\n [23, 15, 0, 15],\n [-11, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -20, 6, 6],\n [-21, 26, -20, -20],\n [10, 4, 10, 10],\n [-5, -14, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 12, -4, 16],\n [-2, 3, -1, 4],\n [-6, 9, -3, 12],\n [8, -12, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -9, 12, -6],\n [3, 14, -11, 9],\n [-8, 6, -18, 6],\n [-26, 0, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 17, 11, 1],\n [16, -10, -10, 4],\n [0, -12, 4, -16],\n [-16, 10, 10, -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[[-3, -4, -1, -3],\n [-3, -4, -1, -3],\n [9, 12, 3, 9],\n [-3, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 2, -2, 4],\n [3, 3, -3, 6],\n [4, 4, -4, 8],\n [-2, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 6, -6, 0],\n [-1, -2, 2, 0],\n [3, 6, -6, 0],\n [1, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 6, -12, -9],\n [-6, 6, -12, -9],\n [-4, 4, -8, -6],\n [-4, 4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 0, -2, 0],\n [-9, 12, -12, 9],\n [0, 4, 2, 3],\n [-3, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 6, -3, 10],\n [-18, -6, 9, -21],\n [9, 6, -3, 10],\n [9, -12, -12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -28, -12, 0],\n [1, 16, 6, 6],\n [0, 0, 0, 0],\n [-11, 6, 4, -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[[-4, -11, 2, 8],\n [-16, 7, -11, 2],\n [-10, 4, -7, 2],\n [-8, -4, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 16, -3, 8],\n [7, 4, -3, -16],\n [-1, -16, 3, -8],\n [6, 0, -2, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -2, -8, 0],\n [12, -4, -16, 0],\n [3, -1, -4, 0],\n [9, -3, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -4, -8, -2],\n [1, -2, -4, -1],\n [1, -2, -4, -1],\n [2, -4, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, -10, 16, -16],\n [-18, -9, 12, -14],\n [-20, -14, 8, -20],\n [-7, -4, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 20, -2, -4],\n [-19, 16, -1, -14],\n [13, 8, 13, 2],\n [6, 16, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 10, 0, -15],\n [5, 10, 0, -15],\n [-16, 2, 0, -3],\n [19, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 0, -2, -5],\n [12, 3, 0, -6],\n [14, 0, -4, -10],\n [6, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -3, -3, -12],\n [-12, -3, -3, -12],\n [-8, -2, -2, -8],\n [8, 2, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -2, -8, -3],\n [-2, 2, -4, 0],\n [10, -10, -4, -6],\n [6, -6, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -3, 8, -13],\n [-16, -12, -4, -16],\n [-5, -3, 2, -7],\n [5, 6, 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 4x4 matrix:\n[[-3, 12, 12, 15],\n [4, -8, -9, -14],\n [5, 4, 1, -7],\n [-3, 4, 5, 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 4x4 matrix:\n[[-12, -9, -12, -9],\n [0, 0, 0, 0],\n [8, 6, 8, 6],\n [16, 12, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -4, -4, -4],\n [2, 8, 8, 7],\n [13, -4, -4, 0],\n [1, -20, -20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, 6, 6, -15],\n [-12, -3, -9, -12],\n [-27, 3, 0, -19],\n [-20, -6, -14, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -32, -8, -16],\n [10, 24, 12, 12],\n [-4, -8, -8, -4],\n [0, 8, -16, 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 4x4 matrix:\n[[-4, 3, 3, 4],\n [12, -9, -9, -12],\n [-12, 9, 9, 12],\n [-8, 6, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 8, 4, 0],\n [-12, -8, -4, 0],\n [-12, -8, -4, 0],\n [-9, -6, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -8, -4, 16],\n [8, -4, 6, -6],\n [24, 2, 13, -25],\n [-25, 2, -15, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 8, -7, 19],\n [-8, 10, 0, 10],\n [-13, 16, -9, 13],\n [-11, 13, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 3, 3, -9],\n [-2, 2, 2, -6],\n [-2, 2, 2, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -3, -6, -3],\n [-8, 2, 4, 2],\n [8, -2, -4, -2],\n [-12, 3, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 8, -8, 6],\n [-2, -4, 4, -3],\n [6, 12, -12, 9],\n [-4, -8, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, 14, 22, 10],\n [-4, -4, -12, -12],\n [0, 7, 16, 13],\n [-8, 13, 24, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-8, 12, -4, 12],\n [8, -12, 4, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 11, 11, -7],\n [-6, -15, -15, 6],\n [-8, -20, -20, 8],\n [24, -12, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -4, 2, -4],\n [0, -4, 2, -4],\n [0, -8, 4, -8],\n [0, 8, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, -1, 2],\n [0, 0, 0, 0],\n [12, 0, -3, 6],\n [-8, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 3, -4, -9],\n [-7, -1, 6, 3],\n [2, 28, 14, -14],\n [-5, -1, 20, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 6, -8, 0],\n [4, -12, 16, 0],\n [-1, 3, -4, 0],\n [-4, 12, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 10, 2, -16],\n [-1, 5, 6, -10],\n [9, 15, 0, -16],\n [0, -2, -23, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 8, 8, -4],\n [-9, -6, -6, 3],\n [9, 6, 6, -3],\n [-6, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[37, -5, -7, 28],\n [15, -3, -9, 4],\n [9, -5, 6, 12],\n [-22, 6, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, -8, 11],\n [-15, 4, 20, -6],\n [-3, -12, 12, -21],\n [12, 0, -16, 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[[4, 4, 4, 6],\n [-8, -8, -8, -12],\n [0, 0, 0, 0],\n [2, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, -1, -4, -1],\n [-14, -5, 0, -1],\n [6, 7, 10, 9],\n [-26, 5, -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[[2, -3, -1, -1],\n [8, 6, -2, -2],\n [-17, -6, 5, 5],\n [-14, -6, 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[[12, -12, -16, -4],\n [6, -6, -8, -2],\n [3, -3, -4, -1],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 16, 14, -2],\n [-7, 0, -9, -13],\n [0, 7, 11, 5],\n [23, -21, -6, 20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 10, -25, -12],\n [14, 1, 4, 4],\n [3, -7, 4, 5],\n [4, -4, -6, 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[[-16, 8, -16, -8],\n [4, -2, 4, 2],\n [4, -2, 4, 2],\n [-4, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -2, 0, -2],\n [0, 0, 0, 0],\n [4, -8, 0, -8],\n [1, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 4, 11, 6],\n [-1, -8, -7, -16],\n [-7, 8, -9, 8],\n [-9, -3, -13, -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[[-9, 18, -2, 8],\n [8, -32, -4, -24],\n [13, -17, 18, 3],\n [4, 13, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -6, 12, -12],\n [-3, 2, -4, 4],\n [6, -4, 8, -8],\n [-12, 8, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -6, 5, 13],\n [4, -4, 8, 6],\n [4, -8, 13, 15],\n [14, 6, -14, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -3, -20, 2],\n [6, 7, 4, -10],\n [8, 2, -8, -4],\n [2, 6, 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[[-14, -8, -7, -6],\n [6, 8, -5, -2],\n [0, -4, 7, 4],\n [-9, -2, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 4, 5, 1],\n [-12, 8, 22, -30],\n [-2, 6, 7, -21],\n [7, -11, 0, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -10, -16, 1],\n [-11, -13, -20, 2],\n [17, 15, 28, 2],\n [-4, -6, -8, 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 4x4 matrix:\n[[-18, 2, -10, 10],\n [-23, -4, -12, 10],\n [-17, -4, -18, 14],\n [-15, -14, -20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 16, -16, -8],\n [-8, -8, 9, 3],\n [12, 12, -6, -12],\n [4, 4, -5, -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 4x4 matrix:\n[[2, -1, -3, 2],\n [-4, 2, 6, -4],\n [6, -3, -9, 6],\n [8, -4, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -13, -9, 6],\n [-12, -18, -10, 10],\n [0, 3, 7, 2],\n [-4, -8, -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[[4, -4, 1, -1],\n [-12, 12, -3, 3],\n [8, -8, 2, -2],\n [-8, 8, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 3, 12, -12],\n [9, 3, 12, -12],\n [-9, -3, -12, 12],\n [-3, -1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -9, -6, 4],\n [0, 3, -6, -4],\n [0, -9, -12, 2],\n [0, 9, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -19, -8, -12],\n [-18, 4, 14, -6],\n [-21, -7, 8, -12],\n [-21, -7, 8, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -21, -3, 3],\n [2, 0, -10, 10],\n [8, 13, -1, 1],\n [16, 28, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 2, -2, 13],\n [9, 23, 10, 4],\n [-24, -2, 19, -18],\n [3, 17, 0, -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 4x4 matrix:\n[[16, -16, -8, 4],\n [12, -12, -6, 3],\n [-16, 16, 8, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -2, -9, -20],\n [8, 4, -2, 8],\n [8, 6, -8, 4],\n [16, 11, -13, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -4, 0, -4],\n [-6, -3, 0, -3],\n [-2, -1, 0, -1],\n [-8, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 9, -4, -3],\n [0, 24, 16, 12],\n [-4, -15, -1, -2],\n [-6, -18, -21, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 4, 12, -4],\n [-4, 18, -6, 17],\n [-2, 7, -3, 7],\n [6, -13, 9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -20, 15, 18],\n [5, -16, 15, 10],\n [0, 20, -13, -20],\n [8, 0, 12, 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 4x4 matrix:\n[[-12, -12, -6, -9],\n [-4, -4, -2, -3],\n [-16, -16, -8, -12],\n [12, 12, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 12, -3, -9],\n [2, 4, -1, -3],\n [2, 4, -1, -3],\n [4, 8, -2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, 7, 15, -3],\n [4, -4, 0, -9],\n [12, -12, 0, -12],\n [9, -9, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -20, -24, -18],\n [10, -6, -8, -8],\n [-12, 8, 0, 12],\n [21, 9, 12, 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[[-12, 16, -16, -16],\n [2, 4, 4, -4],\n [-6, 3, -9, -3],\n [-1, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -3, 5, -13],\n [-12, 3, -9, 9],\n [1, -1, 1, -5],\n [-2, -1, -1, -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 4x4 matrix:\n[[2, 0, 0, 0],\n [12, -1, -3, 3],\n [2, -2, -6, 6],\n [6, -1, -3, 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 4x4 matrix:\n[[-12, -9, -12, 12],\n [-13, -12, -4, 16],\n [-12, -12, 0, 16],\n [-11, -9, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -16, 4, -12],\n [0, -8, 2, -6],\n [0, 16, -4, 12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-3, -12, -12, 0],\n [1, 4, 4, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -4, 1, -2],\n [8, -6, 10, -4],\n [34, -17, 19, -10],\n [-6, 13, -14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 21, -2, 24],\n [8, -8, -6, -10],\n [-18, -1, 11, 2],\n [0, 10, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, -4, -1],\n [-16, 16, 16, 4],\n [-8, 8, 8, 2],\n [12, -12, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 4, 16, -16],\n [1, 0, -4, 0],\n [10, 3, -7, -12],\n [0, -2, -22, 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[[9, -9, -6, -3],\n [-12, 12, 8, 4],\n [-12, 12, 8, 4],\n [12, -12, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-3, 6, -3, 3],\n [-3, 6, -3, 3],\n [-3, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 6, 4, 8],\n [-12, 12, 8, 16],\n [0, 0, 0, 0],\n [-3, 3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -3, 6, 9],\n [-2, -1, 2, 3],\n [8, 4, -8, -12],\n [4, 2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -2, 2, 2],\n [12, 8, -8, -8],\n [3, 2, -2, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 8, -8, -4],\n [4, 1, -7, 1],\n [-5, -24, 0, 18],\n [-8, -28, 4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 6, -6, 9],\n [-1, 2, -2, 3],\n [0, 0, 0, 0],\n [-2, 4, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 2, 0, -2],\n [6, 4, 0, -4],\n [-5, -2, -2, 3],\n [-10, 4, -16, 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 4x4 matrix:\n[[8, 20, -9, -19],\n [-2, -8, 0, 7],\n [0, 12, 9, -9],\n [6, -4, -21, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 16, 0, -16],\n [21, 16, 2, -13],\n [-6, 0, 4, 6],\n [3, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -8, -4, 4],\n [-4, 0, -6, 0],\n [6, -4, 1, 2],\n [4, 2, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -2, 0, -10],\n [-17, 9, 0, -6],\n [-12, 4, 0, -16],\n [-7, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -4, -16, -16],\n [8, 2, 6, 2],\n [-6, -1, -2, 2],\n [0, 2, 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[[0, 0, 0, 0],\n [12, 6, 9, -6],\n [16, 8, 12, -8],\n [-16, -8, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 6, 0, 3],\n [8, 12, 4, 10],\n [-8, -8, 0, -4],\n [0, -8, -8, -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 4x4 matrix:\n[[-8, 19, -17, -16],\n [-13, 13, -7, -4],\n [5, -7, 5, 4],\n [-4, -10, 14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -6, 6, 2],\n [0, 0, 0, 0],\n [2, 6, -6, -2],\n [-2, -6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 4, 4],\n [-12, 12, -12, -12],\n [4, -4, 4, 4],\n [-16, 16, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -8, -16, -4],\n [2, 8, 16, 0],\n [-2, 0, 0, -4],\n [6, 10, 20, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 15, 9, -18],\n [-10, -1, 19, -10],\n [-16, 8, 16, -16],\n [-8, 8, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, 2, 3],\n [-9, -7, 5, 4],\n [-5, -3, 3, 1],\n [8, 0, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 12, -6, -3],\n [4, 8, -4, -2],\n [-6, -12, 6, 3],\n [2, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -10, -4, 4],\n [-6, 4, -16, 0],\n [-4, -20, 20, 4],\n [13, 12, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 0, 8, 13],\n [-18, -25, 6, 16],\n [20, 28, -8, -20],\n [-12, -16, 0, 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 4x4 matrix:\n[[8, -16, -20, -24],\n [-8, 0, 6, 8],\n [16, 16, 2, 0],\n [12, 8, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -1, 3, 3],\n [0, 1, -3, -3],\n [0, 0, 0, 0],\n [0, 4, -12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -1, 0, 3],\n [-1, 13, -12, -4],\n [9, -6, 6, 6],\n [-2, 1, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 24, -10, -2],\n [-18, 24, -12, 2],\n [24, -32, 12, -4],\n [14, -20, 20, 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[[18, -15, 1, -8],\n [-12, 16, 32, 4],\n [-9, 0, -12, -9],\n [-9, 15, 15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -10, -8, 7],\n [12, 24, 17, 9],\n [-8, -2, -2, -6],\n [5, 14, 14, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -12, 4, 4],\n [4, -12, 4, 4],\n [-1, 3, -1, -1],\n [-3, 9, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -5, 23, -8],\n [-8, -16, 5, 8],\n [-4, 8, -3, -16],\n [0, 6, 33, -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[[-9, 6, 4, -1],\n [-12, 0, -8, -4],\n [1, 2, 4, 1],\n [12, 0, 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[[3, -15, -10, -37],\n [-9, 5, -2, 23],\n [0, 2, 1, 8],\n [15, 16, 24, 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[[0, -3, 6, -12],\n [0, -3, 6, -12],\n [0, 0, 0, 0],\n [0, -3, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 15, 0, -3],\n [-8, -10, 0, 2],\n [4, 11, -4, -9],\n [-16, 4, -16, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 13, -16, 10],\n [7, -7, 24, -14],\n [-11, 11, -2, 2],\n [-10, 10, -20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 4, -4, 4],\n [-6, -4, 4, -4],\n [-12, -8, 8, -8],\n [-9, -6, 6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -15, 8, 17],\n [-9, -6, -15, -3],\n [2, 13, -13, -18],\n [4, 11, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 16, 8, 4],\n [0, 0, 0, 0],\n [0, -8, -4, -2],\n [0, 8, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 12, -7, 16],\n [-8, -20, 12, -24],\n [4, 12, -7, 16],\n [2, 5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 3, -4, 4],\n [0, 0, 0, 0],\n [-4, -12, 16, -16],\n [3, 9, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, 2, 0],\n [-10, 8, 10, -12],\n [7, -5, -4, 3],\n [13, -9, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -8, 4, -14],\n [7, 17, -14, 5],\n [-10, -22, 20, 2],\n [6, 16, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -6, -5, -12],\n [1, -6, -1, -12],\n [-7, -2, -4, -4],\n [3, -6, 0, -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 4x4 matrix:\n[[3, -1, -3, 1],\n [9, -3, -9, 3],\n [3, -1, -3, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-22, 16, 10, -10],\n [1, -10, 14, 2],\n [-16, 16, 10, -14],\n [6, 4, -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 4x4 matrix:\n[[-6, -10, -7, 4],\n [2, -6, -7, 8],\n [-14, 2, 9, -16],\n [-6, 6, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -16, 12, 8],\n [0, 4, -3, -2],\n [0, -12, 9, 6],\n [0, -16, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, -12, -4],\n [12, 12, 0, 0],\n [24, 20, 12, 4],\n [-20, -16, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 1, -2, 2],\n [-2, -1, 2, -2],\n [8, 4, -8, 8],\n [4, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 1, -1, -2],\n [2, 2, -2, -4],\n [4, 4, -4, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -1, 4, 1],\n [8, 2, -8, -2],\n [4, 1, -4, -1],\n [-4, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -4, 2, -1],\n [13, 6, -4, 11],\n [-7, -15, 7, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 7, -24, 1],\n [25, -5, 36, 1],\n [11, -7, 12, -9],\n [3, -11, 10, -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 4x4 matrix:\n[[4, 0, 1, 3],\n [12, 0, 3, 9],\n [-8, 0, -2, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 17, -2, 6],\n [-12, -20, 0, -4],\n [0, -2, 12, -16],\n [6, 9, 6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -6, 5, 7],\n [4, -4, 1, -1],\n [-16, 20, -12, -12],\n [-8, 8, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 13, 4, 3],\n [-4, -7, -15, 12],\n [7, 3, 26, -24],\n [-2, 2, -8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [16, -4, -8, 0],\n [0, 0, 0, 0],\n [4, -1, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -6, 8, 4],\n [-6, 9, -12, -6],\n [-8, 12, -16, -8],\n [-6, 9, -12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -9, 15, -5],\n [0, -4, -36, -4],\n [5, 11, 16, 6],\n [-3, 12, -5, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 4, 0, 4],\n [-2, 8, 0, 8],\n [-3, 12, 0, 12],\n [-1, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 9, -12, -6],\n [0, -3, 4, 2],\n [0, -12, 16, 8],\n [0, 9, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 2, -8, 0],\n [-3, 3, -12, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, 2, -8],\n [0, 0, 0, 0],\n [-9, 0, -3, 12],\n [9, 0, 3, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-28, -4, -16, 0],\n [0, 0, 0, 0],\n [5, 5, -1, 9],\n [-16, 2, -13, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 4, -20, -12],\n [-11, -2, -10, -4],\n [14, 2, 14, 6],\n [-5, 1, -9, -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[[-10, 17, -18, -16],\n [-14, 15, -14, -16],\n [-4, 20, -24, -16],\n [4, -20, 24, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, 6, 2],\n [4, -4, 12, 4],\n [0, 0, 0, 0],\n [-2, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 8, -20, -5],\n [-3, -4, 4, -11],\n [-1, -5, 16, 11],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 3, 2, -1],\n [-1, 3, 2, -1],\n [2, -6, -4, 2],\n [1, -3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, -3, 1],\n [-16, 8, 12, -4],\n [-4, 2, 3, -1],\n [-4, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, -14, -14],\n [4, -10, -20, -22],\n [-4, 4, 28, 28],\n [0, -12, 16, 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[[9, 2, -3, 1],\n [-4, 8, -4, -4],\n [-11, -3, 4, -1],\n [9, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -3, -12, 9],\n [0, 0, 0, 0],\n [2, 2, 8, -6],\n [1, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-34, -9, 5, 0],\n [22, -8, 1, -7],\n [-6, -11, 1, -2],\n [16, 16, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-19, 8, -16, -7],\n [6, -2, 4, 3],\n [16, -6, 12, 7],\n [4, 0, 0, 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[[3, -12, 0, -3],\n [1, -4, 0, -1],\n [2, -8, 0, -2],\n [-2, 8, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 4, -6, 2],\n [3, -10, 13, -15],\n [4, 16, -20, 28],\n [9, -8, 11, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [4, 3, -4, 4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 20, 31, 7],\n [-6, -4, -20, -8],\n [-3, 19, -11, -19],\n [-4, -19, -16, -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 4x4 matrix:\n[[-9, -2, -15, -16],\n [-9, -8, 1, -16],\n [6, 3, -15, -14],\n [6, -3, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -4, 14, 9],\n [7, 2, -10, -5],\n [-6, 1, -2, 1],\n [-11, 5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -12, 16, 0],\n [0, 6, -8, 0],\n [0, 12, -16, 0],\n [0, -12, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 16, -12, -4],\n [-6, -12, 9, 3],\n [8, 16, -12, -4],\n [4, 8, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 4, -3, -3],\n [-9, 12, -9, -9],\n [-12, 16, -12, -12],\n [-3, 4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 4, 8, 8],\n [-4, -4, -8, -8],\n [-2, -2, -4, -4],\n [-8, -8, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 3, -6, -6],\n [2, 8, -5, 11],\n [12, -24, -18, 6],\n [-10, 5, 19, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -14, 14, 1],\n [-20, 11, 4, 11],\n [8, -6, 8, 2],\n [-28, 18, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -3, -3, 0],\n [-4, 2, 0, 0],\n [12, 6, 4, 0],\n [12, 12, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 4, 8, 14],\n [-6, -4, -8, -17],\n [6, 4, 8, -1],\n [-9, -6, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[19, 22, -15, 7],\n [19, 22, -15, 7],\n [-20, -24, 16, -4],\n [-4, -8, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 3, -1, 6],\n [18, 18, 10, 20],\n [-8, -6, -2, -8],\n [-12, -18, -14, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -3, 4, 0],\n [4, 0, -8, -4],\n [7, -6, 6, 2],\n [-6, 12, -28, -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[[-16, -12, 12, -8],\n [-16, -12, 12, -8],\n [4, 3, -3, 2],\n [4, 3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -5, -14, 2],\n [-4, 16, 16, -16],\n [-12, -12, -24, 8],\n [-7, 13, 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[[-12, 0, -3, 6],\n [0, 0, 0, 0],\n [-4, 0, -1, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 1, -4, -8],\n [-12, -12, 12, 28],\n [-7, -12, 9, 19],\n [5, -8, -1, -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[[6, 4, -6, 2],\n [3, 2, -3, 1],\n [3, 2, -3, 1],\n [12, 8, -12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, 2, -9, 1],\n [-16, -20, -12, 8],\n [-18, 8, -12, -6],\n [-25, -8, -15, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -16, -16, 16],\n [6, -12, -12, 12],\n [6, -12, -12, 12],\n [-2, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -20, -4, 16],\n [-14, -6, -2, 0],\n [3, -19, -13, -12],\n [0, 20, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -1, -4, 1],\n [0, 0, 0, 0],\n [4, -1, -4, 1],\n [8, -2, -8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 6, -8, 2],\n [-2, 6, -8, 2],\n [4, -12, 16, -4],\n [2, -6, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -24, 0, 15],\n [6, -8, 2, 5],\n [2, -13, 1, 7],\n [7, -4, 3, 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 4x4 matrix:\n[[-4, 9, 12, 0],\n [-4, 14, -8, 12],\n [-2, 8, 1, 6],\n [-7, 7, 11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, -16, -12],\n [0, 0, 0, 0],\n [0, 0, 4, 3],\n [0, 0, -16, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -3, 0, -4],\n [-1, -2, 3, -2],\n [2, -1, 6, 0],\n [-6, -7, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 12, 14, 16],\n [2, 2, 3, 4],\n [18, 0, 6, 12],\n [2, 2, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 2, 8, -6],\n [16, -4, -16, 12],\n [16, -4, -16, 12],\n [-4, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -16, -16, -12],\n [-6, -12, -12, -9],\n [2, 4, 4, 3],\n [4, 8, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -12, -19, -12],\n [6, 6, -11, -16],\n [18, 36, 19, -4],\n [-2, -2, -15, -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[[0, 10, 9, 7],\n [-3, 20, 10, -4],\n [21, 8, 8, 12],\n [-12, 8, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 8, -8, -6],\n [-13, 0, 8, 5],\n [-12, 10, 2, 0],\n [-2, -7, 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, 0, 0, 0],\n [4, -4, 4, 8],\n [3, -3, 3, 6],\n [-3, 3, -3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -9, -24, -15],\n [0, 12, 12, 3],\n [-9, -3, 12, 12],\n [-6, 14, 24, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, 7, 1],\n [6, 4, 18, 9],\n [4, 6, 7, 1],\n [0, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 5, 1, 0],\n [-12, -14, 11, -6],\n [-16, -26, 24, -5],\n [-12, -15, 18, -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 4x4 matrix:\n[[3, 9, -18, -3],\n [-2, 13, -17, -4],\n [3, -1, 12, 5],\n [-11, -4, 7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -9, 14, -3],\n [1, 3, -4, 1],\n [-7, -15, 16, -5],\n [-3, 0, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 2, -6, 9],\n [5, -5, -15, 5],\n [-8, 6, 9, 5],\n [5, 0, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -9, 2, 1],\n [3, 15, 9, 17],\n [-1, -19, -10, -19],\n [-7, -9, -13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 13, 16, -13],\n [-4, 8, 8, -6],\n [-1, -25, -16, 9],\n [7, 13, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -16, -1, -27],\n [6, 4, -13, -8],\n [-10, -6, 13, 4],\n [-12, -28, 14, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [1, -2, -3, -1],\n [0, 0, 0, 0],\n [2, -4, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -1, 7, 0],\n [6, 11, -7, -21],\n [-10, -9, 13, 15],\n [-8, 4, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -10, -8, 0],\n [-6, -4, -2, 4],\n [15, -1, -5, -14],\n [-10, 8, 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[[8, 0, -2, -20],\n [2, 11, 2, 14],\n [-5, -14, -5, -1],\n [-8, -21, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -13, 8, -12],\n [14, -24, 25, -9],\n [0, 4, 4, 12],\n [4, -5, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -12, -8, 4],\n [12, -20, -8, 4],\n [16, -8, 8, -4],\n [14, -2, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -8, 12, -16],\n [-8, -4, 6, -8],\n [8, 4, -6, 8],\n [-8, -4, 6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 2, 0, -6],\n [7, 6, 22, 13],\n [1, 2, 0, -6],\n [3, -2, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 16, -4, -4],\n [-5, 6, -5, 2],\n [-12, 18, -3, -6],\n [-6, 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[[-8, 24, 8, -4],\n [-4, 2, 9, -10],\n [-12, 20, 20, 4],\n [-1, -5, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 2, 0, 8],\n [15, 6, -7, 4],\n [-4, -12, -13, -20],\n [-3, 6, 12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -4, 2, 1],\n [14, 12, 6, 13],\n [6, 16, -11, -8],\n [4, 4, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 6, 8, 0],\n [4, -2, -9, -9],\n [-1, 2, -8, -10],\n [2, -6, 7, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -9, -1, 20],\n [-6, 3, 1, -8],\n [-16, 4, 1, -14],\n [26, 10, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 0, -14, 14],\n [3, -6, 9, -8],\n [-3, 10, 4, -3],\n [-7, 18, -11, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 12, 0, 9],\n [12, 12, 0, 9],\n [-12, -12, 0, -9],\n [-16, -16, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 7, 3, 0],\n [-7, -12, 17, 5],\n [1, 6, -17, -5],\n [-5, -8, 8, 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[[-22, 8, 18, -16],\n [-20, 4, 16, -12],\n [16, -5, -13, 11],\n [-14, 1, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -9, -1, 18],\n [1, 0, 11, -17],\n [14, -14, 14, -8],\n [-4, 5, -9, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 8, 16, 24],\n [16, -8, -16, -24],\n [0, -6, 6, 9],\n [-12, 16, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 12, 2, -10],\n [0, -12, -10, 8],\n [8, 20, 6, -16],\n [-4, -16, -8, 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 4x4 matrix:\n[[-12, 0, -12, 10],\n [11, 9, 21, -5],\n [11, 9, 18, 2],\n [5, 3, 11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, 4, 8],\n [0, 13, -4, -8],\n [0, 2, 4, 8],\n [0, -17, 8, 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[[-11, -4, 10, -15],\n [17, 18, 0, 3],\n [-8, 3, 3, -9],\n [16, 9, 9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 0, -4, -10],\n [-8, 5, 11, 11],\n [4, -5, -6, 6],\n [19, -2, -9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 3, 5, -5],\n [-15, 13, 15, -6],\n [-3, 28, 20, 5],\n [-3, 1, 3, -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[[-7, -20, -3, 10],\n [2, -5, -17, -15],\n [0, 15, -5, -1],\n [-6, -30, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 9, 12, -6],\n [16, 0, 4, -14],\n [16, 16, 20, -6],\n [8, 2, 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[[5, -1, 21, 12],\n [-3, 0, -18, -12],\n [-6, 3, -9, 0],\n [-4, 2, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 3, 0, -3],\n [2, 3, 0, -3],\n [2, 3, 0, -3],\n [-6, -9, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -16, 8, -8],\n [16, 16, -8, 8],\n [4, 4, -2, 2],\n [16, 16, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -2, 0, -8],\n [8, -4, 0, -16],\n [-8, 4, 0, 16],\n [8, -4, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 3, -2, 5],\n [-13, 7, 2, 15],\n [10, -2, 12, 2],\n [8, 0, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 0, -4, -16],\n [-6, 0, -3, -12],\n [-4, 0, -2, -8],\n [4, 0, 2, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, 16, -12, -16],\n [13, -4, 23, -4],\n [12, -12, 33, -12],\n [-6, -4, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -13, 3, 10],\n [-4, 1, -5, -17],\n [12, -12, -3, -3],\n [-3, 0, -2, -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[[-11, 10, -13, 4],\n [-14, 12, 11, -6],\n [4, -2, 28, -4],\n [-15, 13, 18, -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 4x4 matrix:\n[[13, -10, 7, 5],\n [8, -20, -8, 20],\n [7, 5, 13, -10],\n [9, 0, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -5, 13, -14],\n [8, -11, 13, -10],\n [-15, -7, -1, 6],\n [-9, -12, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -3, -4, -7],\n [-15, 12, 10, -13],\n [3, -5, -6, 3],\n [-8, 4, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -10, 8, 1],\n [1, -2, -4, 15],\n [10, 14, -10, 28],\n [-3, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -8, -7, 7],\n [28, -4, -9, 33],\n [-9, 6, 3, -15],\n [4, -28, -11, 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 4x4 matrix:\n[[-4, 6, 4, -6],\n [8, -12, -8, 12],\n [8, -12, -8, 12],\n [6, -9, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 8, 6, 2],\n [12, -16, -12, -4],\n [0, 0, 0, 0],\n [12, -16, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -8, 4, -8],\n [-2, -4, 2, -4],\n [4, 8, -4, 8],\n [2, 4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 4, 14, -8],\n [4, -3, -3, 1],\n [-5, 0, -6, 4],\n [-12, 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[[0, 4, 8, -4],\n [21, 15, 2, -15],\n [-6, 2, 12, -2],\n [0, -8, -16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -20, -17, -3],\n [0, -16, -10, -6],\n [8, 8, 2, 6],\n [-12, -12, -3, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -16, -16, 4],\n [-1, -16, -6, 19],\n [14, -4, -6, 10],\n [6, -12, -4, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 11, -7, -6],\n [2, -6, 12, 13],\n [-20, -5, -3, 10],\n [-20, 14, -4, 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 4x4 matrix:\n[[8, -8, -4, 11],\n [-4, 4, -16, -4],\n [11, -11, -16, 16],\n [-11, 11, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -7, -10, -6],\n [9, 1, -12, 6],\n [12, -24, 10, -30],\n [0, -4, 4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -16, 9, -5],\n [-1, -17, 3, -5],\n [-1, 7, 0, 2],\n [1, -7, 0, -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[[8, -2, -4, -12],\n [-8, 2, 6, 18],\n [-8, 2, -4, -12],\n [-16, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 3, 6, 3],\n [-6, -2, 1, -2],\n [2, 1, 1, 1],\n [-4, -3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, 6, 6],\n [-4, 12, 0, -16],\n [18, 6, 10, 2],\n [7, -3, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 7, 5, -12],\n [-12, 8, 16, -16],\n [14, 2, -14, 0],\n [8, -11, -13, 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[[8, 4, -2, -2],\n [-16, -8, 4, 4],\n [-16, -8, 4, 4],\n [-8, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 21, -9, 3],\n [1, 3, -3, 3],\n [6, -18, 2, 6],\n [-4, -12, 12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, 17, 3, -12],\n [-10, -4, -18, 16],\n [-3, -3, -3, 4],\n [-5, -11, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 8, 16, 12],\n [4, -8, -16, -12],\n [-1, 2, 4, 3],\n [2, -4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, -12, 4],\n [-21, 18, -15, -2],\n [20, -18, 12, -2],\n [-28, 24, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 17, 7, 28],\n [-2, 8, 6, 4],\n [3, -18, -12, -8],\n [-4, -20, -8, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 3, -10, 0],\n [5, 21, -10, 0],\n [4, -12, -8, 0],\n [2, 3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -6, 6, -14],\n [0, -8, 8, -4],\n [-6, 12, -12, 15],\n [6, -4, 4, -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[[-12, 0, 3, 18],\n [-12, 0, 3, 18],\n [-6, -24, 21, -6],\n [6, -8, 5, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 1, 4, -2],\n [6, -3, 1, 6],\n [-11, -1, -4, 2],\n [6, 3, 3, -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[[-8, 8, -2, -2],\n [16, -16, 4, 4],\n [12, -12, 3, 3],\n [-16, 16, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 4, -12, -16],\n [6, 2, -6, -8],\n [0, 0, 0, 0],\n [6, 2, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -10, -15, -13],\n [10, -2, -12, -12],\n [-4, -8, 7, 5],\n [-5, 21, 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[[4, -4, 16, 9],\n [-4, 4, 2, 0],\n [18, -18, 15, 12],\n [-8, 8, -20, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 0, 3, 1],\n [6, 0, 6, 2],\n [-12, 0, -12, -4],\n [6, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, -6, -9, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 8, 4, 5],\n [-6, -28, 1, 0],\n [9, 4, 0, 13],\n [15, 8, 2, 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[[-16, -12, -12, 12],\n [-16, -12, -12, 12],\n [16, 12, 12, -12],\n [8, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -16, -12, -4],\n [10, 8, 13, 6],\n [2, 4, -4, -3],\n [-18, -20, -8, -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[[14, 17, -10, -5],\n [-10, -1, 9, 11],\n [-12, 0, 11, 14],\n [18, 15, -14, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 19, -4, 9],\n [15, -30, 9, -17],\n [-4, -3, 3, 0],\n [0, -5, 2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 2, -18, -8],\n [11, 5, -15, -10],\n [-10, -2, 18, 8],\n [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[[0, 4, 9, -7],\n [-11, -4, -6, 0],\n [-9, -12, -6, 12],\n [16, 10, 5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [4, 4, 1, -2],\n [-12, -12, -3, 6],\n [16, 16, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, 6, -8],\n [-8, 8, 12, -16],\n [8, -8, -12, 16],\n [8, -8, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 6, -9, 9],\n [3, 6, -9, 9],\n [3, 6, -9, 9],\n [-4, -8, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, 0, 8],\n [4, -8, 0, -16],\n [-1, 2, 0, 4],\n [-4, 8, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -12, 3, -12],\n [-3, -12, 3, -12],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -4, 14, 4],\n [9, -10, 7, 10],\n [-9, 2, 13, -2],\n [12, -12, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -3, 0, 12],\n [-8, -4, 0, 16],\n [-8, -4, 0, 16],\n [-2, -1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -4, -24, -20],\n [-4, 20, -6, 10],\n [16, -20, 4, -8],\n [-5, -6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 0, -16, -3],\n [10, 0, -16, -2],\n [-12, -3, 12, 4],\n [-6, -9, 24, 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[[-15, -4, 13, 10],\n [17, 4, -11, -6],\n [-7, -1, 0, -4],\n [8, 2, -6, -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[[-1, 3, 4, 4],\n [5, 14, 6, 18],\n [3, 7, -8, 5],\n [-9, 1, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -8, -3, 4],\n [4, 7, 6, 1],\n [24, 2, 12, 14],\n [28, -1, 12, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -7, -7, 4],\n [-7, -1, -1, -2],\n [-3, 1, 1, -2],\n [9, 2, 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[[10, -4, 24, -2],\n [-9, 12, -1, -10],\n [13, -3, 14, 7],\n [7, -8, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 6, 0, 8],\n [-16, -12, 0, -16],\n [-8, -6, 0, -8],\n [12, 9, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 8, -8, 4],\n [8, -6, -6, 2],\n [-8, 6, 6, -2],\n [28, -6, -18, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, -6, -14, 0],\n [-5, 16, 13, -11],\n [28, -29, -4, 19],\n [-4, 12, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 6, 6, 12],\n [-4, -4, -12, -8],\n [7, 4, -6, 8],\n [3, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 32, 4, -28],\n [-4, 8, 8, -8],\n [2, -8, -1, 7],\n [6, -16, -9, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, -12, 8],\n [9, 12, 0, 17],\n [6, 8, -1, 12],\n [6, 8, -4, 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 4x4 matrix:\n[[0, 7, -12, -2],\n [0, -11, -9, 18],\n [0, 6, -21, 4],\n [0, 14, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 10, -6, 2],\n [-8, 13, -7, 4],\n [-4, -11, 9, 2],\n [-4, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 12, 0, 8],\n [5, 9, -12, 2],\n [9, 15, -12, 6],\n [-3, -3, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 6, 3],\n [0, 0, -4, -2],\n [0, 0, 6, 3],\n [0, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 8, 2, 14],\n [6, 8, 16, -28],\n [16, -36, -25, 0],\n [-10, 8, -2, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 16, 7, 4],\n [8, 16, 7, 4],\n [-9, 6, 9, 12],\n [-5, -3, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -2, 18, -16],\n [-4, 1, 15, -10],\n [-12, 3, -19, 18],\n [4, -1, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 6, 15, 12],\n [6, -15, 9, -18],\n [16, 12, 11, 20],\n [-18, -17, -11, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 12, -12, 0],\n [-5, -17, 17, -16],\n [0, 0, 0, 0],\n [-8, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -16, -4, 5],\n [6, -16, 4, 3],\n [12, -16, -8, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 0, -16, 11],\n [-4, -1, 5, 24],\n [-6, 0, -10, -8],\n [-8, 4, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 0, 1, 2],\n [2, -27, -24, 24],\n [2, 3, 3, -2],\n [7, -18, -14, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 0, 2, 2],\n [-12, 0, 3, 3],\n [-16, 0, 4, 4],\n [8, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 4, 4, 7],\n [-4, -2, -2, 9],\n [-8, 8, 8, 4],\n [2, 4, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -3, -3, 1],\n [12, 12, 12, -4],\n [3, 3, 3, -1],\n [-9, -9, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 12, 12, 3],\n [-1, -4, -4, -1],\n [-4, -16, -16, -4],\n [-1, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -2, 8, -8],\n [12, -16, 4, -8],\n [-9, 10, 5, -2],\n [0, -2, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-2, 6, -2, -4],\n [3, -9, 3, 6],\n [-3, 9, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, 0, -2, 0],\n [-3, -8, -9, 4],\n [-12, 12, 14, -6],\n [-18, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -12, 12, 14],\n [8, 9, -16, -14],\n [-12, 0, 6, 3],\n [0, 9, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -15, 9, 12],\n [9, -15, 33, 6],\n [-2, -13, 16, -6],\n [-5, 13, -25, -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[[-24, -24, 10, -10],\n [20, 16, 3, -13],\n [0, -1, -8, 12],\n [0, 2, 11, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -6, 3, 3],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -8, 4, 0],\n [-6, -8, 4, 0],\n [12, 16, -8, 0],\n [-12, -16, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -6, 20, 18],\n [1, -2, 7, 25],\n [4, 14, -13, -3],\n [4, -2, 14, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 2, 14, 6],\n [16, 4, 18, 9],\n [-16, 4, -22, -3],\n [-12, -10, -10, -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[[0, -6, 0, 6],\n [0, 6, 0, -6],\n [0, -3, 0, 3],\n [0, -6, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 1, 2, -2],\n [-8, -2, -4, 4],\n [-12, -3, -6, 6],\n [-4, -1, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 3, 7, 11],\n [3, -2, -18, -24],\n [-6, -6, -14, -22],\n [3, 0, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, 20, 2, -6],\n [-28, -26, 0, 9],\n [-4, 24, 14, 6],\n [8, -20, -21, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 7, -8, -14],\n [9, -6, -15, 12],\n [7, -2, -17, 4],\n [5, 2, -19, -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[[-9, 12, -6, -3],\n [6, -8, 4, 2],\n [12, -16, 8, 4],\n [6, -8, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-3, 3, 0, 4],\n [3, -3, 0, -4],\n [-9, 9, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -4, -1, 1],\n [1, -4, -1, 1],\n [4, -16, -4, 4],\n [3, -12, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 7, -7, 2],\n [17, 16, -19, 2],\n [-17, -16, 19, -2],\n [-16, -25, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -8, -8, -8],\n [-8, -10, -16, -6],\n [0, -1, 8, -7],\n [-2, -3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 17, 6, -1],\n [5, -9, 5, -7],\n [-2, 8, -23, 24],\n [2, 13, 22, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 20, 7, 16],\n [-1, -12, -2, -14],\n [3, 12, 3, 12],\n [-6, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 4, 6, 6],\n [-20, -12, -20, -8],\n [11, 9, 17, -4],\n [20, 12, 20, 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[[7, -1, 5, 12],\n [5, 4, -3, 15],\n [-11, -5, 1, -16],\n [10, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 8, -16, 4],\n [6, 6, -12, 3],\n [4, 4, -8, 2],\n [2, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 2, 8, 4],\n [-12, -4, -8, -16],\n [7, 4, 18, 6],\n [-6, -3, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -2, 0, 2],\n [-3, 1, 0, -1],\n [6, -2, 0, 2],\n [-3, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 3, 2, -1],\n [-9, 3, 0, -12],\n [8, 2, 4, 14],\n [18, -13, -6, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 8, 4],\n [0, 0, -8, -4],\n [0, 0, 0, 0],\n [0, 0, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-16, -8, 12, 12],\n [-4, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -6, 4, 0],\n [0, -3, 2, 0],\n [0, -3, 2, 0],\n [0, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -24, -2, 2],\n [1, -4, 3, -1],\n [-4, 16, -2, 0],\n [-1, 4, 2, -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 4x4 matrix:\n[[-6, 2, 2, 2],\n [3, -1, -1, -1],\n [-12, 4, 4, 4],\n [-9, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -4, 0, 4],\n [-6, -2, 0, 2],\n [-6, -2, 0, 2],\n [9, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, 6, 0],\n [9, -9, 9, 0],\n [12, -12, 12, 0],\n [12, -12, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -9, 11, 12],\n [0, -12, 20, 0],\n [-6, 0, -4, 12],\n [2, 11, -17, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 16, -1, -5],\n [6, -8, 2, 1],\n [15, -36, 5, 7],\n [4, 0, -7, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -4, -6, -17],\n [-3, 12, 6, 3],\n [-3, 12, 6, 3],\n [-2, 8, 7, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-3, -3, 12, 6],\n [3, 3, -12, -6],\n [-4, -4, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -6, 8, 8],\n [16, -4, -13, -1],\n [-9, 11, 1, -8],\n [6, 10, -5, -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[[20, 20, 0, 1],\n [16, 16, -3, 4],\n [10, 10, -12, 22],\n [-14, -14, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 17, 12, -7],\n [4, 3, 4, -3],\n [-3, 3, -12, 12],\n [3, 4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [2, 2, 0, -1],\n [-6, -6, 0, 3],\n [-2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, -18, -19, -3],\n [12, 10, 10, 0],\n [-3, -6, -13, -21],\n [6, 8, 14, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -14, 8, 0],\n [-18, 11, -20, 16],\n [0, 0, 0, 0],\n [-18, 11, -20, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 10, 0, 0],\n [-16, -14, 0, -12],\n [-15, -5, 9, 2],\n [9, 17, 3, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, 0, 6, -6],\n [6, 0, -6, 6],\n [2, 0, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 12, 4, -4],\n [12, 16, 4, -16],\n [0, -2, -2, -10],\n [2, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 0, -12, 9],\n [0, 0, 0, 0],\n [-4, 0, 4, -3],\n [-8, 0, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 19, 4, -7],\n [15, -16, -10, 0],\n [12, -15, -6, 3],\n [-6, 2, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 16, 16, -8],\n [4, -10, 2, -2],\n [-18, 3, 9, 10],\n [20, 28, -17, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 6, 8, -4],\n [20, 1, 18, -4],\n [14, 1, 13, -3],\n [-8, -4, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 4, -2, 3],\n [10, 14, -16, -13],\n [-16, -4, 10, 14],\n [4, 10, -7, -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[[-1, -14, 18, 1],\n [-4, -24, 28, -4],\n [1, 6, -7, 1],\n [-8, -16, 12, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 1, 7, 8],\n [10, 0, -10, -12],\n [14, -8, -6, -4],\n [10, -5, -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, 0, -11, 12],\n [-8, -11, -1, -8],\n [0, 1, -2, 4],\n [12, -17, -14, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -16, -8, -8],\n [0, 16, 8, 8],\n [0, 8, 4, 4],\n [0, 8, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 3, 6, 6],\n [12, 4, 8, 8],\n [0, 0, 0, 0],\n [-12, -4, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -4, 0, 8],\n [18, 12, 9, -24],\n [-10, -2, 2, 4],\n [4, 6, 7, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [-9, -12, 3, -9],\n [12, 16, -4, 12],\n [-6, -8, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 7, 3, 7],\n [20, 6, -6, 1],\n [-20, -13, 3, -8],\n [-16, -9, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 12, -4, 4],\n [4, 0, 4, -16],\n [-4, -16, 8, -16],\n [7, 20, -8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 15, -4, -13],\n [2, 6, -2, -8],\n [1, 9, -4, -19],\n [3, 1, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 5, -4, 2],\n [12, 6, -12, -12],\n [-24, -4, 16, 24],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 10, 14, 12],\n [-6, 12, 12, 8],\n [26, -16, 1, -3],\n [3, 6, 9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -12, 4, -4],\n [-16, -12, 4, -4],\n [-4, -3, 1, -1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-22, 14, -1, -3],\n [-11, 6, 2, -3],\n [9, -5, 0, 1],\n [-12, 9, -11, 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 4x4 matrix:\n[[-8, 8, 4, -6],\n [16, -16, -8, 12],\n [16, -16, -8, 12],\n [-8, 8, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -8, 5, -3],\n [-11, 8, 1, -7],\n [2, -6, 3, -1],\n [-13, 14, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 2, -3, -3],\n [4, -8, 12, 12],\n [-4, 8, -12, -12],\n [4, -8, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 12, 16, 12],\n [-8, 12, 16, 12],\n [8, -12, -16, -12],\n [-4, 6, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -10, -13, -13],\n [2, -5, 7, 7],\n [9, -1, 14, 14],\n [-9, -2, -11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -12, 8, 4],\n [-6, -13, 2, 4],\n [6, 6, -4, -2],\n [0, -14, -4, 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[[3, -3, 3, 6],\n [-4, 4, -4, -8],\n [4, -4, 4, 8],\n [-2, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [2, 8, 0, -4],\n [1, 4, 0, -2],\n [-4, -16, 0, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -16, -8, 16],\n [-2, 8, 4, -8],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -6, -6, -12],\n [0, 14, -2, -12],\n [13, 10, 6, 10],\n [12, -8, 8, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -2, -4, -8],\n [6, 2, 4, 8],\n [-2, -1, -2, -4],\n [-3, -1, -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[[12, -3, 10, 10],\n [8, 5, 2, 9],\n [16, 4, 8, 16],\n [-16, 14, -20, -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[[-4, -7, -6, 5],\n [-16, -18, -14, 5],\n [-12, -9, -6, -3],\n [0, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -1, 4, 3],\n [2, 1, -4, -3],\n [4, -7, 16, 0],\n [0, 3, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 8, -16, -4],\n [-9, -6, 12, 3],\n [0, 0, 0, 0],\n [-6, -4, 8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -3, 9, -9],\n [-3, -3, 9, -9],\n [2, 2, -6, 6],\n [-2, -2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -16, 8, 4],\n [1, 4, -2, -1],\n [4, 16, -8, -4],\n [4, 16, -8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, -14, -9, 0],\n [2, 14, -6, -12],\n [-6, 2, 6, 0],\n [1, 5, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 4, -11, 0],\n [3, -10, -5, 13],\n [-12, 12, -8, -10],\n [6, -16, -6, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -9, 0, 6],\n [-8, -6, 0, 4],\n [16, 12, 0, -8],\n [12, 9, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -6, -2, 4],\n [-16, -13, -2, 6],\n [-9, -9, -3, 6],\n [14, 8, -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, 8, -14, 0],\n [1, 5, -5, 0],\n [-10, 6, 2, 0],\n [-13, -2, 11, 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[[-2, 5, 1, 1],\n [20, -2, 2, 8],\n [14, -3, 1, 5],\n [2, -9, 17, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 2, 2, 3],\n [-10, -6, -4, 3],\n [-8, 8, 8, 12],\n [-20, -12, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 13, 17, 13],\n [10, 10, 8, 13],\n [10, 9, 9, 11],\n [8, 8, 10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, -15, 8],\n [-6, -3, 14, -5],\n [2, -2, -1, 0],\n [7, 5, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-21, 8, -4, 13],\n [-9, -3, -12, 12],\n [0, 5, 8, -5],\n [21, -13, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -6, -8, -2],\n [3, -9, -12, -3],\n [3, -9, -12, -3],\n [2, -6, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 12, -10, 14],\n [-4, 16, -14, 18],\n [1, -6, 5, -7],\n [-2, 12, -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[[6, -8, -4, 20],\n [-16, 0, 14, -24],\n [0, -16, 5, 12],\n [11, 18, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 0, 0, -2],\n [-9, 0, 0, 3],\n [-3, 0, 0, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 11, 3, 16],\n [-27, 7, 26, 13],\n [-19, 3, 19, 4],\n [-2, -4, -1, 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[[-8, 8, -2, -2],\n [12, -12, 3, 3],\n [16, -16, 4, 4],\n [-16, 16, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 12, 14, 11],\n [19, 6, -5, -13],\n [-13, -8, -14, 5],\n [-14, -16, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 4, 16, 16],\n [-3, -1, -4, -4],\n [-9, -3, -12, -12],\n [3, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 2, 4, -2],\n [0, 8, 12, 4],\n [-2, 6, 10, 0],\n [12, -8, -18, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -6, -12, -15],\n [-12, -7, -12, -12],\n [6, -1, 8, 18],\n [15, -24, -14, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, -7, 5],\n [-3, -3, -6, -5],\n [12, 0, 18, 2],\n [3, -5, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 12, -16, 16],\n [-4, 12, -16, 16],\n [-2, 6, -8, 8],\n [-2, 6, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, -6, -4],\n [0, 0, 0, 0],\n [8, 2, -6, -4],\n [16, 4, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 2, 1, 2],\n [21, -5, 0, 22],\n [-19, -13, -19, -2],\n [14, -8, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 8, -3, 4],\n [4, 4, -6, 8],\n [0, -4, -12, 16],\n [0, 4, 12, -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[[-4, 0, 4, -24],\n [-4, -20, 19, -14],\n [-1, -4, 4, -4],\n [-1, -20, 16, 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 4x4 matrix:\n[[-4, 10, 4, 6],\n [3, 9, -9, 3],\n [-5, -1, 11, -3],\n [-5, -6, 7, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 0, 3, -3],\n [0, 0, 0, 0],\n [4, 0, 2, -2],\n [4, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[21, 16, -1, -10],\n [-2, 8, 17, -5],\n [26, 18, 5, -13],\n [-5, -4, -19, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 2, -4, 2],\n [12, 6, -12, 6],\n [4, 2, -4, 2],\n [-16, -8, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 9, -6, -3],\n [0, -9, 6, 3],\n [0, 9, -6, -3],\n [0, -3, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, 24, 12, 10],\n [16, 16, 9, 9],\n [36, 36, 9, 10],\n [0, 0, 9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 12, -12, -7],\n [0, 24, -12, -3],\n [12, 0, -4, -4],\n [-2, 4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-2, -2, 8, -2],\n [-1, -1, 4, -1],\n [-3, -3, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -3, -3, -3],\n [6, 2, 2, 2],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 1, -2, 3],\n [3, 3, 8, -11],\n [-2, -4, -6, 8],\n [7, 2, 17, -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[[2, -2, 2, 1],\n [6, -6, 6, 3],\n [2, -2, 2, 1],\n [-2, 2, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 3, 1, 14],\n [13, -1, 13, 2],\n [-25, 4, -16, 10],\n [2, 1, 7, 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[[16, 0, 4, 12],\n [12, 0, 3, 9],\n [-12, 0, -3, -9],\n [8, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 1, -3, 16],\n [13, 5, -13, 16],\n [5, 3, -6, 11],\n [-4, 15, 9, -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[[-14, -17, 26, 9],\n [0, -12, 24, 4],\n [8, -10, 16, 10],\n [-10, 11, -23, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 8, 11, -18],\n [-18, -9, -15, 21],\n [10, 9, 12, -21],\n [16, -3, 8, 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 4x4 matrix:\n[[10, -8, -4, -4],\n [0, 4, 6, 2],\n [4, -12, -16, -3],\n [-12, 12, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, 1, 0],\n [0, 0, 0, 0],\n [6, 0, -3, 0],\n [6, 0, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [4, -4, 2, 4],\n [0, 6, -2, -7],\n [-6, -12, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 1, -3, -4],\n [0, 4, -12, -16],\n [0, -1, 3, 4],\n [0, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -17, 16, -13],\n [11, 2, -20, -3],\n [-10, -1, -14, 6],\n [-16, -7, 1, 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 4x4 matrix:\n[[-4, -1, -4, 3],\n [-1, 10, -4, -4],\n [4, 5, -8, 1],\n [-22, 14, -25, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 6, -8, 8],\n [-14, -8, -8, 14],\n [-9, 12, -6, 3],\n [4, 8, 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 4x4 matrix:\n[[-3, 3, 3, 12],\n [-2, 2, 2, 8],\n [1, -1, -1, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -2, 4, 6],\n [-3, 9, 9, 12],\n [-4, 2, 5, 7],\n [-2, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 7, 3, -3],\n [6, 2, -2, 2],\n [3, 3, 1, -1],\n [-24, -20, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 0, -9, 0],\n [4, 0, -3, 0],\n [4, 0, -3, 0],\n [16, 0, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -1, -5, -2],\n [4, 4, 4, -12],\n [9, -2, -8, 1],\n [-5, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 0, 4, 6],\n [0, 0, 0, 0],\n [-6, 0, 4, 6],\n [6, 0, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, -6, 0],\n [16, 0, 8, 0],\n [-8, 0, -4, 0],\n [-16, 0, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 10, -2, -5],\n [-12, -6, 0, 6],\n [0, 0, -2, 5],\n [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[[16, -12, -4, -16],\n [-16, 12, 4, 16],\n [4, -3, -1, -4],\n [8, -6, -2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, -12, 5, 9],\n [8, -12, -1, -9],\n [-8, 12, 1, 9],\n [-17, 16, -5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, -7, 8],\n [-10, 6, 18, -20],\n [-8, 6, 22, -24],\n [-4, -2, 6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -9, -9, -5],\n [1, 9, -4, -2],\n [-14, -18, -4, -4],\n [-19, -12, -7, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, -12, -4, 16],\n [0, -6, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 8, -16, -4],\n [6, -6, 12, 3],\n [-4, 4, -8, -2],\n [6, -6, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 8, -2, 3],\n [6, -16, 6, -8],\n [18, 4, 18, 14],\n [-24, 12, -11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, -2, -6],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-6, 0, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 8, -4, 12],\n [0, -8, 4, -12],\n [10, 16, -13, 14],\n [-2, 4, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -12, 12, 4],\n [20, 7, -12, -1],\n [-10, 3, 3, -5],\n [10, 8, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -3, -4, -16],\n [-4, -9, -12, -6],\n [0, 6, 8, -4],\n [-5, -3, -4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -8, 16, 0],\n [2, 2, -4, 0],\n [6, 6, -12, 0],\n [-2, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 8, -16, -16],\n [6, -4, 8, 8],\n [3, -2, 4, 4],\n [-12, 8, -16, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -1, 2, 5],\n [0, 10, 16, -14],\n [-12, 12, -8, 4],\n [-15, 25, 6, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -8, -16, 8],\n [8, -4, -8, 4],\n [12, -6, -12, 6],\n [12, -6, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, 0, -4],\n [12, -6, 0, 12],\n [16, -8, 0, 16],\n [-8, 4, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 3, 2, -4],\n [6, -6, -4, 8],\n [-3, 3, 2, -4],\n [9, -9, -6, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 17, -5, -10],\n [-4, -4, 1, 2],\n [0, 28, -8, -16],\n [-28, 0, -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 4x4 matrix:\n[[13, 19, 13, 1],\n [-6, -17, -15, -6],\n [9, 9, 6, -2],\n [-1, 8, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 13, -16, -12],\n [12, -1, -8, -2],\n [-7, 2, 4, -1],\n [18, -27, 16, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [8, -12, 8, -12],\n [6, -9, 6, -9],\n [6, -9, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 3, -9, 6],\n [0, 0, 0, 0],\n [-2, -2, 6, -4],\n [-2, -2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 6, -3, -4],\n [8, -4, 1, -3],\n [-22, 13, -7, 14],\n [-10, 31, -25, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 6, 2, 4],\n [4, -3, -1, -2],\n [-4, 3, 1, 2],\n [4, -3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, -6, -2, 9],\n [-13, -12, -17, -4],\n [22, 6, 2, -9],\n [3, -14, 19, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -1, -3, -1],\n [-4, 10, 18, 4],\n [11, -10, -12, -1],\n [2, -5, -9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 4, -2, 0],\n [12, 6, -3, 0],\n [4, 2, -1, 0],\n [-16, -8, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 9, 12, -12],\n [0, 0, 0, 0],\n [4, 3, 4, -4],\n [16, 12, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [4, 4, 3, 4],\n [-16, -16, -12, -16],\n [4, 4, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -6, 11, 4],\n [5, 0, -28, -13],\n [-16, 8, 20, -4],\n [4, -2, -11, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 16, 12, -4],\n [9, -10, -3, 10],\n [4, -23, -9, 1],\n [-7, 15, 8, -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[[17, 19, -7, -3],\n [-16, -25, 11, 6],\n [-13, -24, 13, 9],\n [15, -8, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -11, 18, -1],\n [-1, -8, -10, 15],\n [-22, -23, -4, 24],\n [6, 11, 2, -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[[7, -26, 26, -3],\n [-15, 4, -4, -4],\n [-6, 8, -8, 0],\n [-12, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 4, 2, 2],\n [0, 0, 0, 0],\n [-9, -6, -6, -9],\n [-9, -6, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -6, 11, -2],\n [4, -10, -14, 19],\n [0, -10, 9, -6],\n [-1, 8, 20, -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[[15, 9, 6, 1],\n [-14, 10, 0, -14],\n [17, -1, 12, 11],\n [-13, 5, 3, -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[[-1, -14, 3, 8],\n [-7, 1, 10, 1],\n [5, 16, -9, -10],\n [3, -3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 6, -10, 3],\n [-2, -11, -2, -1],\n [-2, 8, -8, 4],\n [4, 10, -14, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 0, 5, 2],\n [-8, 6, -6, -4],\n [7, -6, 1, 2],\n [16, -15, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -2, 6, -21],\n [-12, -10, 2, -14],\n [-2, -14, -6, -2],\n [-20, -10, 10, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -12, 9, -9],\n [-2, -4, 3, -3],\n [4, 8, -6, 6],\n [8, 16, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -10, -10, 2],\n [3, 6, 18, -6],\n [-5, -6, 2, -2],\n [-6, -9, -12, 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[[5, 10, 10, 4],\n [7, -2, 6, 4],\n [1, 14, 8, 2],\n [-14, -16, -22, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -16, 16, 4],\n [-4, -16, 16, 4],\n [3, 12, -12, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -16, 12, 4],\n [0, -8, 6, 2],\n [0, -16, 12, 4],\n [0, -8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 2],\n [-15, 0, -10, 7],\n [-21, 0, -14, 15],\n [-9, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 13, 12, -7],\n [2, 1, 4, 11],\n [-18, 19, 20, -1],\n [-6, 7, 8, 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 4x4 matrix:\n[[-18, -6, -6, 12],\n [-18, -12, -6, 12],\n [18, 12, 6, -12],\n [-15, -8, -5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 20, -28, 24],\n [1, 7, -15, 12],\n [-4, 2, 5, -3],\n [-2, 10, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -4, 0, 1],\n [-1, -4, 6, -5],\n [4, 16, -14, 10],\n [-3, -12, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -2, 4, 4],\n [6, -2, 4, 4],\n [6, -2, 4, 4],\n [12, -4, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [3, -3, 3, -2],\n [-6, 6, -6, 4],\n [6, -6, 6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 4, -6, -3],\n [-6, 0, 6, 2],\n [3, 4, -6, -3],\n [-3, 16, -9, -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[[-5, -9, -5, -2],\n [6, 12, 6, 3],\n [8, 12, 6, 4],\n [12, -12, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -20, 8, 24],\n [-12, 0, -14, 3],\n [-10, 14, -14, -15],\n [-7, -1, -8, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [-4, 2, 6, 3],\n [-2, -4, 3, -6],\n [-6, -8, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -14, 5, 1],\n [17, 8, 3, -17],\n [17, -4, 19, -7],\n [-8, 18, -12, 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 4x4 matrix:\n[[3, -3, 1, 1],\n [12, -18, -4, 8],\n [-6, 12, 6, -6],\n [-3, 9, 7, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [3, -6, 3, 6],\n [-2, 4, -2, -4],\n [1, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -8, -8, -8],\n [-4, 8, 8, 8],\n [0, 0, 0, 0],\n [3, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 6, -1, -5],\n [-12, 7, 5, 10],\n [-20, -10, 6, 12],\n [12, 8, -16, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -10, -8, 0],\n [12, -3, 16, 7],\n [8, -8, 12, 7],\n [-12, 0, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 1, 2, 11],\n [0, -16, 9, -17],\n [0, -12, 6, -6],\n [4, -2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 6, -8, 8],\n [-16, -12, 16, -16],\n [16, 12, -16, 16],\n [4, 3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -4, 6, 6],\n [-2, 4, -6, -6],\n [-4, 8, -12, -12],\n [-2, 4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 8, -6, -4],\n [4, -6, -4, -2],\n [-22, 25, -6, -5],\n [10, -13, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -12, -8, -8],\n [-4, -3, -2, -2],\n [-12, -9, -6, -6],\n [-4, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [8, 12, -8, 4],\n [0, 0, 0, 0],\n [4, 6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -12, -10, -13],\n [-3, -6, -8, -5],\n [10, 12, 8, 14],\n [-7, -6, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -8, -9, -5],\n [0, -1, -9, -5],\n [7, 9, 6, 2],\n [-25, -19, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -3, 6, 5],\n [5, -7, -10, 1],\n [-17, -12, -3, 21],\n [12, 2, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 9, 11, 2],\n [-17, 6, -1, -7],\n [-17, 6, -1, -7],\n [-3, -15, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 5, -6, 2],\n [2, 6, 4, 1],\n [-3, -19, -6, -4],\n [-3, -11, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 13, -15, 4],\n [-10, -5, 20, 0],\n [-10, 3, 28, 32],\n [10, -7, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -4, -2, 1],\n [-2, -4, -2, 1],\n [-4, -8, -4, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -6, 10, -14],\n [6, 4, -2, 4],\n [16, 10, 2, 2],\n [9, 5, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -12, -6, 9],\n [6, 8, 4, -6],\n [12, 16, 8, -12],\n [6, 8, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 4, 6, 8],\n [6, -4, -6, -8],\n [9, -6, -9, -12],\n [3, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 22, -8, 12],\n [6, 14, -4, 6],\n [6, 14, -4, 6],\n [12, 19, -8, 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 4x4 matrix:\n[[6, -6, 0, -3],\n [-15, 22, -14, -17],\n [5, -4, -2, -6],\n [-2, 4, -4, -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[[15, 33, 26, -20],\n [1, 18, 11, -14],\n [-7, -11, -10, 6],\n [1, -24, -19, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -17, -8, -14],\n [-12, 10, 13, 8],\n [8, -11, 1, -7],\n [-12, -25, 8, -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[[-19, -9, -5, -6],\n [-6, -2, 6, -4],\n [25, 11, -1, 10],\n [-8, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, 4, -16],\n [-4, 4, -2, 8],\n [6, -6, 3, -12],\n [-2, 2, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 7, 6, -1],\n [1, 21, 2, 1],\n [-4, 24, -2, 14],\n [3, -19, 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 4x4 matrix:\n[[3, -6, 3, -3],\n [-7, 5, -3, 8],\n [-5, 1, -1, 6],\n [-3, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -8, 12, -12],\n [0, 0, 0, 0],\n [8, -4, 6, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, 2, 24, -13],\n [-8, 4, 6, -2],\n [12, -12, 10, -10],\n [10, -2, -17, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, -6, -6],\n [3, 3, 3, 0],\n [2, 8, -4, -6],\n [-3, -15, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 9, -9, 9],\n [-12, -12, 12, -12],\n [-12, -12, 12, -12],\n [-9, -9, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -6, -10, -11],\n [4, -4, 4, -2],\n [8, -6, 2, -5],\n [20, -8, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 2, 10, 9],\n [-12, 6, 10, 7],\n [0, -8, 6, 9],\n [0, 2, -4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 5, -5, -15],\n [3, 7, 5, -3],\n [-3, 13, -1, -9],\n [1, -16, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -6, -9, 9],\n [0, -6, -9, 9],\n [0, 8, 12, -12],\n [0, 8, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -7, 28, 14],\n [-1, 0, -26, -16],\n [-1, -18, -2, -28],\n [9, -6, 10, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -3, -12, 12],\n [2, 1, 4, -4],\n [4, 2, 8, -8],\n [4, 2, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 4, -4, 12],\n [2, -14, -10, -2],\n [-4, 12, 12, -4],\n [0, -12, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -1, 2, 0],\n [-4, -4, 8, 0],\n [-2, -2, 4, 0],\n [-4, -4, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -6, -2, 2],\n [-8, -12, -8, 12],\n [1, 6, 2, -2],\n [-16, 12, -8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 0, 4, -2],\n [-1, 0, -2, 1],\n [0, 0, 0, 0],\n [-1, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -12, 9, -9],\n [-15, -21, 15, -21],\n [-8, -16, 12, -12],\n [2, 4, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -3, -9, 23],\n [-1, -11, -7, -7],\n [10, 10, 2, 18],\n [0, -18, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -10, 12, 14],\n [8, 10, -16, -10],\n [-8, 8, 16, -8],\n [-10, -2, 20, 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 4x4 matrix:\n[[-16, 22, 19, 4],\n [22, -17, -14, -7],\n [-22, 21, 17, 9],\n [-8, 0, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 10, -14, -14],\n [8, 8, -20, 4],\n [-20, 14, -9, 7],\n [-4, 8, -11, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-3, 3, 3, -6],\n [-1, 1, 1, -2],\n [2, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, -9, 6, -1],\n [-5, 8, -5, 3],\n [-6, 0, 0, 3],\n [10, -15, 11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -3, 0, 4],\n [8, -6, 0, 8],\n [-4, 3, 0, -4],\n [8, -6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 27, -14, 6],\n [-1, 7, -3, -1],\n [-16, -7, 1, -11],\n [11, 13, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -4, -5, -7],\n [13, 5, 2, -8],\n [-28, -2, -1, 1],\n [4, 16, 10, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 1, 1, 20],\n [16, -1, -1, -20],\n [-8, 6, 2, 8],\n [14, 6, 1, -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[[-8, -16, -8, -8],\n [4, 14, 11, 7],\n [6, -6, -15, -3],\n [-4, 10, 17, 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, -3, 3, 12],\n [9, -18, 2, -20],\n [-4, 11, -3, 8],\n [-7, -9, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 4, 2, -6],\n [-6, 6, 3, -9],\n [6, -6, -3, 9],\n [4, -4, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 0, 3, 0],\n [-1, 0, -3, -9],\n [6, 0, -3, 12],\n [-2, 0, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, -3, 6],\n [-11, -6, 7, -3],\n [-7, 9, -5, -9],\n [11, -15, 12, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, -8, -2],\n [-4, -14, 20, 8],\n [4, 6, -4, 0],\n [6, 6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 16, -12, -12],\n [-4, 0, 13, 13],\n [16, -12, -4, -4],\n [-8, 8, -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[[6, 0, 12, 6],\n [0, 0, 0, 0],\n [8, 0, 16, 8],\n [-6, 0, -12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 26, 2, 20],\n [-1, -11, 2, -8],\n [9, -15, 12, -24],\n [-10, 4, -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[[-2, -8, 2, 2],\n [4, 16, -4, -4],\n [4, 16, -4, -4],\n [-1, -4, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -5, -19, 13],\n [0, -6, -6, 3],\n [-2, 14, -6, -5],\n [-3, 9, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -15, 10, 3],\n [-13, 9, 7, 15],\n [18, -30, 6, -12],\n [-31, 19, 20, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, 5, -6, -10],\n [-34, 5, -6, -22],\n [21, 6, 11, 13],\n [17, -13, -13, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 6, 0, 6],\n [4, 3, 0, 3],\n [16, 12, 0, 12],\n [16, 12, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -7, 5, 15],\n [-28, -11, -7, 5],\n [-21, 10, -17, -11],\n [9, 21, -6, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 10, 9, -5],\n [1, -5, 2, 5],\n [6, -6, -8, 2],\n [0, -6, 5, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 9, 9, 3],\n [-8, -24, -24, -4],\n [1, -15, -15, 2],\n [4, -12, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 7, -16, -6],\n [0, -1, 12, -5],\n [16, -5, 20, 3],\n [-4, 3, 6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -9, -3, -12],\n [-6, -6, -2, -8],\n [-9, -9, -3, -12],\n [-3, -3, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 12, 3, 3],\n [0, -12, -3, -3],\n [0, 8, 2, 2],\n [0, -16, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 2, -4, -2],\n [-12, 6, -12, -6],\n [12, -6, 12, 6],\n [-12, 6, -12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -8, 4, 16],\n [-3, 8, -7, -8],\n [-4, 11, -10, -10],\n [-1, 3, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -12, 12, 4],\n [-22, 24, -24, 24],\n [4, -12, 12, 0],\n [18, -24, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -5, -9, -1],\n [0, -8, 0, -7],\n [2, 2, 2, 1],\n [-2, -10, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -27, -20, -22],\n [2, 17, 8, 16],\n [-22, -1, 4, 6],\n [0, -1, 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[[-9, 12, -9, 6],\n [-10, 4, -10, 9],\n [2, 4, 2, -3],\n [8, 16, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 2, -3, -2],\n [29, -12, 13, 12],\n [22, -10, 12, 6],\n [-26, 26, -26, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -3, -18, -3],\n [-5, 0, -14, -2],\n [-9, 11, 10, 3],\n [5, -10, -18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -12, 7, 9],\n [-1, -5, -5, -18],\n [8, -4, 6, -8],\n [5, -7, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 8, 8, 8],\n [-2, 2, 2, 2],\n [8, -8, -8, -8],\n [6, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 8, 8, -8],\n [0, 0, 0, 0],\n [1, 4, 4, -4],\n [-1, -4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 6, -6, 6],\n [12, 8, -8, 8],\n [0, 0, 0, 0],\n [3, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -16, 16, 16],\n [-8, 16, -16, -16],\n [4, -8, 8, 8],\n [4, -8, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -2, -8, -6],\n [0, 0, 0, 0],\n [-4, -4, -16, -12],\n [3, 3, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, -3, 4],\n [4, -2, -3, 4],\n [-12, 6, 9, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -2, 0, -1],\n [6, 4, 0, 2],\n [-6, -4, 0, -2],\n [-9, -6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 8, -14, 2],\n [-3, 3, 3, 3],\n [-7, 5, 7, -4],\n [2, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 0, 2, -3],\n [0, 0, 0, 0],\n [3, 0, 2, -3],\n [-12, 0, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -4, -12, 4],\n [1, 1, 3, -1],\n [1, 1, 3, -1],\n [-3, -3, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-19, -19, 24, 2],\n [-5, -5, 7, 0],\n [9, 9, 3, -12],\n [-8, -8, 19, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 20, 10, 14],\n [8, 3, -17, -11],\n [18, -1, -18, -14],\n [0, -1, -24, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, -2, -3, 1],\n [-12, -6, -9, 3],\n [-8, -4, -6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 2, -23, -11],\n [4, 4, -10, -27],\n [8, 8, 16, 18],\n [-14, -12, 0, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 4, 4, 12],\n [7, -3, -7, -17],\n [4, 0, 8, 16],\n [-9, 2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, -2, -6],\n [-4, 8, -2, -6],\n [4, -8, 2, 6],\n [2, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -16, -4, -12],\n [-3, 12, 3, 9],\n [-1, 4, 1, 3],\n [-1, 4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -1, -16, -3],\n [5, 6, -11, -4],\n [-13, -18, 15, -2],\n [-6, -8, -2, -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[[-10, -12, -9, 3],\n [-4, -4, -8, -4],\n [1, 0, 6, 3],\n [14, 19, 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[[8, 0, 12, -12],\n [-6, 0, -9, 9],\n [-4, 0, -6, 6],\n [4, 0, 6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 2, 14, -2],\n [1, 4, -2, 10],\n [-10, 4, 14, -2],\n [0, 2, 8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -3, 12, -3],\n [9, 3, -12, 3],\n [-6, -2, 8, -2],\n [-12, -4, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 3, 1, -4],\n [3, -3, -1, 4],\n [3, -3, -1, 4],\n [6, -6, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, 0, -4, 4],\n [8, 0, 8, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -8, 0, -4],\n [-8, -4, 0, -2],\n [-8, -4, 0, -2],\n [-8, -4, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 4, -6, 2],\n [-8, 4, -2, 6],\n [-4, 8, 2, 18],\n [16, -4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 2, 6, -2],\n [-16, 0, 10, 4],\n [-6, -15, -9, -3],\n [-6, -14, -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[[1, 3, 10, 11],\n [-12, 4, -16, -12],\n [7, -9, -8, -13],\n [16, -12, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -8, 4, 2],\n [-6, -8, 4, 2],\n [0, 0, 0, 0],\n [9, 12, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 8, 2, -6],\n [2, -4, -1, 3],\n [-2, 4, 1, -3],\n [8, -16, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -6, 10, 8],\n [0, 2, -6, 0],\n [25, 14, -17, -25],\n [21, 12, -15, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[33, 5, 15, -14],\n [-12, 6, -12, 0],\n [-4, -12, 4, 24],\n [1, -20, 19, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -6, -4, -6],\n [0, -12, -8, -12],\n [0, -6, -4, -6],\n [0, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -6, -2, 8],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [8, -12, -4, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 14, 6, 4],\n [-14, 16, 0, 2],\n [4, -2, 6, 2],\n [0, 3, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 20, 0, 4],\n [-8, 6, -3, -5],\n [2, -11, -5, -13],\n [12, 10, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 0, 8, 8],\n [4, 0, -4, -4],\n [6, 0, -6, -6],\n [4, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, -1, -10, 28],\n [-9, 6, 1, -14],\n [4, -1, -1, -1],\n [-13, 1, 7, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 12, 4, -4],\n [0, 0, 0, 0],\n [-3, 9, 3, -3],\n [3, -9, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 3, 9, 3],\n [4, -2, -6, -2],\n [-6, 3, 9, 3],\n [2, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 3, 9, -6],\n [8, 2, 6, -4],\n [-8, -2, -6, 4],\n [-8, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -21, -9, -24],\n [3, -21, -9, -24],\n [-21, -3, -12, -7],\n [-12, 6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -4, 4, -9],\n [2, -18, -2, -1],\n [14, 8, -6, -1],\n [-5, -6, 2, 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[[0, 12, 11, 2],\n [5, -21, 4, 18],\n [2, -11, 6, 13],\n [-7, -4, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, -8, 0, 1],\n [4, -5, 2, -1],\n [10, -16, 0, 2],\n [-3, -5, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[34, -10, -20, 26],\n [18, -2, -8, 10],\n [-5, -7, -6, 9],\n [-2, 0, -5, 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 4x4 matrix:\n[[-28, 4, 5, -8],\n [3, 0, -6, 3],\n [1, 2, 4, 11],\n [10, -1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -9, -12, 3],\n [-9, -9, -12, 3],\n [0, 0, 0, 0],\n [-12, -12, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [4, 16, -4, -8],\n [1, 4, -1, -2],\n [2, 8, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 16, -4, -16],\n [22, -1, 16, -5],\n [-30, -7, -11, 13],\n [-2, 12, -18, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 5, -4, -10],\n [0, -1, 0, 1],\n [2, -7, 16, -7],\n [10, 6, -8, -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 4x4 matrix:\n[[-2, 1, -3, 0],\n [-8, 4, -12, 0],\n [2, -1, 3, 0],\n [8, -4, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -10, -11, 5],\n [1, 2, -1, 7],\n [2, -10, -9, 0],\n [4, -2, -9, 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, 6, 12],\n [1, -4, 2, 4],\n [3, -12, 6, 12],\n [-1, 4, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [3, 12, 6, 9],\n [0, 0, 0, 0],\n [3, 12, 6, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 4, 4, 30],\n [4, 16, -4, -8],\n [5, -5, 0, -14],\n [12, 32, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -12, 6, 25],\n [20, 0, 4, 12],\n [7, -6, 6, 5],\n [-4, -3, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 2, -3, 11],\n [13, -12, 3, 37],\n [7, 8, -1, 3],\n [-13, 1, 0, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 4, -7, -12],\n [-2, 2, -2, -3],\n [5, 10, -1, 3],\n [-7, 2, -5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 9, 6, 0],\n [10, -12, -19, 1],\n [18, -18, -24, 2],\n [-6, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -2, -4, 15],\n [0, -8, -24, 10],\n [-22, -8, 16, 7],\n [-16, -4, 28, -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[[1, -2, -4, -4],\n [-4, 12, -8, -4],\n [1, -2, -4, -4],\n [8, -20, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-1, 1, 4, -4],\n [3, -3, -12, 12],\n [4, -4, -16, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -6, 14, -5],\n [2, -8, 4, 6],\n [1, -5, 1, 5],\n [-8, 12, -20, 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[[16, 8, 7, -5],\n [29, -8, 1, 4],\n [5, -12, -4, -5],\n [25, -6, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 11, 3, -6],\n [11, 14, 3, -15],\n [1, 4, 1, -3],\n [20, 20, 4, -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[[-24, -24, -12, 32],\n [2, 9, 9, -6],\n [2, 14, 9, -8],\n [6, 8, 6, -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[[-7, 7, 12, 10],\n [8, -8, 16, 9],\n [-7, 7, 12, 10],\n [-1, 1, 20, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 8, -4, 12],\n [-12, -6, 3, -9],\n [16, 8, -4, 12],\n [-8, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 12, 0, 3],\n [2, -4, 0, -1],\n [-2, 4, 0, 1],\n [2, -4, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 0, 4, 3],\n [-8, 4, 4, 8],\n [14, -6, 6, -6],\n [-5, 5, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -3, 0, -3],\n [3, -3, 0, -3],\n [-4, 4, 0, 4],\n [2, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -4, -16, -8],\n [-12, 4, 16, 8],\n [-6, 2, 8, 4],\n [3, -1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -22, -4, 15],\n [5, -5, -11, 10],\n [9, -9, 29, -22],\n [14, -24, -6, 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[[-4, 1, -1, -1],\n [0, 0, 0, 0],\n [-16, 4, -4, -4],\n [12, -3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[15, -11, -7, 16],\n [-9, 6, 12, -12],\n [-4, 2, 14, -8],\n [7, -5, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -3, 3, 4],\n [6, -6, 6, 8],\n [9, -9, 9, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 5, 4, -15],\n [8, 20, 12, -10],\n [-12, -21, -12, 3],\n [-8, -5, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 5, 6, -20],\n [-3, -2, 1, -24],\n [30, -2, 4, 12],\n [-28, -4, -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[[-2, 3, 2, -3],\n [0, 0, 0, 0],\n [4, -6, -4, 6],\n [2, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, -4, -3],\n [12, -12, -12, -9],\n [-12, 12, 12, 9],\n [12, -12, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -2, -12, 10],\n [18, 2, 8, -8],\n [-19, -1, -6, 3],\n [-37, -3, 0, 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 4x4 matrix:\n[[16, 6, -7, 0],\n [-19, -6, 0, -5],\n [-5, 8, -6, -17],\n [25, 12, 5, 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 4x4 matrix:\n[[7, -17, 2, -15],\n [-6, -6, -20, 6],\n [1, -27, -10, -19],\n [3, -5, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -6, -2, -8],\n [-4, -9, 2, -16],\n [4, 7, -1, 12],\n [-20, -13, -6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, 0, -6, -3],\n [3, 0, 2, 1],\n [-3, 0, -2, -1],\n [12, 0, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -11, 7, 12],\n [6, -3, 3, 12],\n [12, -20, 12, 16],\n [-9, 8, -6, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 0, -6, 8],\n [6, 0, -9, 12],\n [-4, 0, 6, -8],\n [8, 0, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -8, -8, -12],\n [3, -6, -6, -9],\n [2, -4, -4, -6],\n [2, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -7, -7, -1],\n [12, 20, 16, 6],\n [-17, -21, -22, 3],\n [-2, 0, 9, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -15, -33, 5],\n [-4, -10, 11, -6],\n [1, 16, 9, 2],\n [-2, 5, 0, -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[[-6, -9, -12, 12],\n [-4, -6, -8, 8],\n [8, 12, 16, -16],\n [6, 9, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -1, -4, -7],\n [2, -6, -6, 6],\n [-7, -8, -1, 15],\n [6, -1, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -3, -6, -9],\n [-1, -3, -2, 1],\n [5, -1, -6, -13],\n [-9, -3, 6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 3, -9, 12],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [8, 4, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, -4, -4],\n [-2, -4, 2, 2],\n [3, 6, -3, -3],\n [-1, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 16, -2, 16],\n [6, -12, 6, 0],\n [-2, 13, -2, 12],\n [-8, 25, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -17, 5, -12],\n [-5, -23, -4, -14],\n [-17, 13, -16, 12],\n [13, -19, 12, -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[[-3, 3, -6, -9],\n [-2, 2, -4, -6],\n [3, -3, 6, 9],\n [3, -3, 6, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -8, 8, 8],\n [1, -2, 2, 2],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -8, 0, 8],\n [8, 8, 6, -10],\n [4, -3, -14, 8],\n [-13, -10, -13, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, 7, 1],\n [14, -6, 0, 1],\n [8, -18, 21, 0],\n [10, -2, -1, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [-14, -22, 2, -14],\n [3, 10, 0, -1],\n [-22, -22, -2, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, 0, -1],\n [-2, 4, -6, -2],\n [22, -20, -6, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 20, 20, 12],\n [6, 6, 2, 2],\n [-6, -4, 2, 0],\n [-6, -2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -9, 6, 12],\n [0, 3, -2, -4],\n [0, 12, -8, -16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, 0, 10, -20],\n [-4, 0, -16, -12],\n [-24, 0, 4, -22],\n [-1, 0, 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[[18, -10, -22, 6],\n [12, -12, -5, 0],\n [9, -3, -18, 0],\n [-12, 8, 4, -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[[3, -6, 3, -4],\n [-4, -9, 6, 23],\n [-5, -18, 14, 13],\n [7, 12, -14, 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 4x4 matrix:\n[[-13, 12, 16, 12],\n [8, 0, -2, -6],\n [1, 4, 4, 0],\n [-15, 4, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -2, 0, -6],\n [-2, -2, 0, -6],\n [0, 0, 0, 0],\n [-3, -3, 0, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -11, 3, -5],\n [-10, 8, 7, -16],\n [2, -6, -4, 6],\n [12, -14, -3, 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[[-10, 9, -11, 11],\n [10, -6, 14, -14],\n [13, -9, 17, -17],\n [-7, 3, -11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -12, -9, 2],\n [1, 3, 2, 0],\n [-2, -6, 0, -8],\n [-4, -12, -11, 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[[-22, 0, -20, 2],\n [5, 4, 6, -7],\n [-13, -6, -14, 11],\n [13, 6, 14, -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[[4, -1, 0, -2],\n [8, -2, 0, -4],\n [16, -4, 0, -8],\n [-8, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, -10, 21, -12],\n [-6, -14, 6, 4],\n [0, -12, 0, 8],\n [6, 8, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -21, 18, 28],\n [5, -2, 2, 6],\n [16, -19, 19, 32],\n [-12, -3, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 6, 10, 12],\n [-1, -1, -14, -16],\n [-3, -2, 10, 16],\n [4, 5, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 8, -15, 12],\n [15, 6, -16, 9],\n [7, -4, 5, -6],\n [5, 4, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 5, -2, -3],\n [-12, 0, 7, -12],\n [15, 7, -14, 15],\n [-15, -3, 11, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -8, -4, 6],\n [-6, -8, -4, 6],\n [-12, -16, -8, 12],\n [12, 16, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -8, -8, 0],\n [12, -6, -6, 0],\n [4, -2, -2, 0],\n [4, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 9, 12, -9],\n [-3, -9, -12, 9],\n [9, 9, -2, -3],\n [13, 12, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 6, 9, -3],\n [6, 10, 7, -5],\n [-3, 22, 1, -11],\n [-12, -8, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -4, -3, 1],\n [-11, -4, -12, -8],\n [-1, 3, -9, -12],\n [-7, 3, -9, -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, 6, -1, -3],\n [8, 12, -10, 6],\n [14, 20, -14, 6],\n [-6, -8, 4, 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[[-4, -4, 0, -18],\n [5, 9, 9, -11],\n [8, 9, 4, 11],\n [-17, -23, -17, 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 4x4 matrix:\n[[7, 8, -14, 0],\n [1, 2, -3, 1],\n [-16, -8, 20, 12],\n [-2, -4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 10, -8, -4],\n [-3, 1, 8, 2],\n [0, -2, -5, -1],\n [-3, -1, 3, 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[[0, -2, -2, 4],\n [0, -4, -4, 8],\n [0, 4, 4, -8],\n [0, 4, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -8, 16, 0],\n [1, -2, 4, 0],\n [3, -6, 12, 0],\n [1, -2, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -2, 2, 6],\n [0, 1, -1, -3],\n [0, 0, 0, 0],\n [0, 3, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -6, -4, 5],\n [6, -6, 0, 3],\n [-11, -4, -12, 8],\n [-9, 4, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -7, -10, -20],\n [0, 6, -4, -8],\n [0, 9, -6, -12],\n [-8, 2, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-3, -12, 3, 12],\n [-3, -12, 3, 12],\n [4, 16, -4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 0, 4, 1],\n [1, 0, 4, 1],\n [4, -2, 8, 10],\n [2, -3, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -6, 4, 16],\n [-3, 9, 0, -12],\n [-17, 3, -8, -20],\n [-4, 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[[-9, 0, -5, -4],\n [-12, -10, -5, -2],\n [-21, -4, -11, -8],\n [-6, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 16, -4],\n [2, -4, 17, 0],\n [3, -3, 12, -3],\n [10, -4, 13, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 18, -6, -6],\n [3, -13, -13, 6],\n [-1, -8, 6, 3],\n [0, -6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -5, 14, -3],\n [-6, -2, -20, -6],\n [-3, 7, 6, 9],\n [12, -6, 20, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -4, 8, 12],\n [4, -1, 2, 3],\n [-4, 1, -2, -3],\n [-4, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 8, 8, 12],\n [-12, 16, 16, 3],\n [-11, -7, -27, -21],\n [6, -2, -10, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [9, -10, 9, -6],\n [9, -10, 9, -6],\n [-12, 12, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -4, 0, -4],\n [-2, -1, 0, -1],\n [-2, -1, 0, -1],\n [-6, -3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -4, -4, -12],\n [0, -3, -3, -9],\n [0, 0, 0, 0],\n [0, 1, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 4, 0, -8],\n [6, -3, 0, 6],\n [0, 0, 0, 0],\n [2, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -6, 8, 4],\n [0, -1, 4, -7],\n [12, 10, 4, -9],\n [-4, -4, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 9, 6, 3],\n [-17, -19, 14, 7],\n [-18, -22, 12, 6],\n [7, 5, -10, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 18, -9, 27],\n [12, 16, 2, 14],\n [0, -12, 3, -15],\n [-8, 4, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -2, -2, -6],\n [1, -1, -1, -3],\n [0, 0, 0, 0],\n [1, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, 2, 3, 3],\n [-13, -10, -3, -9],\n [2, -6, 1, -4],\n [0, 14, -1, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, -5, -1],\n [12, -12, 6, 9],\n [-4, 4, 8, -1],\n [0, 0, 5, 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 4x4 matrix:\n[[3, -3, 8, -3],\n [0, 0, 0, 0],\n [4, -4, 8, -6],\n [0, 0, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -15, -10, -7],\n [6, 11, 8, 6],\n [6, 14, 12, 10],\n [-3, -7, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, -4, -16],\n [16, 8, 6, 8],\n [6, 6, 4, 8],\n [18, 6, 5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, -4, 1],\n [-15, 11, -15, 7],\n [4, 12, 4, 12],\n [-11, -5, -11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 4, 0, 9],\n [-10, 7, 9, 0],\n [-12, 6, 10, -4],\n [10, -4, -8, 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[[-4, -15, 22, -1],\n [12, -2, -6, 12],\n [-4, -3, 4, -3],\n [0, -13, 12, 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 4x4 matrix:\n[[-16, 0, 4, -12],\n [-4, 0, 1, -3],\n [0, 0, 0, 0],\n [16, 0, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, 12, 0],\n [4, 0, -4, 0],\n [-8, 0, 8, 0],\n [16, 0, -16, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 2, 2, 4],\n [0, 8, 8, 16],\n [0, 0, 0, 0],\n [0, 8, 8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 2, -6, -10],\n [4, -16, -12, -10],\n [0, -12, -12, -12],\n [-8, 14, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 16, -7, 5],\n [-7, 9, 5, -11],\n [-3, 5, -7, 9],\n [-9, 13, -5, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [6, 4, -6, 0],\n [-6, -4, 6, 0],\n [6, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, -6, -10, -1],\n [-18, 8, 6, 4],\n [0, -6, -4, 0],\n [-6, -11, 24, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -6, 3, 12],\n [-12, -6, 3, 12],\n [12, 6, -3, -12],\n [4, 2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -1, -4, 4],\n [-2, 2, 8, -8],\n [-4, 4, 16, -16],\n [2, -2, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 4, 2, -4],\n [-4, 2, -11, -2],\n [-7, 2, -1, -8],\n [10, -2, 6, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 12, 4, 4],\n [-4, -3, -1, -1],\n [12, 9, 3, 3],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 8, 4, 6],\n [12, -12, -6, -9],\n [-12, 12, 6, 9],\n [-4, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 1, -4, 3],\n [0, 0, 0, 0],\n [-2, 1, -4, 3],\n [2, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -9, 7, 1],\n [6, 15, -13, 5],\n [-3, 3, -4, 8],\n [6, 12, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 12, 0, 12],\n [12, -16, 0, -16],\n [-12, 16, 0, 16],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 0, -1, 3],\n [8, 0, 4, -12],\n [-8, 0, -4, 12],\n [4, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 15, -9, 21],\n [1, -18, 13, -23],\n [3, -3, 0, -3],\n [13, -14, 23, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -4, 17, 16],\n [8, 4, 28, 0],\n [4, 2, -13, 12],\n [-16, -12, -12, 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[[1, -2, -4, -1],\n [11, -14, 4, -19],\n [-4, 2, -20, 10],\n [-6, 10, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -13, 0, 11],\n [-7, -7, -15, -1],\n [-2, 13, 0, -11],\n [3, 5, 7, -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 4x4 matrix:\n[[8, -12, 4, 7],\n [17, 2, 16, -16],\n [24, -3, 18, -18],\n [3, -1, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, -6, 9, -12],\n [0, 0, 0, 0],\n [0, -4, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -4, 0, -8],\n [3, 1, 0, 2],\n [-6, -2, 0, -4],\n [9, 3, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -16, -7, 3],\n [-14, -12, 0, 4],\n [11, 18, 6, -4],\n [-11, -8, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 6, 2, 6],\n [-8, 3, 1, 6],\n [16, 9, 3, -2],\n [8, 3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 12, 2, -8],\n [-6, 12, 3, -12],\n [-8, -4, 1, -4],\n [-3, -4, 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 4x4 matrix:\n[[0, 12, -12, 8],\n [0, 6, -6, 4],\n [0, 0, 0, 0],\n [0, -12, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 12, 6, 0],\n [-4, 4, 2, 0],\n [-12, 12, 6, 0],\n [8, -8, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 10, -17, -1],\n [12, 12, 9, -11],\n [4, 29, -7, 9],\n [12, 21, 5, -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 4x4 matrix:\n[[8, 4, 4, -12],\n [4, 2, 2, -6],\n [-4, -2, -2, 6],\n [2, 1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 3, -6, 0],\n [9, 3, -6, 0],\n [-3, -1, 2, 0],\n [9, 3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 8, 8, -4],\n [6, 12, 12, -6],\n [8, 16, 16, -8],\n [6, 12, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[32, 8, -4, 28],\n [-4, 4, -17, -6],\n [4, -2, 10, 5],\n [-12, 2, -16, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -6, -2, -3],\n [-2, 12, 4, 11],\n [-4, 3, 1, 1],\n [24, -13, 9, -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[[-2, 0, 8, 6],\n [-3, 3, -6, -3],\n [4, -4, 8, 4],\n [2, -1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 1, -1, -3],\n [2, -2, 0, 0],\n [-11, -4, -3, -9],\n [-4, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [1, -2, 3, -3],\n [-1, 2, -3, 3],\n [-3, 6, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, -10, 6, -12],\n [2, -3, 4, 1],\n [1, 2, -19, 11],\n [-26, 14, 2, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 16, 12, 8],\n [8, 8, 6, 4],\n [4, 4, 3, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -2, -9, 3],\n [14, -5, -17, 13],\n [-16, 6, 20, -16],\n [-8, 4, 12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 19, -15, -12],\n [-21, 27, -9, -12],\n [0, -1, 20, -10],\n [6, -10, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, -8, 12, 12],\n [0, -4, 6, 6],\n [0, -8, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 7, 9, 2],\n [-8, -13, -9, 4],\n [0, 3, 3, 0],\n [4, 8, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 20, -1, 6],\n [-7, 9, -17, 1],\n [2, -15, 12, -9],\n [-2, 11, 16, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 4, -12, 8],\n [-32, 24, 5, -22],\n [-10, 14, 0, 4],\n [-10, 6, -5, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -1, -5, 0],\n [8, 4, -12, 0],\n [-21, -3, 9, -12],\n [8, 6, 6, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 4, 4, -6],\n [-28, 28, 4, 6],\n [-8, 8, 1, 2],\n [-8, 8, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -4, 0, 1],\n [8, 16, 0, -4],\n [4, 8, 0, -2],\n [-6, -12, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 12, -3, -9],\n [6, -8, 2, 6],\n [-6, 8, -2, -6],\n [-6, 8, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -6, 0, -2],\n [-4, 3, 0, 1],\n [12, -9, 0, -3],\n [-16, 12, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -6, -3, 6],\n [6, -4, -2, 4],\n [-3, 2, 1, -2],\n [6, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-15, 17, 3, -4],\n [-13, 19, 9, -4],\n [-12, 4, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 6, 9, -12],\n [0, 0, 0, 0],\n [-8, 4, 6, -8],\n [4, -2, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, -1, 4],\n [4, -2, 1, -4],\n [-16, 8, -4, 16],\n [4, -2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -20, 6, 0],\n [-11, 5, -6, 10],\n [-5, -13, 3, 2],\n [-17, -1, -6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -6, 15, -9],\n [3, -6, 15, -9],\n [8, 14, 10, -14],\n [1, -2, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, 0, -6],\n [-4, 8, 12, 24],\n [0, 0, 0, 0],\n [1, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 4, -4, -8],\n [-15, 13, 15, -18],\n [-12, 10, 11, -14],\n [6, -10, -18, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -8, 6, 8],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, 4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, -2, 4],\n [16, -8, 8, -16],\n [0, 0, 0, 0],\n [-12, 6, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -3, 4, -5],\n [-6, -6, 12, -6],\n [-4, 4, -4, 8],\n [-18, -2, 12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [8, -6, -2, -8],\n [0, 0, 0, 0],\n [-12, 9, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 14, 22, 2],\n [-4, -16, -28, -4],\n [1, -8, -9, 1],\n [-4, -4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, 8, -8],\n [0, 0, 0, 0],\n [-3, -3, -2, 2],\n [-9, -9, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, -4, 2],\n [10, -11, 14, -4],\n [2, -1, 2, 0],\n [-12, 15, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -16, 16, 4],\n [12, -16, 16, 4],\n [12, -16, 16, 4],\n [9, -12, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -24, -36, 26],\n [16, 8, 16, -12],\n [-9, -8, -17, 22],\n [3, -2, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -3, 12, 9],\n [0, 0, 0, 0],\n [-6, -3, 12, 9],\n [8, 4, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -4, 8, 6],\n [13, 14, -4, -13],\n [12, 8, -16, -12],\n [11, 10, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [1, -14, 18, 1],\n [-4, -4, 12, 2],\n [10, 0, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 8, 0, -8],\n [12, -12, 0, 12],\n [-16, 16, 0, -16],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 13, -8, -3],\n [-3, -5, 2, 1],\n [-3, 1, -6, -1],\n [9, -3, 18, 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, 5, 12, -9],\n [1, 1, 8, -6],\n [13, -7, -16, 12],\n [7, -5, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 9, 9, -6],\n [0, -3, -3, 2],\n [0, 6, 6, -4],\n [0, -6, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 14, 0, 24],\n [4, -4, 0, -4],\n [1, -4, 0, -5],\n [-4, -2, 0, -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 4x4 matrix:\n[[-3, 10, -4, 3],\n [4, -10, 7, -4],\n [-3, -6, 7, -5],\n [1, -3, -8, 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[[12, 6, 0, 0],\n [16, 8, 0, 0],\n [16, 8, 0, 0],\n [12, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 9, -12, 0],\n [-6, -6, 8, 0],\n [6, 6, -8, 0],\n [-9, -9, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 12, 4, -2],\n [4, -12, 4, 22],\n [-6, 4, 8, 16],\n [-10, 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[[0, 12, -12, -4],\n [0, -6, 6, 2],\n [0, 0, 0, 0],\n [0, -3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -4, 4, 0],\n [22, -20, -12, -12],\n [-6, 10, 6, 10],\n [-28, 35, 13, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -3, 2, 13],\n [-1, 12, -3, -4],\n [-6, 3, 1, -5],\n [-5, 3, -4, -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[[-12, 10, -8, 2],\n [-15, 21, 1, -13],\n [-15, -8, -13, 4],\n [0, -28, -8, 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[[-13, -8, -1, -8],\n [-16, 7, -4, -20],\n [-22, 2, -10, -4],\n [-7, -8, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -6, 2, 0],\n [13, 3, 6, 0],\n [-3, 3, -2, 0],\n [-18, -8, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 11, -12, -10],\n [-10, 13, -12, -2],\n [-4, 1, 0, 4],\n [-22, 16, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -3, 16, -2],\n [1, -1, 8, -2],\n [14, -7, 28, 0],\n [-9, 0, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 4, 2, -7],\n [-16, 0, 8, 4],\n [3, -14, 2, 7],\n [0, -12, 3, 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[[-17, -11, -25, 31],\n [18, 18, 19, -19],\n [24, 32, 18, -10],\n [-5, -11, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, -8, -12],\n [-3, -6, 9, 6],\n [1, 2, -3, -2],\n [4, 10, -16, -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 4x4 matrix:\n[[0, 0, -3, 15],\n [-1, 0, 2, 6],\n [3, 0, -8, -8],\n [1, 0, -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[[3, 5, -4, 1],\n [0, -4, -1, 4],\n [-20, -4, 22, 8],\n [-14, 2, 13, 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[[16, -16, 12, -12],\n [-13, 18, -9, 13],\n [-21, 6, -18, 6],\n [-11, 6, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -7, -7, -15],\n [-4, 0, 0, -2],\n [-4, 1, 1, 1],\n [12, -8, -8, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 5, 1, -2],\n [-4, -2, 3, 0],\n [-21, -15, -3, 6],\n [25, 17, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 0, -9, 0],\n [3, 0, 9, 0],\n [-2, 0, -6, 0],\n [-1, 0, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -15, -12, 6],\n [-13, -2, 8, -2],\n [-12, -15, 3, -8],\n [13, -4, 4, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, -1, 12, -6],\n [14, -13, -20, 13],\n [-12, -1, -4, -4],\n [24, 15, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, -21, 3],\n [-16, 13, 8, 6],\n [3, 0, -8, -17],\n [16, -14, 22, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 12, -16, 0],\n [4, -8, -16, 4],\n [7, 22, -18, 1],\n [-7, 6, 32, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, -1, 6, -7],\n [1, -3, -16, 9],\n [-4, 4, 30, -14],\n [3, -1, -14, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 8, 0, 3],\n [-14, 12, 2, 4],\n [14, -12, -2, -4],\n [-11, 18, 11, 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 4x4 matrix:\n[[12, 0, -4, 0],\n [12, 0, -4, 0],\n [-3, 0, 1, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -5, 3, 9],\n [3, -7, 5, 7],\n [9, -3, 3, -3],\n [-9, 3, -3, 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 4x4 matrix:\n[[12, 8, 8, -8],\n [9, 6, 6, -6],\n [6, 4, 4, -4],\n [-9, -6, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 9, 0, 0],\n [-9, -9, 0, 0],\n [0, 0, 0, 0],\n [9, 9, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -7, -17, -13],\n [8, 33, -13, 1],\n [-14, -14, -3, -3],\n [-16, -17, 1, -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[[-8, -14, -8, 5],\n [6, 4, -20, 19],\n [2, -2, -20, 18],\n [2, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, -16, 6, -24],\n [-13, -3, 23, -6],\n [-10, -12, -10, -15],\n [-16, -13, 2, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -12, -16, 8],\n [0, 0, 0, 0],\n [-8, 12, 16, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -13, -18, 21],\n [-16, -8, 13, -4],\n [11, 5, -24, 0],\n [3, 1, -7, 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[[-27, -7, -6, 19],\n [-8, 4, -22, 4],\n [-3, 6, -18, 6],\n [-8, -4, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 2, 8, -2],\n [0, 0, 0, 0],\n [-2, -2, -8, 2],\n [3, 3, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[25, 7, -2, -16],\n [24, 0, 2, -19],\n [-14, -2, 0, 10],\n [-17, 1, -2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -4, -3, 8],\n [0, 12, -4, 0],\n [-10, -34, 8, -10],\n [-6, 17, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -4, -1, 0],\n [-25, -2, 15, 30],\n [1, 10, -11, 7],\n [1, 16, -19, -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[[17, -2, -6, -5],\n [0, -9, -10, 3],\n [-3, 3, 4, 0],\n [4, -10, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 24, 6, -12],\n [11, 4, -16, 2],\n [-18, 8, 17, -6],\n [3, -8, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 6, -20, 17],\n [3, 5, -12, 10],\n [0, -12, 12, -9],\n [-3, 3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 7, 13, 1],\n [-17, 2, 3, -10],\n [-7, 4, 1, 4],\n [-6, 5, 20, -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 4x4 matrix:\n[[-3, -9, 3, 3],\n [3, 9, -3, -3],\n [1, 3, -1, -1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -9, -29, 10],\n [12, 2, -2, -20],\n [8, 0, -6, -15],\n [6, 3, 1, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 13, -2, -11],\n [-3, -9, 0, 9],\n [15, 5, 8, -13],\n [-3, -9, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, -4, 8],\n [8, -16, 8, -16],\n [0, 0, 0, 0],\n [-6, 12, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 12, 0, 12],\n [2, 4, 0, 4],\n [8, 16, 0, 16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 16, 4, 12],\n [-16, 16, 4, 12],\n [16, -16, -4, -12],\n [-12, 12, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 3, -3, 5],\n [-3, -7, -3, -5],\n [-12, 2, -12, 10],\n [-9, 1, -9, 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[[2, 8, -6, -2],\n [2, 8, -6, -2],\n [1, 4, -3, -1],\n [-4, -16, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -18, 3, -21],\n [0, 16, -4, 16],\n [0, 8, -2, 8],\n [2, 14, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 6, -4, -2],\n [4, -3, 2, 1],\n [8, -6, 4, 2],\n [12, -9, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 16, 8, -4],\n [12, 16, 8, -4],\n [-6, -8, -4, 2],\n [-6, -8, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -4, 0, 19],\n [-8, -6, 4, 20],\n [-5, -9, 9, -8],\n [12, 14, -12, -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 4x4 matrix:\n[[20, 22, -4, 3],\n [-20, -22, 4, -3],\n [-20, 6, 16, -3],\n [11, -3, -16, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -12, 8, 2],\n [12, 3, -16, 2],\n [-13, -3, 19, -2],\n [32, -12, -16, 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[[0, 0, 0, 0],\n [-6, -12, -3, -6],\n [6, 12, 3, 6],\n [-8, -16, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -6, -16, 15],\n [5, -2, -2, 4],\n [-10, 14, 9, -16],\n [-20, 12, -8, -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[[3, 9, -18, 3],\n [24, 9, -4, 10],\n [4, 12, -24, 4],\n [3, 9, -18, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[34, -22, 0, 15],\n [-11, 1, 4, -8],\n [-2, 0, 14, -1],\n [17, -15, 16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, 2, 5],\n [-2, -8, -1, 5],\n [-6, -8, -3, 3],\n [6, 0, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 8, -4, -14],\n [4, 6, 12, -13],\n [12, 2, 20, -7],\n [4, -8, -2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [8, 0, 6, -8],\n [4, 0, 3, -4],\n [16, 0, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -6, -12, -9],\n [2, -2, -4, -3],\n [-4, 4, 8, 6],\n [-8, 8, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -12, 7, -5],\n [4, 9, -2, -6],\n [2, -6, 6, -10],\n [-1, 12, -9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 5, 13, -18],\n [1, 13, 17, -18],\n [-10, -8, -12, 12],\n [16, -2, -10, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -13, 1, 12],\n [-5, -5, 1, 4],\n [-9, -9, 1, 8],\n [11, 11, 1, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 2, -6, 0],\n [3, -1, 3, 0],\n [6, -2, 6, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[30, 11, 2, -8],\n [-8, -5, 11, 4],\n [18, -6, 9, 0],\n [7, -15, 13, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -4, -8, 24],\n [17, 11, -2, -3],\n [-16, -10, 0, -3],\n [20, 8, -4, 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[[1, -7, -13, 7],\n [3, 0, 3, -3],\n [0, 12, 12, -6],\n [1, -3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 0, -2, 8],\n [0, 8, -12, -16],\n [-24, 3, 21, 0],\n [0, 5, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -9, 15, 21],\n [0, 5, -8, -11],\n [8, 12, -20, -28],\n [12, 8, -14, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 8, -6, 4],\n [-3, -4, 3, -2],\n [0, 0, 0, 0],\n [6, 8, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -12, 12, -24],\n [-15, -6, 19, -6],\n [-2, 10, -16, 16],\n [22, -8, 2, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -13, 9, -4],\n [-5, -7, -6, 2],\n [1, -1, 3, -4],\n [-12, -20, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 1, -3, 0],\n [0, -3, 5, 0],\n [1, 10, -16, 0],\n [-5, 4, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, -20, 12],\n [11, 8, 11, 0],\n [-1, -13, 14, -15],\n [5, 2, 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[[12, -8, -16, -8],\n [-9, 6, 12, 6],\n [9, -6, -12, -6],\n [-6, 4, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -16, 17, 3],\n [-3, -12, 10, -6],\n [-1, 16, -15, 3],\n [5, -8, 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[[-8, -8, 0, -20],\n [8, 10, -4, 18],\n [-2, -5, 6, -2],\n [4, 7, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 19, 0, -14],\n [12, -20, 0, 20],\n [3, 3, -6, 6],\n [1, -1, -17, -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[[-16, -8, -8, -12],\n [-8, -4, -4, -6],\n [0, 0, 0, 0],\n [4, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 2, 8, 0],\n [8, 4, -4, -8],\n [6, 5, 5, -6],\n [-2, -6, -19, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -8, 1, 4],\n [9, -10, 5, -6],\n [-15, 18, -7, 6],\n [-9, 11, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 9, -9, 8],\n [-16, 7, -7, 16],\n [12, -8, 8, -12],\n [-21, 3, -3, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 3, 16, -2],\n [-9, 12, -6, 12],\n [-18, 10, 16, 4],\n [14, -7, -14, -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 4x4 matrix:\n[[0, -6, 0, 6],\n [-1, 11, 4, -7],\n [-2, 13, 8, -5],\n [3, 0, -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[[3, 0, -1, -3],\n [9, 3, -4, -6],\n [-9, -15, 8, -6],\n [9, 6, -5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 1, 2, 1],\n [12, 3, 6, 3],\n [0, 0, 0, 0],\n [-12, -3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-37, 21, 14, -37],\n [-11, 15, 22, -5],\n [-8, 6, 6, -7],\n [20, -6, 4, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 4, 2, -4],\n [-4, -2, -1, 2],\n [16, 8, 4, -8],\n [-4, -2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -6, 0, 0],\n [6, 16, 8, -4],\n [0, 6, 0, 0],\n [18, -6, 24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -5, 11, -7],\n [0, 1, -1, 3],\n [4, 1, -13, -13],\n [1, -3, 0, -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[[-6, -1, 5, -4],\n [2, 5, -18, -8],\n [0, -6, 21, 12],\n [-2, -7, 25, 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, 8, -6, 10],\n [-10, -6, 4, -6],\n [-7, -2, 5, -13],\n [-5, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -5, -4, 15],\n [-14, -8, 14, 5],\n [3, -1, 4, 23],\n [-5, -1, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -6, -4, 0],\n [-12, 9, 6, 0],\n [-4, 3, 2, 0],\n [-12, 9, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 8, -13, -5],\n [3, 5, 11, 12],\n [-7, 15, -13, 2],\n [-2, 13, 0, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 2, 0, -2],\n [-2, -3, 7, -5],\n [4, 0, 3, 3],\n [14, -5, -15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -1, -6, -2],\n [-1, 7, -13, -7],\n [-12, -22, -7, 25],\n [-3, 21, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 4, 16, 16],\n [8, 4, 16, 16],\n [2, 1, 4, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, -20, -8, -14],\n [-18, 21, 12, 12],\n [6, -17, -23, 4],\n [-8, 15, 15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -1, 5, -13],\n [-6, 12, 14, 2],\n [9, -13, -15, 3],\n [12, 10, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -9, -12, -9],\n [6, 6, 8, 6],\n [6, 6, 8, 6],\n [12, 12, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -8, -4, 4],\n [8, 0, -12, 4],\n [-8, 16, -4, -4],\n [-12, 6, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -4, -18, 5],\n [1, 0, -6, 3],\n [-17, 5, 22, -8],\n [-1, 6, -2, -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[[-7, 12, -4, -24],\n [-21, -4, -12, 8],\n [-5, 16, 10, -5],\n [8, -18, -24, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 12, 12, 6],\n [-12, -16, -16, -8],\n [-9, -12, -12, -6],\n [-6, -8, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -8, -1, -15],\n [-6, -19, -2, 30],\n [-2, -15, -5, 27],\n [28, 28, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, 6, -18, -4],\n [-11, 0, -12, 1],\n [-7, 11, -15, -4],\n [-18, 8, -24, -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[[0, -12, 8, -16],\n [0, -12, 8, -16],\n [0, -12, 8, -16],\n [0, 6, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, -10, 17, -5],\n [14, -21, -6, 6],\n [-11, 19, 3, -7],\n [-12, 8, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -9, -7, -4],\n [14, 2, 16, 4],\n [15, -15, -3, -8],\n [-19, 14, -5, 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 4x4 matrix:\n[[-21, 7, -11, -1],\n [6, -1, -11, -16],\n [8, -4, 2, -7],\n [-16, 6, 0, 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[[15, 7, 9, 8],\n [-1, 7, 12, -7],\n [9, 3, 0, 15],\n [24, 2, 1, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -8, -8, -8],\n [-1, 2, 2, 2],\n [4, -8, -8, -8],\n [4, -8, -8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -6, -8, 0],\n [4, 6, 8, 0],\n [0, 0, 0, 0],\n [-4, -6, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, -4, -8],\n [0, 0, 2, 4],\n [0, 0, 3, 6],\n [0, 0, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 15, -9, 0],\n [-9, 7, -3, 3],\n [14, -18, 10, -2],\n [9, -7, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -1, -1, -3],\n [-8, -4, -4, -12],\n [-4, -2, -2, -6],\n [2, 1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -4, 0, -8],\n [-7, -22, 0, -2],\n [0, 18, -3, -2],\n [11, -7, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -10, 5, -3],\n [-17, -7, 15, -10],\n [-2, 5, -16, 9],\n [-12, -2, 20, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -15, 12, -6],\n [3, -3, -12, 6],\n [2, 10, -8, 4],\n [2, 7, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, -16, 16, -16],\n [-9, 12, -12, 12],\n [-9, 12, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -4, 8, 0],\n [8, 2, -4, 0],\n [-8, -2, 4, 0],\n [-4, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [3, 4, 4, 2],\n [-3, -4, -4, -2],\n [3, 4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -4, 0, 6],\n [14, -3, 6, 3],\n [9, 11, 2, -1],\n [20, 7, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 4, 0, -12],\n [-12, -4, 0, 12],\n [-6, -2, 0, 6],\n [-6, -2, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 1, -3, -2],\n [-14, 7, 24, 1],\n [13, 10, -7, 1],\n [9, 15, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -8, 8, -16],\n [8, 8, -8, 16],\n [0, 0, 0, 0],\n [-6, -6, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -2, 12, -14],\n [-17, 4, 0, -1],\n [4, -9, -8, 2],\n [2, -4, 6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -7, 10, -1],\n [-3, 10, -9, -1],\n [-5, 7, -7, 3],\n [5, -13, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -6, 3, 12],\n [-12, -2, -1, 0],\n [0, -8, 2, 12],\n [16, 8, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 0, 20, -3],\n [-4, 0, 12, -2],\n [2, 0, 0, -2],\n [0, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -1, -11, 17],\n [14, 10, 6, -24],\n [8, 8, -4, -11],\n [8, 7, 1, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -12, 12, 8],\n [1, -3, 3, 2],\n [-4, 12, -12, -8],\n [2, -6, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -3, 1, -4],\n [0, -9, 5, 4],\n [3, -3, 2, 4],\n [-10, 7, -5, -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 4x4 matrix:\n[[4, 4, 2, -1],\n [16, 16, 8, -4],\n [4, 4, 2, -1],\n [12, 12, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -8, -9, -10],\n [12, 8, 9, 10],\n [16, 8, 10, 12],\n [-4, -8, -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 4x4 matrix:\n[[-26, 2, -2, -24],\n [19, 5, 1, 20],\n [24, 3, 0, 28],\n [-2, 12, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, -12, -8],\n [12, 0, 12, 8],\n [9, 0, 9, 6],\n [-9, 0, -9, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 2, -4, 1],\n [-4, -8, 16, -4],\n [-1, -2, 4, -1],\n [-1, -2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 16, 25, 13],\n [-9, 11, -11, 5],\n [-12, 10, -24, -2],\n [-2, 3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 2, 3, 0],\n [-2, -8, 7, -3],\n [16, -7, 13, -4],\n [4, -7, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 10, 3, -14],\n [0, 2, 0, 1],\n [4, 20, 0, -22],\n [9, 4, -9, -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[[-25, -12, -11, 12],\n [24, 16, 10, -9],\n [-5, -12, -1, -3],\n [-13, 4, -7, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -16, 4, 12],\n [2, -8, 2, 6],\n [-2, 8, -2, -6],\n [-3, 12, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -2, -6, -16],\n [4, -7, -5, 4],\n [10, -2, -3, -5],\n [-10, -11, -4, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 6, -20, -26],\n [22, 18, -10, -18],\n [-6, -6, 4, -10],\n [-1, -3, 9, -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[[-2, -4, 6, -5],\n [4, 6, -4, 8],\n [-8, -4, -24, -8],\n [-4, -7, 8, -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 4x4 matrix:\n[[-1, 3, -4, 5],\n [4, -12, 10, 4],\n [3, -9, 9, -3],\n [0, 0, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, 17, -11, -6],\n [-1, 9, -7, -2],\n [-18, 15, -15, -9],\n [-10, -5, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 0, -6, -12],\n [-10, -20, 12, -11],\n [-14, 8, -12, -10],\n [-5, 20, -18, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -20, 4, -14],\n [-11, -18, 6, -5],\n [-3, -4, 2, 1],\n [-9, -17, 4, -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[[0, -20, -24, 3],\n [-8, -3, -18, 1],\n [-17, 11, -8, -9],\n [-3, 10, 14, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 16, 11, 24],\n [-6, 0, -2, -22],\n [6, -13, -8, -5],\n [2, -3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -1, 3, -1],\n [-11, 3, -9, -8],\n [-20, 4, -12, -8],\n [-2, -2, 6, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -6, -4, -12],\n [6, -9, 6, 0],\n [-3, 4, 0, 4],\n [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 4x4 matrix:\n[[4, -4, 14, -2],\n [20, 10, 28, 14],\n [-9, -15, -7, -14],\n [0, 10, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 3, -8, 1],\n [10, 13, -28, 11],\n [-18, -29, 24, 2],\n [16, 28, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -6, 18, 8],\n [-22, -5, -4, -25],\n [6, 1, 2, 7],\n [18, 7, -4, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -8, 8, -16],\n [9, -8, 10, -12],\n [-8, -10, 18, -4],\n [-13, -4, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 6, -6, -12],\n [2, 2, -2, -4],\n [-6, -6, 6, 12],\n [-2, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 2, 2, -4],\n [-6, 3, 3, -6],\n [4, -2, -2, 4],\n [-6, 3, 3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 0, -16, -16],\n [6, 0, 12, 12],\n [-6, 0, -12, -12],\n [8, 0, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 1, -2, 4],\n [-6, 2, -4, 8],\n [6, -2, 4, -8],\n [-3, 1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -27, 12, -15],\n [-2, -7, -8, -6],\n [-6, 0, -20, -7],\n [15, -31, 16, -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[[16, 12, -4, 4],\n [-16, -12, 4, -4],\n [-12, -9, 3, -3],\n [12, 9, -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[[-2, -4, -1, 3],\n [-10, 0, -17, 15],\n [-6, 8, -15, 9],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -3, -3, 9],\n [-12, 3, 3, -9],\n [12, -3, -3, 9],\n [8, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 4, -1],\n [3, 0, 14, -8],\n [9, 6, 26, -12],\n [3, 6, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -1, 25, 2],\n [-3, -8, 2, -6],\n [9, 9, 9, 8],\n [9, -6, 24, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -16, -10, 1],\n [-17, -12, -1, 12],\n [-12, 8, -6, -5],\n [10, -8, -20, -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[[-11, -3, -1, 8],\n [16, -12, -4, -28],\n [18, -6, -2, -24],\n [-6, 6, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -4, 6, 0],\n [-2, -2, 3, 0],\n [0, 0, 0, 0],\n [6, 6, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 6, 0, 20],\n [0, -1, 1, 3],\n [14, -14, -4, -16],\n [-12, 6, 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[[16, 12, -16, 0],\n [12, 9, -12, 0],\n [0, 0, 0, 0],\n [-12, -9, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -6, 3, -9],\n [16, 8, -4, 12],\n [4, 2, -1, 3],\n [16, 8, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 4, -3, 4],\n [-10, 12, 2, 1],\n [-12, 16, 4, 0],\n [-2, 0, -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[[8, 0, 4, 8],\n [-4, 0, -2, -4],\n [-12, 0, -6, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -3, 2, 1],\n [-8, 12, -8, -4],\n [0, 0, 0, 0],\n [-4, 6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 5, 2, 2],\n [-24, 15, 24, 24],\n [-5, -6, 1, 1],\n [-4, -8, 12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -2, 3, -3],\n [-8, -8, 0, 0],\n [-2, -2, 2, -2],\n [8, 8, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -7, -10, -7],\n [-8, -6, -14, 8],\n [-21, 9, 12, 15],\n [4, -3, -8, -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[[-8, -14, -1, -14],\n [-1, -10, -5, -7],\n [-16, -16, 4, -16],\n [1, -2, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 10, -2, 8],\n [7, -7, 7, -4],\n [-5, 5, 6, 6],\n [3, -3, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 20, 12, -12],\n [-6, 4, 20, 13],\n [0, -8, 8, 16],\n [6, -14, -10, 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[[-3, 2, -6, 5],\n [0, -2, 4, -1],\n [-18, -4, -4, 22],\n [0, 8, -16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 4, 3, -4],\n [9, 11, 6, 16],\n [-12, -6, -2, -24],\n [-6, -5, -4, 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 4x4 matrix:\n[[12, -12, 0, 4],\n [25, -1, 16, -5],\n [-9, 9, 0, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -14, -8, -10],\n [-1, -7, 9, 13],\n [4, 4, -20, -28],\n [-3, 12, 5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 16, 25, -16],\n [-1, -10, -1, 10],\n [-3, -3, -12, 3],\n [-1, -1, -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[[-3, 3, 4, 0],\n [3, -6, -25, -9],\n [0, -2, -14, -6],\n [-12, 10, 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[[-1, -3, -6, -12],\n [-15, 13, -6, 12],\n [-4, 6, -4, 4],\n [-19, 21, -6, 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, 0, 0, 0],\n [4, 8, 8, -4],\n [6, 12, 12, -6],\n [4, 8, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -15, 10, 0],\n [0, -20, 16, 20],\n [-6, 8, -4, -2],\n [5, -23, 17, 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 4x4 matrix:\n[[-9, -4, -3, 6],\n [9, 0, 9, -12],\n [-12, -4, -6, 10],\n [12, 10, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 13, -22, 0],\n [15, 6, 6, 21],\n [10, 11, -14, 6],\n [-4, -3, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 6, -12, -2],\n [-5, 8, 3, 22],\n [1, -7, -21, 13],\n [-3, 0, 15, 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[[2, 2, 4, 6],\n [13, 11, 16, 8],\n [11, 1, -6, -1],\n [-12, 3, 14, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 4, -28, 0],\n [-15, -13, 19, 0],\n [12, 20, 4, 0],\n [16, 24, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, -2, -2],\n [8, 8, -2, -2],\n [8, 8, -2, -2],\n [4, 4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 0, 12, 0],\n [2, 4, 8, 0],\n [6, 2, 8, 0],\n [20, 0, 16, 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 4x4 matrix:\n[[2, 0, -10, -16],\n [0, 1, 3, 4],\n [0, 0, 0, 0],\n [6, 7, -9, -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[[-11, 8, 18, 18],\n [0, 6, 8, 8],\n [-4, 4, 8, 8],\n [-4, -8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -8, 3, 5],\n [21, -5, -6, 11],\n [-12, 4, 2, -6],\n [6, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -4, -8, 12],\n [6, 2, 4, -6],\n [12, 4, 8, -12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -9, 0, 0],\n [0, 12, 0, 0],\n [0, -9, 0, 0],\n [0, -12, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -8, 4, 16],\n [0, 0, 0, 0],\n [8, -4, 2, 8],\n [16, -8, 4, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 14, 10, 4],\n [-7, -11, -7, -1],\n [12, 12, 12, 12],\n [-1, -5, -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[[22, 4, -24, 11],\n [-4, 2, 8, -8],\n [-14, -5, 12, -3],\n [-34, -10, 32, -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 4x4 matrix:\n[[-4, 6, -4, 8],\n [4, -10, -11, -12],\n [-4, -2, 2, 0],\n [-16, -4, -21, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 16, 6, -4],\n [8, 6, 6, -2],\n [2, -4, 6, 0],\n [16, 1, 21, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 6, 5, 6],\n [12, -8, 2, -8],\n [6, -4, 6, -4],\n [-6, 4, -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[[0, -16, 22, -4],\n [0, -16, 22, -4],\n [-5, -17, 24, 2],\n [10, 2, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -10, 2, 6],\n [-22, 10, 4, 6],\n [-13, 4, 4, 7],\n [-7, -5, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, -1, 1],\n [2, 8, -1, -2],\n [8, 0, 4, 0],\n [6, -4, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 7, 9, 7],\n [12, -5, -8, -5],\n [-8, 3, 5, 3],\n [0, 2, 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[[12, 1, 0, 16],\n [12, -9, -12, 0],\n [-8, -4, -4, -16],\n [16, -7, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 12, 4, -1],\n [-20, 3, 5, -13],\n [10, 3, -1, 6],\n [14, -6, 1, -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 4x4 matrix:\n[[10, -21, 11, -4],\n [18, -15, -3, -12],\n [0, -4, 4, 8],\n [23, -16, -7, -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 4x4 matrix:\n[[8, -1, -13, 12],\n [-4, 3, 3, -4],\n [-7, 12, 9, -6],\n [-11, 20, 11, -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[[-20, 20, 16, -16],\n [-10, 0, 12, 3],\n [-8, 4, 8, -2],\n [6, 2, -8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -2, -2, 2],\n [2, -3, -1, -11],\n [-12, -12, -9, -9],\n [16, 16, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[19, 8, 2, -6],\n [20, 6, 4, -6],\n [-5, 13, -19, -9],\n [-16, 4, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, -4, 26, 22],\n [-14, -6, 11, 0],\n [-7, -11, 7, 20],\n [8, 24, 3, -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[[3, 3, 6, 9],\n [-2, -2, -4, -6],\n [-1, -1, -2, -3],\n [-1, -1, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 10, 0, 0],\n [-5, 0, 10, -10],\n [7, 9, 13, -13],\n [2, 4, 8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -2, 5, 5],\n [-6, -14, -9, -9],\n [-4, -8, -4, -4],\n [-12, -20, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 5, 6, 3],\n [-6, 1, 9, 6],\n [2, -7, 2, 3],\n [0, -16, 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[[-2, 6, -2, 4],\n [5, -1, 25, 3],\n [7, 5, -13, 3],\n [-8, 0, 40, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [-4, 16, -4, 16],\n [-3, 12, -3, 12],\n [4, -16, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 4, -4, 3],\n [2, 8, -8, 6],\n [3, 12, -12, 9],\n [-2, -8, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -4, -8, -6],\n [-3, -6, -12, -9],\n [1, 2, 4, 3],\n [-4, -8, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[23, -29, 19, 6],\n [-10, -2, -22, 16],\n [-23, 23, -16, -18],\n [8, -14, -1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -1, 3, -1],\n [2, -1, 3, -1],\n [0, 0, 0, 0],\n [2, -1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -8, 8, 4],\n [8, -16, 16, 8],\n [2, -4, 4, 2],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 15, -16, -9],\n [6, 9, -11, -4],\n [-2, -15, 17, 8],\n [8, 24, -28, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 10, -37, -1],\n [-8, 8, 0, 4],\n [-2, -16, -10, 14],\n [-5, 4, -27, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 3, 3, -3],\n [3, -1, 2, -3],\n [10, -3, 3, -5],\n [15, -4, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, 0, 4],\n [0, -6, 0, -4],\n [0, -6, 0, -4],\n [0, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[27, -22, 9, -11],\n [-16, 12, 15, 20],\n [27, -22, 9, -11],\n [-11, 22, 15, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 7, 3, 15],\n [-12, 0, -9, -17],\n [12, 0, 6, 9],\n [-9, -9, -3, -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 4x4 matrix:\n[[-4, 12, -2, 0],\n [-2, 6, 2, 0],\n [-1, 3, 4, 0],\n [3, -9, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 9, -9, -23],\n [-22, -3, 3, 31],\n [-8, 1, -1, 14],\n [-4, -8, 8, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -4, 2, -8],\n [-16, -8, 4, -16],\n [8, 4, -2, 8],\n [-12, -6, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -2, 1, -7],\n [4, 2, 4, 6],\n [-18, -16, 31, 5],\n [-10, -4, 9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -3, 1, 0],\n [0, 0, 0, 0],\n [-2, 3, -1, 0],\n [-2, 3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -8, 4, -12],\n [4, -2, 1, -3],\n [-4, 2, -1, 3],\n [-12, 6, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -3, 2, 1],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [6, -9, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -6, 0, 12],\n [-8, 2, 3, -11],\n [2, 22, -21, 5],\n [1, 6, -6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -1, 1, -5],\n [3, -24, 2, 14],\n [-14, -24, 8, -8],\n [-2, 7, 1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -2, -14, 6],\n [-1, -6, 9, -3],\n [3, -4, 15, -7],\n [3, -8, 1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 12, 20, -14],\n [5, 9, -6, -12],\n [3, -3, 6, 0],\n [-6, -8, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -2, 0, 3],\n [-12, 8, 0, -12],\n [6, -4, 0, 6],\n [6, -4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 20, 12, 13],\n [-18, -14, 3, 8],\n [10, -2, -9, -13],\n [14, 10, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 2, -5, 5],\n [-3, -8, 3, 14],\n [28, 20, -4, -16],\n [-10, -20, 10, 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[[-3, -13, -2, -17],\n [23, 5, 14, 5],\n [6, 4, -4, -4],\n [16, 12, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -3, -3, -1],\n [4, 9, 9, -3],\n [4, -6, -6, 7],\n [-28, -12, -12, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 1, -20, 21],\n [9, -7, 14, -12],\n [-8, 12, -16, 12],\n [3, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, -9, 2],\n [8, 6, 7, 2],\n [-20, -20, -12, -8],\n [-14, -18, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -2, 1, 0],\n [12, 8, -4, 0],\n [12, 8, -4, 0],\n [-12, -8, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 0, -3, 6],\n [3, 0, 1, -2],\n [-12, 0, -4, 8],\n [-12, 0, -4, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -3, -4, 4],\n [-9, -21, 22, 3],\n [-6, -18, 18, 3],\n [-8, 0, 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[[4, -4, -8, -8],\n [0, 0, 0, 0],\n [6, -6, -12, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -1, -4, 3],\n [-6, 2, 8, -6],\n [3, -1, -4, 3],\n [9, -3, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -13, -9, -1],\n [-6, -11, -3, 3],\n [8, 15, 3, -5],\n [6, 11, 3, -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 4x4 matrix:\n[[-9, -9, 6, 0],\n [-12, -12, 8, 0],\n [-12, -12, 8, 0],\n [6, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, 17, -22, -16],\n [8, 8, -16, -16],\n [-11, -11, 18, 16],\n [-16, -16, 16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -3, -1, 5],\n [-12, -7, 5, 13],\n [3, 5, -24, -13],\n [18, 10, -4, -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 4x4 matrix:\n[[12, 0, -16, 8],\n [-12, 0, 16, -8],\n [9, 0, -12, 6],\n [9, 0, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 7, -10, 13],\n [3, -3, 6, -9],\n [2, 6, -4, 2],\n [-2, 2, -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[[3, -7, -2, -1],\n [8, 15, -6, -21],\n [-24, -6, 28, -2],\n [16, -6, -20, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 34, 13, -16],\n [-11, -2, -16, 19],\n [12, -24, -14, 14],\n [-11, 36, 12, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, -2, 4],\n [0, 0, 0, 0],\n [0, 0, -3, 6],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -14, -11, 19],\n [-10, 2, -2, -6],\n [-7, -14, -15, 23],\n [1, 14, 9, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 1, 1, 5],\n [-12, -6, 4, 5],\n [-6, -2, 2, 4],\n [9, 17, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -14, 13, 13],\n [13, 15, -10, -10],\n [10, 4, 2, 2],\n [13, 8, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 0, 3, -1],\n [3, 0, 3, -1],\n [9, 0, 9, -3],\n [3, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, 2, 2],\n [-8, 8, -4, -4],\n [-12, 12, -6, -6],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 8, -13, -3],\n [28, -2, -18, 9],\n [-15, 0, 9, 3],\n [-7, 14, -13, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, 8, 5, 3],\n [-7, -13, -10, -3],\n [10, 10, 8, 2],\n [9, 6, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 7, -12, 8],\n [-10, -7, 16, -13],\n [6, 6, -12, 9],\n [-20, -8, 24, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -16, 4, 12],\n [4, 0, 4, 24],\n [-17, -20, 3, 3],\n [-13, -16, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 8, 4, 12],\n [9, -6, -3, -9],\n [-12, 8, 4, 12],\n [6, -4, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -8, 3, 20],\n [-9, -12, -3, 24],\n [-1, -4, 2, 12],\n [-6, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -2, 0, -4],\n [0, -4, 0, -8],\n [0, -4, 0, -8],\n [0, -4, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -12, -12, -6],\n [12, -16, -16, -8],\n [-6, 8, 8, 4],\n [-12, 16, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -4, 4, -12],\n [-8, -28, -20, 12],\n [10, 9, 11, -13],\n [9, 25, 19, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 12, -12, -2],\n [-32, 0, 0, -12],\n [0, 18, -18, -3],\n [8, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 0, -12, -2],\n [0, -18, -2, -8],\n [22, -4, 22, 3],\n [12, 0, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -16, 8, 0],\n [4, -16, 8, 0],\n [3, -12, 6, 0],\n [-2, 8, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, -16, -4],\n [-12, -22, -9, 3],\n [9, -1, 10, -1],\n [-7, 15, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -8, 6, -2],\n [9, -12, 9, -3],\n [6, -8, 6, -2],\n [-3, 4, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -12, 16, -20],\n [-5, 0, 2, 9],\n [-4, 12, -9, -1],\n [-2, -3, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 8, -6, 2],\n [-6, -8, 6, -2],\n [-3, -4, 3, -1],\n [-9, -12, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 22, 2, -8],\n [0, -4, -1, 0],\n [3, -9, -4, -4],\n [-6, 6, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -5, 0, 3],\n [12, 10, 0, -7],\n [4, 5, 0, -4],\n [12, 9, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, 0, 4],\n [0, -1, 0, -2],\n [0, -4, 0, -8],\n [0, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, -6, -2],\n [0, 0, -3, -1],\n [0, 0, 12, 4],\n [0, 0, -6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, -5, 4, 12],\n [-4, 1, 16, 0],\n [-24, -2, 12, 16],\n [-9, -9, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 7, 1, -9],\n [-8, 0, -9, -10],\n [3, -7, -1, 9],\n [-6, 6, -3, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, 3, -1],\n [18, 12, -18, 2],\n [-1, -1, 3, -5],\n [-11, -10, 12, -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[[3, 9, 0, 6],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 9, -6, -9],\n [-4, 6, -4, -6],\n [2, -3, 2, 3],\n [-4, 6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -4, -10, 24],\n [30, -2, 8, 4],\n [-1, -4, -7, 6],\n [13, -10, -11, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 8, 2, -8],\n [-3, 12, 3, -12],\n [4, -16, -4, 16],\n [2, -8, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 6, -23, -5],\n [-6, -8, -2, -2],\n [10, 7, 0, -11],\n [-1, 18, -7, 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 4x4 matrix:\n[[12, -4, -2, -4],\n [-22, 8, 10, 15],\n [14, -8, -14, -18],\n [22, -8, -10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 12, 10, -5],\n [-15, -27, -7, -23],\n [13, 27, 7, 17],\n [0, 15, 9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -3, -9, -6],\n [-4, -1, 10, -1],\n [-6, -2, 15, -4],\n [4, 6, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -14, -10, -17],\n [-13, -12, -24, -31],\n [24, 40, -8, 8],\n [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[[-1, -1, -2, 4],\n [-1, -3, -3, 4],\n [-4, -6, -9, 16],\n [0, 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[[-2, 19, 18, 8],\n [6, 11, -4, 11],\n [8, -9, -17, 0],\n [22, 6, -13, 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 4x4 matrix:\n[[4, -5, 15, 1],\n [0, 4, -8, 0],\n [0, 4, -8, 0],\n [0, -4, 8, 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[[-9, 2, 2, 14],\n [-9, 14, 14, 8],\n [-2, -8, 2, 24],\n [2, 4, 0, -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[[-13, -9, -3, 10],\n [16, 30, -12, 0],\n [-8, -20, 12, 2],\n [3, 0, 3, -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[[-22, 0, 8, 14],\n [7, -22, 7, -10],\n [4, 18, -1, 1],\n [14, 16, -11, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, 2, -2, -6],\n [-9, -1, -7, -9],\n [9, -3, -3, 0],\n [4, -4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -4, -17, -3],\n [0, 0, 0, 0],\n [0, 4, 3, 1],\n [-12, -24, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 9, 0, 3],\n [-4, 6, 0, 2],\n [-6, 9, 0, 3],\n [6, -9, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 5, -5, -13],\n [-18, 16, 16, -3],\n [-6, 16, 7, -18],\n [4, 2, -2, -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[[6, 4, 2, 6],\n [0, 0, 0, 0],\n [3, 2, 1, 3],\n [3, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 1, 8, 28],\n [21, -13, -10, 4],\n [7, -9, -1, -4],\n [-10, -4, 13, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 2, -4, -22],\n [1, 9, 7, -9],\n [5, 12, 11, -6],\n [8, -5, 0, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 10, 12, 6],\n [-18, -2, -12, 12],\n [13, 3, 10, -7],\n [2, -25, -21, -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 4x4 matrix:\n[[-17, -1, -2, 24],\n [13, -1, -2, -18],\n [-4, -2, -4, 6],\n [-12, -1, -2, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -9, -3, 6],\n [1, -3, -1, 2],\n [10, 12, 4, -8],\n [-7, 3, 1, -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[[7, 2, -3, 0],\n [-9, -13, -16, -3],\n [-20, -13, -7, -3],\n [-10, -20, -36, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -12, 0, 2],\n [12, -5, 18, -7],\n [10, -7, 20, -11],\n [-6, 0, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, 3, -3],\n [-8, -8, 2, -2],\n [-4, -4, 1, -1],\n [4, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -8, 3, 4],\n [8, 16, -4, -4],\n [2, -4, 0, -1],\n [-2, 28, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 13, -6, 11],\n [-18, -23, -6, -24],\n [-13, -18, -7, -19],\n [18, 23, 6, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 2, 0, 0],\n [-14, 6, 6, 2],\n [-18, 10, 18, 6],\n [-2, 0, -3, -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[[-3, -1, 1, 0],\n [-3, 6, 12, 6],\n [-4, 0, 20, 4],\n [22, -17, 0, -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 4x4 matrix:\n[[-4, -7, -9, -2],\n [-2, 8, -5, -9],\n [-6, 8, -16, -16],\n [-2, -8, -19, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 12, -18, 0],\n [-11, -14, 21, 0],\n [3, 2, -3, 0],\n [12, 16, -24, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 3, 15, 3],\n [-7, -7, -14, -7],\n [-5, -5, 3, -5],\n [-1, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 2, 8, -6],\n [0, 0, 0, 0],\n [-6, 2, 8, -6],\n [-3, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 4, -4, -9],\n [6, 2, -4, -3],\n [-12, -5, 16, 3],\n [-10, -1, -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[[1, 3, -1, 4],\n [3, 9, -3, 12],\n [2, 6, -2, 8],\n [1, 3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 0, 0, -4],\n [0, 3, 3, -8],\n [-9, -9, -9, 12],\n [-6, -3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 6, -12, 3],\n [-4, -4, 16, 12],\n [12, 4, 0, 16],\n [-19, -11, 28, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -4, -4, 1],\n [8, 8, 8, -2],\n [0, 0, 0, 0],\n [-8, -8, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -9, -15, 14],\n [-9, 15, -9, 0],\n [9, -6, 7, 1],\n [18, -12, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 0, -9, 21],\n [5, -4, -5, 5],\n [1, 4, -1, 9],\n [3, -3, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 3, -3, 4],\n [8, -14, -1, -2],\n [5, -11, 5, -8],\n [-10, 18, 0, 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[[-7, 10, 4, 9],\n [-4, 4, 4, -12],\n [6, -7, -5, 8],\n [9, -13, -5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, -4, -4],\n [-2, -4, 7, 3],\n [2, -2, -4, 0],\n [-2, 10, 0, -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 4x4 matrix:\n[[-3, 28, -1, 10],\n [-3, 32, -3, 12],\n [-3, -4, -17, -6],\n [3, -24, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 6, 1, -9],\n [0, 3, 3, -12],\n [4, -7, -2, 13],\n [12, -10, 5, -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[[12, 5, -8, -7],\n [-18, -13, 4, 11],\n [3, -7, -14, -1],\n [6, 8, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -7, 5, -7],\n [-9, -7, 17, -5],\n [-12, -3, -13, 5],\n [-14, -14, 8, -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[[8, 2, -2, 8],\n [-12, 4, 12, -12],\n [8, -5, -11, 8],\n [16, -3, -13, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 12, 8, 12],\n [6, -3, -17, -24],\n [6, 9, -9, -12],\n [8, 24, -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[[6, 6, 6, 6],\n [-6, -6, -6, -6],\n [-8, -8, -8, -8],\n [-8, -8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 0, 4, 16],\n [16, 0, 4, 16],\n [8, 0, 2, 8],\n [16, 0, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 0, 4, -1],\n [9, 0, -12, 3],\n [6, 0, -8, 2],\n [12, 0, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 8, -4, 7],\n [-5, -9, 16, -9],\n [8, 3, 29, 9],\n [-17, -3, -3, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, -6, 8],\n [-25, -9, 13, -28],\n [-24, -12, 15, -28],\n [24, 12, -15, 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[[7, 13, 7, -24],\n [12, 18, 12, -9],\n [5, 8, 5, 6],\n [-6, -4, -6, -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[[20, 8, -8, 12],\n [4, -2, -10, -18],\n [4, 4, 4, 16],\n [-2, -2, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, 4, 4],\n [-9, 0, -6, -6],\n [-12, 0, -8, -8],\n [12, 0, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -1, 3, 4],\n [-6, 2, -6, -8],\n [-3, 1, -3, -4],\n [6, -2, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -3, -1, -2],\n [-9, 9, 3, 6],\n [0, 0, 0, 0],\n [12, -12, -4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 0, -9, -3],\n [-12, 0, 9, 3],\n [-4, 0, 3, 1],\n [-16, 0, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 4, 2, 12],\n [-6, -4, -3, -15],\n [-8, 4, -4, -6],\n [2, -4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 3, 3, 6],\n [1, 3, -1, 6],\n [1, 3, -1, 6],\n [-11, -9, 11, -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[[15, -21, 10, 1],\n [4, -10, 4, 2],\n [4, 3, -27, 4],\n [-2, 10, -30, 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[[12, 12, 0, 8],\n [9, 9, 0, 6],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, 20, 1, -28],\n [-11, 6, -2, -12],\n [16, -30, 13, 36],\n [1, 2, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -9, 17, 16],\n [-4, -12, -12, -8],\n [-7, 6, -7, -7],\n [-1, -19, -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[[6, -6, 3, -9],\n [-2, 2, -1, 3],\n [2, -2, 1, -3],\n [4, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -9, -5, 0],\n [0, 11, -5, -1],\n [-10, -12, 17, 0],\n [-7, 9, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-25, 13, 5, 2],\n [5, 7, 15, -22],\n [-8, 8, 8, -8],\n [-14, 2, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, 9, -12],\n [2, -2, 3, -4],\n [-8, 8, -12, 16],\n [4, -4, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 7, -2, 6],\n [7, 24, -8, -7],\n [0, 12, -12, -8],\n [-2, 14, -20, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 12, -16, -16],\n [12, -9, 12, 12],\n [16, -12, 16, 16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, 6, -8],\n [-8, 4, -3, 10],\n [0, 0, 0, 0],\n [0, 8, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 12, -14, -18],\n [4, 3, 3, 2],\n [-10, 9, -13, -16],\n [-4, 6, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 18, -8, 8],\n [9, 0, -24, 15],\n [-5, -21, 4, -6],\n [-1, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 1, -2, -2],\n [2, -1, 2, 2],\n [6, -3, 6, 6],\n [4, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, -4, -6],\n [-22, 16, 2, -2],\n [8, 19, -7, -14],\n [17, 8, 5, -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[[0, 0, 0, 0],\n [-4, -2, 1, -1],\n [0, 0, 0, 0],\n [16, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -18, 15, -6],\n [-1, -13, 25, 3],\n [-14, -30, 9, -18],\n [-14, -26, 2, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 2, -4, 6],\n [-12, 3, -6, 9],\n [-8, 2, -4, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -10, -12, 14],\n [-1, 5, 7, 8],\n [4, -4, -8, -16],\n [-14, -6, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 4, -6, 8],\n [-2, 6, 0, 6],\n [3, 5, 7, 1],\n [16, 1, 20, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 5, -26, 0],\n [16, -1, -20, 3],\n [-33, 2, 16, -13],\n [21, 7, -30, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 12, -12, 18],\n [18, 12, -6, 12],\n [6, 4, -6, 8],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -7, -5, -11],\n [-6, -4, -4, -7],\n [-2, 2, -2, 1],\n [4, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -5, -8, -2],\n [13, 2, 1, -19],\n [-2, -9, -2, 14],\n [4, -3, -26, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -2, 0, -10],\n [0, -8, -10, 4],\n [-5, 10, 6, 11],\n [14, 20, 9, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, 4, -4],\n [0, 0, 0, 0],\n [-4, -4, 4, -4],\n [-2, -2, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 6, 4, 4],\n [0, 0, 0, 0],\n [-2, 3, 2, 2],\n [-4, 6, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 9, -9, 6],\n [-4, 3, -6, -1],\n [5, -6, 9, -1],\n [-6, 6, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 13, 5, 14],\n [8, -20, -12, -24],\n [-6, 5, -11, -2],\n [2, 5, 17, 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, -12, 4, -4],\n [-3, -6, -6, -12],\n [6, 7, 3, 9],\n [12, 9, -3, 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 4x4 matrix:\n[[2, -3, -4, 2],\n [3, 1, -5, 5],\n [17, 4, -5, 15],\n [5, -16, 5, -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 4x4 matrix:\n[[16, -6, -4, 4],\n [15, -14, -1, -3],\n [-7, 10, 0, 8],\n [17, -11, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 4, 1, -4],\n [10, 10, 6, -2],\n [-7, 1, -5, -13],\n [-11, -7, -7, -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 4x4 matrix:\n[[-6, -4, 8, -4],\n [9, 8, -7, -10],\n [-10, -8, 10, 4],\n [-4, -2, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, -12, -8],\n [-9, -9, 9, 6],\n [12, 12, -12, -8],\n [6, 6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 2, -2, -8],\n [5, -2, -1, -4],\n [1, -1, 0, 0],\n [1, -1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 9, 0, 6],\n [0, 0, 0, 0],\n [8, -6, 0, -4],\n [12, -9, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -1, -3, 4],\n [0, 0, 0, 0],\n [0, -2, -6, 8],\n [0, 2, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -6, -8, -4],\n [-6, 7, -11, 0],\n [6, -16, -20, -2],\n [3, -4, 7, 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 4x4 matrix:\n[[-4, 4, 1, 1],\n [-4, 4, 1, 1],\n [0, 0, 0, 0],\n [-16, 16, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 2, 3, -1],\n [-3, 6, 9, -3],\n [1, -2, -3, 1],\n [4, -8, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -12, 0, -4],\n [9, 0, -2, -3],\n [10, -9, 6, 5],\n [-4, -21, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 3, 2, 4],\n [8, -1, -3, 8],\n [-28, -4, 3, -28],\n [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 4x4 matrix:\n[[-16, -8, 10, 18],\n [-25, 19, 6, 8],\n [-1, 10, 4, 3],\n [-23, 12, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -7, -1, -5],\n [6, -9, 6, 6],\n [-4, 0, 1, -3],\n [0, 22, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 6, -6, 4],\n [8, 6, -6, 4],\n [0, 0, 0, 0],\n [-16, -12, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 9, 4, -9],\n [-13, 6, 1, 0],\n [-4, -7, -5, -3],\n [5, -5, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 6, 6, -18],\n [-5, 6, 0, -5],\n [8, 10, 0, -13],\n [9, -20, 8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 16, -16, -4],\n [4, 8, -8, -2],\n [-2, -4, 4, 1],\n [4, 8, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 7, 0, -22],\n [13, -1, -25, -4],\n [5, -1, -11, 0],\n [5, 3, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -5, 11, -16],\n [-11, 3, -5, 5],\n [0, 20, 12, -2],\n [-1, -12, -9, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -8, -12, 8],\n [0, 0, 0, 0],\n [8, 8, 12, -8],\n [2, 2, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -3, 9, -2],\n [-4, -10, 14, 4],\n [2, -10, 8, 8],\n [8, 5, -13, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 2, 1, -2],\n [-2, -5, 16, 6],\n [-9, -11, 15, 16],\n [-15, 0, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 2, 8, -14],\n [2, 17, 3, 6],\n [2, 2, 8, -14],\n [4, 28, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -6, 6, -8],\n [-1, 3, -3, 4],\n [0, 0, 0, 0],\n [4, -12, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -3, 3, -2],\n [-9, 9, -9, 6],\n [0, 0, 0, 0],\n [-6, 6, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 12, -12, 4],\n [-25, -24, 6, -8],\n [13, 12, 2, 5],\n [12, 21, 4, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 5, 10, 2],\n [-28, 6, 4, -4],\n [-18, -6, -4, 8],\n [23, -3, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -6, 2, 6],\n [4, 9, -7, -8],\n [0, -3, 1, 3],\n [12, 0, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -25, 7, 4],\n [6, -2, 14, 16],\n [8, 2, 12, 20],\n [3, -21, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 6, -3, 6],\n [-12, -8, 4, -8],\n [-9, -6, 3, -6],\n [9, 6, -3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -4, -13, 4],\n [3, 2, 5, -11],\n [-1, -9, -16, 6],\n [-9, 9, 24, -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[[16, -9, -5, 11],\n [-26, 18, 4, -28],\n [14, -6, 4, 16],\n [-12, 5, -3, -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[[2, 2, 0, -1],\n [8, 8, 0, -4],\n [-2, -2, 0, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [1, 4, -1, -2],\n [4, 16, -4, -8],\n [-3, -12, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, -6, 1, -15],\n [-2, -1, 1, 5],\n [-8, 6, -2, 6],\n [8, -1, -1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 9, 2, 1],\n [-1, 9, 7, 10],\n [-9, -1, 7, 4],\n [-11, 10, 15, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -3, -2, -3],\n [-4, -7, 18, 9],\n [2, -1, -12, -9],\n [2, 20, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -3, 4, -1],\n [4, -3, 4, -1],\n [0, 0, 0, 0],\n [4, -3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 12, 9, -3],\n [0, 0, 0, 0],\n [-1, 4, 3, -1],\n [2, -8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 20, 0, 17],\n [10, 12, -16, 16],\n [-8, -12, 4, -12],\n [1, -4, 14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 4, -15, -13],\n [-4, 16, -4, 4],\n [6, -12, -4, -10],\n [2, -2, -3, -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[[5, -7, -4, -1],\n [-14, 16, 7, 1],\n [3, 3, 6, 3],\n [0, -6, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 2, -2, 2],\n [0, 0, 0, 0],\n [4, 2, -2, 2],\n [-4, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 37, 16, -17],\n [4, 5, -6, 5],\n [6, 7, -16, 13],\n [-11, -15, -1, 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 4x4 matrix:\n[[6, -12, -6, -8],\n [-4, 8, 4, 0],\n [5, -10, -5, -12],\n [8, -16, -8, -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 4x4 matrix:\n[[10, 9, 8, 6],\n [4, 2, -3, 7],\n [1, -4, -9, 9],\n [3, -2, 17, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -6, -4, -9],\n [7, 22, 8, 18],\n [0, -8, -17, -12],\n [-2, -12, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 9, -6, -6],\n [6, 6, -4, -4],\n [6, 6, -4, -4],\n [-6, -6, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [3, 6, -9, -9],\n [0, 0, 0, 0],\n [-2, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 8, 0, 6],\n [8, 8, 0, 6],\n [16, 16, 0, 12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -8, 0, 15],\n [16, -16, -15, 16],\n [-24, 21, 24, -21],\n [12, -5, -16, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 11, 5, -29],\n [-10, -4, -10, 5],\n [7, 6, 8, -4],\n [7, 6, 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[[10, 12, 6, -5],\n [-5, -18, -3, -5],\n [15, 26, 16, 5],\n [22, 16, 23, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -10, 8, 10],\n [2, 3, -1, 2],\n [4, -2, -6, 8],\n [26, 3, -10, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -6, -2, -2],\n [-2, -6, -2, -2],\n [4, 12, 4, 4],\n [-1, -3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-28, 1, 20, -3],\n [26, 4, -12, 11],\n [-27, -10, 12, -12],\n [32, 9, -32, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -2, -6, -4],\n [-4, 1, 3, 2],\n [4, -1, -3, -2],\n [-8, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 3, 1, 4],\n [-6, -9, -3, -12],\n [4, 6, 2, 8],\n [4, 6, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 3, -6, -12],\n [-9, 2, 10, -4],\n [-5, -4, 10, 14],\n [-20, -4, 16, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -1, 7, 12],\n [13, -15, 17, 15],\n [-1, -1, -1, -3],\n [-16, 12, -20, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, 13, 3, -20],\n [-4, 2, 6, 8],\n [17, -13, -3, 20],\n [-12, 8, 8, 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 4x4 matrix:\n[[3, -4, -2, 2],\n [-9, 12, 6, -6],\n [-3, 4, 2, -2],\n [12, -16, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -5, 2, 9],\n [-7, 16, -19, 27],\n [-10, -8, 8, 6],\n [14, -8, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -2, -3, 4],\n [-12, -4, 4, 12],\n [11, -3, -7, -3],\n [10, 0, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, -6, 0, 0],\n [-18, -8, 21, 9],\n [-11, -15, -3, -12],\n [-14, -16, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 17, -4, -15],\n [-12, -4, -4, -2],\n [-20, -1, -2, -2],\n [-11, 12, -16, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 16, -12, -8],\n [-6, -8, 6, 4],\n [0, 0, 0, 0],\n [3, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -12, 9, -12],\n [7, 8, -6, 14],\n [8, 8, -6, 16],\n [-6, -16, 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[[-6, 6, 4, -6],\n [-7, -8, -9, -3],\n [-5, -3, -2, -8],\n [1, 8, 7, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 10, 7, -16],\n [17, -1, 1, 5],\n [-4, -8, -6, 12],\n [-22, 6, 2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 3, 3, 2],\n [0, -3, -3, -2],\n [0, -12, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 2, 4, 3],\n [12, 4, 8, -15],\n [-16, -2, -4, 15],\n [16, 2, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 2, -6, 0],\n [-2, 0, 6, 8],\n [-3, 1, 6, 12],\n [2, -5, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 0, -13, -1],\n [6, 2, 5, 4],\n [-2, 3, -12, 9],\n [3, 4, 9, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 4, 1, 3],\n [8, 8, 2, 6],\n [-16, -16, -4, -12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -15, -15, -21],\n [0, 4, 2, 3],\n [0, 12, 16, 22],\n [0, -11, -13, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 12, -4, -4],\n [18, -19, 1, 11],\n [-18, 0, -2, 4],\n [10, -17, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -21, -6, 0],\n [-4, -27, -9, 18],\n [-40, -6, -4, -10],\n [4, -6, -5, 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[[3, 0, -9, 0],\n [-4, 17, 4, -25],\n [22, -4, -6, 12],\n [16, -12, -20, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 9, -6, -11],\n [1, 7, -2, -5],\n [-3, -12, 6, 12],\n [-1, -13, 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[[-5, 11, -18, -6],\n [-3, -9, 30, 0],\n [-17, 29, -10, -15],\n [7, 8, -36, 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[[0, 0, 0, 0],\n [0, 0, -3, -1],\n [0, 0, -12, -4],\n [0, 0, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, -3, 4],\n [9, -1, -3, -13],\n [-3, 1, 2, 3],\n [0, -6, -9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 4, -2, -4],\n [1, 4, -2, -4],\n [-2, -8, 4, 8],\n [-3, -12, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, -5, 10, -8],\n [-8, -12, 8, 0],\n [-22, -5, 15, -14],\n [4, 10, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -3, 4, 1],\n [2, -3, 4, 1],\n [0, 0, 0, 0],\n [-6, 9, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 2, 22, -16],\n [-2, 11, -7, 8],\n [-5, -9, -9, 22],\n [0, 23, 7, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -4, -8, 12],\n [8, 2, 4, -6],\n [0, 0, 0, 0],\n [4, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, 0, 4],\n [0, 6, 0, 3],\n [0, 2, 0, 1],\n [0, -6, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 4, 1, -3],\n [1, 4, 1, -3],\n [1, 4, 1, -3],\n [1, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -16, -6, 20],\n [6, 4, 4, -6],\n [-22, 12, -8, -10],\n [-12, -8, -8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -8, -8, 2],\n [8, -8, -8, 2],\n [16, -16, -16, 4],\n [-4, 4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 14, -4, -9],\n [8, -26, 8, 15],\n [20, -6, -12, 13],\n [16, -6, -12, 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, 6, 8, 16],\n [2, 8, -5, -3],\n [4, 10, 5, 19],\n [1, 5, 9, 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[[2, -2, -8, -18],\n [-7, 8, -3, 3],\n [9, 3, 6, 9],\n [0, -14, -3, -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, 6, -12],\n [-3, -6, -6, 12],\n [2, 4, 4, -8],\n [-3, -6, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 6, -8, 0],\n [-12, -9, 12, 0],\n [12, 9, -12, 0],\n [-16, -12, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 9, -13, 5],\n [0, -8, 12, -8],\n [3, -5, 6, 7],\n [3, -3, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, -8, -12, 11],\n [-22, 8, 12, -11],\n [6, 6, 4, 3],\n [-4, -19, -16, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, -6, -6],\n [0, 0, 0, 0],\n [-12, 8, 12, 12],\n [9, -6, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 4, 16, -12],\n [8, 2, 8, -6],\n [-4, -1, -4, 3],\n [12, 3, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 16, -1, -16],\n [-4, -8, 1, 10],\n [9, 12, -3, -21],\n [-4, 8, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 10, 2, 17],\n [12, 9, 3, 21],\n [8, 6, 2, 14],\n [-12, -8, -4, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -2, 4, -6],\n [12, 0, 4, -2],\n [9, -18, 24, -14],\n [-9, 0, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, -6, 0],\n [0, 8, -12, 0],\n [0, 0, 0, 0],\n [0, -4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -4, 0, 20],\n [-9, 7, 16, -3],\n [1, -3, -4, 7],\n [1, 5, 4, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -8, -8, -2],\n [0, 0, 0, 0],\n [-3, -12, -12, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 12, -16, 12],\n [0, -3, 4, -3],\n [0, -3, 4, -3],\n [0, 12, -16, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-3, 4, 17, 15],\n [-1, 0, 9, 9],\n [1, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, -1, 0],\n [2, -2, 0, 1],\n [-12, -16, 14, -20],\n [8, 14, -11, 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[[-8, 4, 16, -2],\n [-7, -10, -17, -7],\n [-12, 4, 8, -10],\n [-6, 6, 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[[0, -3, -3, 8],\n [-26, 4, 28, 2],\n [2, 14, 2, 4],\n [5, -16, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 6, -1],\n [-22, 6, -2, -13],\n [-28, 2, 5, -18],\n [3, -1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -6, -5, 1],\n [8, -18, -22, 10],\n [0, -12, -12, 4],\n [-2, -9, -8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 12, 8, 4],\n [-16, 12, 8, 4],\n [16, -12, -8, -4],\n [-4, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -8, -18, 9],\n [2, 5, 1, -2],\n [1, -5, 4, -5],\n [-1, -4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 9, -6, -12],\n [0, 0, 0, 0],\n [3, -9, 6, 12],\n [1, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -2, -4, 4],\n [-12, 32, 20, -48],\n [17, -7, 9, 4],\n [14, -19, 2, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 4, 10, -6],\n [6, -2, -7, 11],\n [10, -4, -12, 14],\n [10, -8, -14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, -4, -6],\n [-2, 4, -2, -3],\n [6, -12, 6, 9],\n [4, -8, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -22, -9, -5],\n [15, 8, -12, 1],\n [-10, -3, 1, -1],\n [8, 2, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 6, -11, 12],\n [-15, 6, -13, 12],\n [11, -10, 17, -20],\n [-6, 6, -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[[-28, -4, 8, -4],\n [25, 7, -7, 5],\n [1, 7, 0, 3],\n [-4, -28, 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[[-2, 8, -4, -2],\n [1, 4, -6, -4],\n [6, -8, -4, -4],\n [6, 0, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 3, 0, 0],\n [16, 12, 0, 0],\n [16, 12, 0, 0],\n [-12, -9, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 0, -8, -4],\n [-8, 7, -6, 4],\n [8, -1, -6, -4],\n [-12, 9, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, 3, 0],\n [0, 0, 0, 0],\n [0, 16, -12, 0],\n [0, -12, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -3, 4, -4],\n [8, 6, -8, 8],\n [0, 0, 0, 0],\n [12, 9, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 12, -8, -4],\n [0, 0, 0, 0],\n [9, 9, -6, -3],\n [-3, -3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 3, 9, 9],\n [0, 0, 0, 0],\n [8, 4, 12, 12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 18, 3, -21],\n [2, 4, -4, -8],\n [-4, -8, 8, 16],\n [-3, 10, 18, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 16, -16, -16],\n [6, -8, 8, 8],\n [-3, 4, -4, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -9, 2, 5],\n [-8, 6, 5, -4],\n [-10, 0, 19, -2],\n [-7, -1, 15, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 0, 4, -4],\n [-2, 0, -4, 4],\n [-1, 0, -2, 2],\n [1, 0, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, -8, 0],\n [0, 3, -12, 0],\n [0, -2, 8, 0],\n [0, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -4, 8, 8],\n [-4, -2, 4, 4],\n [-12, -6, 12, 12],\n [12, 6, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -12, 11, -10],\n [-6, 23, -28, 23],\n [2, 18, -19, 12],\n [-5, 11, -15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 4, 14, 8],\n [0, 12, 18, 16],\n [1, -10, -14, -13],\n [-2, -4, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 2, 12, 19],\n [-6, -4, -14, 2],\n [6, -7, 8, 21],\n [0, -11, -1, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 4, -1, 7],\n [-16, -12, 4, -12],\n [-11, 0, -1, -9],\n [12, 20, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, 1, 3],\n [16, 0, 4, 12],\n [8, 0, 2, 6],\n [-8, 0, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 9, 6, -21],\n [-1, -4, 9, -1],\n [18, 0, -10, 26],\n [-9, 9, 11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -16, 7, -1],\n [6, -12, -4, -8],\n [0, 3, -1, 1],\n [6, 8, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 5, 3, -5],\n [2, 7, 5, 1],\n [3, 10, 7, 0],\n [4, 10, 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[[4, -20, -24, 20],\n [0, 0, 0, 0],\n [1, -3, -3, 1],\n [-1, -5, -9, 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 4x4 matrix:\n[[0, 4, 12, 12],\n [0, -2, -6, -6],\n [0, 2, 6, 6],\n [0, -1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 24, 4, -24],\n [-4, 16, 2, -15],\n [0, -8, 0, 6],\n [-6, 22, 3, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-12, 6, 9, 0],\n [-8, 4, 6, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -7, 13, 13],\n [-3, 6, -10, -10],\n [0, -1, 3, 3],\n [9, -12, 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[[-2, 8, 14, -16],\n [4, -16, 0, 18],\n [-1, 4, 7, -8],\n [3, -12, 15, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -1, -12, 11],\n [8, -2, -12, 6],\n [-14, 11, 14, -7],\n [-12, 8, 25, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 8, 0, -1],\n [4, 4, -14, 20],\n [0, 4, -14, 18],\n [-4, -12, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -4, 13, -13],\n [-20, -5, 18, -18],\n [8, -2, -4, 4],\n [-10, 0, 7, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, 19, 12, 2],\n [9, 3, 12, 6],\n [7, 9, 4, 0],\n [-12, -4, -16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -1, -13, 2],\n [29, -23, -25, -15],\n [-12, 16, 6, 17],\n [10, -10, -16, -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[[14, 28, 5, -10],\n [-19, -12, -19, 11],\n [-12, -12, -3, 0],\n [13, 28, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, -1, -6],\n [-5, -5, -8, -8],\n [5, 5, 8, 8],\n [-6, -6, -11, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 0, 0, 12],\n [8, 0, 0, -16],\n [-4, 0, 0, 8],\n [-6, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 20, 2, -1],\n [-28, -17, -2, 2],\n [10, 5, 12, 9],\n [8, -2, 0, -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, -13, -9, -15],\n [-1, 2, 3, -2],\n [6, -8, -6, -8],\n [18, -25, -21, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -9, -12, -6],\n [0, -9, -12, -6],\n [2, 9, 4, 2],\n [0, 9, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -16, -4, 8],\n [-4, 0, -8, 8],\n [-5, 12, -4, 1],\n [-3, 12, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 8, -13],\n [12, 20, 8, 25],\n [12, 18, 9, 21],\n [-8, -12, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -15, 9, -13],\n [3, -3, -1, 17],\n [-3, 9, -3, -9],\n [3, -21, 11, -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[[10, -11, -2, -10],\n [-6, 5, -1, -11],\n [-14, 13, 0, -4],\n [-10, 7, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -3, -6, 3],\n [0, 0, 0, 0],\n [8, 2, 4, -2],\n [8, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 11, 2, 1],\n [-6, -7, -14, 13],\n [6, -25, -2, -5],\n [8, -24, 2, -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 4x4 matrix:\n[[3, 1, -2, 4],\n [3, -3, -5, -25],\n [11, 15, -7, 21],\n [-4, 4, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -6, 3, 0],\n [-6, 6, 6, 9],\n [2, -2, 4, 3],\n [8, -8, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -6, -4, -4],\n [-8, -6, -4, -4],\n [-12, -7, -6, -4],\n [16, -24, 8, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 4, 26, 6],\n [-18, -8, 8, -9],\n [4, 6, -22, 10],\n [-20, 2, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -1, 4, 4],\n [5, 8, -15, -18],\n [-8, -4, 16, 16],\n [-5, 14, -5, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -12, -3, -6],\n [-4, -8, -2, -4],\n [-4, -8, -2, -4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -9, 6, 6],\n [2, 3, -2, -2],\n [-4, -6, 4, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -4, 2, 8],\n [14, 6, 2, -12],\n [8, 7, -1, -14],\n [18, 7, 3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -10, 0, -10],\n [-15, 10, -15, -5],\n [8, -4, 8, 4],\n [-20, 0, -20, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 22, 2, -1],\n [12, 6, 26, -8],\n [-26, 7, 17, -25],\n [10, 10, -2, 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, -3, 12, 9],\n [-13, -3, 5, 4],\n [7, -17, 14, 7],\n [6, 4, 14, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 2, -8, 0],\n [12, -3, 12, 0],\n [8, -2, 8, 0],\n [-8, 2, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, -4, 2],\n [12, 28, 5, -6],\n [4, 0, 4, -2],\n [8, 0, 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[[9, 0, 0, -3],\n [-3, 0, 0, 1],\n [6, 0, 0, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 2, -7, 6],\n [12, -2, 16, -12],\n [12, 2, 2, 0],\n [4, 2, -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[[2, 12, -2, -2],\n [11, 0, -2, -5],\n [-15, -2, 3, 7],\n [-24, 10, 3, 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[[21, -13, 2, -4],\n [6, -5, 13, 4],\n [-3, 19, 2, 16],\n [-6, 8, -18, -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[[-10, -6, -9, 6],\n [3, 1, 9, 12],\n [0, 2, 0, -3],\n [9, 5, 3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 25, 5, -2],\n [6, -5, 0, -8],\n [3, 17, 2, 2],\n [9, -1, 1, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 16, 14, 18],\n [0, 2, -1, 1],\n [12, 18, 13, 19],\n [9, 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 4x4 matrix:\n[[0, -2, 2, -4],\n [0, 3, -3, 6],\n [0, 4, -4, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, -4],\n [-17, 1, -6, 1],\n [-14, 2, -4, -6],\n [2, -1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 15, 9, -4],\n [1, 3, -6, 7],\n [-11, 21, 12, -5],\n [7, -12, -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[[8, 4, 4, -12],\n [-2, -1, -1, 3],\n [6, 3, 3, -9],\n [8, 4, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 16, -17, -7],\n [13, 12, -10, -8],\n [-12, -8, 5, 7],\n [2, 8, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 8, 14, 5],\n [5, 18, 18, 4],\n [15, 0, 18, 3],\n [3, 14, 14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -16, 8, 0],\n [0, 0, 0, 0],\n [-2, -4, 2, 0],\n [-4, -8, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, 19, 14, -12],\n [-12, -4, -24, 0],\n [-6, -13, -3, 9],\n [-14, -3, -9, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 8, -1, -18],\n [17, -4, -8, -5],\n [4, -13, 6, 13],\n [-9, -1, -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[[4, -6, 16, 16],\n [1, -11, 7, -12],\n [10, 4, -18, -18],\n [-9, 14, -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 4x4 matrix:\n[[1, -2, 1, -3],\n [-4, 8, -4, 12],\n [3, -6, 3, -9],\n [-4, 8, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 11, 12, -6],\n [-14, 14, 8, 16],\n [13, -10, 0, -17],\n [2, -1, 4, -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 4x4 matrix:\n[[8, 8, 9, -14],\n [-12, -12, -7, -5],\n [-12, -12, -7, -5],\n [12, 12, 11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -8, 2, -18],\n [-9, -18, -3, -9],\n [-3, 30, 3, 21],\n [4, 29, 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[[2, 4, -1, 0],\n [-4, -8, 2, 0],\n [2, 4, -1, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[22, 11, 6, 6],\n [-4, 14, 12, -4],\n [0, -9, -19, -6],\n [-14, 11, 8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -4, -7, -4],\n [2, 8, 9, 8],\n [-7, -15, -25, -15],\n [-3, -9, -12, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -11, -19, 15],\n [12, -24, 0, 16],\n [8, -22, -8, 18],\n [-13, 7, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 12, -20, -18],\n [-3, 11, -10, -11],\n [-10, 2, -5, 4],\n [3, 29, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -1, 2, 0],\n [4, -1, 2, 0],\n [-16, -11, 22, 0],\n [-12, -7, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 6, 4, 9],\n [-12, -8, 0, -12],\n [3, 2, 0, 3],\n [-9, -6, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -15, -2, -1],\n [9, -2, -4, 5],\n [2, -8, 0, -2],\n [12, 3, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -7, -9, 20],\n [0, -6, -12, 0],\n [0, 12, 24, 0],\n [-6, -1, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 10, -8, -6],\n [6, -6, -4, -6],\n [-6, -6, 7, 6],\n [0, 16, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -7, -4, -8],\n [8, -5, 1, -7],\n [-16, -4, -5, -3],\n [0, -7, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 12, -4, -6],\n [-12, 0, 8, 0],\n [-6, 4, 0, -2],\n [9, -22, 16, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 6, 12, -12],\n [0, 11, 3, -14],\n [4, 21, -3, -22],\n [12, -2, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -1, -4, 2],\n [4, 4, 16, -8],\n [-4, -4, -16, 8],\n [-1, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -7, -11, 0],\n [24, 14, 30, 28],\n [-5, -6, -6, -14],\n [-8, -3, -16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 6, -2, -8],\n [4, 4, 16, -17],\n [-4, -8, -10, 13],\n [0, 0, -16, 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[[31, 5, 28, -4],\n [18, 7, 16, -7],\n [15, 2, 4, -7],\n [-4, 12, -8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -16, -16, -4],\n [0, -16, -16, -4],\n [0, 16, 16, 4],\n [0, 8, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -20, 12, -1],\n [-6, -4, 4, 3],\n [4, -24, 14, -2],\n [-4, -24, 16, 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 4x4 matrix:\n[[-12, -12, 12, 16],\n [-3, -3, 3, 4],\n [-12, -12, 12, 16],\n [-6, -6, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 9, -9, 9],\n [0, 12, -12, 12],\n [0, -9, 9, -9],\n [0, 9, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[25, 25, 19, -13],\n [-16, -16, -16, 4],\n [25, 25, 19, -13],\n [-8, -8, -8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -18, 14, -10],\n [3, -10, 6, -7],\n [-9, -2, 18, 8],\n [18, -2, -15, -22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 12, 16, 0],\n [4, -3, -4, 0],\n [8, -6, -8, 0],\n [-8, 6, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -4, -11, -10],\n [8, -25, -4, 4],\n [-20, -4, -12, -12],\n [-5, -4, 5, 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[[-2, 2, 1, -2],\n [-2, -7, -8, -14],\n [-6, -6, -9, -22],\n [-4, 10, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 16, 4, 0],\n [4, 16, 4, 0],\n [0, 0, 0, 0],\n [-4, -16, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -1, 1, 2],\n [-12, -3, 3, 6],\n [0, 0, 0, 0],\n [-12, -3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 9, -6, -3],\n [4, -12, 8, 4],\n [-3, 9, -6, -3],\n [-2, 6, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 1, -2, 3],\n [8, -2, -1, -11],\n [4, 2, -2, 8],\n [6, -3, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -1, -3, -2],\n [0, 3, 9, 6],\n [0, -2, -6, -4],\n [0, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 12, 9, 3],\n [-4, 4, 3, 1],\n [-4, 4, 3, 1],\n [-16, 16, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[28, -13, 18, 20],\n [-12, -8, -5, -14],\n [24, -9, 15, 18],\n [-16, 11, -11, -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[[-4, 0, 8, -12],\n [2, 0, -4, 6],\n [1, 0, -2, 3],\n [3, 0, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 24, 0, -8],\n [-14, 20, -1, -4],\n [-6, 4, -5, 12],\n [16, -24, 0, 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 4x4 matrix:\n[[1, 6, -3, 8],\n [25, -4, -24, -14],\n [19, 4, -16, -10],\n [17, -8, -18, -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[[6, 0, -16, 8],\n [-9, 4, 20, -4],\n [-12, 24, 8, 32],\n [6, 0, -16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 3, -3, -12],\n [0, -4, 4, 16],\n [0, 4, -4, -16],\n [0, -4, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 3, -16, -6],\n [-27, 21, -4, -14],\n [-9, 0, 0, -3],\n [-11, 6, -8, -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[[9, 6, 0, 12],\n [-1, 6, 8, -20],\n [-7, -3, 2, -14],\n [8, 7, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -12, -6, -6],\n [0, 12, 6, 6],\n [0, 0, 0, 0],\n [0, -16, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -10, -16, -4],\n [1, 5, 8, 2],\n [2, -6, -8, -8],\n [-5, -9, -16, 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 4x4 matrix:\n[[5, -7, 11, 7],\n [11, -1, -11, 5],\n [9, 3, -10, -2],\n [3, -13, 17, 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[[-16, -12, 26, 24],\n [4, -6, -20, 0],\n [-14, -4, 5, 10],\n [-5, 1, 18, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -6, -8, 0],\n [-3, 3, 10, -8],\n [-1, 15, 8, 16],\n [-3, 18, 15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -15, 28, 15],\n [-4, 6, -8, -6],\n [-12, 11, -12, -11],\n [10, 6, -16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -4, 0, 6],\n [6, -19, 11, -6],\n [-12, 9, -13, 0],\n [-9, 7, -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[[6, -16, -14, -8],\n [19, -14, 25, 1],\n [-24, 22, -16, 4],\n [1, -7, -9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -24, -16, -16],\n [6, -4, -4, -6],\n [5, -6, -4, -4],\n [-4, 0, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 14, -6, 14],\n [5, -2, -14, 4],\n [3, 0, -3, 12],\n [-7, 6, 9, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 8, -9, 2],\n [26, -10, -28, 8],\n [9, 6, -6, 1],\n [17, -15, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-21, 6, 8, 16],\n [15, -18, -2, -4],\n [-3, 4, 0, 2],\n [-17, 15, 3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 2, 7, -1],\n [13, 9, -25, -9],\n [3, 7, 25, -2],\n [15, 15, -19, -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[[20, -4, 12, 4],\n [-4, -2, -4, 1],\n [2, -6, -2, 4],\n [16, -6, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 3, -6, 0],\n [11, 1, -2, 5],\n [14, 4, -13, 1],\n [-11, -7, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 12, 8, 8],\n [-2, 6, 4, 4],\n [3, -9, -6, -6],\n [4, -12, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 1, -13, -1],\n [1, -1, 3, 7],\n [7, 11, -14, -17],\n [-10, -3, 19, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -2, 3, -1],\n [-16, 8, -12, 4],\n [-8, 4, -6, 2],\n [8, -4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -2, 3, -2],\n [-4, -12, 12, -4],\n [0, -20, 18, -4],\n [-4, -2, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 12, -6, 6],\n [-6, 8, -4, 4],\n [0, 0, 0, 0],\n [3, -4, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -1, -5, 14],\n [0, -3, 3, 12],\n [1, 0, 3, -2],\n [-24, 4, -28, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 1, 0],\n [-2, -2, -4, -1],\n [2, 2, 0, 1],\n [-6, -6, -13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -3, 4, -3],\n [2, 10, -12, 12],\n [-8, 8, -16, 0],\n [-2, 5, -8, 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 4x4 matrix:\n[[26, 8, -10, -12],\n [-22, -8, 6, 8],\n [-14, 16, -18, -6],\n [3, -8, 5, 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 4x4 matrix:\n[[5, -11, 14, 3],\n [8, -14, 8, 3],\n [0, 14, -16, -12],\n [-3, -5, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 5, -10, 3],\n [-4, 6, 4, -6],\n [10, -6, -10, -6],\n [0, -5, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -4, -2, -2],\n [12, 16, 8, 8],\n [0, 0, 0, 0],\n [12, 16, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 28, 8, -5],\n [-10, 25, 14, 2],\n [14, 6, 8, -2],\n [21, -1, 15, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [16, -16, 0, -12],\n [-8, 8, 0, 6],\n [-16, 16, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-16, -8, 8, -8],\n [4, 2, -2, 2],\n [16, 8, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 3, -4, 4],\n [-6, 2, -8, 14],\n [-1, -5, 4, -1],\n [-5, -1, -4, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [3, 12, 3, -9],\n [-2, -8, -2, 6],\n [-1, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 8, -6, -2],\n [0, -8, 6, 2],\n [0, 0, 0, 0],\n [0, -12, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 14, 6, -20],\n [2, -8, -6, -4],\n [-6, 16, 10, -4],\n [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[[2, 5, -1, -23],\n [8, 7, -5, -5],\n [-8, 6, 6, -19],\n [-18, -6, 12, 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[[7, 0, 2, 8],\n [4, 6, 34, -8],\n [13, -15, 18, -18],\n [3, -3, 23, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -1, 4, 4],\n [7, -8, 5, -13],\n [-2, -8, -6, 6],\n [4, 7, 8, -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[[-2, -3, 3, 0],\n [-4, -6, 6, 0],\n [6, 9, -9, 0],\n [8, 12, -12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -12, -16, -12],\n [-13, 1, -4, 13],\n [-9, 9, 12, 9],\n [-15, 6, 4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 9, -8, 13],\n [0, 10, 2, 10],\n [19, -12, 11, -16],\n [-34, 16, -6, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -3, -2, -3],\n [12, 28, 12, 28],\n [-9, -7, -10, -11],\n [0, -16, -6, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -11, 6, -2],\n [4, 14, -8, 0],\n [-6, -9, 4, -8],\n [6, 12, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, -9, -3, -21],\n [-18, -5, 3, -21],\n [-12, 4, 12, -12],\n [12, 7, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -1, -4, 1],\n [12, 3, 12, -3],\n [-12, -3, -12, 3],\n [-4, -1, -4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 0, -15, -16],\n [14, 0, -3, -10],\n [16, 0, 0, -8],\n [-4, 0, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -16, -5, 8],\n [16, 8, 6, 10],\n [12, 16, 7, 0],\n [4, 0, 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[[-21, 2, 8, -19],\n [-10, -3, 1, -14],\n [9, 14, 10, 3],\n [7, -3, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -8, -8, -2],\n [-12, 16, 16, -4],\n [-5, -12, -12, 17],\n [-13, 4, 4, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -12, -3, 12],\n [12, -16, -4, 16],\n [12, -16, -4, 16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 12, -3, -9],\n [0, 0, 0, 0],\n [-9, -12, 3, 9],\n [9, 12, -3, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -3, -6, 4],\n [-12, 6, -6, -8],\n [-3, 3, 0, -4],\n [-9, 15, 6, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 3, -2, 3],\n [4, 6, -4, 6],\n [8, 12, -8, 12],\n [-6, -9, 6, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[22, -1, 16, -14],\n [-4, 4, -2, -17],\n [26, 2, 20, -12],\n [-4, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-21, -25, -16, -6],\n [3, 7, 16, -6],\n [3, 1, -8, 6],\n [-18, -20, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 1, 2, -2],\n [16, -9, 6, 4],\n [5, -4, 0, 2],\n [18, 5, 2, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, -13, 1],\n [-16, 2, -10, 4],\n [12, -1, 6, -3],\n [-28, 4, -19, 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 4x4 matrix:\n[[8, -3, -4, -12],\n [14, -9, -6, -20],\n [9, -9, -3, -12],\n [-4, -6, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 6, 15, -9],\n [14, 7, 12, 6],\n [-12, -6, -9, -9],\n [4, 2, 3, 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 4x4 matrix:\n[[6, -6, 3, 0],\n [0, 0, 0, 0],\n [2, -2, 1, 0],\n [6, -6, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -3, 12, -6],\n [-2, -1, 4, -2],\n [-8, -4, 16, -8],\n [-4, -2, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-3, 1, -3, -3],\n [-12, 4, -12, -12],\n [6, -2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 6, -6, 8],\n [0, -9, 9, -12],\n [0, 9, -9, 12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 12, 0, -3],\n [-6, -12, 0, 3],\n [-2, -4, 0, 1],\n [6, 12, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -22, 18, 11],\n [-8, 2, 2, 5],\n [6, -18, 9, 3],\n [-3, -10, 11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -4, 4, 6],\n [2, -4, 4, 6],\n [-4, 8, -8, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 4, 6, -6],\n [4, 4, 6, -6],\n [-6, -6, -9, 9],\n [8, 8, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -6, 3, -8],\n [2, -18, -2, -6],\n [-7, 12, -7, -4],\n [4, 18, 8, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 1, 2, 4],\n [-6, 7, -2, -2],\n [-6, 2, -4, -7],\n [-8, 6, -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[[0, 6, 6, 4],\n [0, -3, -3, -2],\n [0, -9, -9, -6],\n [0, 12, 12, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 17, -20, -21],\n [-4, -20, 8, 12],\n [25, -2, -2, 6],\n [-15, -17, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -12, -7, -3],\n [-2, -6, 13, 21],\n [-2, -2, 8, 12],\n [11, -17, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -12, -9, -12],\n [-4, 4, 3, 4],\n [2, -12, -14, -8],\n [-8, 8, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, -18, 27, -19],\n [-17, -20, 12, -4],\n [1, 10, 3, -3],\n [18, 30, -9, 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 4x4 matrix:\n[[0, -1, -2, -6],\n [10, -10, -12, 6],\n [0, 8, -1, -21],\n [6, 6, -7, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -15, 9, -6],\n [2, 2, -8, -4],\n [2, 6, 10, 12],\n [-2, 0, 17, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -2, -7, 5],\n [1, 0, -1, 3],\n [-3, 0, 3, -9],\n [4, 0, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, -6, -6],\n [0, 0, 9, 9],\n [0, 0, 6, 6],\n [0, 0, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 3, 18, 12],\n [-4, 0, 18, 8],\n [-16, 10, -3, 12],\n [-4, 0, 18, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, 0, 14],\n [-3, 3, 9, 18],\n [7, 7, 0, 2],\n [12, 8, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -22, -20, -16],\n [13, 23, 22, 16],\n [-12, -12, -8, -8],\n [0, -25, -25, -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[[21, -11, -16, -3],\n [20, -5, -11, 1],\n [10, 5, 3, 7],\n [-4, 0, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 6, 6, -2],\n [14, -6, -14, 14],\n [14, -6, -14, 14],\n [-2, 6, 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[[10, 4, 8, 2],\n [-4, 4, -6, -8],\n [9, 12, 3, -9],\n [-8, 8, -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[[-4, -20, 3, 2],\n [-5, -8, 7, -4],\n [-11, -7, 5, -1],\n [8, 20, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -6, -9, -3],\n [-12, -16, -14, -14],\n [2, 0, 5, -3],\n [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, 4, 12, -4],\n [-2, -1, -3, 1],\n [-8, -4, -12, 4],\n [2, 1, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, -5, -2],\n [8, 5, 5, 9],\n [-12, -7, -8, -13],\n [-12, -2, -13, -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 4x4 matrix:\n[[12, 7, -7, -2],\n [5, 18, 13, 27],\n [-4, -26, 8, -16],\n [-13, 7, 7, 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[[10, 2, -10, 10],\n [-5, -3, 10, -5],\n [-8, -4, 14, -8],\n [4, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -14, -4, 2],\n [8, 20, 0, 4],\n [2, 8, -2, 4],\n [-6, -3, -8, 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 4x4 matrix:\n[[12, 8, -12, -12],\n [6, 4, -6, -6],\n [12, 8, -12, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -2, 0, -2],\n [16, 8, 8, 8],\n [9, 7, 8, 7],\n [14, 12, 14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -11, 1, 7],\n [5, 10, 6, -11],\n [-5, 0, 13, -6],\n [-7, 7, 1, -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 4x4 matrix:\n[[12, 0, -28, 4],\n [9, -9, -12, 9],\n [-6, 9, 5, -8],\n [12, -24, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 4, -2, 0],\n [24, -8, -4, -16],\n [12, -4, -2, -8],\n [-28, 4, 6, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -1, 2, -2],\n [-2, 1, -2, 2],\n [2, -1, 2, -2],\n [8, -4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 8, 16, -12],\n [-16, -8, -16, 12],\n [0, 0, 0, 0],\n [16, 8, 16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -13, -11, 15],\n [-2, 15, 21, -11],\n [4, 16, 14, 8],\n [-4, -16, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -1, -4, -1],\n [0, -2, -8, -2],\n [0, -2, -8, -2],\n [0, -3, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -8, 6, 6],\n [9, -10, 9, 3],\n [3, -14, 11, 9],\n [-6, -4, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 8, 8, 0],\n [1, 4, 4, 0],\n [-1, -4, -4, 0],\n [1, 4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 0, 1, -2],\n [-12, 0, -3, 6],\n [0, 0, 0, 0],\n [-12, 0, -3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, -28, 9, 9],\n [-14, -16, 3, 8],\n [0, 4, -6, 5],\n [12, 20, -12, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 4, -3, -1],\n [-12, 16, -12, -4],\n [-6, 8, -6, -2],\n [6, -8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, -20, -6, -9],\n [12, -10, -4, -6],\n [20, -12, -2, -3],\n [-4, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-12, -3, 0, -12],\n [-12, -3, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 12, 9, -9],\n [3, 4, 3, -3],\n [9, 12, 9, -9],\n [12, 16, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -6, 6, 4],\n [-24, -21, 12, 5],\n [-19, -15, 3, -2],\n [-21, -18, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -7, -9, -4],\n [10, 21, -10, -2],\n [-16, -15, 11, 3],\n [-14, 5, 17, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -2, 5, -6],\n [2, 2, 2, -1],\n [9, -5, 6, -6],\n [20, -18, 14, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 3, 6, 9],\n [0, 0, 0, 0],\n [-1, -1, -2, -3],\n [-2, -2, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -7, -4, 13],\n [-1, -3, 0, 5],\n [-4, -2, 4, 2],\n [5, -5, -8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -6, -1, 8],\n [-24, -3, -3, 9],\n [24, 3, 3, -9],\n [2, -12, 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[[10, 5, -5, 6],\n [9, 17, -3, 11],\n [12, 16, -9, 16],\n [10, 7, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -1, -3, 2],\n [0, 0, 0, 0],\n [2, 7, 5, -8],\n [-1, -5, -7, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-6, -12, 12, -6],\n [4, 8, -8, 4],\n [8, 16, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -1, -4, 0],\n [6, 3, 12, 0],\n [6, 3, 12, 0],\n [-2, -1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[18, 15, -15, 14],\n [13, 9, -3, -5],\n [6, 3, 3, -12],\n [8, 5, -7, -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 4x4 matrix:\n[[2, -1, 0, 1],\n [11, 5, -6, 7],\n [-4, 2, 0, -2],\n [-5, 6, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 12, 16, -4],\n [-12, -12, -16, 4],\n [0, 0, 0, 0],\n [6, 6, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -16, 12, -16],\n [9, -12, 9, -12],\n [-3, 4, -3, 4],\n [12, -16, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -6, 4, 6],\n [-6, 9, -6, -9],\n [8, -12, 8, 12],\n [-6, 9, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, 5, 4],\n [-26, -12, -1, 7],\n [22, 4, -8, -5],\n [-10, 12, 25, -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[[6, -1, 7, 17],\n [12, -12, 4, 4],\n [-6, 0, -8, -20],\n [12, -8, 8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -6, -9, 3],\n [-3, -2, -3, 1],\n [-3, -2, -3, 1],\n [-12, -8, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -6, 2, 2],\n [-13, -21, 7, 5],\n [-9, -9, 3, 9],\n [-10, -12, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, 4, 3],\n [0, 4, 8, 6],\n [0, -2, -4, -3],\n [0, -8, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-16, 4, 8, 8],\n [0, 0, 0, 0],\n [12, -3, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -12, -12, 0],\n [-8, 8, 8, 0],\n [0, 4, 6, 6],\n [16, -14, -13, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 6, 3, -9],\n [1, 2, 1, -3],\n [4, 8, 4, -12],\n [1, 2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[18, -18, 8, -18],\n [-4, 6, 12, -20],\n [6, -11, 6, -14],\n [28, -29, 10, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -1, 0, 1],\n [3, 3, 0, -3],\n [-1, -1, 0, 1],\n [-4, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -8, 12, -4],\n [-3, 2, -3, 1],\n [-3, 2, -3, 1],\n [-9, 6, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -14, 11, 13],\n [0, 2, 19, 5],\n [5, -14, -4, 8],\n [8, -24, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -4, -8, 2],\n [-12, -2, -12, 8],\n [0, 0, 0, 0],\n [-12, 1, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 6, -4, -8],\n [-3, 0, 2, 1],\n [0, -6, -2, 5],\n [-9, 0, 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[[-23, -1, 11, -1],\n [-12, 24, -10, 6],\n [6, 2, -2, -10],\n [-18, 3, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 12, 6, -21],\n [-1, 12, -9, -6],\n [-4, 4, 8, -13],\n [3, 0, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 3, -5, 7],\n [0, 1, 9, -14],\n [16, 6, 8, -4],\n [-5, 0, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -4, 2, -1],\n [-8, 8, 2, 2],\n [2, -4, 5, -1],\n [0, -4, 11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [6, -8, 2, 8],\n [-3, 4, -1, -4],\n [3, -4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 2, 4, 3],\n [2, -2, -8, -4],\n [1, -1, -4, -2],\n [15, 9, 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[[-2, -1, 2, 2],\n [-8, -4, 8, 8],\n [-8, -4, 8, 8],\n [-4, -2, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 0, -15, 0],\n [-15, 3, -13, -18],\n [4, -4, -4, 8],\n [-11, -20, 4, 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 4x4 matrix:\n[[16, 10, -1, 5],\n [-13, -3, 4, 3],\n [4, -2, -4, -4],\n [-10, -10, 4, -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[[0, -4, 1, -4],\n [0, -4, 1, -4],\n [0, -8, 2, -8],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -11, 0, -5],\n [3, 1, -9, 3],\n [20, -4, -10, 4],\n [-16, -10, 4, -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[[6, 0, 6, 3],\n [-2, -2, -2, -6],\n [-16, 8, -16, 12],\n [14, -10, 14, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 16, -16, -20],\n [15, 0, 12, 3],\n [17, -6, 16, 10],\n [15, -10, 16, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 6, -6, -12],\n [12, 6, 0, -3],\n [16, 8, -4, -10],\n [4, 2, -8, -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 4x4 matrix:\n[[-4, 7, 2, -11],\n [-4, 6, 0, -2],\n [6, -10, -2, 12],\n [-3, 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 4x4 matrix:\n[[5, 5, -12, 13],\n [0, 0, 0, 0],\n [7, -1, 0, 3],\n [13, 1, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 1, 1, 1],\n [-1, 1, 3, 0],\n [-2, -2, -8, 1],\n [16, 0, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 12, 12, 11],\n [-9, 29, -8, 15],\n [-5, 13, -4, 7],\n [-1, 4, 0, 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[[0, -32, -4, 8],\n [0, -8, -1, 2],\n [-15, 3, -23, -14],\n [0, -20, 21, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -4, 10, 7],\n [-18, 12, -14, -5],\n [10, -8, 8, 2],\n [-15, 12, -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 4x4 matrix:\n[[-8, 0, 16, 10],\n [12, 15, -4, 5],\n [-4, 9, 20, 17],\n [-12, -18, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, -16, 8],\n [-2, 2, -8, 4],\n [-2, 2, -8, 4],\n [-4, 4, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 2, 10, 7],\n [6, -4, -4, -2],\n [9, 4, 24, 17],\n [-6, -3, -3, -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 4x4 matrix:\n[[11, 2, -1, 15],\n [1, 14, -13, 0],\n [-10, 3, 0, -9],\n [34, -10, -2, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -20, 8, 14],\n [-12, -9, -2, 0],\n [12, 9, 2, 0],\n [-4, -7, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -1, -1, -10],\n [-6, -18, -18, 8],\n [3, -15, 6, 1],\n [-4, 6, -16, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 2, 6, -1],\n [-5, -2, -6, 1],\n [2, 12, -4, -2],\n [3, -3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 6, 3, -1],\n [-4, 6, 3, -1],\n [16, -20, -11, 4],\n [-4, -14, -2, -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 4x4 matrix:\n[[8, -7, -13, -21],\n [-1, -3, 13, -4],\n [-5, 2, 18, 11],\n [-1, -6, 25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 3, 4, -4],\n [4, -7, -4, 20],\n [0, -3, 0, 12],\n [-16, 16, 16, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -3, -12, -9],\n [0, 3, 12, 9],\n [0, 1, 4, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -8, 16, 2],\n [3, 9, -4, -2],\n [-12, 8, 16, -4],\n [2, 11, -6, -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[[-12, -8, 0, -15],\n [-4, 2, 7, 2],\n [20, 4, -14, 11],\n [-12, 0, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 1, -2, 12],\n [11, 4, -8, 4],\n [-6, 2, 0, 24],\n [6, 4, -7, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 11, 4, -4],\n [-4, -5, -4, -4],\n [16, 14, 4, -8],\n [-24, -22, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -16, 8, 4],\n [0, 12, -6, -3],\n [0, 12, -6, -3],\n [0, 8, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -3, 17, 16],\n [4, 4, -16, 0],\n [-4, 0, -2, -7],\n [-2, -1, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 0, 8, 0],\n [12, 9, 6, -6],\n [4, 15, 2, -10],\n [-16, -15, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 8, 0, 4],\n [12, 12, 0, 6],\n [-8, -8, 0, -4],\n [8, 8, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -8, 6, 4],\n [-8, -16, 12, 8],\n [0, 0, 0, 0],\n [2, 4, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 25, -24, -9],\n [16, -22, 20, 10],\n [13, -18, 17, 7],\n [2, -4, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -3, 12, 0],\n [0, 12, 12, -8],\n [-3, -1, 4, 0],\n [-9, 0, 15, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 4, 0, 4],\n [-12, -16, 0, -16],\n [3, 4, 0, 4],\n [3, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 2, -6, 8],\n [20, -20, 24, -16],\n [6, 8, 3, -16],\n [-1, -3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -6, 14, -10],\n [7, -2, -5, 9],\n [-2, -3, 6, 5],\n [-8, -12, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 0, 0, 6],\n [2, -1, 1, 4],\n [2, -3, 3, 4],\n [-1, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 8, 0, 12],\n [-4, 8, 12, 6],\n [-14, -12, -8, -14],\n [6, -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[[8, -2, -5, 9],\n [-2, 8, 8, -3],\n [10, 2, 2, 18],\n [32, 12, -23, -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[[-12, -9, 9, -3],\n [-8, 6, 9, 1],\n [-16, -12, 12, -4],\n [-16, 12, 18, 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 4x4 matrix:\n[[8, 2, 8, 2],\n [4, 1, 4, 1],\n [12, 3, 12, 3],\n [-4, -1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, 12, 26, 0],\n [-2, 19, 12, 9],\n [-8, -20, -4, -12],\n [18, 0, -6, 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[[-12, -12, -8, 4],\n [9, 9, -16, -13],\n [2, 2, 10, 1],\n [-1, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 12, 16, 16],\n [-4, -3, -4, -4],\n [-8, -6, -8, -8],\n [-12, -9, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -7, 3, 0],\n [-10, 15, 14, -13],\n [-4, 12, 20, -16],\n [-8, 9, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, 4, -10, 17],\n [7, -4, 2, 9],\n [0, 12, 0, -24],\n [-7, 8, -8, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 2, -3, 17],\n [0, -2, 3, -5],\n [8, 16, 11, -6],\n [16, -8, 19, 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[[-2, -5, -7, 3],\n [-3, -4, -4, -1],\n [-12, -16, -10, -12],\n [23, 5, 37, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 4, 6, 6],\n [-12, -8, -12, -12],\n [-12, -8, -12, -12],\n [3, 2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 4, -6, 8],\n [6, -17, -1, -18],\n [11, -7, 4, -9],\n [-6, -4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -2, -5, -21],\n [-10, -4, -9, -13],\n [32, -12, 16, 12],\n [-14, 2, -18, -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 4x4 matrix:\n[[-5, -7, 1, 6],\n [-6, -3, -15, 9],\n [1, 2, -2, -1],\n [7, 5, 13, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -6, -8, -8],\n [-3, 1, -3, -3],\n [-1, -8, 1, -2],\n [-1, -3, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 0, 0, -8],\n [2, 0, 0, -8],\n [-3, 0, 0, 12],\n [-4, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -2, 4, 0],\n [-12, 8, -16, 0],\n [6, -4, 8, 0],\n [-6, 4, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 4, 0, -3],\n [0, -12, 0, 9],\n [0, -8, 0, 6],\n [0, -8, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -8, 12, -16],\n [-12, -6, 9, -12],\n [-12, -6, 9, -12],\n [16, 8, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 12, 9, 6],\n [4, 12, 21, 4],\n [4, 12, 9, 0],\n [8, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -20, 20, -9],\n [-4, -24, 24, -10],\n [-9, -24, 24, -9],\n [-14, -24, 24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 21, 4, 7],\n [-19, -9, -2, -5],\n [7, 17, 3, 4],\n [12, 19, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -6, 2, 0],\n [2, 7, -6, -1],\n [-15, 6, 9, 3],\n [-10, -9, 14, 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 4x4 matrix:\n[[20, -4, 12, -8],\n [0, 18, 8, 4],\n [18, 10, 17, -2],\n [17, -20, 3, -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 4x4 matrix:\n[[-25, 15, -41, -8],\n [-4, -2, 8, -15],\n [-24, 8, -40, -9],\n [-5, -7, -17, 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[[24, 0, 3, -19],\n [-9, -15, 12, -1],\n [9, -9, 9, -12],\n [21, 3, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -6, -2, -6],\n [-4, 12, 4, 12],\n [4, -12, -4, -12],\n [-3, 9, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 8, 14, 36],\n [-5, -12, -8, -8],\n [9, 8, 7, 18],\n [-15, 8, -3, -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[[7, 2, 1, -13],\n [2, -8, -4, 2],\n [-16, 4, 2, 21],\n [-13, 22, 11, 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[[17, 4, 0, 4],\n [9, 0, -2, 4],\n [17, 4, 0, 4],\n [20, -8, -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[[-14, 2, 20, -8],\n [3, -3, -4, -2],\n [-16, 10, 22, 2],\n [2, -8, -2, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -21, 14, -33],\n [24, -24, 0, -3],\n [-14, 10, 4, -1],\n [1, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 6, 3, 18],\n [9, 12, -4, 2],\n [15, 6, 4, -8],\n [22, 7, -9, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 3, -3, -9],\n [0, 0, 0, 0],\n [-12, -3, 3, 9],\n [-16, -4, 4, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [8, -8, -4, -12],\n [-2, 2, 1, 3],\n [6, -6, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 16, 12, -2],\n [-14, -12, -14, 19],\n [6, 8, 8, -8],\n [-3, -24, -18, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -6, -8, 2],\n [-1, 3, 4, -1],\n [-3, 9, 12, -3],\n [-1, 3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 6, 1, -14],\n [-16, 9, -11, -19],\n [8, 9, -2, 9],\n [2, -6, 17, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -4, 8, -12],\n [2, 1, -2, 3],\n [-8, -4, 8, -12],\n [8, 4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -4, -12, -4],\n [0, -2, -6, -2],\n [0, -2, -6, -2],\n [0, -2, -6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 6, -16, 9],\n [18, 1, 8, -14],\n [-4, 12, -17, -3],\n [6, -7, 22, -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[[-16, 4, 0, 4],\n [-16, 4, 0, 4],\n [-16, 20, 32, -28],\n [-16, 14, 20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -18, 10, -4],\n [8, 12, -12, 0],\n [2, 3, -3, 0],\n [-8, 6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, 13, 0, 3],\n [5, -4, 4, 1],\n [3, -14, -20, -17],\n [9, -5, -28, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, -4, -6],\n [6, 12, 6, 9],\n [-4, 12, -4, -6],\n [-2, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -1, 15, -16],\n [-8, 17, -11, -8],\n [-1, 21, -8, -22],\n [-15, 5, -13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 7, -16, 0],\n [5, -5, 8, -6],\n [-13, 7, -16, 0],\n [4, -6, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -5, 5, -12],\n [11, 14, 1, 0],\n [-5, -12, -8, 9],\n [-2, -9, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 11, 3, -15],\n [-25, -15, -9, -14],\n [-17, -11, -9, -17],\n [12, -8, 0, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -10, -4, -2],\n [7, -1, 6, 3],\n [1, 2, -9, 0],\n [10, -21, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -6, -6, 2],\n [16, -20, 20, -12],\n [-4, 2, -8, 4],\n [-2, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [4, -3, 1, -2],\n [16, -12, 4, -8],\n [4, -3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[17, 9, 6, -2],\n [14, -10, -12, -20],\n [-5, 5, 14, 14],\n [-5, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -12, -3, 9],\n [9, -12, -3, 9],\n [9, -12, -3, 9],\n [9, -12, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 0, 12, -16],\n [-17, 11, -6, 13],\n [5, -5, -12, 15],\n [-4, -3, -12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 4, 2, -2],\n [-12, 16, 8, -8],\n [12, -16, -8, 8],\n [9, -12, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -6, -6, -5],\n [-6, 5, 9, -9],\n [-11, -13, -12, -19],\n [-1, 2, 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[[8, 18, 6, 12],\n [12, 6, -6, 12],\n [-3, 10, 13, -1],\n [12, 23, 16, 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[[11, -14, 10, -20],\n [-20, 20, -16, 32],\n [-13, -8, -2, 4],\n [-19, 16, -14, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, 8, -8],\n [-8, 8, 16, -16],\n [8, -8, -16, 16],\n [-8, 8, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-9, -3, -9, -3],\n [-3, -1, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 0, -6, 3],\n [1, 0, 2, -1],\n [0, 0, 0, 0],\n [-4, 0, -8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 6, 2, -6],\n [-8, 6, 2, 8],\n [2, -6, 8, -3],\n [0, -6, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -9, 12, 9],\n [3, 0, 12, 6],\n [13, -8, 1, 5],\n [-5, 6, 2, -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[[0, 9, 9, -6],\n [0, 9, 9, -6],\n [0, 6, 6, -4],\n [0, 12, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -16, 8, -15],\n [3, -13, 5, -11],\n [1, 10, -2, 7],\n [17, -3, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 9, -12, -3],\n [12, -12, 16, 4],\n [-12, 12, -16, -4],\n [12, -12, 16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, -16, 13, -12],\n [17, 16, -13, 12],\n [-4, -16, 4, 16],\n [16, 25, -13, -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 4x4 matrix:\n[[16, 0, -10, 4],\n [-10, -12, 7, -4],\n [-3, -18, 3, -3],\n [-10, -12, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -8, -7, -16],\n [-12, -15, 5, -11],\n [-38, -11, -10, -31],\n [36, 6, 13, 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 4x4 matrix:\n[[-6, 12, 0, 0],\n [4, -8, 0, 0],\n [6, -12, 0, 0],\n [4, -8, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 8, 0, 8],\n [3, 12, 0, 12],\n [2, 8, 0, 8],\n [3, 12, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -2, -24, 9],\n [9, -5, 14, -9],\n [1, -3, -11, 3],\n [-5, -1, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 9, 4, -2],\n [4, -12, -8, 0],\n [12, -24, -8, 8],\n [7, -15, -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 4x4 matrix:\n[[0, 8, 16, 12],\n [0, -4, -8, -6],\n [0, -8, -16, -12],\n [0, -6, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 3, 18, 6],\n [-1, -5, 18, 14],\n [4, 2, 12, 4],\n [9, 6, 20, 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[[10, -6, -6, 1],\n [-10, 4, 14, -9],\n [-16, 10, 8, 0],\n [-14, 6, 18, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -1, 0, 0],\n [4, -2, 0, 0],\n [0, 0, 0, 0],\n [8, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 4, 0, 1],\n [2, 8, 0, 2],\n [4, 16, 0, 4],\n [-3, -12, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -4, 3, -3],\n [-3, 4, -3, 3],\n [6, -8, 6, -6],\n [-9, 12, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 6, -6, 1],\n [-8, -8, 8, -4],\n [-4, -4, 4, -2],\n [-8, -18, 18, 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[[-4, 3, 3, 2],\n [12, -28, -16, -20],\n [-12, 28, 16, 20],\n [-16, -7, 5, -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 4x4 matrix:\n[[0, -21, -12, 9],\n [-6, 3, -12, -9],\n [-3, 12, 0, -9],\n [2, 20, 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[[6, 6, -1, -7],\n [8, -6, -3, -1],\n [14, 10, -2, -14],\n [0, 24, -2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -5, 17],\n [3, -1, -7, 13],\n [-8, 12, 2, -28],\n [11, -13, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -8, 16, -8],\n [-8, -4, 8, -4],\n [-4, -2, 4, -2],\n [-16, -8, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 0, 9, 0],\n [-11, 0, -6, 0],\n [3, 0, 3, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -3, 9, -6],\n [-12, 8, -8, 16],\n [14, -7, 9, -14],\n [12, -8, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -11, 5, 9],\n [8, -16, 4, 8],\n [-10, 13, -1, -3],\n [-8, 9, 0, -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 4x4 matrix:\n[[4, 8, -16, 4],\n [-1, -2, 4, -1],\n [2, 4, -8, 2],\n [2, 4, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -16, -12, 4],\n [24, 28, 20, -12],\n [-8, -16, -12, 4],\n [12, 19, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 8, -6, -8],\n [-9, 12, -9, -12],\n [-3, 4, -3, -4],\n [-9, 12, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -7, 0, -20],\n [11, -6, 12, -23],\n [8, 12, -18, -8],\n [-2, 2, 22, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, -10, 1, -5],\n [-22, 12, 2, -2],\n [-7, 4, 0, 1],\n [-22, 12, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -12, 6, -12],\n [-9, 12, -6, 12],\n [-12, 16, -8, 16],\n [-3, 4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 6, 3, -6],\n [4, -8, -4, 8],\n [1, -2, -1, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [16, -8, 0, -16],\n [4, -2, 0, -4],\n [4, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 3, -9, 3],\n [4, 8, -2, 2],\n [0, -4, -2, -2],\n [-2, -8, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, 13, -23, -20],\n [2, 0, 15, -1],\n [-9, -12, -7, 2],\n [-4, -1, -1, 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 4x4 matrix:\n[[8, 12, 16, 12],\n [-2, -3, -4, -3],\n [2, 3, 4, 3],\n [8, 12, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 2, -1, -2],\n [-4, -8, 4, 8],\n [-4, -8, 4, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 6, -6, 0],\n [4, -12, 12, 0],\n [3, -9, 9, 0],\n [-4, 12, -12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, 8, 0],\n [-8, 4, 8, 0],\n [16, -8, -16, 0],\n [4, -2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 4, -9, -3],\n [2, 14, 9, -15],\n [-8, -14, -9, -3],\n [-9, -18, 9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, 0, 3, -10],\n [-2, 2, -2, 8],\n [-15, -5, -7, 20],\n [-8, -2, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[24, 4, 12, 8],\n [-12, 2, -6, -2],\n [4, 2, 2, 2],\n [20, 2, 10, 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 4x4 matrix:\n[[-8, -8, 16, 12],\n [-2, -2, 4, 3],\n [0, 0, 0, 0],\n [-4, -4, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -5, -27, 11],\n [-10, 0, 16, -8],\n [-4, 3, 11, -1],\n [-2, -1, -7, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 12, -12, -6],\n [6, -3, 12, 15],\n [2, 3, 4, 9],\n [-6, 3, -12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 18, 3, 12],\n [23, 7, 10, -14],\n [-10, -5, -16, 8],\n [-3, -12, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -6, 12, -8],\n [0, 8, -16, 16],\n [0, -6, 12, -12],\n [-3, -1, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 3, 4, -3],\n [-8, 16, -12, -16],\n [4, -5, 5, 5],\n [-2, 10, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 1, -4, 0],\n [-3, 1, -4, 0],\n [-6, 2, -8, 0],\n [12, -4, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, 4, -8, 18],\n [12, 18, 24, -4],\n [-15, -15, -24, 9],\n [-19, -16, -28, 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, -4, 4, 16],\n [2, -1, 1, 4],\n [-4, 2, -2, -8],\n [-8, 4, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-27, -4, 7, -9],\n [-2, 7, 0, 3],\n [-19, 12, -1, 3],\n [-25, -7, -1, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 8, 16, 8],\n [0, 0, 0, 0],\n [6, 4, 8, 4],\n [-6, -4, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -6, 14, 4],\n [-9, 0, 5, -11],\n [0, -2, 0, 2],\n [3, -4, -7, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 27, -4, -2],\n [-8, 27, -7, -6],\n [-7, -8, -8, 1],\n [11, -19, -2, -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[[3, -4, 3, -4],\n [3, -4, 3, -4],\n [9, -12, 9, -12],\n [9, -12, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 16, 0, -4],\n [0, 1, -1, 3],\n [-6, -5, -3, 11],\n [21, 25, 3, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, -2, 8, -6],\n [0, -1, 4, -3],\n [0, -1, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 6, 8, -8],\n [2, -6, -8, 8],\n [3, -9, -12, 12],\n [-2, 6, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, -2, 2],\n [16, -9, 11, -4],\n [-2, 3, 3, -2],\n [-5, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -3, 6, 3],\n [12, -3, 6, 3],\n [8, -2, 4, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -8, 8, -16],\n [-6, -10, -4, -2],\n [8, 17, 4, 7],\n [14, 5, 16, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 5, -20, 0],\n [13, 15, 20, 20],\n [-4, -7, 2, -13],\n [2, 0, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -2, 2, -2],\n [24, -15, 12, 5],\n [24, -9, 6, 3],\n [8, 1, -3, 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[[-7, -2, -4, -1],\n [-11, -18, 16, 17],\n [3, -14, 8, -21],\n [14, -12, 20, -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 4x4 matrix:\n[[-4, 0, 0, 2],\n [-8, 0, 0, 4],\n [-8, 0, 0, 4],\n [6, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, 3, -2],\n [12, 0, 4, -3],\n [16, -20, 10, 3],\n [20, -16, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 18, 10, 1],\n [4, 2, 4, 2],\n [9, -4, -3, 10],\n [-12, -4, 2, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -5, 8, 1],\n [-10, 0, 2, -6],\n [-5, 5, -7, -4],\n [11, -2, 1, 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, -13, -3, 19],\n [-3, 19, 7, -15],\n [9, 8, -1, 0],\n [-20, -10, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -2, 17, 20],\n [2, 8, -3, -6],\n [15, 9, 6, 3],\n [7, 3, -13, -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[[2, 10, 0, -16],\n [-1, -2, -16, 9],\n [8, 15, -16, -3],\n [-11, -5, 4, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 0, -2, -4],\n [8, 0, -8, -16],\n [0, 0, 0, 0],\n [8, 0, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 4, -14, 8],\n [12, 8, -16, 8],\n [2, 6, -6, -6],\n [7, -18, 12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 2, 2, -7],\n [11, -8, -14, -5],\n [4, 12, -10, -22],\n [1, -6, 1, 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 4x4 matrix:\n[[-8, 24, -16, 8],\n [4, 4, -15, -14],\n [-4, 12, -13, 6],\n [8, -18, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -6, -4, 0],\n [2, 6, 4, 0],\n [4, 12, 8, 0],\n [4, 12, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 3, 4, -1],\n [-1, -3, -4, 1],\n [0, 0, 0, 0],\n [-2, -6, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -5, 1, -7],\n [-8, 6, 2, 10],\n [16, 4, -4, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 11, 6, -3],\n [3, 1, 1, -3],\n [18, -10, 2, 2],\n [18, -11, 13, 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 4x4 matrix:\n[[4, -16, 12, -12],\n [-3, 12, -9, 9],\n [2, -8, 6, -6],\n [3, -12, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -7, -10, 8],\n [4, -2, -6, -4],\n [0, -2, -4, 0],\n [-8, -4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 2, 0, 6],\n [0, -1, 0, -3],\n [0, 1, 0, 3],\n [0, -2, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 22, -3, 0],\n [-4, -8, -12, -16],\n [-1, -10, 21, 16],\n [7, 18, -9, 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[[11, 6, -11, -21],\n [13, 5, 21, -1],\n [8, 6, 22, 2],\n [1, -5, -20, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, -3, -8, 4],\n [-4, 4, 14, -12],\n [-4, -4, -4, 32],\n [11, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 12, 4, -16],\n [-3, -2, -5, 20],\n [-18, -10, 0, -24],\n [-10, 18, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 0, -21, -3],\n [-6, -16, -2, 14],\n [19, 4, -24, -7],\n [11, -4, -18, 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[[8, -4, 8, -2],\n [4, -7, 5, -14],\n [-2, 1, -15, 20],\n [5, -10, -16, 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[[20, 8, 18, -7],\n [4, 0, 6, -5],\n [0, 4, 4, -4],\n [-16, -10, -14, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [4, -2, -4, -1],\n [16, -8, -16, -4],\n [8, -4, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-12, -8, -16, 8],\n [-6, -4, -8, 4],\n [-9, -6, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -16, 5, 24],\n [8, 22, -19, 8],\n [-1, 14, 13, -21],\n [20, 2, 29, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -16, 20, -30],\n [-8, 20, -19, 25],\n [14, 4, -9, 18],\n [-4, 28, -29, 41]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -9, 1, -10],\n [-1, -9, -16, 7],\n [13, 1, -12, -7],\n [5, -3, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -2, 0, 2],\n [-2, 2, 0, -2],\n [0, 0, 0, 0],\n [2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, -4],\n [-6, 12, 18, -10],\n [3, -6, -9, 7],\n [3, -6, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 4, -16, 2],\n [4, 2, -14, -8],\n [-6, 1, 1, 8],\n [-12, 2, 2, 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[[12, -18, -12, -21],\n [-6, -6, -12, -3],\n [-6, 4, 0, 6],\n [3, -12, -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[[9, 12, -6, 3],\n [9, 12, -6, 3],\n [0, 0, 0, 0],\n [-3, -4, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [4, -20, 2, 0],\n [-2, 10, 4, -20],\n [0, -4, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 2, -4, -10],\n [6, 6, 0, -22],\n [10, -2, -8, -6],\n [8, -4, -8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -4, 14, -7],\n [-6, 6, -9, 6],\n [-8, 10, 1, 4],\n [-8, 10, 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[[0, 12, 15, -7],\n [0, 12, 16, -4],\n [0, -6, -2, 20],\n [0, 3, 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[[4, 4, -8, -4],\n [12, 12, -10, -2],\n [-12, -12, -4, -8],\n [6, 6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -7, -14, 3],\n [-14, -2, -16, -2],\n [30, -18, -6, 12],\n [-32, 19, -4, -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[[4, 0, 4, 4],\n [4, 0, 4, 4],\n [-6, 0, -6, -6],\n [8, 0, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 16, 25, -4],\n [-27, 9, 18, -18],\n [-1, -3, 0, 0],\n [-5, 5, 8, -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[[-5, 21, 3, 0],\n [-13, 1, 15, 15],\n [-2, -10, 2, 4],\n [3, -3, 11, 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[[-4, -8, -4, -16],\n [-4, 16, 16, 4],\n [-2, 2, 3, -3],\n [-8, -4, 2, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 28, 5, 31],\n [8, 2, 16, 2],\n [5, 17, 1, 20],\n [6, 9, 16, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 12, 12, 12],\n [12, 12, 12, 12],\n [3, 3, 3, 3],\n [3, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 2, -7, 5],\n [3, 16, 3, -10],\n [-17, -28, 8, 0],\n [15, -14, -11, -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[[6, 2, -6, 4],\n [12, 4, -12, 8],\n [12, 4, -12, 8],\n [9, 3, -9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -1, -1, 4],\n [0, -2, -2, 8],\n [0, -3, -3, 12],\n [0, 4, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -6, 9, -9],\n [0, -6, 9, -9],\n [0, -4, 6, -6],\n [0, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[19, -3, -19, 6],\n [-16, -3, 16, -1],\n [-4, -12, 4, 8],\n [-11, -3, 11, 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, 0, 2, -4],\n [0, 0, -6, 12],\n [0, 0, 0, 0],\n [0, 0, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, 9, -9],\n [16, 16, -12, 12],\n [-16, -16, 12, -12],\n [-12, -12, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -8, -1, 3],\n [3, -12, 12, 9],\n [4, -16, 16, 12],\n [-18, -8, -7, 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 4x4 matrix:\n[[8, 4, 0, -4],\n [8, 16, -24, 14],\n [-8, -10, 12, -5],\n [8, 12, -16, 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 4x4 matrix:\n[[7, -8, -3, 8],\n [-12, 12, 6, -14],\n [8, -16, 0, 8],\n [-8, -8, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 4, -12, -16],\n [-8, -4, 10, 22],\n [12, 2, -9, 1],\n [-4, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -9, 0, 6],\n [2, 6, 0, -4],\n [8, 14, -6, -2],\n [5, 10, -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[[-2, -6, -4, -9],\n [20, -8, -6, -6],\n [1, -8, -11, -24],\n [-3, -4, -5, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -6, 2, -4],\n [5, -19, -12, -9],\n [-8, -20, -20, -8],\n [12, 12, 16, 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 4x4 matrix:\n[[-1, 21, -10, -15],\n [0, 0, 16, 0],\n [-4, -12, 20, 4],\n [6, -6, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 0, 3, -3],\n [3, 0, -3, 3],\n [-3, 0, 3, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 3, 1, -3],\n [0, 9, 3, -9],\n [0, -9, -3, 9],\n [0, 12, 4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 4, 8, -8],\n [7, -9, 6, 10],\n [9, -15, 6, 18],\n [-6, 2, -8, 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[[3, -4, 12, -6],\n [-2, 7, 0, -5],\n [-4, 12, -12, 8],\n [4, -15, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 0, -1, 2],\n [-10, -6, 5, -4],\n [6, 12, -9, 6],\n [0, 14, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -20, -4, 16],\n [-10, 16, 10, -9],\n [26, -8, 2, 25],\n [2, 10, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [12, 6, -9, 3],\n [-8, -4, 6, -2],\n [16, 8, -12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -4, -2, 18],\n [-12, 4, -4, 16],\n [0, -2, 11, -3],\n [3, -1, 1, -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 4x4 matrix:\n[[-2, 0, -6, 10],\n [-14, -10, -12, 10],\n [-9, -6, -9, 9],\n [-5, -2, -9, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 2, -1, -4],\n [-24, 8, -1, -16],\n [8, -8, -11, 16],\n [-24, 8, -1, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 3, -4, 2],\n [3, 3, -4, 2],\n [-6, -6, 8, -4],\n [3, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 3, -9, -4],\n [-10, 2, -6, -11],\n [-5, 7, -21, -1],\n [-12, 4, -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[[-1, -4, 5, -3],\n [-1, 3, 22, -4],\n [-6, 2, 16, -8],\n [-5, -1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 6, 4, -4],\n [-16, -12, -8, 8],\n [16, 12, 8, -8],\n [16, 12, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -3, 2, -1],\n [-8, 12, -8, 4],\n [0, 0, 0, 0],\n [-6, 9, -6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-21, -2, -13, -12],\n [3, 14, -8, -12],\n [-11, -22, -28, 5],\n [36, 8, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [1, 0, -1, 1],\n [-4, 0, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 10, 3, -11],\n [12, -9, 10, 15],\n [0, -6, 2, 0],\n [0, -9, 5, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -1, -3, 2],\n [3, 1, 3, -2],\n [3, 1, 3, -2],\n [3, 1, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 8, -6, 20],\n [7, -12, 10, -4],\n [8, -7, 7, 8],\n [5, 8, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-17, 1, -20, 12],\n [-1, -2, -1, -1],\n [-20, 16, -18, -2],\n [12, -11, 15, -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[[4, 8, -8, 8],\n [2, 4, -4, 4],\n [2, 4, -4, 4],\n [8, 16, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 12, -3, 6],\n [-6, -12, 3, -6],\n [-2, -4, 1, -2],\n [-8, -16, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 1, -9, -16],\n [-12, 4, 0, -16],\n [-3, -2, -9, -4],\n [0, 4, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -16, 7, 10],\n [-7, -2, -1, -10],\n [11, -8, 5, 14],\n [-3, -12, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -2, -19, 11],\n [-14, -4, -20, 14],\n [-2, 6, -6, -2],\n [-2, 2, 7, -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[[12, -7, 2, -2],\n [-8, 10, -12, 12],\n [12, -8, 4, -4],\n [16, -15, 14, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -6, 2, 2],\n [-6, -6, 2, 4],\n [-6, -9, 3, 9],\n [-2, 3, -1, -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[[8, 8, -12, 18],\n [3, 17, 12, 1],\n [-5, 1, -4, -3],\n [0, 16, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 16, -16, -16],\n [-16, -16, 16, 16],\n [-16, -16, 16, 16],\n [-12, -12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -15, 12, -18],\n [1, -7, 8, -10],\n [-9, 3, -12, 10],\n [-1, 6, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 2, 18, -9],\n [-26, -24, 10, 12],\n [-24, -24, 4, 13],\n [0, -10, -10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 8, 8, 14],\n [-1, 2, 5, 2],\n [1, 8, 10, 13],\n [2, -2, -7, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 11, 4, -16],\n [-16, 11, 10, 4],\n [-18, 8, 10, 12],\n [16, -11, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 0, -4, 4],\n [4, 0, 1, -1],\n [-12, 0, -3, 3],\n [4, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -19, -15, -3],\n [4, 4, -3, 11],\n [2, 2, 3, -3],\n [-21, 1, 12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 8, 0, -2],\n [8, -8, 0, 2],\n [4, -4, 0, 1],\n [-8, 8, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -16, -14, -10],\n [-22, 21, 18, 15],\n [13, 2, 3, -6],\n [9, -10, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 16, -12, -4],\n [3, 4, -3, -1],\n [6, 8, -6, -2],\n [3, 4, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 15, 2, 11],\n [-9, 2, -3, 1],\n [7, -11, -1, -8],\n [-11, 10, -1, 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[[-12, -4, 16, 16],\n [-6, -2, 8, 8],\n [6, 2, -8, -8],\n [-6, -2, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 15, -8, 4],\n [24, -20, 28, 16],\n [18, -10, 4, 18],\n [17, 1, 0, 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[[4, -1, 1, 3],\n [16, -4, 4, 12],\n [-4, 1, -1, -3],\n [16, -4, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 9, 3, 2],\n [0, -8, -7, -5],\n [-4, -4, 2, 8],\n [12, 16, 10, -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[[12, -8, -8, 0],\n [-3, 2, 2, 0],\n [-6, 4, 4, 0],\n [3, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -6, 0, 8],\n [-6, 4, 12, 2],\n [7, -3, -5, 4],\n [0, 19, 21, -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[[0, 12, 12, 0],\n [6, 5, -4, 12],\n [33, 23, 2, 9],\n [3, 1, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 2, -4, 2],\n [-4, -2, 12, 14],\n [-1, 2, -2, 6],\n [2, -6, 8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 4, -6, 2],\n [4, 8, -12, 4],\n [-3, -6, 9, -3],\n [1, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 12, 0, -16],\n [-17, -9, 3, 16],\n [12, -4, -4, 0],\n [14, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -8, -12, 20],\n [-15, 16, 4, -5],\n [3, -4, -2, 3],\n [-3, 10, 11, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -6, -15, -6],\n [-3, 3, 6, 11],\n [-1, 1, -1, 7],\n [-1, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 2, 0, 2],\n [0, 0, 0, 0],\n [-3, 1, 0, 1],\n [9, -3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -24, 28, 8],\n [18, 8, -6, -16],\n [11, 6, -5, -10],\n [-4, 16, -20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 11, -4, -8],\n [3, 3, 12, 6],\n [-3, -21, 2, 2],\n [-5, -4, -5, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -2, -6, -1],\n [-3, 9, 12, 9],\n [4, -13, -14, -14],\n [2, -4, -12, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 4, 24, -4],\n [-8, 16, 20, -19],\n [8, -14, -20, 16],\n [8, 6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 9, -9, -12],\n [12, -9, 9, 12],\n [-16, 12, -12, -16],\n [4, -3, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 7, -4, 0],\n [-14, -1, 2, 15],\n [-13, -5, 4, 12],\n [-2, 8, -4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, 26, -20],\n [-18, 9, -12, 6],\n [-8, -12, -20, 16],\n [14, 14, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, 16, -4],\n [8, -7, 16, -11],\n [10, -22, 3, -19],\n [0, -11, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 2, 0, -6],\n [-12, 4, 0, -12],\n [-12, 4, 0, -12],\n [-9, 3, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 3, -4, 0],\n [1, 3, -4, 0],\n [-4, -12, 16, 0],\n [-3, -9, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 6, 2, -2],\n [-2, 3, 1, -1],\n [-4, 6, 2, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 20, 28, 0],\n [0, -18, -20, -7],\n [16, -26, -32, -13],\n [-2, 34, 40, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 0, -4, -12],\n [0, 1, -3, 4],\n [-16, -3, 13, 0],\n [-12, 1, 0, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 6, 12, 12],\n [16, 8, 16, 16],\n [-8, -4, -8, -8],\n [-16, -8, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 6, -3, -4],\n [6, -8, 4, 2],\n [12, 16, -8, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 6, -8, 8],\n [0, -9, 12, -12],\n [0, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 6, -40, -5],\n [-23, 6, -12, -2],\n [-2, 2, 4, -2],\n [9, 2, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 6, 6, -3],\n [0, 0, 0, 0],\n [-6, 4, 4, -2],\n [-6, 4, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 12, 8, 10],\n [-10, 10, 12, 13],\n [0, 0, 8, 7],\n [-2, 2, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 13, -13, -12],\n [9, -13, 7, 15],\n [15, 11, -11, -9],\n [14, 2, -6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -9, 12, -12],\n [4, -3, 4, -4],\n [-16, 12, -16, 16],\n [-8, 6, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 11, 11, -10],\n [-11, -5, 5, -2],\n [-2, -6, -6, 4],\n [12, 4, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 6, 9, 0],\n [0, 0, 0, 0],\n [-3, 2, 3, 0],\n [-9, 6, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 12, -6, -9],\n [4, 16, -8, -12],\n [-3, -12, 6, 9],\n [4, 16, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, 0, 3],\n [-2, 2, 0, -3],\n [5, -11, 0, 8],\n [-8, 14, -15, -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[[12, -12, 12, 16],\n [-12, 12, -12, -16],\n [-9, 9, -9, -12],\n [-12, 12, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 14, 11, -16],\n [-16, 5, 4, -18],\n [4, 1, 1, -2],\n [-32, 16, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -6, 5, 4],\n [8, 0, -12, 0],\n [-10, -9, 9, 6],\n [-12, -6, 14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-22, 7, 0, -11],\n [-14, 3, -4, -15],\n [14, -3, 4, 15],\n [19, -6, 1, 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[[-4, 16, -17, -13],\n [1, -11, 6, 5],\n [4, -24, 19, 15],\n [-1, 11, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -1, 4, 2],\n [-12, 3, -12, -6],\n [-4, 1, -4, -2],\n [16, -4, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, 7, 13, 9],\n [-10, -20, -12, 12],\n [7, 2, -2, -6],\n [-4, 16, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -9, -3, 4],\n [-6, 6, 0, 2],\n [2, -10, -1, -1],\n [16, -8, 1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 0, -12, 6],\n [-2, 0, -4, 2],\n [-2, 0, -4, 2],\n [4, 0, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -6, 2, -8],\n [3, 20, -6, 30],\n [-6, -12, 14, -14],\n [5, -6, -12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -10, 6, 6],\n [19, -6, 19, -16],\n [-16, 9, -17, 18],\n [5, -14, 8, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -12, 4, 4],\n [-4, -12, 4, 4],\n [1, 3, -1, -1],\n [3, 9, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 2, -12, 10],\n [-10, -8, 20, -14],\n [0, -10, -24, 20],\n [-4, -3, 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[[3, -4, 3, 2],\n [3, -4, 3, 2],\n [-9, 12, -9, -6],\n [-6, 8, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, 18, -20, -2],\n [15, 12, -8, 14],\n [-11, -4, 8, -6],\n [-3, 3, -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[[3, 3, 0, -3],\n [-3, -3, 0, 3],\n [-3, -3, 0, 3],\n [6, 6, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -11, -21, -20],\n [-6, -15, -3, -3],\n [-8, -13, 11, 3],\n [-7, -8, 16, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 2, -2, 4],\n [-12, -3, 3, -6],\n [-8, 5, -1, -8],\n [-10, -13, 7, 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[[4, 3, 3, 0],\n [4, 5, 5, -16],\n [0, -2, -2, 16],\n [-10, -6, -6, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, -13, -2, 15],\n [-16, -12, 8, -12],\n [-8, 1, 2, -6],\n [-8, 15, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 4, 2, 2],\n [-1, -22, -13, -17],\n [12, 40, 28, 28],\n [2, 8, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -8, 2, 0],\n [0, 4, -1, 0],\n [0, 12, -3, 0],\n [0, -12, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -1, 1, 2],\n [0, -4, 4, 8],\n [0, 0, 0, 0],\n [0, 3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -1, -3, 4],\n [0, 3, 9, -12],\n [0, -1, -3, 4],\n [0, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -12, 2, 5],\n [16, 20, 8, 3],\n [0, -12, 0, 3],\n [-12, -12, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -2, 5, 12],\n [2, -1, 0, 1],\n [2, -4, 6, 16],\n [-6, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 5, -22, 9],\n [2, 10, -12, 8],\n [14, -3, -24, 15],\n [5, 2, 4, 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[[12, 9, -3, 9],\n [-6, -8, 4, 8],\n [-10, -7, 13, 27],\n [-17, -9, 7, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, -14, 3, 15],\n [-4, 0, 2, 3],\n [16, 16, 0, -12],\n [-8, 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[[-4, 2, -1, 3],\n [-12, 6, -3, 9],\n [16, -8, 4, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 4, -3, -1],\n [-9, -3, 0, 3],\n [4, -4, -12, 16],\n [4, -4, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 9, 0, 9],\n [-9, -1, 10, 17],\n [6, -10, 16, 17],\n [-21, -9, -9, -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[[4, 16, 8, -12],\n [1, 4, 2, -3],\n [-4, -16, -8, 12],\n [4, 16, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 5, -16, -2],\n [0, 2, 8, -4],\n [6, 15, 6, -18],\n [2, 5, 2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 5, 6, -20],\n [-19, -25, -2, 4],\n [-10, -14, -2, 4],\n [-16, -13, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 9, -3, 6],\n [4, 3, -1, 2],\n [4, 3, -1, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -10, -9, -8],\n [0, 4, -12, 8],\n [-4, -10, 4, -12],\n [8, 20, -8, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -8, 16, 0],\n [1, 2, -4, 0],\n [1, 2, -4, 0],\n [-3, -6, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -21, 6, 3],\n [10, 2, 2, -5],\n [-14, -16, 2, 7],\n [-4, 8, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, -4, 12],\n [0, 0, 4, -12],\n [0, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 12, 4, 4],\n [-3, -4, 2, 0],\n [0, 2, -6, -2],\n [0, -1, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [8, 4, 8, -8],\n [2, 1, 2, -2],\n [-8, -4, -8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -8, 4, -16],\n [-14, -10, -14, -27],\n [-16, -18, 13, -2],\n [8, 8, -1, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 4, 4, -4],\n [-9, 6, 6, -6],\n [9, -6, -6, 6],\n [3, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -9, -14, -1],\n [-12, 0, 14, -14],\n [-4, -9, -4, -11],\n [-18, -3, 17, -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[[2, 6, -3, -12],\n [3, 14, 3, -8],\n [1, 2, -3, -8],\n [0, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -5, 3, 5],\n [-28, 9, 14, 6],\n [-12, 5, 2, -2],\n [-8, 0, 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[[2, 2, -3, 1],\n [-2, -2, 3, -1],\n [8, 8, -12, 4],\n [4, 4, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 6, 0, 9],\n [-4, 8, 0, 12],\n [4, -8, 0, -12],\n [2, -4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -10, -1, 10],\n [-1, 14, 1, -8],\n [1, -3, -1, 4],\n [-13, -8, 13, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -2, -8, -8],\n [0, 0, 0, 0],\n [-12, -4, -16, -16],\n [9, 3, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 6, 9, 3],\n [12, 6, 9, 3],\n [4, 2, 3, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 0, 14, -19],\n [1, 3, -2, 4],\n [9, 3, 12, -15],\n [14, 18, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -24, 0, 24],\n [12, 14, -5, -4],\n [-9, -8, 5, -2],\n [0, -4, -2, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 2, -3, -3],\n [-11, 6, 1, 11],\n [-4, 0, 2, 4],\n [4, 4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -2, -4, 1],\n [9, -6, -12, 3],\n [3, -2, -4, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 3, 12, 9],\n [0, 0, 0, 0],\n [-3, -1, -4, -3],\n [2, -2, -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[[-6, -3, -6, -9],\n [-4, -2, -4, -6],\n [2, 1, 2, 3],\n [8, 4, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 1, 4, 1],\n [4, -4, -16, -4],\n [1, -1, -4, -1],\n [-4, 4, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 1, -12, 10],\n [-1, 13, 6, -10],\n [-1, 16, 12, -16],\n [-5, 11, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -4, -1, -2],\n [2, -8, -2, -4],\n [3, -12, -3, -6],\n [-2, 8, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 12, 3, 9],\n [1, -4, -1, -3],\n [-4, 16, 4, 12],\n [3, -12, -3, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -8, 4, 12],\n [8, 8, -4, -12],\n [-6, -6, 3, 9],\n [-8, -8, 4, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 0, -3, -9],\n [0, 0, 0, 0],\n [-1, 0, 1, 3],\n [-1, 0, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -8, -6, -4],\n [6, 10, -8, 6],\n [4, 16, -14, 6],\n [-2, -6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 0, 1, 4],\n [1, -17, 5, -14],\n [2, 22, -6, 20],\n [-1, 10, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -2, 4, -4],\n [0, -4, 8, -8],\n [0, 3, -6, 6],\n [0, -4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 8, -6, -6],\n [0, 0, 0, 0],\n [-8, -10, 6, 7],\n [16, 16, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 2, -4, 6],\n [-3, 6, 0, 6],\n [0, 0, 0, 0],\n [8, -8, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 6, -16, -4],\n [3, 0, 0, -4],\n [2, -2, 18, 2],\n [-4, -7, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 20, -9, 11],\n [6, 1, 2, 4],\n [-4, 8, -18, 2],\n [-2, 19, -5, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 2, -6, 4],\n [-8, 2, -6, 4],\n [16, -4, 12, -8],\n [8, -2, 6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-12, -9, 3, 6],\n [16, 2, -6, -12],\n [20, 5, -7, -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 4x4 matrix:\n[[-9, 6, -3, -9],\n [0, 0, 0, 0],\n [3, -2, 1, 3],\n [-3, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -6, -5, -11],\n [10, 7, -7, 0],\n [16, 11, -13, -2],\n [-7, -5, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 5, -8, -3],\n [-3, -15, 12, 12],\n [0, -3, 0, 3],\n [1, 13, -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[[-20, -2, 6, -5],\n [-2, 6, -1, -14],\n [-6, 6, 0, -16],\n [23, 7, -10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -12, 11, -9],\n [-24, 6, -18, 12],\n [6, 0, 7, 15],\n [0, 12, -15, -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 4x4 matrix:\n[[-12, 11, -13, -6],\n [-22, 23, -7, -8],\n [6, -10, 8, 2],\n [-4, 13, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 8, -12, 14],\n [-3, -4, 16, -9],\n [-7, -1, 4, -1],\n [-7, -13, 12, -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[[0, 12, -3, 3],\n [0, 16, -4, 4],\n [0, 8, -2, 2],\n [0, -12, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, -26, 4, -15],\n [4, -11, 12, -6],\n [0, 7, -18, 0],\n [20, -9, -10, 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[[24, 8, -8, -4],\n [-9, -2, 3, 1],\n [6, -2, -2, 1],\n [-9, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -10, 10, -20],\n [-4, -4, 6, -12],\n [0, 0, 0, 0],\n [-1, -6, 4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -1, -7, -2],\n [-27, 25, 20, 10],\n [4, -11, 13, -22],\n [20, -19, -16, -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, 4, 0, 0],\n [2, 2, 2, -1],\n [-1, 8, 14, -7],\n [1, 4, 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[[-6, -6, -3, 6],\n [-4, -4, -2, 4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -16, -14, 6],\n [2, 13, 10, -4],\n [0, -6, -8, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, -2, 2],\n [0, 4, -2, 2],\n [0, 2, -1, 1],\n [0, 6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, 9, 12, -12],\n [-4, -3, -4, 4],\n [16, 12, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 12, 8, -4],\n [0, -6, -4, 2],\n [0, 3, 2, -1],\n [0, 3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 12, -3, 0],\n [12, -8, -16, 4],\n [-6, -6, 15, -3],\n [-5, -10, 16, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -2, 4, 0],\n [-2, -1, 2, 0],\n [4, 2, -4, 0],\n [8, 4, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -6, 6, -6],\n [3, 0, -2, 1],\n [4, 8, -24, 16],\n [0, -6, 16, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -4, 0, 0],\n [6, 0, 4, 0],\n [3, 3, 4, 0],\n [4, 14, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 10, -9, 6],\n [-3, -15, -6, -6],\n [-1, -6, -5, -2],\n [0, 4, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -7, -9, 5],\n [2, -7, -9, -3],\n [-1, -14, -10, 15],\n [10, 11, 5, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -3, 12, 6],\n [0, 0, 0, 0],\n [6, -3, 12, 6],\n [8, -4, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-30, 19, -1, -10],\n [-14, 25, 3, -11],\n [24, -20, 12, 16],\n [-4, 20, -2, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 6, -6, 4],\n [-16, -12, 12, -8],\n [0, 0, 0, 0],\n [4, 3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 13, 3, -2],\n [-18, 12, -8, 2],\n [-6, 5, -1, 0],\n [-9, 0, -14, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -23, 15, -3],\n [-12, 16, -8, 4],\n [11, -6, -4, -3],\n [10, -9, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 12, 4, 4],\n [16, -14, 0, -5],\n [-16, 16, -4, 6],\n [-12, 13, -5, 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[[16, -10, -11, 0],\n [-13, 27, 15, 5],\n [6, 4, -4, -2],\n [-18, 16, 19, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -9, 9, -9],\n [-13, -2, -14, 7],\n [-18, -17, 1, -10],\n [-12, -1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 8, -4, -12],\n [0, -8, 4, 6],\n [6, 4, -2, -12],\n [-11, 6, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, 0, -3, 6],\n [-13, 2, -7, 10],\n [-4, 8, -12, 8],\n [0, 6, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -12, -8, -12],\n [-16, 12, 8, 12],\n [12, -9, -6, -9],\n [4, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, 14, -5],\n [-28, 24, -20, 0],\n [24, -20, 20, -1],\n [-15, 13, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -10, -13, -12],\n [-1, -16, -19, -6],\n [2, -15, -11, -17],\n [-1, 0, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -12, 0, 16],\n [-9, 0, 9, -12],\n [-13, -12, 9, 4],\n [12, 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[[9, -12, -12, 9],\n [-9, 12, 12, -9],\n [12, -16, -16, 12],\n [-3, 4, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 2, 18, -6],\n [-12, 20, 32, 8],\n [9, -9, -5, 1],\n [0, 0, 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[[4, 2, 7, 1],\n [16, -3, 6, 15],\n [16, -2, 8, 14],\n [-8, 3, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 2, 8, 8],\n [4, 4, 16, 16],\n [-4, -4, -16, -16],\n [3, 3, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 4, 3, 1],\n [6, -8, -6, -2],\n [-12, 16, 12, 4],\n [12, -16, -12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 9, -3, 6],\n [-24, 15, 3, -12],\n [-4, 10, -2, 3],\n [12, -9, -1, 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[[4, -6, -12, -13],\n [-12, -4, 3, 6],\n [-8, 4, 12, 14],\n [-8, -10, -9, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -21, -5, 1],\n [14, -3, -11, 3],\n [-15, 9, 13, 0],\n [16, 12, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -13, -7, -2],\n [19, 8, -7, -2],\n [4, 5, -1, -4],\n [4, -7, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 8, -8, -8],\n [-8, 8, -8, -8],\n [-4, 4, -4, -4],\n [16, -16, 16, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, 0, 0],\n [0, -8, 0, 0],\n [0, 8, 0, 0],\n [0, -8, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 6, 6, 6],\n [-3, 9, 9, 9],\n [1, -3, -3, -3],\n [-3, 9, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 2, 2, -8],\n [-8, 4, 4, -16],\n [0, 0, 0, 0],\n [8, -4, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 0, -20, 20],\n [9, 0, 12, -6],\n [9, -2, 17, -14],\n [-12, 1, -16, 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[[3, -2, 0, -3],\n [-6, 4, 0, 6],\n [-6, 4, 0, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-17, -3, 3, 4],\n [-20, 0, 0, -8],\n [-15, 0, 0, -6],\n [16, -1, 1, 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 4x4 matrix:\n[[-12, 8, 5, -19],\n [13, 11, 9, 11],\n [16, -6, 26, 16],\n [-8, -18, -15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, 5, 2, 12],\n [-9, 10, -15, 3],\n [4, 3, -8, -2],\n [8, -8, 14, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 11, 1, 9],\n [-28, -8, 7, -5],\n [-24, -9, 6, -6],\n [20, 5, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 7, 5, 1],\n [-3, -14, -4, -12],\n [3, 1, -1, 3],\n [-2, 8, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -9, 12, 3],\n [0, 0, 0, 0],\n [-4, 3, -4, -1],\n [12, -9, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 18, 0, 0],\n [-4, -23, -13, -9],\n [8, 10, -14, 6],\n [-16, 6, 8, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 3, -3, 6],\n [-9, 3, -3, 6],\n [9, -3, 3, -6],\n [-6, 2, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 27, -9, -15],\n [-16, 23, -16, -5],\n [9, -6, 18, -13],\n [17, -4, 10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 8, -8, -8],\n [0, 2, -2, -2],\n [0, -6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 2, -7, 18],\n [-14, 10, -20, -3],\n [-5, 0, -3, -7],\n [4, 0, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 1, 7, 5],\n [-8, 7, 4, 8],\n [-12, 3, 7, 0],\n [12, 15, -9, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 9, -12, -9],\n [-1, 3, -4, -3],\n [-3, 9, -12, -9],\n [2, -6, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 12, -12, 0],\n [12, -9, 9, 0],\n [-4, 3, -3, 0],\n [16, -12, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 0, -4, 2],\n [4, 0, 4, -2],\n [-2, 0, -2, 1],\n [4, 0, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 0, -4, 4],\n [14, 1, 10, -10],\n [2, -7, -20, 20],\n [-2, 3, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -16, 12, 20],\n [0, 5, -3, -9],\n [3, -3, 0, 12],\n [-9, -11, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 1, 2, -7],\n [8, 4, 6, -6],\n [-3, -3, -4, -1],\n [-11, -7, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -1, -6, -1],\n [-16, -8, 0, -8],\n [-22, -14, -4, -14],\n [10, 8, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -2, -13, -11],\n [18, -4, 28, 34],\n [-18, 24, -22, -8],\n [-7, 0, -16, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 1, 2, 1],\n [8, -4, -8, -4],\n [-6, 3, 6, 3],\n [8, -4, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, -22, -15],\n [7, 16, 4, -10],\n [-7, 6, 5, -2],\n [15, -12, -22, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-6, 2, 6, 8],\n [12, -4, -12, -16],\n [-6, 2, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, -8, 16, 4],\n [18, -8, 12, 2],\n [1, 3, -1, 7],\n [13, -1, -5, 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 4x4 matrix:\n[[8, -4, -6, -2],\n [-8, 4, 6, 2],\n [12, -6, -9, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -6, 4, 1],\n [-20, -1, -3, 9],\n [16, 2, 2, -8],\n [8, 3, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -12, -4, 26],\n [3, 2, 4, 5],\n [-5, -9, -8, 5],\n [-10, -21, -17, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 16, 0, 0],\n [2, -12, 2, -2],\n [8, 0, -10, -26],\n [14, 7, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -13, -5, 3],\n [-18, -14, 8, -20],\n [-13, -31, -2, -12],\n [5, 6, -3, 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 4x4 matrix:\n[[-16, 8, 13, 10],\n [3, -6, 9, -6],\n [-7, 3, 16, 22],\n [-2, 4, -13, -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, 0, 4, -2],\n [0, 0, -6, 3],\n [0, 0, 0, 0],\n [0, 0, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -8, 8, 12],\n [-25, -1, 1, 40],\n [-10, -4, 4, 16],\n [-2, -28, 28, -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[[-3, 17, -22, 28],\n [9, -7, 20, -32],\n [-8, 16, -28, 40],\n [6, 6, 20, -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 4x4 matrix:\n[[16, 6, -12, 8],\n [10, 3, 0, -4],\n [18, 5, 4, -12],\n [0, 2, -20, 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[[-8, 3, -15, 2],\n [15, 0, 9, 3],\n [-14, -1, -5, -4],\n [15, 5, -8, 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 4x4 matrix:\n[[-6, 6, 0, 16],\n [6, -6, 0, -16],\n [-1, -10, 22, -1],\n [-1, -10, 22, -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[[-3, 2, 2, -2],\n [-9, 6, 6, -6],\n [-9, 6, 6, -6],\n [-3, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 5, 2, 5],\n [-24, 4, -8, -8],\n [4, 4, 0, 2],\n [-8, 20, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 12, 3, -3],\n [0, 0, 0, 0],\n [-4, 16, 4, -4],\n [2, -8, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 3, -5, 10],\n [-3, 5, -6, 13],\n [17, -11, -5, 0],\n [6, 2, -15, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[30, 8, 36, 25],\n [-10, 15, -20, -15],\n [12, -8, 6, 3],\n [6, 5, 6, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-21, -7, -8, 9],\n [-3, 25, -16, -3],\n [9, 37, -16, -9],\n [-18, -11, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 2, 7, -4],\n [-13, 3, 16, 16],\n [-7, 1, 6, 8],\n [-13, 3, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 12, -12, 0],\n [-4, 4, -4, 0],\n [4, -4, 4, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 4, -2, 4],\n [0, -8, 6, -14],\n [0, 4, -3, 7],\n [-2, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 25, -16, -16],\n [-12, -5, 11, -4],\n [8, -10, -4, 16],\n [12, 5, -11, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 8, -16, 16],\n [-2, -4, 8, -8],\n [-1, -2, 4, -4],\n [-1, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 1, 3],\n [0, 0, 4, 12],\n [0, 0, -4, -12],\n [0, 0, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -6, 6, 12],\n [0, -16, 0, -8],\n [2, -14, -2, -12],\n [-2, -10, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 2, 12, 6],\n [17, 6, 5, 1],\n [25, 12, 16, 5],\n [-1, 2, 14, 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 4x4 matrix:\n[[1, -1, 3, -1],\n [-1, 1, -3, 1],\n [-4, 4, -12, 4],\n [3, -3, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -6, 0, 1],\n [12, 10, -28, 17],\n [12, -22, 4, 1],\n [-4, 18, -12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 8, 0, -2],\n [-8, 8, 0, -2],\n [4, -4, 0, 1],\n [-16, 16, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 22, -16, -11],\n [-8, 10, 14, -4],\n [-6, -6, 12, -1],\n [-8, 11, 13, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -2, -10, -22],\n [-2, -4, -12, -20],\n [6, -4, -4, 4],\n [16, -16, -24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 1, 8, -5],\n [29, 11, 21, -11],\n [-7, 9, -1, 2],\n [16, -7, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 20, -3, -4],\n [5, 12, 1, 8],\n [-6, -15, 0, -6],\n [0, 8, -6, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -3, -1, 4],\n [-2, -12, 2, 2],\n [-13, 6, 5, -15],\n [6, 15, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -8, 2, 6],\n [9, 9, 9, -6],\n [21, -8, -9, 9],\n [0, -7, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 9, 6, 12],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, -9, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -8, -28, 19],\n [13, 7, 24, -17],\n [4, 18, 24, -8],\n [11, -4, 8, -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 4x4 matrix:\n[[1, -2, -6, -1],\n [-4, 17, 6, 19],\n [-4, 11, 18, 9],\n [12, 9, 6, -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[[5, -19, 7, -3],\n [-12, -12, -6, 12],\n [6, -12, -5, -11],\n [-3, 9, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, 9, 2, 4],\n [12, -12, 6, -14],\n [6, 6, 2, 2],\n [1, 9, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 0, 2, -8],\n [-14, 6, -10, 22],\n [14, -6, 10, -22],\n [-4, 3, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 9, 8, 3],\n [11, -11, -7, -2],\n [-9, 9, 3, 0],\n [18, -18, -11, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -6, 9, 5],\n [-3, -9, 15, 12],\n [-12, -6, 4, -10],\n [6, 6, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -3, 3, -2],\n [8, -10, 2, -1],\n [-17, 25, 7, -6],\n [12, -18, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 1, -1, 8],\n [14, -10, 0, -24],\n [-5, 11, 4, 4],\n [-3, -9, -6, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[17, 2, 18, 7],\n [-18, 13, -13, -5],\n [3, 15, -10, 15],\n [13, -8, 23, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -1, 0, -9],\n [-2, -4, 4, -8],\n [-18, 8, -12, -12],\n [-3, -6, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, 0, -6],\n [12, -12, 0, 12],\n [15, -7, -2, 13],\n [-6, -2, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -12, 2, -10],\n [4, 3, -1, 3],\n [-4, 0, 4, -4],\n [-18, -15, 3, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -10, -2, 17],\n [-2, -8, 2, 4],\n [0, 2, 1, -5],\n [2, 10, -1, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -4, -8, 8],\n [1, -1, -2, 2],\n [-2, 2, 4, -4],\n [-1, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -10, 12, -15],\n [-14, -10, 12, -9],\n [14, -1, 4, -10],\n [-10, -8, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-8, 8, 16, 12],\n [-4, 4, 8, 6],\n [6, -6, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 1, 3, 3],\n [0, 1, 3, 3],\n [0, 4, 12, 12],\n [0, 3, 9, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -6, -14, 8],\n [-3, -3, -3, 4],\n [-2, -3, -1, 4],\n [10, 6, 14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 14, -5, 13],\n [7, 10, -7, 15],\n [-18, 4, 5, -7],\n [-16, 0, 6, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 0, -10, -5],\n [5, 10, 0, 5],\n [-9, -9, 3, -3],\n [-15, 0, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, -12],\n [0, 0, 0, -3],\n [0, 0, 0, -3],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, 14, 0],\n [7, 16, -16, -9],\n [7, 16, -16, -9],\n [13, 4, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 12, 12, -12],\n [-9, -9, -9, 9],\n [3, 3, 3, -3],\n [-6, -6, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -8, 8, 10],\n [8, -12, 16, 14],\n [-1, 3, -2, -4],\n [3, -5, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 8, -16, -20],\n [-8, 0, 16, -12],\n [-8, -4, 8, 10],\n [12, 4, -16, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -19, -13, 13],\n [4, 4, -2, -20],\n [-16, -4, -13, 12],\n [-20, -17, -19, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 1, -3, 2],\n [21, -9, 6, -3],\n [-5, 3, 5, -4],\n [-25, 11, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -5, -10, -8],\n [5, -10, -14, 17],\n [8, -10, -8, 8],\n [13, -11, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -12, -6, 6],\n [22, 2, -21, 21],\n [-9, 6, 8, -8],\n [4, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -8, 4, 7],\n [-13, 20, -10, -19],\n [-3, 24, -12, -21],\n [10, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, 8, -4],\n [0, 0, 0, 0],\n [12, -12, 12, -6],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 3, -3, 0],\n [0, -1, 1, 0],\n [0, -4, 4, 0],\n [0, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -1, -6, -5],\n [9, -12, -6, -6],\n [-9, 5, 8, 7],\n [3, -25, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -6, -6, 6],\n [8, 6, 6, -6],\n [8, 6, 6, -6],\n [-4, -3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 4, -6, -8],\n [-4, 8, -12, -16],\n [0, 0, 0, 0],\n [-4, 8, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -9, -10, 9],\n [16, 0, 4, 16],\n [12, -24, -32, -4],\n [-10, -3, -5, -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[[3, 3, 4, -4],\n [-12, -12, -16, 16],\n [-9, -9, -12, 12],\n [12, 12, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -12, 10, 20],\n [-12, -4, 8, 16],\n [-6, 8, 5, 10],\n [-8, -16, 4, 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[[19, 8, 4, 5],\n [24, -12, -7, -13],\n [-9, 20, 5, 14],\n [3, 4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 1, -3, 0],\n [4, -1, 3, 0],\n [4, -1, 3, 0],\n [8, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 11, 3, -6],\n [3, 16, -3, -9],\n [-3, 2, 3, 4],\n [9, 18, -9, -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[[-2, -4, -1, 0],\n [4, 8, 2, 0],\n [-4, -8, -2, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -4, -2, 14],\n [2, 1, 1, -4],\n [5, 1, 3, -6],\n [4, -4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 6, 6, -4],\n [8, -12, -12, 8],\n [6, -9, -9, 6],\n [6, -9, -9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 8, 10, -12],\n [-11, 5, 9, -6],\n [-2, -5, -7, 7],\n [-11, -8, -9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 1, -1, -1],\n [3, 1, -1, -1],\n [-3, -1, 1, 1],\n [-3, -1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [3, 2, 3, -2],\n [12, 8, 12, -8],\n [6, 4, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 0, -10, -10],\n [2, -22, 4, -20],\n [-11, 1, -3, -9],\n [-4, -2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, -5, 2, 8],\n [-12, -9, 4, 8],\n [8, 5, -7, -5],\n [-12, -12, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 7, -7, -3],\n [-6, -5, 4, 1],\n [-18, -5, 10, 19],\n [15, 1, 11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, 0, -8],\n [-2, 10, -6, 10],\n [-8, -2, -4, 12],\n [7, -3, 6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -21, -15, 12],\n [5, -21, -4, 19],\n [-6, -16, 1, 9],\n [11, -15, 9, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, -4, 2],\n [0, 0, 0, 0],\n [0, 0, -6, 3],\n [0, 0, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-9, 0, 15, 21],\n [4, 16, -16, -16],\n [-1, 8, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 4, -8, 6],\n [-8, 4, -8, 6],\n [12, -6, 12, -9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 3, -2, 4],\n [-3, -5, -10, -14],\n [4, -1, -22, -16],\n [-4, 0, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 12, -4, 4],\n [4, -9, 1, -1],\n [-2, 17, -3, 3],\n [-4, 9, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -11, -6, -3],\n [11, 0, 9, -12],\n [-8, -5, -12, 11],\n [-12, -4, -12, 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[[-6, 6, 8, -6],\n [-6, 6, 8, -6],\n [0, 0, 0, 0],\n [6, -6, -8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, -9, 9, -6],\n [0, -3, 3, -2],\n [0, -3, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 4, -6, -2],\n [-1, 2, -3, -1],\n [0, 0, 0, 0],\n [1, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 16, -5, -8],\n [-4, 8, 2, -12],\n [6, -12, -15, 26],\n [4, 12, 3, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -1, -5, -4],\n [13, -11, -11, 6],\n [18, -10, -18, 0],\n [-17, 9, 19, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 0, 8, -12],\n [4, 0, 4, -6],\n [-4, 0, -4, 6],\n [-4, 0, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 1, 32, 7],\n [1, 3, -21, -20],\n [5, -3, -16, 5],\n [-9, -13, 14, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -14, -10, -11],\n [10, 13, 11, 9],\n [16, 15, 9, 8],\n [-4, 1, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 10, -8, 1],\n [4, 8, -16, -4],\n [-4, 24, 0, 12],\n [4, -20, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, 13, 13, 7],\n [20, -15, -20, -14],\n [-9, 10, 9, 9],\n [9, -6, -9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 4, -2, 6],\n [9, -6, 3, -9],\n [-12, 8, -4, 12],\n [12, -8, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -12, 6, 3],\n [-9, 12, -6, -3],\n [12, -16, 8, 4],\n [-6, 8, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 0, 16, 0],\n [0, 0, 0, 0],\n [6, 0, -12, 0],\n [-6, 0, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 18, 16, -1],\n [-16, -16, -4, 16],\n [8, 15, 5, -13],\n [11, 2, 0, -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[[7, -3, -12, -12],\n [3, 1, 2, 4],\n [-9, 1, 5, 0],\n [-8, -8, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 6, 0, 0],\n [-4, -3, 0, 0],\n [12, 9, 0, 0],\n [4, 3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 10, 10, -12],\n [7, 3, -1, -14],\n [5, 15, 25, 8],\n [-12, -8, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -12, 12, -16],\n [-12, 9, -9, 12],\n [0, 0, 0, 0],\n [-4, 3, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 1, 3, -4],\n [-12, 4, 12, -16],\n [6, -2, -6, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 1, -1, -2],\n [0, 2, -2, -4],\n [0, 3, -3, -6],\n [0, -1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -12, -16, -12],\n [-8, 6, 8, 6],\n [-8, 6, 8, 6],\n [8, -6, -8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 5, 27, 1],\n [37, -1, 7, -7],\n [8, 20, 15, 1],\n [8, 0, 31, 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 4x4 matrix:\n[[9, -7, 9, 2],\n [0, 0, 0, 0],\n [18, -19, 0, -10],\n [-5, 5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -12, -6, -15],\n [10, -24, 0, -18],\n [7, -20, 4, -11],\n [8, -16, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -8, -2, 4],\n [0, 0, 0, 0],\n [2, 4, 1, -2],\n [8, 16, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -3, 15, -6],\n [12, 3, 11, -10],\n [6, -11, 3, 10],\n [-3, -12, -5, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 8, 4, 24],\n [24, 8, 10, 4],\n [-4, -6, -18, 11],\n [-8, 2, 16, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -16, -16, 4],\n [-9, -20, -4, -1],\n [-3, -8, 0, -1],\n [-9, -16, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -9, -6, 9],\n [9, 9, 6, -9],\n [12, 12, 8, -12],\n [6, 6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 11, 6, 2],\n [6, 15, -12, -14],\n [5, -1, -6, -6],\n [3, 18, -3, 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 4x4 matrix:\n[[8, -8, 8, 4],\n [2, -8, 4, 7],\n [-10, -8, -4, 13],\n [10, 2, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 12, -15, -4],\n [2, 8, -2, 0],\n [-8, -5, 20, -3],\n [8, 2, -20, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 5, 5, -6],\n [-8, 5, 5, -6],\n [16, -10, -10, 12],\n [-4, 11, 11, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 19, -4, 0],\n [12, -15, -12, 0],\n [8, 20, -8, 0],\n [12, -6, -12, 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[[-14, 5, -4, 14],\n [-1, 10, 10, 22],\n [-20, 8, -6, 20],\n [-7, 13, 8, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 1, 3, -1],\n [-4, 4, 12, -4],\n [-3, 3, 9, -3],\n [1, -1, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -6, -10, 20],\n [-12, -7, -13, 24],\n [0, -4, -4, 12],\n [-12, -3, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-6, -4, 2, 8],\n [6, 4, -2, -8],\n [-12, -8, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 18, 15, 6],\n [-12, -12, -6, 0],\n [28, 4, -6, -8],\n [-20, -14, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 12, -6, 0],\n [3, -4, 2, 0],\n [-9, 12, -6, 0],\n [-3, 4, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 4, -2, 4],\n [-2, -2, -10, 13],\n [-4, -4, -2, 5],\n [1, -3, -7, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, 6, -8, 0],\n [18, -3, 4, -3],\n [-13, -6, 8, 8],\n [8, 15, -20, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -2, -1, -3],\n [9, -6, -3, -9],\n [9, -6, -3, -9],\n [3, -2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -24, 1, -4],\n [28, 4, 0, -8],\n [-5, -3, -4, -16],\n [-11, 11, -6, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -4, 4, 4],\n [0, 0, 0, 0],\n [8, -8, 8, 8],\n [-4, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 12, 12, -11],\n [5, 16, -4, 5],\n [-8, -4, -8, 12],\n [-16, -28, 0, 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[[-9, -15, -19, 2],\n [-12, 20, 0, -4],\n [5, -15, -4, 15],\n [-10, -5, -14, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 9, -10, 5],\n [6, 4, -6, 2],\n [3, -8, 5, -5],\n [0, 15, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -5, -8, 18],\n [12, -19, 8, 4],\n [-14, 8, 24, -8],\n [8, -14, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -16, 16, 4],\n [-4, 4, -4, -1],\n [12, -12, 12, 3],\n [12, -12, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 12, 0, 9],\n [2, 4, 0, 3],\n [-2, -4, 0, -3],\n [4, 8, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 4, 3, 0],\n [12, 16, 12, 0],\n [12, 16, 12, 0],\n [-9, -12, -9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 5, -3, 14],\n [6, -5, -6, 8],\n [3, 8, -3, 18],\n [3, 5, -3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, -4, -16],\n [0, 1, 1, 4],\n [0, -2, -2, -8],\n [0, 2, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -3, -6, 1],\n [10, -16, 10, -11],\n [-14, -1, -14, 5],\n [4, -1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -4, 5, -9],\n [-28, 12, -8, 20],\n [-5, 3, 5, -2],\n [8, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, -2, 8],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-8, 8, 2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -5, -8, -6],\n [-8, 2, -8, 0],\n [16, -4, 16, 0],\n [14, 3, 16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, -9, 0, 0],\n [-16, 20, 12, 6],\n [-29, 8, 3, -3],\n [-7, -4, 15, -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 4x4 matrix:\n[[-1, 14, 15, 3],\n [0, 5, 6, 0],\n [-4, -4, -12, 12],\n [-4, 1, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 4, 1, 3],\n [-1, -4, -1, -3],\n [3, 12, 3, 9],\n [-4, -16, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 8, 8, 2],\n [-6, -3, 18, 9],\n [4, -6, 15, 10],\n [9, -6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -2, -5, 5],\n [-2, 13, -18, 16],\n [-6, 7, -10, 12],\n [6, -5, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -7, -4, 3],\n [-4, 6, 12, -4],\n [-8, 8, 20, -6],\n [6, -9, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -12, 9, 12],\n [-2, -8, 6, 8],\n [1, 4, -3, -4],\n [2, 8, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 1, -4, 1],\n [-10, -10, -8, 8],\n [-20, -5, -28, 13],\n [4, -2, 8, -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 4x4 matrix:\n[[-3, 13, 7, -7],\n [-3, 9, 9, -6],\n [-1, 3, 3, -2],\n [-4, 12, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 16, -24, 16],\n [-24, 8, -24, 4],\n [-5, -8, 8, -12],\n [-4, 16, -15, 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 4x4 matrix:\n[[12, 9, 3, -12],\n [22, 15, 4, -22],\n [-24, -16, -4, 24],\n [2, 3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, -18, -8, -6],\n [11, 6, 2, 6],\n [19, 8, 2, 12],\n [-4, 12, 8, -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 4x4 matrix:\n[[9, -41, -41, 3],\n [5, 9, 9, -11],\n [-8, -4, -4, 8],\n [-9, 34, 34, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -8, 17, -8],\n [9, -9, 4, -11],\n [14, -14, 0, -16],\n [7, -7, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -9, -15, 5],\n [-4, 0, -6, 4],\n [-1, -15, -14, 1],\n [2, -6, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 2, 1, 4],\n [0, 4, 2, 8],\n [0, -2, -1, -4],\n [0, -8, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 8, 5, -4],\n [-24, -8, -8, 20],\n [10, 8, -16, 33],\n [2, 2, -10, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -9, 6, -5],\n [-6, -9, 9, -3],\n [12, -3, 0, -3],\n [-8, -5, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -4, -12, -28],\n [-2, -25, 9, 0],\n [0, 28, -12, -4],\n [8, 9, 3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 5, -5, 17],\n [0, -3, -1, -3],\n [-2, 0, -4, 8],\n [1, -1, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, -16, -6, -6],\n [9, -12, -17, -17],\n [3, 12, 9, 9],\n [-13, -4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 12, 6, -14],\n [0, -12, -5, 3],\n [6, 36, 24, -3],\n [-4, -16, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 10, 18, 14],\n [-13, 20, 10, 11],\n [16, -16, -12, -20],\n [-13, -9, -28, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[37, -27, 13, 25],\n [-9, -3, 9, 2],\n [8, -11, 13, 1],\n [-5, 3, -5, 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 4x4 matrix:\n[[-30, 24, 6, 17],\n [-19, 19, 10, 15],\n [3, -10, -15, -10],\n [-14, 14, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [3, 0, -1, -2],\n [-3, 0, 1, 2],\n [-9, 0, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 3, -3, 3],\n [0, 8, 8, -4],\n [0, 11, 5, -1],\n [0, 2, -6, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, 1, 1],\n [-30, 16, -16, -18],\n [-3, 6, 25, 22],\n [-3, -6, -3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 16, 8, -16],\n [0, 4, 2, -4],\n [0, 12, 6, -12],\n [0, -12, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -4, -8, 18],\n [5, 6, -18, 3],\n [-3, -2, 2, 3],\n [-14, -8, 2, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -8, 4, -8],\n [4, 20, -16, 6],\n [-9, -6, -12, 9],\n [24, 12, -10, -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 4x4 matrix:\n[[3, -4, 3, -1],\n [9, -8, 3, 1],\n [8, -4, -2, 4],\n [-15, 12, -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[[-12, -12, 0, 6],\n [16, 16, 0, -8],\n [0, 0, 0, 0],\n [16, 16, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -3, 1, -2],\n [-3, -3, 1, -2],\n [6, 6, -2, 4],\n [9, 9, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -4, 8, 4],\n [0, 6, -12, -6],\n [0, 2, -4, -2],\n [0, -6, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 8, 0, -16],\n [6, -4, 0, 8],\n [3, -2, 0, 4],\n [12, -8, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -4, 2, 4],\n [-1, -4, 2, 4],\n [12, -24, 8, 12],\n [-7, 8, -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[[2, 1, 2, -4],\n [8, 7, 5, -8],\n [2, 7, -4, 12],\n [-6, -3, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 7, -15, 9],\n [-2, -10, -6, -6],\n [14, 5, -23, 27],\n [10, 19, -1, -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[[-9, 12, 12, 0],\n [-12, 16, 16, 0],\n [3, -4, -4, 0],\n [-9, 12, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 12, -1, -10],\n [-14, 8, -10, -2],\n [6, 12, 3, -12],\n [-16, 4, -11, 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[[7, -4, -1, 10],\n [-3, -24, -6, 6],\n [-2, 24, 6, -12],\n [3, 24, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 4, 3, 3],\n [-6, -8, -6, -6],\n [6, 8, 6, 6],\n [-3, -4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 1, 10, 3],\n [-5, 13, 13, -12],\n [20, -13, 12, 1],\n [-16, 16, 7, -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 4x4 matrix:\n[[-8, 8, 8, 6],\n [-16, 6, 4, 0],\n [-8, 8, 8, 6],\n [0, 15, 18, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 16, 1, -7],\n [3, -17, -2, 4],\n [16, -4, -4, -12],\n [6, -8, -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[[-6, -11, -5, -2],\n [-15, -2, -19, -10],\n [-18, -12, -18, -12],\n [18, 18, 5, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -1, 3, -7],\n [-2, -8, -6, 4],\n [2, 13, 9, -5],\n [14, 1, 9, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 18, -10, 12],\n [3, 2, 2, 6],\n [-4, 4, -6, -3],\n [1, -10, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 6, 1, 24],\n [6, -2, 4, 5],\n [-8, 6, -7, 0],\n [0, -4, 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[[8, -8, 8, 0],\n [8, -8, 8, 0],\n [-8, 8, -8, 0],\n [8, -8, 8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -1, 1, 1],\n [-1, 1, -1, -1],\n [10, 6, 10, -6],\n [28, 12, 28, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -12, -11, 3],\n [-12, -10, -7, -17],\n [-14, -4, -24, -4],\n [-6, -15, 5, -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[[11, -8, -5, -11],\n [1, -4, -3, -1],\n [-18, 0, -2, 18],\n [15, 12, 11, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 10, -8, 6],\n [-24, 8, -10, 6],\n [20, 4, 0, -14],\n [-8, 1, 0, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 2, 2, -6],\n [4, -7, 3, -9],\n [4, -13, 1, -3],\n [-1, -8, -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[[-16, -8, 4, -8],\n [-4, -2, 1, -2],\n [16, 8, -4, 8],\n [-16, -8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 4, -16, -8],\n [6, -3, 12, 6],\n [0, 0, 0, 0],\n [-8, 4, -16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 0, -2, -4],\n [-6, 0, 6, 12],\n [-2, 0, 2, 4],\n [-6, 0, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 6, 8, 8],\n [0, -12, -6, -16],\n [-3, 3, 3, 4],\n [-15, 3, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-29, 19, -7, -21],\n [7, -4, -2, 1],\n [2, 6, -22, -14],\n [17, -10, 4, 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 4x4 matrix:\n[[24, -8, 17, -16],\n [-4, 0, -3, 0],\n [9, -6, 6, -12],\n [-1, 6, 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[[-9, 7, -10, -7],\n [-20, -14, -16, -14],\n [1, 14, -2, 0],\n [7, -16, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 1, 0, 3],\n [-1, 1, 0, 3],\n [1, -1, 0, -3],\n [-1, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -4, 4, 0],\n [-6, 4, -4, 0],\n [3, -2, 2, 0],\n [9, -6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 0, 2, 4],\n [2, 0, -2, -4],\n [-8, 0, 8, 16],\n [8, 0, -8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, 6, -3],\n [-1, 2, 9, -5],\n [3, -6, -3, 9],\n [6, -4, 22, -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[[-20, 2, 6, 8],\n [12, -4, 0, -4],\n [3, 6, -9, -3],\n [-2, 3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -8, 4, -1],\n [15, -1, -1, -2],\n [-4, 8, -8, -4],\n [2, 6, -10, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, 6, 15, -10],\n [1, -14, -9, 7],\n [6, 7, 0, 0],\n [-1, -22, -15, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 15, -15, -9],\n [8, 4, 2, 6],\n [-4, -8, 6, 2],\n [-15, -3, -9, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-8, -4, 0, -6],\n [16, 8, 0, 12],\n [-4, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 6, 8, -4],\n [-16, 12, 16, -8],\n [-4, 3, 4, -2],\n [-12, 9, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, 17, -5, 16],\n [-13, -21, 4, -12],\n [2, 9, 13, 9],\n [-12, -7, 33, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -12, 6, 3],\n [1, 4, -2, -1],\n [2, 8, -4, -2],\n [-3, -12, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -2, 0, 4],\n [-12, 4, 0, -8],\n [3, -1, 0, 2],\n [-12, 4, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 4, 8, 16],\n [-12, 3, 6, 12],\n [0, 0, 0, 0],\n [-16, 4, 8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 3, -1, 4],\n [-4, 6, -2, 8],\n [-14, -21, 21, -22],\n [1, 0, -17, 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[[-4, 0, 2, 0],\n [16, 0, -8, 0],\n [16, 0, -8, 0],\n [-16, 0, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -1, -15, -3],\n [1, -2, -9, -2],\n [-14, -22, 6, -2],\n [16, 28, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 20, -14, 2],\n [-8, -5, 4, -7],\n [-5, -1, 1, -4],\n [-15, -3, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -12, 9, -3],\n [-9, -12, 9, -3],\n [3, 4, -3, 1],\n [9, 12, -9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, 10, 2, 13],\n [-9, -8, -2, -10],\n [8, -10, -8, -7],\n [-20, -24, -8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -10, 4, -4],\n [-6, -10, -9, -1],\n [-2, -7, 8, -4],\n [-2, -4, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -2, -3, -3],\n [-16, 8, 12, 12],\n [-16, 8, 12, 12],\n [-16, 8, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, -4, -14, -5],\n [-6, -28, -13, -18],\n [9, 12, 12, 9],\n [-6, 12, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -13, 14, 5],\n [-2, -13, 4, 7],\n [5, 12, -22, -10],\n [-2, 15, -14, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 6, -6, 4],\n [-6, 6, -6, 4],\n [12, -12, 12, -8],\n [6, -6, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 9, -2, -6],\n [-11, -6, 5, 10],\n [2, 9, 0, -8],\n [-4, 9, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -12, 6, -9],\n [3, -12, 6, -9],\n [2, -8, 4, -6],\n [4, -16, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 15, 9, 19],\n [-6, 10, -21, 15],\n [-2, -14, 2, -18],\n [2, 7, 17, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 3, 1, 12],\n [-23, 18, 14, 6],\n [-9, -10, -11, 5],\n [-13, 2, -1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -8, 0, 8],\n [-6, -12, 0, 12],\n [0, 0, 0, 0],\n [8, 16, 0, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -1, -1, 14],\n [0, 1, 1, -6],\n [8, 4, 4, 8],\n [-10, -3, -3, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 0, -16, 12],\n [19, 18, 12, 6],\n [-25, -27, -16, -9],\n [7, 8, -28, 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[[5, -4, 8, -7],\n [0, -16, -8, 12],\n [-4, 8, -4, 2],\n [-4, 4, -6, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 6, 11, 17],\n [8, -4, -6, -10],\n [10, -6, -7, -13],\n [-8, -4, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 8, 24, 2],\n [-16, 8, 12, 20],\n [-17, -5, -13, 1],\n [21, 0, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -4, 4, -2],\n [4, 2, -2, 1],\n [-12, -6, 6, -3],\n [12, 6, -6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -9, -2, 13],\n [-8, 8, 1, 2],\n [11, -7, -2, -5],\n [-6, 10, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -4, 4, -8],\n [3, 2, -2, 4],\n [3, 2, -2, 4],\n [-3, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -4, 8, -5],\n [-19, 6, -11, 6],\n [9, -8, 10, -1],\n [-8, -10, 7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 0, -8, 4],\n [16, -15, 8, -4],\n [8, 6, 4, -2],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -12, -12, 0],\n [2, -8, -8, 0],\n [-3, 12, 12, 0],\n [1, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 14, 7, -9],\n [1, 10, 6, -7],\n [9, -22, -6, 2],\n [-5, 16, 5, -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, -19, -19, -23],\n [-10, -5, 4, -2],\n [-16, -7, 6, 0],\n [1, -4, -5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 0, 12, 0],\n [-6, 0, 3, -9],\n [14, 0, 5, 12],\n [18, 0, 7, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 16, -8, 0],\n [8, 8, -4, 0],\n [16, 16, -8, 0],\n [-4, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 4, 1, -2],\n [6, 12, 3, -6],\n [-8, -16, -4, 8],\n [8, 16, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 12, -12, 12],\n [-8, -13, 13, 3],\n [-4, -14, 14, -6],\n [-2, -10, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 8, 12, -16],\n [-8, -8, -12, 16],\n [-6, -6, -9, 12],\n [-6, -6, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -6, 12, -2],\n [13, -5, 2, 5],\n [-19, -3, 14, -8],\n [-24, -6, 21, -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[[9, -21, -9, -3],\n [5, 19, 17, 11],\n [9, -15, -3, 3],\n [15, -7, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 0, 14, -2],\n [-22, 0, -22, -2],\n [-36, 12, -24, 12],\n [17, 8, 25, 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[[0, -3, 1, 4],\n [0, -3, 1, 4],\n [0, 12, -4, -16],\n [0, 6, -2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-2, 0, -2, 4],\n [-6, 0, -6, 12],\n [2, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-16, -4, -16, 12],\n [-4, -1, -4, 3],\n [-12, -3, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -15, 0, 11],\n [-12, -3, 19, 6],\n [-12, 18, -9, -15],\n [8, 0, -10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -14, 1, 17],\n [-2, 6, 0, -7],\n [2, -10, -4, 9],\n [6, -18, 0, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 1, -3, -2],\n [6, -9, 9, 2],\n [9, -10, 3, -4],\n [-12, 10, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -3, 3, -3],\n [-4, -1, 1, -1],\n [-12, -3, 3, -3],\n [-4, -1, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -8, 16, -8],\n [-7, 18, -11, 21],\n [0, -6, 2, -8],\n [-26, -18, -19, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -1, 11, 4],\n [8, 4, -8, -4],\n [17, 21, -9, -20],\n [9, 21, 3, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 0, 0, -6],\n [19, -7, -11, -5],\n [23, -16, 2, 1],\n [6, 0, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -16, -16, 0],\n [-4, -4, -4, 0],\n [0, 0, 0, 0],\n [12, 12, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 16, 1, -2],\n [0, 0, 0, 0],\n [-12, -16, -12, 8],\n [9, 14, 5, -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 4x4 matrix:\n[[-4, 1, 25, 29],\n [6, 17, 16, 1],\n [5, 9, 7, 13],\n [-5, -10, -1, 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 4x4 matrix:\n[[4, 1, 6, -4],\n [2, -1, 2, -3],\n [6, -3, 6, -9],\n [-2, -2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -18, -8, -2],\n [-10, 2, -14, -4],\n [-6, 16, 10, 12],\n [-8, 16, 4, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -5, -15, -9],\n [0, 0, 0, 0],\n [-20, 7, -24, 0],\n [-6, 1, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -8, 8, 8],\n [0, 0, 0, 0],\n [-12, 16, -16, -16],\n [3, -4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 4, -4, 4],\n [0, 16, -16, 16],\n [0, 16, -16, 16],\n [0, -12, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 8, -3, 12],\n [8, 0, -12, -16],\n [-5, 6, 3, 16],\n [5, -2, -6, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 8, 3, -11],\n [20, 17, -3, -14],\n [12, 12, -3, -9],\n [8, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -5, -11, 0],\n [20, 23, -26, 18],\n [-16, 12, 8, -8],\n [-12, 28, -2, -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[[-4, -4, 2, -2],\n [-14, -12, -2, -10],\n [2, -20, -1, -2],\n [2, 16, -9, 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[[-6, 9, -2, 8],\n [5, -6, 1, -5],\n [-14, 15, -2, 12],\n [-19, 21, -3, 17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -11, -6, -4],\n [10, 1, -6, 0],\n [13, -5, -18, -12],\n [-13, 5, 18, 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 4x4 matrix:\n[[-4, 2, -2, -3],\n [4, -2, 2, 3],\n [8, -4, 4, 6],\n [4, -2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -8, 7, -14],\n [-2, -2, 12, -5],\n [6, 8, -14, 15],\n [-4, -2, 18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -4, -8, -6],\n [-10, -4, -4, -11],\n [9, 5, 12, 5],\n [10, 6, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -8, -6, -5],\n [0, -4, 2, -1],\n [0, 0, -10, -3],\n [0, -14, 12, -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 4x4 matrix:\n[[-3, 1, -3, -3],\n [5, 2, 3, 3],\n [-22, -32, 6, 22],\n [11, 13, -3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -9, 12, 12],\n [2, -12, 15, 15],\n [-6, 6, -5, -5],\n [-1, 9, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 5, -4, -20],\n [-9, 5, -8, -10],\n [-2, 2, 0, -12],\n [-4, 0, -8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, 3, -9, -9],\n [0, 0, 0, 0],\n [6, -2, 6, 6],\n [-12, 4, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 10, -10, -6],\n [-16, -12, 18, 11],\n [-4, -12, 0, -4],\n [-4, 17, -17, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -22, -22, -20],\n [-3, -5, -5, 1],\n [12, -2, -2, -1],\n [6, -22, -22, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 1, -1, 1],\n [8, 2, -2, 2],\n [-12, -3, 3, -3],\n [-8, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 5, 9, -8],\n [0, -10, 6, 4],\n [0, -12, 6, 3],\n [-13, 6, 18, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 7, -2, 2],\n [-20, -5, 0, 14],\n [4, 8, 12, -14],\n [-6, 11, 14, -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[[6, 6, -8, 6],\n [-15, -11, 16, -9],\n [-9, -1, 4, 3],\n [18, 12, -18, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 16, 4, -8],\n [24, -24, -9, -2],\n [-20, 20, 10, 8],\n [8, -8, -1, 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[[0, -4, -2, -14],\n [-2, 0, 1, -3],\n [-10, 6, 8, 6],\n [12, -4, -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[[4, -8, 12, 8],\n [6, 0, -1, 0],\n [11, -9, -3, 14],\n [21, -8, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -15, -2, 6],\n [1, -11, 7, -1],\n [11, 19, 5, -11],\n [-14, -11, -18, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 2, 2, -1],\n [-1, -4, 0, -1],\n [13, -4, -8, 5],\n [-10, 2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 0, 8, -6],\n [-16, 8, 16, -12],\n [11, 0, -12, 14],\n [13, -16, -12, 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[[5, -4, -13, 9],\n [-13, -19, 9, 12],\n [-1, -17, -15, 18],\n [-12, -4, 28, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -16, 4],\n [0, 8, -16, 4],\n [0, 8, -16, 4],\n [0, 6, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 0, 12, 0],\n [6, 0, 6, 0],\n [3, 0, 3, 0],\n [-12, 0, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -9, -24, 19],\n [10, -2, -22, 12],\n [-5, 1, 11, -6],\n [8, 11, 16, -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[[17, 14, -18, 6],\n [-16, -8, 16, -16],\n [26, 14, -24, 12],\n [15, 8, -14, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 0, 6, -2],\n [0, 0, 0, 0],\n [-12, 0, -9, 3],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -6, -6, 6],\n [12, -6, -6, 6],\n [-4, -2, 4, -6],\n [8, -2, -5, 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 4x4 matrix:\n[[4, 0, 8, -4],\n [-8, 0, -16, 8],\n [-2, 0, -4, 2],\n [4, 0, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 3, -1, -3],\n [0, -6, 2, 2],\n [-16, 21, -15, 3],\n [8, -12, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -3, 0, -4],\n [2, 6, 0, 8],\n [1, 3, 0, 4],\n [-3, -9, 0, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 6, -3, 12],\n [2, 4, -2, 8],\n [-2, -4, 2, -8],\n [-1, -2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 0, -6, 8],\n [12, 0, 20, -20],\n [-12, 0, -8, 14],\n [-6, 0, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, 4, -12],\n [14, 9, 8, 18],\n [-16, -24, 12, 4],\n [0, 3, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, -6, -9],\n [4, 0, 4, 6],\n [-8, 0, -8, -12],\n [2, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 8, 2, 0],\n [-2, 8, 2, 0],\n [3, -12, -3, 0],\n [-3, 12, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [3, 3, 9, 9],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-25, 20, 0, 25],\n [10, 0, 0, -10],\n [-18, 14, 0, 18],\n [15, -10, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, 2, -4],\n [-8, 0, 8, -16],\n [6, 0, -6, 12],\n [2, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -2, 4, -3],\n [0, 0, 0, 0],\n [-12, -6, 12, -9],\n [8, 4, -8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 8, 22, 30],\n [-8, -4, -4, 6],\n [4, -8, -4, -9],\n [-4, -4, 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[[-17, 18, 25, 12],\n [1, 12, 13, -12],\n [-10, 12, 14, -6],\n [23, -18, -23, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -2, -16, -1],\n [13, 4, 20, 11],\n [-7, -12, 12, -21],\n [9, 4, -4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -12, 6, -3],\n [16, 16, -8, 4],\n [16, 16, -8, 4],\n [4, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -14, 10, -3],\n [-15, 2, 2, 3],\n [-15, 10, 10, 3],\n [8, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, -20, -5, 14],\n [20, -22, -12, 10],\n [-20, 18, 11, -6],\n [32, -29, -4, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-12, 6, -3, 3],\n [-12, 6, -3, 3],\n [-16, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -3, -16, 0],\n [3, 18, 14, 5],\n [-6, -12, -20, -2],\n [-6, 7, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 11, -8, 15],\n [19, 22, -8, 19],\n [-5, 16, 8, 19],\n [8, -13, -24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -24, 10, -12],\n [9, 8, -13, 4],\n [4, -4, 3, -2],\n [-5, 8, 15, 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 4x4 matrix:\n[[12, -9, 12, -6],\n [-12, 9, -12, 6],\n [-16, 12, -16, 8],\n [12, -9, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -3, -1, 1],\n [-4, 6, 2, -2],\n [6, -9, -3, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -5, -2, -6],\n [-4, 7, -8, -6],\n [-3, 15, -6, 2],\n [2, -8, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, 16, -8],\n [-12, 17, -16, 10],\n [16, 4, 20, -8],\n [20, -7, 22, -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[[3, 15, 18, 6],\n [-3, 0, -3, -6],\n [0, 5, 19, 10],\n [0, 4, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-21, -6, 6, -9],\n [-4, -18, -20, -10],\n [-12, 8, 22, -8],\n [2, 15, 16, 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[[12, 1, 9, 16],\n [-9, -12, -18, -12],\n [6, 2, 6, 8],\n [-9, 3, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -6, 0, 8],\n [12, 12, 0, -16],\n [3, 3, 0, -4],\n [-12, -12, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, 0, -2],\n [-8, 0, 0, -4],\n [6, 0, 0, 3],\n [-6, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -11, -25, 13],\n [3, 5, 11, -5],\n [-3, -1, -1, -2],\n [-3, 3, 9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 8, 8],\n [-1, 1, -2, -2],\n [-2, 2, -4, -4],\n [4, -4, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -1, -16, -9],\n [16, -11, 8, 7],\n [0, -8, 20, 12],\n [19, -12, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 0, 0, 12],\n [-8, 0, 0, 16],\n [4, 0, 0, -8],\n [-8, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 2, 6, 4],\n [10, -7, 0, 4],\n [-6, 3, 2, 0],\n [-22, 13, 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[[12, 10, -13, -3],\n [-9, -12, 12, 9],\n [9, 18, -15, -18],\n [6, 14, -11, -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[[-1, -2, 9, 2],\n [-2, -2, -3, -10],\n [-2, 3, -10, -17],\n [-4, -16, 3, -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 4x4 matrix:\n[[2, -2, -8, 2],\n [1, -1, -4, 1],\n [-2, 2, 8, -2],\n [4, -4, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -4, 1, -1],\n [6, -18, 3, -5],\n [10, -22, 1, -7],\n [-8, 20, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, -2, 0],\n [4, -2, -2, 2],\n [4, -5, -8, 5],\n [12, 0, 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[[6, -19, 14, -11],\n [2, -14, 15, -14],\n [0, 24, 4, -4],\n [-12, 8, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 8, -6, -6],\n [-16, 16, -12, -12],\n [0, 0, 0, 0],\n [-16, 16, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 1, 2, -3],\n [-1, -1, -2, 3],\n [-3, -3, -6, 9],\n [-4, -4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, -16, 9],\n [14, -10, 0, -11],\n [4, -4, -4, -3],\n [-3, 6, 8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -18, -4, -8],\n [-12, 12, 28, 32],\n [0, 16, 12, 16],\n [-12, -12, 10, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -9, 0, 12],\n [2, 6, 0, -8],\n [2, 6, 0, -8],\n [-4, -12, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 3, -20, 1],\n [-12, -5, -4, -11],\n [1, 1, 12, 5],\n [-1, -1, -12, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 9, -24, -12],\n [17, 1, 8, -12],\n [0, 5, -20, -11],\n [-1, 4, 28, 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 4x4 matrix:\n[[16, 0, -4, -24],\n [3, -15, -7, 3],\n [8, 0, -2, -12],\n [2, -6, -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[[-6, 6, 3, 6],\n [-6, 6, 3, 6],\n [0, 0, 0, 0],\n [-4, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -9, 2, 7],\n [-12, 21, 13, 2],\n [40, 7, 15, 26],\n [15, 19, 14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 1, -4, -1],\n [3, 1, -4, -1],\n [-12, -4, 16, 4],\n [12, 4, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 5, 12, -3],\n [-2, -13, -4, -14],\n [-19, -3, -8, 4],\n [4, 10, 28, -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 4x4 matrix:\n[[-12, -6, 4, -2],\n [-9, -3, 4, -1],\n [3, -9, -8, -3],\n [-6, 12, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 8, 4, 16],\n [-9, 6, 3, 12],\n [6, -4, -2, -8],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -9, 12, 3],\n [-4, -6, 8, 2],\n [8, 12, -16, -4],\n [2, 3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 8, -12, 4],\n [-4, 8, -12, 4],\n [1, -2, 3, -1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 10, -14, -6],\n [-18, 12, -3, -6],\n [22, 2, -13, 6],\n [0, 18, -18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -1, 0, -3],\n [6, 3, 0, 9],\n [6, 3, 0, 9],\n [4, 2, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, 8, 26, -20],\n [-9, 9, -2, -2],\n [9, -12, -2, 14],\n [13, -1, -14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 8, -6, 2],\n [-21, -1, -1, 5],\n [11, -29, 23, -11],\n [-25, 2, -3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 0, -12, 4],\n [-8, 0, 6, -2],\n [12, 0, -9, 3],\n [-8, 0, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, -6, -3],\n [0, 0, -4, -2],\n [0, 0, -8, -4],\n [0, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -6, -8, -14],\n [18, 6, 16, 6],\n [-11, 0, 4, 8],\n [15, 1, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 12, 6, -9],\n [-15, -18, -10, 17],\n [9, 12, 6, -9],\n [21, 25, 14, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, 0, 4],\n [0, 4, 0, -4],\n [0, 2, 0, -2],\n [0, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, 8, -7, 22],\n [-7, -4, -12, 12],\n [2, 0, 8, -8],\n [31, 12, 1, 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[[1, 0, -1, 9],\n [-13, 9, 13, 0],\n [-5, 4, 5, 7],\n [-2, 0, 2, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 5, -12, -14],\n [-12, -19, 25, 17],\n [13, 16, -17, -9],\n [-2, 6, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 4, -3, -2],\n [-2, -15, -3, 5],\n [-2, -8, 7, -6],\n [0, -3, -7, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -2, -6, 4],\n [-8, -4, -2, 0],\n [-4, -12, -16, 8],\n [-14, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -3, 6, -3],\n [-19, -3, -13, 11],\n [-2, -8, 3, 3],\n [-17, 2, -13, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -3, 12, -12],\n [-2, -1, 4, -4],\n [-2, -1, 4, -4],\n [4, 2, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 4, -14, 8],\n [-4, 10, -3, 4],\n [-4, -18, 9, -4],\n [-20, -3, -11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 20, -14, -14],\n [2, 12, -6, -6],\n [17, 16, 9, 9],\n [4, 8, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -8, 8, -4],\n [0, -2, 2, -1],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 6, 4, 0],\n [-6, -9, -6, 0],\n [8, 12, 8, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 0, 1, 4],\n [-21, 11, 4, -6],\n [9, -5, -2, 2],\n [-6, 0, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -3, 4, -1],\n [6, 9, -12, 3],\n [8, 12, -16, 4],\n [-4, -6, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -4, 16, -4],\n [-8, -4, 16, -4],\n [-4, -2, 8, -2],\n [-8, -4, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 6, 18, 12],\n [-8, 12, 12, 24],\n [4, 2, -14, 4],\n [4, -2, -10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 12, -9, -6],\n [6, -12, 9, 6],\n [-4, 8, -6, -4],\n [-4, 8, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 6, -5, 3],\n [0, 6, 1, 3],\n [0, 14, -1, 7],\n [0, 2, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -2, 13, -3],\n [9, -1, -16, -6],\n [9, 7, -8, 18],\n [-9, -3, 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 4x4 matrix:\n[[12, -5, -10, 0],\n [6, 8, 16, 14],\n [-6, -5, -10, -10],\n [18, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, -4, -12],\n [0, 4, -20, 24],\n [0, -3, 9, 6],\n [0, 0, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 3, -1, 4],\n [18, 15, -9, 12],\n [0, 4, 4, 16],\n [-3, -3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 6, -2, 11],\n [0, 22, -2, 16],\n [-8, -8, 14, -12],\n [4, 5, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -12, -16, 12],\n [2, -3, -4, 3],\n [-4, 6, 8, -6],\n [4, -6, -8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 8, -12, -16],\n [-1, -4, 2, -3],\n [10, 20, -14, 4],\n [-1, 6, -1, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, -2, 4],\n [0, 4, 2, -4],\n [0, 0, 0, 0],\n [0, -8, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -12, 12, -16],\n [6, -9, 9, -12],\n [8, -12, 12, -16],\n [-2, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -12, -13, -29],\n [6, -10, -6, 4],\n [3, 12, 5, 19],\n [-5, 6, 8, 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[[-1, -11, -28, -15],\n [-2, -4, 0, -4],\n [7, 7, 16, 10],\n [11, -11, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 10, 24, 10],\n [-1, 5, 8, 15],\n [1, 1, 4, -3],\n [2, 4, 12, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -7, 4, 3],\n [-3, 6, -1, 12],\n [0, 2, 0, 6],\n [9, -9, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 13, 12, 8],\n [4, 7, -12, 2],\n [-1, 11, 20, 8],\n [0, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 3, -4, 8],\n [12, -4, 16, 0],\n [15, 2, 4, 12],\n [-8, 12, -32, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 16, 4, 4],\n [-3, 4, 1, 1],\n [-6, -12, 12, -3],\n [9, -12, -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[[0, -21, -15, 3],\n [0, -4, -14, -14],\n [0, -2, 6, 10],\n [0, -12, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 0, -18, 0],\n [-16, 9, -18, 3],\n [12, -12, 16, -4],\n [-18, -3, -14, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -4, -1, 2],\n [12, 16, 4, -8],\n [12, 16, 4, -8],\n [-6, -8, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -4, 2, -15],\n [-5, 9, 6, -17],\n [-7, 10, 5, -23],\n [1, 28, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -19, 11, 4],\n [0, -2, 9, -4],\n [-4, -12, 11, 6],\n [-20, -15, 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[[16, 6, -8, 16],\n [-8, 4, 4, 6],\n [-8, -2, 4, -6],\n [12, 8, -6, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -4, -11, 15],\n [0, -28, 0, -4],\n [13, 0, -31, 17],\n [-7, 6, 21, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 6, 6, 12],\n [0, 0, 0, 0],\n [-16, 8, 8, 16],\n [4, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 20, 4, -4],\n [2, 16, 2, -8],\n [1, 8, 1, -4],\n [12, 5, -2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 9, -6, -6],\n [6, -6, 8, 2],\n [6, -6, 4, 4],\n [6, -6, 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[[16, -4, -16, 16],\n [-12, 3, 12, -12],\n [0, 0, 0, 0],\n [-4, 1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 13, -18, 1],\n [4, 14, -23, -7],\n [8, 23, -21, -17],\n [8, 3, -11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 0, -4, 3],\n [-16, 7, -6, 15],\n [-6, 0, -4, 3],\n [-12, 3, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 4, -16, -16],\n [0, 1, -4, -4],\n [0, 3, -12, -12],\n [0, -3, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 13, 19, 5],\n [8, 4, 28, 8],\n [-1, 4, 4, 1],\n [5, 7, 25, 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 4x4 matrix:\n[[-12, -12, 9, 9],\n [-4, -4, 3, 3],\n [-12, -12, 9, 9],\n [-12, -12, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 0, 2, 2],\n [-1, 8, 6, -10],\n [-5, -2, 2, 6],\n [5, 2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 2, -1, 3],\n [0, 0, 0, 0],\n [4, -8, 4, -12],\n [-1, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -1, 3, 25],\n [-14, 3, 4, 16],\n [8, -4, 0, 16],\n [-22, 7, 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[[21, -16, -23, 25],\n [12, -7, 4, 0],\n [-8, 0, 9, -14],\n [19, -14, -10, 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[[-2, -1, -1, -3],\n [-9, -12, 18, -11],\n [-6, -3, -3, -9],\n [-7, -11, 19, -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 4x4 matrix:\n[[12, 20, 32, 20],\n [-13, -3, -8, -7],\n [8, -10, -12, -5],\n [18, 2, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -1, 4, 0],\n [0, -4, 16, 0],\n [0, -2, 8, 0],\n [0, -2, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 8, 5, 7],\n [4, -12, 0, -5],\n [0, 10, -2, 4],\n [10, -15, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 6, -4, 3],\n [-8, 8, -12, -11],\n [24, -24, 28, 15],\n [-7, 7, -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[[-15, -12, -18, -6],\n [-3, 1, -8, 11],\n [2, -4, 4, -8],\n [-10, -6, -4, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-9, 6, -6, -12],\n [-12, 8, -8, -16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 2, 2, -6],\n [-8, -2, -2, 6],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -6, -13, -1],\n [22, -6, -11, 4],\n [10, 4, -10, -2],\n [-24, 0, 16, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-12, 8, -8, -4],\n [-6, 4, -4, -2],\n [6, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, -4, 8],\n [-24, -16, 0, 6],\n [2, 30, -19, -22],\n [-5, -6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -22, 22, -2],\n [-6, -11, 11, 2],\n [-9, 4, -5, 5],\n [-4, 8, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -4, -24, -8],\n [7, -7, -12, -4],\n [-16, -24, 6, 22],\n [2, 3, 23, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [2, 4, -4, 8],\n [-1, -2, 2, -4],\n [1, 2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, -4, -6],\n [4, 0, 4, 6],\n [-2, 0, -2, -3],\n [-2, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 4, 3, 11],\n [-4, 8, -7, 6],\n [-19, 16, -27, -3],\n [-6, 16, -9, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 4, -5, -2],\n [-19, -1, 10, 18],\n [-16, -4, 12, 16],\n [17, -7, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, 6, -6],\n [2, 0, -6, 6],\n [-4, 0, 12, -12],\n [1, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -10, -9, -3],\n [-4, 1, 1, 14],\n [4, 14, 11, 1],\n [3, -3, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -4, -4, 0],\n [4, -8, -6, 1],\n [16, -18, -10, 4],\n [-8, 8, 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[[-8, -5, -7, 2],\n [-19, 3, 11, 9],\n [10, -6, -14, -6],\n [9, 3, 3, -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 4x4 matrix:\n[[-4, -1, 0, -1],\n [0, 3, -4, 2],\n [8, -1, 4, 0],\n [8, 5, -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[[-8, 8, -2, -12],\n [8, -1, -5, -2],\n [12, -8, -1, 10],\n [16, -8, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, 13, -6],\n [10, 3, 10, -13],\n [-26, -3, 2, 17],\n [6, -3, -17, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 8, -12, -10],\n [5, 16, -3, 8],\n [-3, 12, -9, -3],\n [4, 8, 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[[-8, 0, 0, 12],\n [-8, 0, 0, 12],\n [6, 0, 0, -9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -6, -14, -9],\n [10, -4, 4, 6],\n [-19, 5, -10, -12],\n [-2, -7, -8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, 8, -17, -15],\n [-6, 10, -15, 14],\n [-9, -2, 8, 1],\n [10, -2, 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 4x4 matrix:\n[[0, 2, -4, 6],\n [0, -2, 4, -6],\n [0, -2, 4, -6],\n [0, 4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -8, 6, 7],\n [0, 24, 18, 2],\n [13, -32, -4, 7],\n [-1, -4, -1, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -14, 12, -9],\n [-12, 10, 0, 1],\n [-4, 18, -12, 6],\n [-1, 5, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 6, 8, -6],\n [-1, -2, -7, -11],\n [0, -2, -6, -8],\n [0, 2, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 12, -5, 10],\n [4, 4, -5, 5],\n [0, 12, -9, 12],\n [0, 12, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [6, 0, 3, -3],\n [8, 0, 4, -4],\n [-2, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 12, -10, -10],\n [-9, 0, -8, -8],\n [-13, -8, -16, -16],\n [22, 7, 24, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, -6, 20],\n [-15, 9, -8, -14],\n [0, -1, -3, 6],\n [21, -2, 3, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -20, 4, -8],\n [0, 0, 0, 0],\n [1, 4, 0, 1],\n [-1, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, 0, 2],\n [0, 2, 0, 2],\n [0, 4, 0, 4],\n [0, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -2, 3, 8],\n [4, -24, -10, 16],\n [-4, 22, 3, -12],\n [6, 3, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 0, 9, 0],\n [2, 6, -12, 12],\n [-11, -14, 9, -28],\n [4, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 3, 22, -1],\n [0, -17, 2, 19],\n [-16, 4, -16, -4],\n [-13, -19, -7, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[26, -7, -7, -2],\n [-4, 5, 14, -20],\n [12, 13, 2, -15],\n [0, 16, 8, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 6, 3, 12],\n [-12, 8, 4, 16],\n [-6, 4, 2, 8],\n [-6, 4, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 20, -4, 20],\n [-11, -9, 9, -1],\n [-14, -18, 8, -11],\n [2, 12, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -18, -12, 18],\n [1, -5, -8, 18],\n [-5, 1, 16, -6],\n [3, 25, 16, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 10, 19, -12],\n [7, 7, -10, 25],\n [9, 0, -13, 18],\n [-7, -1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, 10, 7, 0],\n [-1, 16, 1, -10],\n [-4, -14, -14, 2],\n [2, -17, -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[[0, 0, 0, 0],\n [-12, -12, 4, -4],\n [9, 9, -3, 3],\n [3, 3, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 0, -8, -16],\n [-2, 15, -28, 4],\n [9, -1, 12, 20],\n [-9, 1, -12, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -8, -5, -10],\n [1, 10, 8, 4],\n [2, -1, -5, 5],\n [0, 7, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -8, -4, 8],\n [-2, -4, -2, 4],\n [2, 4, 2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -6, 9, -7],\n [-8, -6, 8, 2],\n [0, 0, -1, 7],\n [0, -3, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 4, 2, -3],\n [0, 0, 0, 0],\n [-3, 12, 6, -9],\n [1, -4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 5, -3, -3],\n [18, -1, -21, 15],\n [7, 1, -9, 5],\n [8, -6, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -4, -2, 4],\n [-6, -8, 4, 6],\n [12, 4, 2, -4],\n [-9, -6, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, 10, -5, -6],\n [6, 10, 9, -1],\n [-19, -2, -19, 8],\n [-17, 6, -11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -4, 2, -2],\n [2, 4, -2, 2],\n [4, 8, -4, 4],\n [4, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -9, 3, 9],\n [4, 12, -4, -12],\n [0, 0, 0, 0],\n [3, 9, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -16, 16, 6],\n [44, 0, 5, -4],\n [-28, 12, -8, 16],\n [12, 8, -9, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -6, -2, -16],\n [4, 9, -5, 12],\n [20, 12, -14, 5],\n [-28, -9, 17, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 9, 6, 3],\n [-4, 12, 8, 4],\n [4, -12, -8, -4],\n [-1, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -20, -20, -10],\n [-21, 21, 19, -3],\n [-4, 4, 4, -1],\n [2, -12, -15, -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 4x4 matrix:\n[[6, 0, -4, 10],\n [6, 20, -18, 16],\n [-9, -2, -7, -18],\n [-12, 12, 32, -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[[8, -8, -20, 8],\n [-3, 3, -15, -8],\n [-16, 16, 4, -24],\n [-7, 7, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 9, 6, 9],\n [11, 9, 8, -23],\n [-4, 10, 3, 2],\n [10, 16, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 12, 6, 12],\n [-16, -16, -8, -16],\n [12, 12, 6, 12],\n [4, 4, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -5, -7, -5],\n [14, -11, -9, -11],\n [0, 0, -6, 2],\n [22, -25, -18, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, -1, 2],\n [0, -8, -2, 4],\n [0, -8, -2, 4],\n [0, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, 7, 10, 2],\n [1, -1, -1, -2],\n [-10, -6, 10, -8],\n [9, 7, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, 9, -6],\n [2, -2, -3, 2],\n [-8, 8, 12, -8],\n [4, -4, -6, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 3, 4, -4],\n [3, 3, 4, -4],\n [-3, -3, -4, 4],\n [3, 3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -3, 0, -6],\n [-4, 1, 0, 2],\n [-12, 3, 0, 6],\n [16, -4, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 0, -6, 3],\n [-5, 2, 10, -5],\n [2, 7, -4, 2],\n [-6, -3, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -2, 6, 4],\n [3, 3, -9, -6],\n [2, 2, -6, -4],\n [3, 3, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 2, 9, 2],\n [-4, 3, 6, -8],\n [7, -4, -6, 16],\n [-1, 4, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, -20, 15, -28],\n [-13, -14, -1, -16],\n [23, 19, 1, 24],\n [19, 17, -7, 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 4x4 matrix:\n[[2, 16, 16, -7],\n [8, -4, 24, -16],\n [-4, -4, -32, 12],\n [5, 23, -12, -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[[0, -2, 4, -9],\n [-16, -6, -16, 5],\n [0, 0, 4, -8],\n [-8, -8, -1, -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[[14, 1, -4, -4],\n [-2, -23, 4, 4],\n [15, -3, -3, -3],\n [8, 20, -16, -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[[-12, -9, -11, -5],\n [-8, 4, -28, 3],\n [12, 18, -1, 14],\n [16, 7, 26, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -9, 6, 3],\n [-14, -7, 11, 12],\n [-2, 4, 0, 4],\n [-11, -3, 3, 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[[16, 20, -13, 7],\n [-2, 10, -12, -10],\n [6, -13, 16, 8],\n [-2, 0, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -2, -33, -12],\n [0, -13, -15, -15],\n [11, -1, -22, -14],\n [31, 9, -2, -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[[6, -2, -4, 4],\n [3, -1, -2, 2],\n [-3, 1, 2, -2],\n [-3, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -6, 0, 6],\n [8, -4, 12, 16],\n [-10, 11, 3, -8],\n [-8, 7, -3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -6, -22, -20],\n [0, 6, -10, -4],\n [4, 0, 16, 12],\n [4, 9, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -6, -1, 14],\n [8, 7, 2, -15],\n [4, 0, 1, -2],\n [20, -5, -12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 6, -4, 2],\n [0, 3, -2, 1],\n [0, 0, 0, 0],\n [0, 6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 6, 0, -26],\n [10, 1, -2, -25],\n [9, -11, -15, -6],\n [-5, 4, 0, 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[[8, -16, -6, 16],\n [8, -23, 0, 17],\n [10, -3, -12, 9],\n [-6, 6, 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 4x4 matrix:\n[[8, 0, 0, -13],\n [10, -11, -11, -19],\n [-4, 10, 10, 9],\n [-8, 4, 4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[17, 0, 7, 3],\n [7, -5, 21, -8],\n [-12, 3, -12, 3],\n [16, -2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 12, 0, 9],\n [-6, -4, 0, -3],\n [15, 10, 12, 15],\n [3, 2, 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[[-12, 12, 0, -3],\n [0, 0, 0, 0],\n [-12, 12, 0, -3],\n [4, -4, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 3, -4, 3],\n [4, 12, -16, 12],\n [-2, -6, 8, -6],\n [1, 3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -8, -8, -16],\n [15, -13, -16, -17],\n [15, -14, -18, -16],\n [-3, 2, 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[[6, 9, 12, 6],\n [0, 0, 0, 0],\n [0, 4, 0, -16],\n [2, 0, 4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, 14, 10, -4],\n [12, -9, -6, 0],\n [20, -20, -16, 16],\n [6, -7, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -2, -3, 1],\n [-2, 2, 3, -1],\n [6, -6, -9, 3],\n [-2, 2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 4, -8, 0],\n [-12, -8, 16, 0],\n [9, 6, -12, 0],\n [3, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, 8, -6],\n [8, -2, 4, -6],\n [2, -4, -20, 9],\n [4, -4, -16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -5, 2, 5],\n [5, 0, 7, -10],\n [21, 12, -9, -6],\n [-8, -1, -8, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -2, 1, 3],\n [8, -5, -3, -9],\n [-20, 11, 7, 21],\n [-6, 3, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 5, 5, -9],\n [4, -12, 12, 0],\n [0, -2, 4, -4],\n [7, -3, -15, 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 4x4 matrix:\n[[0, -2, 8, 4],\n [-8, 6, 20, -8],\n [2, -2, -3, 3],\n [-2, 2, 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[[8, 10, 0, 10],\n [-13, -17, -9, -8],\n [-6, -8, -6, -2],\n [11, 14, 3, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -4, -2, -3],\n [4, -8, -4, -6],\n [4, -8, -4, -6],\n [-2, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-18, 4, 16, 12],\n [-4, 24, 20, 8],\n [-1, -2, -3, -4],\n [-14, 12, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -2, -3, 4],\n [0, 4, 6, -8],\n [0, 0, 0, 0],\n [0, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -3, 6, -3],\n [-16, 23, -4, -5],\n [-6, -6, -3, 6],\n [-6, 15, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-6, 4, 8, -8],\n [3, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 10, -1, -16],\n [8, -2, 17, 8],\n [-8, 2, -17, -8],\n [8, 8, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 12, 4, 2],\n [-4, 2, -1, -5],\n [1, 9, 8, 0],\n [-1, 20, 15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 4, -4, 0],\n [6, -6, 6, 0],\n [-2, 2, -2, 0],\n [-6, 6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 3, -6, -4],\n [22, 15, 0, 4],\n [-16, -32, -12, -16],\n [0, 24, 44, 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[[-4, -12, -16, -16],\n [4, 12, 16, 16],\n [-1, -3, -4, -4],\n [2, 6, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 4, -4, -6],\n [6, 6, -6, -9],\n [-8, -8, 8, 12],\n [6, 6, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -2, 6, -2],\n [0, 1, -3, 1],\n [0, 1, -3, 1],\n [0, -4, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -16, 0, 4],\n [-2, -8, 8, -9],\n [-10, 17, 2, -7],\n [4, -8, 0, 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 4x4 matrix:\n[[-4, 2, 1, -4],\n [12, -6, -3, 12],\n [12, -6, -3, 12],\n [12, -6, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, -16, 32],\n [6, 0, -4, 8],\n [-12, 0, 8, -16],\n [-15, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -3, 3, -20],\n [-4, -14, -12, -9],\n [6, 17, 15, 8],\n [2, 16, 6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 12, -6, -6],\n [0, -4, 2, 2],\n [0, 12, -6, -6],\n [0, 12, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, -8, -7, 7],\n [-23, 6, 5, -5],\n [13, 13, 9, -18],\n [-4, 1, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-21, 5, -14, -18],\n [3, -19, 6, 2],\n [-6, 17, -5, 17],\n [6, 27, -3, -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[[7, 7, -6, 3],\n [-6, -6, 13, -1],\n [11, 11, -13, 4],\n [-3, -3, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -4, 0, -8],\n [12, -4, -14, -1],\n [-8, 2, 8, 0],\n [4, -8, -18, -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, 8, 12, 4],\n [-2, -1, 4, 5],\n [-1, -5, -13, -8],\n [2, 1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 4, 4, 4],\n [0, -4, -4, -4],\n [0, -6, -6, -6],\n [0, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 3, -6, -18],\n [-8, 2, 9, 1],\n [16, -4, -3, 13],\n [-12, 3, -12, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 6, -8, 2],\n [0, -6, 3, -12],\n [-2, 9, -7, 13],\n [8, -2, 11, 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[[-1, 2, -2, -2],\n [7, -13, 15, 10],\n [-1, 3, -1, 0],\n [0, -18, -18, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 12, 12, 12],\n [2, -8, -8, -8],\n [2, -8, -8, -8],\n [-3, 12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 9, -1, -5],\n [-13, -3, -3, 9],\n [13, -8, 10, -8],\n [17, 5, 1, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 12, -5, 5],\n [5, 6, -4, 0],\n [4, 0, -5, 6],\n [-10, 4, 5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 11, 13, 21],\n [16, 11, 10, -6],\n [13, 13, 5, -3],\n [7, 12, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, 7, 8, -11],\n [1, -5, 2, -14],\n [-8, 0, -6, 17],\n [-28, -20, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, -8, 8],\n [-8, 8, 8, -8],\n [-2, 2, 2, -2],\n [-2, 2, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 7, 5, -4],\n [8, 16, 4, -6],\n [-11, 0, -2, 11],\n [22, 19, 15, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 3, -4, 3],\n [-18, 20, -7, 2],\n [-2, 1, -16, 9],\n [-1, 5, -14, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 2, 16, 3],\n [0, -6, 24, 3],\n [6, 14, -20, -1],\n [0, -8, 32, 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, 0, 0, 0],\n [8, -12, -16, -8],\n [0, 0, 0, 0],\n [-4, 6, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 8, 2, 4],\n [16, 16, 4, 8],\n [16, 16, 4, 8],\n [16, 16, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 6, 9, -9],\n [2, 4, 6, -6],\n [-3, -6, -9, 9],\n [3, 6, 9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 8, 18, -28],\n [11, -17, 28, -25],\n [-7, 9, -16, 15],\n [9, -7, -4, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -8, -11, -5],\n [4, 12, 12, 12],\n [-2, -2, -5, 1],\n [6, 6, 15, -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 4x4 matrix:\n[[-4, -3, -1, 0],\n [-12, -9, -3, 0],\n [8, 6, 2, 0],\n [4, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 2, -4, -7],\n [-10, -4, 16, -1],\n [-5, 0, 4, 15],\n [5, 7, -8, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -12, 18, -9],\n [-12, -6, -6, 9],\n [-8, -6, 4, 0],\n [8, 10, -20, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 6, 6, -10],\n [-4, -8, 4, 4],\n [-8, 11, 8, -16],\n [14, -8, -14, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -3, 3, 6],\n [0, 3, -3, -6],\n [0, 3, -3, -6],\n [0, 4, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[30, -16, 28, -6],\n [0, 9, 0, -11],\n [14, -6, 14, -2],\n [14, -20, 10, 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 4x4 matrix:\n[[-6, -12, -6, -3],\n [34, 20, 6, 11],\n [10, -13, -6, 2],\n [2, -19, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -6, 9, 3],\n [-9, 6, -9, -3],\n [6, -4, 6, 2],\n [3, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 12, 8, -4],\n [-12, 12, 8, -4],\n [9, -9, -6, 3],\n [-6, 6, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 8, -12, 16],\n [-12, 6, -9, 12],\n [12, -6, 9, -12],\n [-4, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -15, 0, 9],\n [13, -1, -19, -7],\n [9, -13, -7, 5],\n [3, -1, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 0, 6, -2],\n [8, 8, 12, -12],\n [8, 4, 12, -8],\n [-2, -6, -3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -16, -12, 8],\n [10, -2, 16, -24],\n [-9, -1, -20, 28],\n [14, -14, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -10, -5, 6],\n [6, -3, 6, 9],\n [2, 10, 2, -6],\n [11, 4, 11, 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[[0, -6, 1, 4],\n [-12, 12, -8, 4],\n [-2, -6, 0, 6],\n [-4, -12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 8, -8, 6],\n [-4, 8, -8, 6],\n [4, -8, 8, -6],\n [6, -12, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -6, 12, -9],\n [1, 2, -4, 3],\n [3, 6, -12, 9],\n [3, 6, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, 0, 0],\n [-3, -3, 0, 0],\n [3, 3, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 7, 6, -1],\n [-13, 13, 10, 5],\n [1, -1, 6, 4],\n [22, -22, 10, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -4, 8, -4],\n [-4, -8, -5, 1],\n [-4, 2, 10, -4],\n [20, 12, -17, 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[[-7, 1, 2, -2],\n [6, 2, -6, 16],\n [10, -2, -2, 0],\n [4, 0, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -12, -12, 1],\n [-7, -16, -16, 6],\n [-6, -16, -16, 8],\n [-8, -16, -16, 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 4x4 matrix:\n[[1, -15, -4, -5],\n [1, 7, 4, -3],\n [28, -25, 28, -15],\n [-18, -4, -24, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, 0, -25, -12],\n [-19, -1, 19, 17],\n [8, -4, 6, -16],\n [22, 4, -31, -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[[3, 0, -6, -12],\n [-3, 4, 5, 13],\n [0, 16, -4, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 0, -16, -7],\n [-2, 13, -2, 6],\n [-7, 14, -2, 10],\n [6, -7, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, 12, -12, 18],\n [12, 12, -12, 16],\n [14, 10, -10, 16],\n [20, 16, -16, 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 4x4 matrix:\n[[-6, -9, 3, 9],\n [-2, -4, 1, 7],\n [-2, -1, 1, -5],\n [-4, -5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, -9, -6],\n [-2, 7, 17, 5],\n [-21, 10, 4, -9],\n [11, -7, -6, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 9, -9, -9],\n [5, -7, -1, 7],\n [20, -28, -4, 28],\n [10, -14, -2, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 2, 2, -1],\n [3, -6, 0, 0],\n [4, -8, 2, -1],\n [-1, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -6, 2, 0],\n [3, -9, 3, 0],\n [4, -12, 4, 0],\n [-4, 12, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 0, -9, -3],\n [4, 0, -12, -4],\n [-2, 0, 6, 2],\n [1, 0, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -12, -4, 4],\n [-1, 3, 1, -1],\n [-4, 12, 4, -4],\n [4, -12, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -8, 8, -7],\n [0, -6, 6, 6],\n [5, 17, -17, -2],\n [4, 16, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 15, -18, 14],\n [-12, -7, 2, -6],\n [0, -8, 10, -16],\n [7, 6, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -12, -8, -3],\n [-12, -8, -10, -2],\n [2, -4, -3, -1],\n [4, -24, -20, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-8, -16, 4, -16],\n [0, 0, 0, 0],\n [4, 8, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -1, -3, -3],\n [-16, 16, -12, 8],\n [4, -3, 3, -1],\n [-16, 10, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [8, 4, -12, 4],\n [4, 2, -6, 2],\n [2, 1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -9, -6, 6],\n [1, 3, 2, -2],\n [3, 9, 6, -6],\n [4, 12, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 17, 2, -2],\n [5, -6, 3, 2],\n [3, 3, -6, 8],\n [-2, 2, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -10, -18, 1],\n [-12, 18, -10, 19],\n [6, -23, -9, -13],\n [4, 11, 11, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-2, -6, 6, 6],\n [-3, -9, 9, 9],\n [3, 9, -9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -1, 8, 6],\n [-2, 0, 3, 1],\n [3, 0, -1, 3],\n [2, 0, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -2, 4, 2],\n [-3, 4, -2, 0],\n [1, 0, 6, 4],\n [6, -6, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -6, -14, -2],\n [4, 0, 0, -28],\n [4, -9, 14, -10],\n [-2, 1, -6, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -8, -2, 0],\n [-6, 9, -9, 9],\n [3, -3, -12, 9],\n [11, -15, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 6, -14, -4],\n [-4, -3, -9, -6],\n [-12, -9, -7, -8],\n [12, 9, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 4, -3, 0],\n [0, 0, 0, 0],\n [16, -16, 12, 0],\n [8, -8, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, 7, 9, 0],\n [12, 2, 6, 0],\n [3, 2, 6, 0],\n [15, 4, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 12, -18, 4],\n [-3, 3, -6, 1],\n [-6, 6, -11, 2],\n [9, -9, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -2, 1, 0],\n [-14, -4, -2, 0],\n [-19, -8, -7, 0],\n [-2, -4, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 12, 12, -4],\n [0, 0, 0, 0],\n [4, 6, 6, -2],\n [2, 3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -12, 12, 6],\n [12, 16, -16, -8],\n [6, 8, -8, -4],\n [-12, -16, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -2, 4, 8],\n [-3, -1, 2, 4],\n [-3, -1, 2, 4],\n [-6, -2, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -2, -4, 0],\n [3, 1, 2, 0],\n [-3, -1, -2, 0],\n [-3, -1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 9, -3, 6],\n [4, 6, -2, 4],\n [-4, -6, 2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -13, 18, 4],\n [-10, -5, 4, -18],\n [0, 5, -2, 10],\n [-4, 1, -6, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -9, 3, -9],\n [9, -21, 3, 3],\n [-10, 24, -4, 0],\n [-2, 6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, -4, -12],\n [9, 0, -3, -9],\n [0, 0, 0, 0],\n [-3, 0, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, 2, 0],\n [1, -1, 1, 0],\n [-2, 2, -2, 0],\n [1, -1, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 12, -8, 16],\n [0, -9, 6, -12],\n [0, -3, 2, -4],\n [0, 12, -8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-28, 11, 19, -4],\n [-16, 6, 10, -2],\n [12, -3, -3, 0],\n [20, -9, -17, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 6, 6, -13],\n [-12, 6, 9, -9],\n [0, 8, 0, 12],\n [20, -8, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 4, 8, 0],\n [16, 2, 17, -22],\n [-8, -7, 1, 18],\n [4, -3, -1, -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 4x4 matrix:\n[[0, -4, 4, -1],\n [-2, -16, 16, -5],\n [-2, -8, 8, -3],\n [8, -12, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 10, 13, 7],\n [-3, -3, -12, -12],\n [14, -10, -4, 4],\n [-11, 7, 1, -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[[-8, -11, -1, -2],\n [8, 8, 2, 0],\n [-12, -18, -1, -4],\n [0, -9, 3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 3, 12, -9],\n [-12, -4, -16, 12],\n [0, 0, 0, 0],\n [-3, -1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -7, -1, 0],\n [-4, 0, 6, 0],\n [-3, 11, -1, 0],\n [-3, 15, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -11, 3, 3],\n [12, 9, 9, 3],\n [-14, 2, -12, -6],\n [18, 1, 15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [1, -1, 3, 4],\n [2, -2, 6, 8],\n [2, -2, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 0, -9, -9],\n [0, 0, 0, 0],\n [8, 0, -6, -6],\n [8, 0, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -2, 0, -8],\n [1, 13, -20, -8],\n [-2, -8, 12, 4],\n [-16, -10, 12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -12, 27, 12],\n [10, 12, -6, 4],\n [8, 8, 2, 22],\n [5, 4, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -29, -13, -30],\n [-6, -14, -8, -14],\n [4, -4, 4, 0],\n [-12, 4, 0, -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[[15, -12, -30, 12],\n [33, -21, -6, 22],\n [-10, 5, 28, -9],\n [21, -15, -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 4x4 matrix:\n[[1, 0, -6, 12],\n [4, -6, 9, -12],\n [9, -12, 12, -12],\n [17, -20, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 6, -9, 12],\n [-9, -6, 9, -12],\n [9, 6, -9, 12],\n [9, 6, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, -4, -6],\n [3, -3, -6, -9],\n [2, -2, -4, -6],\n [-4, 4, 8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 6, -3, 6],\n [4, -2, 1, -2],\n [16, -8, 4, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 8, -4, -18],\n [-3, 4, -4, -2],\n [-1, -2, 0, 8],\n [12, -16, 16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -16, -12, -16],\n [2, 4, 3, 4],\n [4, 8, 6, 8],\n [2, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -2, -19, 9],\n [-3, 1, -5, 1],\n [-3, 15, 8, -11],\n [-6, -4, -9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 2, 2, 10],\n [-1, 22, 7, 15],\n [-4, 20, 9, 9],\n [6, -3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 12, 4, 4],\n [-2, -6, 14, 8],\n [0, -8, 8, 4],\n [2, 0, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -5, -4, 1],\n [-18, -3, -2, -2],\n [8, 10, 12, -8],\n [16, -13, -1, -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, 2, 2, 28],\n [-1, -10, 7, -4],\n [-2, 12, -13, -8],\n [6, -12, 16, 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[[-4, -4, 2, 6],\n [4, 4, -2, -6],\n [-4, -4, 2, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 4, -5, -13],\n [-26, 3, -2, -13],\n [28, -4, 6, 18],\n [16, -18, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, -4, 8],\n [-6, 3, -6, 12],\n [8, -4, 8, -16],\n [-4, 7, -5, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 12, -12, -3],\n [3, 0, 15, 9],\n [0, 4, 16, 11],\n [0, -4, -16, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 4, -9, 0],\n [2, 20, 3, 0],\n [7, 4, -6, 0],\n [-1, 8, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 8, 8, 7],\n [2, 4, -12, 14],\n [4, -11, -4, -13],\n [-20, -16, 0, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -9, 8, -22],\n [-8, 14, 2, 17],\n [-16, 16, 0, 12],\n [2, 7, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [20, -3, -7, -11],\n [20, -3, -7, -11],\n [20, -7, -3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, -16, -16],\n [6, -3, -15, -24],\n [-8, 0, 20, 16],\n [-8, 4, 20, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, -4, 8],\n [-3, -15, -6, 0],\n [0, -1, 2, -4],\n [-3, -10, -16, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 10, -10, 8],\n [12, -4, -2, 4],\n [20, -12, 4, 0],\n [-2, -2, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 4, 0, -16],\n [-4, -1, 0, 4],\n [-8, -2, 0, 8],\n [16, 4, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 16, -12, -8],\n [4, -4, 3, 2],\n [4, -4, 3, 2],\n [4, -4, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 2, 3, -2],\n [0, -8, -12, 8],\n [0, -2, -3, 2],\n [0, -6, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -9, -1, 12],\n [14, -12, 10, -20],\n [12, 5, 13, 19],\n [21, -1, 19, -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 4x4 matrix:\n[[7, 13, 5, 11],\n [-16, -10, -2, -20],\n [-2, -12, -14, -10],\n [-1, -5, 15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -12, 6, -18],\n [4, -6, 6, -28],\n [2, -12, 25, 4],\n [2, 3, 5, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 2, 8, -6],\n [-3, 3, 12, -9],\n [2, -2, -8, 6],\n [2, -2, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -11, -11, -5],\n [5, -15, -28, -21],\n [5, 3, 4, 4],\n [0, 16, 22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 12, 9, 6],\n [-2, -4, -3, -2],\n [-8, -16, -12, -8],\n [-2, -4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -2, -9, 7],\n [-20, 7, -18, 12],\n [-8, -13, -6, 8],\n [-2, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 2, 2, -3],\n [-2, -4, -4, 6],\n [-3, -6, -6, 9],\n [4, 8, 8, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, 20, 0, 7],\n [8, 0, -20, 2],\n [4, 2, -3, 1],\n [16, 10, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 21, 7, -16],\n [12, -18, -10, 16],\n [0, -3, 3, 0],\n [9, -3, -18, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 30, 1, -26],\n [-14, -14, 0, 10],\n [-21, -7, -6, -1],\n [7, 0, -4, -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 4x4 matrix:\n[[-4, -13, 5, -13],\n [4, -11, -5, -5],\n [-2, 13, -3, 13],\n [-12, 17, 15, 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 4x4 matrix:\n[[4, 2, -6, -6],\n [-8, -4, 12, 12],\n [8, 4, -12, -12],\n [-4, -2, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, -17, 13, 2],\n [0, 5, -17, -8],\n [4, 2, 6, 4],\n [-1, -8, 24, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -4, 6, 2],\n [4, 8, -12, -4],\n [4, 8, -12, -4],\n [2, 4, -6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -2, 2, 2],\n [8, 2, -2, -2],\n [0, 0, 0, 0],\n [12, 3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -9, -10, -2],\n [-22, 3, -33, 20],\n [6, -1, 9, -8],\n [10, -3, 14, -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 4x4 matrix:\n[[2, 0, -2, 1],\n [8, 0, -8, 4],\n [8, 0, -8, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [3, -1, -3, 2],\n [-9, 3, 9, -6],\n [3, -1, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 8, 0, 6],\n [-2, -8, 0, -6],\n [2, 8, 0, -18],\n [0, 0, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 16, 12, -16],\n [12, -16, -12, 16],\n [0, 0, 0, 0],\n [-12, 16, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -19, -1, -3],\n [-2, 5, 0, 1],\n [8, -19, -1, -3],\n [0, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -5, 5, 5],\n [-4, 10, -20, -10],\n [-10, 1, 6, -1],\n [2, -2, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -9, 1, -12],\n [-2, 0, 5, 12],\n [1, 5, 9, 4],\n [-3, -1, -14, 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 4x4 matrix:\n[[2, 8, 6, -4],\n [3, 12, 9, -6],\n [-3, -12, -9, 6],\n [3, 12, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -6, 10, 4],\n [4, -7, 12, 6],\n [-11, -4, -9, -8],\n [8, 3, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-24, 1, -13, 0],\n [18, -7, -9, 5],\n [-8, -1, 13, -8],\n [3, -1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 7, -8, 16],\n [2, 7, -8, 16],\n [2, 7, -8, 16],\n [8, 8, -12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -8, -10, -20],\n [0, 4, -1, 2],\n [-4, -16, 10, 0],\n [2, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, -3, -3, 24],\n [-14, 16, 14, -37],\n [15, 11, 7, 17],\n [13, -13, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -9, 6, -9],\n [-4, 3, -2, 3],\n [-8, 6, -4, 6],\n [-16, 12, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 17, 9, -14],\n [28, -19, -11, 10],\n [-4, 1, 1, 2],\n [-4, 7, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 6, 8, -8],\n [8, 10, -24, 12],\n [-7, -9, 16, -7],\n [-3, -3, 24, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 10, 0, 10],\n [10, 0, -10, -10],\n [-8, 12, -4, 8],\n [-4, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 4, -4, 16],\n [-4, -2, 2, -8],\n [0, 0, 0, 0],\n [-8, -4, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -16, 8, 16],\n [-28, -8, -4, 32],\n [-12, -12, 6, 12],\n [13, 18, -11, -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[[-16, -10, 15, -10],\n [-8, -6, 9, -14],\n [-19, -10, 15, 5],\n [6, 2, -3, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, -5, 10, 21],\n [5, 2, 4, 3],\n [2, -14, -4, 14],\n [-7, 1, 0, -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[[-5, 23, -5, 7],\n [10, -9, 25, -15],\n [-6, 14, -14, 12],\n [2, 1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[34, 16, 18, -9],\n [6, -24, 2, 0],\n [-4, 20, -3, -3],\n [11, 4, 7, -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[[16, 26, -17, 27],\n [2, 0, 5, 14],\n [-12, -12, 19, -13],\n [-4, -20, 5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 3, -3, -3],\n [0, -12, 12, 12],\n [0, -6, 6, 6],\n [0, -12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 5, -38, -33],\n [-6, 4, -16, -12],\n [-8, 3, -14, -7],\n [0, -11, 14, 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[[6, 2, 6, -6],\n [-6, -14, 0, -6],\n [9, -1, 11, -13],\n [-6, -6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 8, -20, -12],\n [-10, 7, 1, -12],\n [-6, 4, 16, -4],\n [6, -16, 24, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -8, 8, -16],\n [-2, 14, 2, 0],\n [6, 6, -6, 12],\n [-2, 14, 2, 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[[-17, -4, -2, -10],\n [-17, -4, -2, -10],\n [-14, 0, 0, -8],\n [25, -4, -2, 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[[6, -8, -4, -6],\n [-8, 0, 8, 4],\n [-4, 0, 4, 2],\n [-3, 12, 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[[18, 18, -7, 18],\n [-14, -14, 4, -11],\n [16, 16, -8, 16],\n [2, 2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 13, -25, -5],\n [6, 9, -5, 5],\n [-9, -12, 12, -3],\n [12, 18, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -6, 6, 4],\n [9, 8, 11, 1],\n [-4, -6, 0, 2],\n [1, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 10, 2, -2],\n [-4, -4, 12, -12],\n [-2, -4, 4, -4],\n [-1, 5, 9, -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[[-2, 3, 4, -4],\n [-10, 8, 11, -9],\n [14, 0, -1, -5],\n [-6, 2, 3, -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 4x4 matrix:\n[[18, -2, -12, 14],\n [0, -22, 16, -14],\n [-8, -4, 10, -10],\n [-10, 6, 7, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, -14, -31],\n [8, -2, -6, -9],\n [28, 4, 0, 12],\n [0, -2, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 28, 1, 16],\n [-8, -8, -2, -2],\n [-12, 20, -3, 17],\n [0, -24, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -6, -4, 10],\n [8, 12, -9, -11],\n [-2, 3, 18, -25],\n [-4, 10, -20, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -12, 0, -12],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 12, 6, -9],\n [0, -8, -4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 23, 5, 1],\n [14, 23, -1, 11],\n [5, 3, -9, 17],\n [-2, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -20, -12, 20],\n [-17, 14, -8, -12],\n [10, -6, 1, -1],\n [-21, 0, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 0, -4, 8],\n [-3, 0, -6, 12],\n [3, 0, 6, -12],\n [3, 0, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -5, -10, -6],\n [18, 0, -11, 9],\n [-10, 1, 2, -5],\n [-6, 0, 14, -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, -9, 3, 0],\n [-4, -6, 2, 0],\n [8, 12, -4, 0],\n [-4, -6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -8, -2, -3],\n [7, 8, -6, -1],\n [13, -16, -6, -7],\n [4, -16, 0, -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[[-3, 6, -21, -12],\n [13, -14, 19, 16],\n [-5, 2, 13, 4],\n [-18, 16, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -1, -3, 4],\n [-6, -2, -6, 8],\n [3, 1, 3, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -17, 16, -21],\n [-18, 1, 7, 0],\n [-4, 6, 12, 10],\n [-6, -4, 7, -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 4x4 matrix:\n[[1, -3, -3, 1],\n [3, -9, -9, 3],\n [-4, 12, 12, -4],\n [1, -3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 2, -14, 1],\n [16, 4, 8, 8],\n [7, -2, 14, -1],\n [21, 9, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 20, 8, -6],\n [16, -28, 0, -4],\n [-3, -9, -9, 6],\n [-3, 9, 3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, 8, 15],\n [-9, 8, 5, 0],\n [-6, 10, 7, 9],\n [-9, 6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 3, 19, 16],\n [13, 3, 21, 4],\n [-11, -21, -17, 2],\n [-10, -18, -14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, 16, 12],\n [-3, 0, 12, 9],\n [4, 0, -16, -12],\n [2, 0, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 10, -10, -20],\n [-2, 6, -6, -12],\n [-3, 5, -5, -10],\n [3, -3, 3, 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[[9, 25, 1, -11],\n [-12, 3, 6, 0],\n [-9, 10, 6, -3],\n [12, 33, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 9, 6, -12],\n [0, 0, 0, 0],\n [-9, 9, 6, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -4, -4, -16],\n [12, 4, 4, 16],\n [-3, -1, -1, -4],\n [6, 2, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 4, -16, 8],\n [1, -7, 9, -7],\n [-5, 11, -6, 8],\n [5, -11, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, 16, -8],\n [0, 0, 0, 0],\n [0, 8, 16, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [20, 4, 4, 0],\n [-28, -4, -12, 0],\n [0, 2, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 12, 3, 33],\n [-24, 0, 18, 0],\n [-5, -3, 1, -7],\n [-11, -6, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -12, -9, -9],\n [2, -1, -6, 1],\n [-12, -14, 0, -14],\n [6, 7, 0, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[19, -4, 9, 1],\n [-2, 22, 23, -2],\n [12, -2, 7, 0],\n [-16, 6, -1, -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 4x4 matrix:\n[[-12, 8, 19, -7],\n [-2, -8, -6, 0],\n [0, 1, -9, 8],\n [11, 28, 5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -11, 7, -15],\n [6, -11, 7, -15],\n [-6, 11, -7, 15],\n [-4, -6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 2, 2, -3],\n [2, -1, -1, 0],\n [-4, 2, 2, 0],\n [-17, 1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, -1, -3],\n [0, 0, -3, -9],\n [-1, 2, 1, 7],\n [-8, 16, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 0, 1, -1],\n [9, 0, 3, -3],\n [-6, 0, -2, 2],\n [-6, 0, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -1, 22, -15],\n [-9, -14, -8, 16],\n [2, -1, 12, -9],\n [-2, -9, -7, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 0, 0, -4],\n [14, -4, -6, 8],\n [-8, 0, 0, -4],\n [-5, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 3, -6, 12],\n [3, 1, -2, 4],\n [0, 0, 0, 0],\n [-12, -4, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, 15, 12, -12],\n [10, 2, 6, -6],\n [0, 8, 9, -9],\n [3, -1, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 13, -8, 3],\n [-12, -24, 12, -12],\n [-6, 16, -1, 25],\n [-6, -19, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 7, 6, 2],\n [18, -16, -10, -8],\n [11, -3, 5, -3],\n [13, -14, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 3, -9, 9],\n [12, 3, -9, 9],\n [-8, -2, 6, -6],\n [-4, -1, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 16, 12, -8],\n [0, 0, 0, 0],\n [4, 16, 12, -8],\n [-2, -8, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -2, 1, -4],\n [-6, -6, 3, -12],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, -4, 8],\n [0, 3, -2, 4],\n [0, 12, -8, 16],\n [0, -9, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [8, -12, -16, 8],\n [4, -6, -8, 4],\n [6, -9, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[18, -10, -4, 12],\n [2, -10, -6, -2],\n [-1, -11, -7, -5],\n [-11, 7, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 6, -14, 2],\n [2, 0, 5, 4],\n [-2, 2, -13, -6],\n [0, -3, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -3, 9, -9],\n [4, -12, -4, 16],\n [6, -20, 0, 18],\n [6, -21, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, 4, -4],\n [6, -3, -6, 6],\n [0, 0, 0, 0],\n [-6, 3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 0, 0, 4],\n [12, -3, 3, -8],\n [-28, -9, 9, -8],\n [12, -3, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -20, 0, 10],\n [16, 4, 4, -15],\n [-16, -30, -10, 10],\n [-4, -12, 7, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -16, 16, -8],\n [0, 6, -1, -7],\n [8, -2, -5, 13],\n [-8, -10, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 16, -16, 12],\n [-3, 0, 0, 6],\n [-8, -12, 12, -14],\n [12, 16, -16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 9, -6, -3],\n [-6, 9, -6, -3],\n [-2, 3, -2, -1],\n [8, -12, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-19, 17, -1, -10],\n [-9, 6, -7, -6],\n [11, 11, 8, 14],\n [-12, 18, -5, -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 4x4 matrix:\n[[4, 4, -7, 2],\n [-3, 24, -15, -6],\n [-7, 8, 1, -6],\n [-5, 28, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 2, -11, -16],\n [6, -6, -12, -20],\n [0, 0, 15, 16],\n [-11, 11, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 8, -3, 9],\n [30, -6, 19, -5],\n [12, -6, 8, -4],\n [-30, 12, -20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, 9, -19],\n [-2, 4, 10, -18],\n [-19, 18, -8, 20],\n [23, -24, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -15, -15, -4],\n [-5, -2, -16, -14],\n [22, 18, 10, 8],\n [-18, -14, -11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 2, -10, 0],\n [-4, 6, -9, 7],\n [8, -4, 8, -4],\n [-12, 10, -17, 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[[2, -4, 2, 4],\n [8, -16, 8, 16],\n [-4, 8, -4, -8],\n [2, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 9, -15, -9],\n [14, -9, 15, 9],\n [-8, 0, -6, -9],\n [2, 13, -5, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 8, -2, -4],\n [18, 16, 8, 0],\n [1, -12, 12, 14],\n [-6, -4, 2, 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[[0, -9, -4, 9],\n [4, -11, 4, 11],\n [-3, 6, -4, -6],\n [-6, 3, -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 4x4 matrix:\n[[16, -16, 8, -16],\n [-16, 16, -8, 16],\n [-4, 4, -2, 4],\n [-8, 8, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -8, 6, 14],\n [0, 5, -3, -2],\n [0, -7, 4, 1],\n [0, -6, 3, -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 4x4 matrix:\n[[6, 8, 16, 9],\n [-13, -15, -4, -7],\n [-1, -7, 12, -4],\n [19, 20, 16, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, -2, 1, -2],\n [0, -4, 2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 1, 1, -14],\n [-20, 8, -8, 28],\n [6, -14, 12, -28],\n [6, 36, -23, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 0, 8, -6],\n [3, -12, -6, 3],\n [2, -8, -4, 2],\n [5, 4, 10, -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[[4, 2, -7, 1],\n [20, 4, -20, 8],\n [-5, 1, 0, -3],\n [12, 4, -16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 2, -3, -1],\n [2, 2, -3, -1],\n [0, 0, 0, 0],\n [-8, -8, 12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 9, -12, -6],\n [-4, 12, -16, -8],\n [3, -9, 12, 6],\n [-4, 12, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -1, -4, -16],\n [9, 0, -5, -22],\n [-7, 22, 20, 6],\n [-6, -3, 3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-3, -9, -6, 3],\n [2, 6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -8, -14, 15],\n [6, -10, -12, 11],\n [13, -2, -24, 11],\n [-11, 2, 22, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 3, -4, 4],\n [4, -6, 8, -8],\n [-2, 3, -4, 4],\n [8, -12, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -5, -16, 18],\n [0, 0, 0, 0],\n [4, 3, 4, -8],\n [-6, 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[[0, 0, 0, 0],\n [12, 12, 8, -8],\n [-6, -6, -4, 4],\n [6, 6, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 24, -1, 6],\n [13, 16, -1, 8],\n [-14, -32, 3, -6],\n [-10, -40, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -9, 9, 21],\n [4, -12, -8, -2],\n [8, 2, -10, -2],\n [-2, -7, -1, -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 4x4 matrix:\n[[0, 12, 6, 9],\n [0, 0, 0, 0],\n [0, 4, 2, 3],\n [0, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 4, 15, 23],\n [12, -16, 0, 4],\n [-13, 24, 15, 11],\n [6, -8, -10, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, 9, -12],\n [-12, 0, 9, -12],\n [-12, 0, 9, -12],\n [12, 0, -9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 1, 10, 7],\n [-5, -7, 8, -5],\n [22, 10, -20, -18],\n [9, 3, -12, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 1, -2, 0],\n [-4, -1, 2, 0],\n [8, 2, -4, 0],\n [-12, -3, 6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-12, -22, -20, -12],\n [6, -1, -6, 6],\n [0, 9, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 6, -6, 6],\n [-8, 6, -6, 6],\n [-12, 9, -9, 9],\n [-4, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 13, -7, 5],\n [-1, -14, 11, -5],\n [10, -3, -6, -2],\n [7, 10, -13, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 6, -6, -8],\n [4, 6, -6, -8],\n [-2, -3, 3, 4],\n [-6, -9, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -4, -4, 6],\n [6, 6, 6, -9],\n [-6, -6, -6, 9],\n [2, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -7, -4, 0],\n [-11, -11, -14, -10],\n [-5, -6, -7, 15],\n [-6, -2, -12, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, 16, 12],\n [-3, 0, 12, 9],\n [-4, 0, 16, 12],\n [-2, 0, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 8, 6, 2],\n [2, 8, 6, 2],\n [-1, -4, -3, -1],\n [-2, -8, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 3, 9, 6],\n [0, 0, 0, 0],\n [4, -2, -6, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -12, 12, 12],\n [-2, -6, 6, 6],\n [-1, -3, 3, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, -10, -1, 1],\n [5, 0, 7, 3],\n [5, 0, 7, 3],\n [0, -10, -8, -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 4x4 matrix:\n[[-5, -8, -2, 7],\n [24, 28, 7, 8],\n [2, 0, 0, 10],\n [4, 8, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -7, 8, -19],\n [-12, -12, 16, 4],\n [-2, -2, -10, -10],\n [-4, -4, -2, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 4, 8, -6],\n [1, -3, -8, 7],\n [-4, 0, 8, -10],\n [-4, -2, 4, -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[[2, -8, -18, 14],\n [-7, -14, -9, 5],\n [-2, 8, 18, -14],\n [-6, -4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 2, 14, -5],\n [-13, 16, -2, -4],\n [19, -4, 14, 1],\n [-7, 7, 1, -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 4x4 matrix:\n[[-3, -3, 3, -1],\n [-6, -6, 6, -2],\n [-3, -3, 3, -1],\n [6, 6, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 2, 2, 0],\n [1, 2, 2, 0],\n [0, 0, 0, 0],\n [4, 8, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 4, 0, 0],\n [-8, -10, 2, -4],\n [-17, -2, 12, -24],\n [11, 8, -4, 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[[4, 3, 1, -2],\n [12, 9, 3, -6],\n [16, 12, 4, -8],\n [-16, -12, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 8, 16, -16],\n [0, 2, 4, -4],\n [0, 0, 0, 0],\n [0, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, 1, 1],\n [-4, 0, 1, 1],\n [4, 0, -1, -1],\n [16, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [8, 6, -8, -6],\n [12, 9, -12, -9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -4, 6, -2],\n [0, -10, 11, -3],\n [-2, 8, -4, -2],\n [-3, -6, 13, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -8, -16, 16],\n [-4, 10, 0, 4],\n [12, -22, -4, -4],\n [-8, -12, 16, -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 4x4 matrix:\n[[3, 15, 0, 1],\n [17, -7, -4, 0],\n [0, 0, 0, 0],\n [-5, -5, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -18, 1, 2],\n [12, 24, 1, -10],\n [4, 7, 0, -2],\n [-8, 1, 5, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 8, 4, -6],\n [-10, 1, 28, -3],\n [-22, -1, 4, 3],\n [-2, -3, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 5, -15, 9],\n [-15, 17, 1, 1],\n [-11, -1, 17, -7],\n [0, -12, 14, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 16, -4, -12],\n [1, 4, -2, -2],\n [6, 4, 3, -7],\n [4, 16, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, 6, 2],\n [0, 0, 0, 0],\n [-5, 0, -2, -4],\n [-12, -8, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 6, 24, -15],\n [-13, -15, -19, 3],\n [2, -4, -10, 14],\n [-15, -6, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -3, -4, -4],\n [0, 0, 0, 0],\n [-3, -9, -12, -12],\n [-1, -3, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 8, -4, -4],\n [8, -8, 4, 4],\n [0, 0, 0, 0],\n [-8, 8, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 24, -4, 8],\n [6, 16, -8, 10],\n [-9, -20, 6, -9],\n [6, -14, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, -32, 12, 4],\n [16, -20, 0, 10],\n [-12, 16, 4, -12],\n [-4, 0, -20, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-26, 8, 21, 7],\n [-4, 10, -18, 0],\n [4, -22, 6, -4],\n [-6, 24, -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[[-8, 4, -8, 0],\n [3, 12, -22, -10],\n [10, 0, 8, 2],\n [8, 0, 12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -12, -4, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, -6, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 6, 0, 0],\n [0, 0, 0, 0],\n [-16, -8, 0, 0],\n [-8, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, -2, 12],\n [-16, 12, -6, 20],\n [-6, 3, -3, 12],\n [20, -16, 7, -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, 6, 4, -8],\n [0, 5, -10, -8],\n [-5, 0, 10, 1],\n [-8, -4, 24, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, 14, -2],\n [8, 13, -9, 6],\n [2, 4, 0, 0],\n [-20, -33, 25, -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[[-8, -23, 3, -20],\n [20, 2, -2, -12],\n [9, 15, -1, 11],\n [2, -1, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -1, -1, -1],\n [2, 1, 1, 1],\n [-6, -3, -3, -3],\n [2, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 6, -12, -6],\n [-6, -6, 12, 6],\n [8, 8, -16, -8],\n [2, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -13, 13, 10],\n [-12, 2, -14, 0],\n [-6, 13, -13, -10],\n [-1, 3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 4, -8, -4],\n [9, -6, 12, 6],\n [-6, 4, -8, -4],\n [-6, 4, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 8, 2, 4],\n [2, 2, -1, 6],\n [-16, 14, 2, 12],\n [-4, -4, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -3, 3, 3],\n [4, -5, 5, 5],\n [11, 3, 12, -23],\n [10, -6, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 3, -2, 10],\n [2, 1, -2, 2],\n [16, -1, -4, -8],\n [-6, 3, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -6, 4, 2],\n [-1, 3, -10, -3],\n [-2, 0, -4, -1],\n [-9, -9, 6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-3, -3, -2, 1],\n [0, 0, 0, 0],\n [6, 6, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 3, -1, -1],\n [-4, -12, -4, 0],\n [0, 18, 2, -8],\n [-10, 9, -7, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, -20, -6, 8],\n [7, -17, -5, 3],\n [-1, -18, -7, 2],\n [4, -29, -14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [3, 12, 12, 9],\n [3, 12, 12, 9],\n [-3, -12, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, -4, -8, 6],\n [0, 8, 16, -12],\n [0, 6, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -6, -4, -4],\n [0, 0, 0, 0],\n [-8, -12, -8, -8],\n [-2, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -2, 18, 2],\n [15, 10, 3, -16],\n [15, 8, -1, -12],\n [17, 12, 1, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -15, 21, -12],\n [-12, -12, 21, -15],\n [8, 0, 1, 1],\n [-8, -4, 13, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 1, 6, 2],\n [13, -2, -9, -3],\n [16, -2, -12, -4],\n [-17, 4, 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[[-20, -4, -24, 12],\n [2, 2, 6, -8],\n [20, 4, 24, -12],\n [-11, 1, -6, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -8, -6, -13],\n [16, 4, 20, 28],\n [-8, 1, -10, -13],\n [4, -11, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, 8, 6],\n [6, 6, -12, -9],\n [12, 6, -12, -7],\n [-8, -8, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[21, 18, -6, 3],\n [22, 17, -3, 4],\n [12, 8, 2, -1],\n [-7, -2, -12, 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[[12, -8, -16, 16],\n [9, -6, -12, 12],\n [-12, 8, 16, -16],\n [-9, 6, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 14, -17, -10],\n [1, 2, 4, 5],\n [4, 0, 12, 0],\n [0, 0, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 10, -8, -2],\n [-14, 10, 2, 8],\n [-40, 34, 0, 14],\n [10, -16, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-6, 6, 8, -6],\n [-3, 3, 4, -3],\n [9, -9, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 4, -10, 2],\n [-14, -8, -12, -4],\n [-2, -24, 4, -12],\n [14, 8, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -3, -9, -10],\n [-28, 18, 10, -16],\n [14, -9, -5, 8],\n [22, -19, -7, 20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -12, -20, 4],\n [4, -2, -9, -1],\n [4, 2, -8, -4],\n [-4, -2, 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[[20, -4, 6, 11],\n [-20, -20, -8, 12],\n [16, -10, 4, 15],\n [16, -4, 22, 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 4x4 matrix:\n[[4, -4, -4, 4],\n [-9, -4, 2, -8],\n [-2, -4, -2, -5],\n [-2, 4, 4, 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 4x4 matrix:\n[[8, -2, -1, 13],\n [4, -10, -5, -7],\n [12, -18, -9, -3],\n [12, -6, -3, 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[[6, -6, -6, 0],\n [0, 0, 0, 0],\n [-2, 2, 2, 0],\n [-2, 2, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 12, 32, -27],\n [0, 4, 8, -9],\n [-16, -4, -24, 21],\n [6, 28, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -12, -8, -12],\n [-6, -6, -4, -6],\n [-3, -3, -2, -3],\n [-9, -9, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 1, 4, 0],\n [8, 4, 16, 0],\n [-8, -4, -16, 0],\n [4, 2, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -3, 1, -6],\n [-3, 3, -10, 15],\n [9, -9, -15, 0],\n [12, -12, 1, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 17, 6, 1],\n [0, -8, -2, 0],\n [-4, 9, 4, 1],\n [-4, -3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -15, -10, -17],\n [13, -12, -3, -16],\n [-22, -14, -22, -11],\n [0, -36, -28, -40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 4, 16, -10],\n [0, -1, 3, -1],\n [-3, 9, 15, -12],\n [-4, 15, 11, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -22, -18, -6],\n [12, -3, 0, 0],\n [-3, -9, -9, -3],\n [-7, -8, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 1, -1],\n [4, 16, -17, -7],\n [1, 4, -5, -1],\n [2, 8, -7, -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[[8, 10, 11, 1],\n [0, -14, -9, 5],\n [4, 12, 10, -2],\n [3, -12, -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[[2, -2, 1, 3],\n [-6, 6, -3, -9],\n [2, -2, 1, 3],\n [4, -4, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 13, 4, 7],\n [0, 12, 8, 4],\n [4, 7, 7, 1],\n [-8, 16, 6, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -15, -20, -4],\n [-7, -3, 7, 10],\n [18, 10, -20, -16],\n [-9, 1, 21, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 1, 7, 6],\n [-2, -9, -7, -12],\n [-4, -3, -5, -6],\n [-5, 5, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -8, 6, 12],\n [-10, 2, 12, 15],\n [-11, -2, 9, 13],\n [10, 4, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -6, -4, -6],\n [-12, -9, -6, -9],\n [12, 9, 6, 9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -4, 18, -12],\n [0, 0, 0, 0],\n [6, 0, 10, -6],\n [-3, -8, 11, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 21, -12, 6],\n [0, 8, -6, -7],\n [11, -17, 10, -3],\n [12, -4, 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[[11, 5, 6, 7],\n [11, -2, -9, 17],\n [2, -1, -3, 4],\n [-7, 0, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 4, -3, 2],\n [-16, -16, 12, -8],\n [16, 16, -12, 8],\n [-8, -8, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 24, 23, 3],\n [-4, 8, 9, -3],\n [0, -8, -13, -1],\n [0, -16, -25, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 3, 2, -12],\n [2, 0, 7, -12],\n [-8, 7, -7, -8],\n [-10, 7, -14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 2, 6, -10],\n [-10, 18, 4, 0],\n [-10, 18, 4, 0],\n [4, 4, -8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, -3, 2],\n [1, 4, 3, -1],\n [-4, 4, 6, -4],\n [2, 8, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -1, 7, 0],\n [4, 2, 7, -3],\n [-4, -7, 8, 3],\n [4, 3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 8, 4, -6],\n [-4, 4, 2, -3],\n [12, -12, -6, 9],\n [4, -4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 16, -24, -12],\n [6, 10, -6, 12],\n [-11, -7, 3, -23],\n [-9, -9, 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[[16, 0, -4, 8],\n [16, 0, -4, 8],\n [0, 0, 0, 0],\n [-8, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 3, 0, -1],\n [4, -3, 0, 1],\n [16, -12, 0, 4],\n [8, -6, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, 12, -40, -16],\n [-9, 6, 6, 15],\n [12, 16, -24, -4],\n [6, 2, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -4, -1, -4],\n [-6, -8, -2, -8],\n [0, 0, 0, 0],\n [-6, -8, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -5, 5, -11],\n [12, -14, 9, -13],\n [-4, -1, 1, 11],\n [-16, 15, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 0, 2, 0],\n [-8, 0, -8, -2],\n [10, 0, 18, 4],\n [-28, 0, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, 3, -7, -5],\n [24, 12, 12, 12],\n [1, 1, 19, 13],\n [-8, -1, 16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 0, 0, -9],\n [6, 0, 0, -6],\n [9, 0, 0, -9],\n [6, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 4, -16, 16],\n [8, 4, -16, 16],\n [0, 0, 0, 0],\n [4, 2, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 8, 12, 18],\n [-7, -13, -23, -21],\n [-9, 21, -3, 0],\n [-5, -16, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 8, -11, 3],\n [-1, -4, -10, -6],\n [-4, -8, 20, -4],\n [-2, 0, -9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -12, 8, -12],\n [0, 6, -4, 6],\n [0, -3, 2, -3],\n [0, -3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 1, -2, 2],\n [3, 12, 6, 9],\n [-4, 10, 0, 10],\n [-4, -3, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 8, 0, 0],\n [-6, 8, -2, 0],\n [4, -6, 2, 0],\n [8, -10, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-12, 9, 12, 12],\n [16, -12, -16, -16],\n [16, -12, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 0, -2, -1],\n [-8, 0, -8, -4],\n [-6, 0, -6, -3],\n [-6, 0, -6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-3, -2, 2, 0],\n [-12, -8, 8, 0],\n [-9, -6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 7, 13, -4],\n [10, 19, 7, -10],\n [16, 19, 13, -6],\n [-14, -5, -13, -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[[9, 6, -12, -9],\n [18, 3, -3, 0],\n [-9, -6, 12, 9],\n [-6, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -9, 12, -3],\n [4, 12, -16, 4],\n [4, 12, -16, 4],\n [-1, -3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, 14, 15, -3],\n [12, 16, 16, 0],\n [7, 14, 15, -3],\n [11, 10, 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[[16, 16, -8, -8],\n [-16, -12, 16, 8],\n [-16, -12, 16, 8],\n [4, 6, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -6, 6, -12],\n [8, 4, -4, 8],\n [12, 6, -6, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -16, 12, 4],\n [0, 12, -9, -3],\n [0, -16, 12, 4],\n [0, -8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, 0, 4],\n [-4, 0, 0, 8],\n [-1, 0, 0, 2],\n [-3, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-4, 0, -6, 0],\n [2, 0, 3, 0],\n [-8, 0, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-6, 12, -3, -3],\n [4, -8, 2, 2],\n [4, -8, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -7, -9, -13],\n [10, 1, 4, 8],\n [13, 10, 10, 11],\n [8, 2, 5, 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 4x4 matrix:\n[[11, 4, 16, 4],\n [-1, -2, -2, -2],\n [-6, 6, -6, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -3, -12, -9],\n [-3, -1, -4, -3],\n [-12, -4, -16, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -9, 12, 9],\n [-9, 12, -2, -18],\n [-3, 4, -6, -6],\n [6, 4, -18, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 16, -16, -10],\n [16, 0, 0, -4],\n [-15, -12, 12, 9],\n [-14, -8, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -11, -4, 4],\n [6, -7, -3, 8],\n [-12, 16, 6, -8],\n [-2, -1, 1, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 2, 0, 1],\n [6, -6, 0, -3],\n [6, -6, 0, -3],\n [2, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -2, 6, -2],\n [-12, -4, 12, -4],\n [12, 4, -12, 4],\n [12, 4, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, 9, -9],\n [-6, 0, -9, 9],\n [6, 0, 9, -9],\n [8, 0, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 4, -6, -8],\n [-1, -2, 3, 4],\n [2, 4, -6, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 1, 5, 20],\n [-12, 8, 12, -8],\n [6, 0, 2, 12],\n [-9, 5, 7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 6, -15, -13],\n [-13, -21, 12, 10],\n [-1, -5, 8, -2],\n [6, 10, -7, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -16, 8, 4],\n [0, -16, 8, 4],\n [0, 0, 0, 0],\n [0, -12, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, 8, 10],\n [2, -2, -2, -1],\n [-2, 18, 8, -20],\n [8, -4, -14, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 12, 9, -3],\n [-3, -12, -9, 3],\n [-1, -4, -3, 1],\n [2, 8, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -1, -6, -1],\n [-13, 0, -15, -4],\n [-4, -10, 0, 13],\n [8, -1, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 12, 0, 0],\n [6, -9, 0, 0],\n [8, -12, 0, 0],\n [-8, 12, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -5, 2, -9],\n [-2, -4, -2, 0],\n [-2, 14, 4, 6],\n [-17, -7, -8, 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[[-11, 8, 24, 12],\n [16, -28, 12, 12],\n [-2, 6, -2, -6],\n [15, -25, -3, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 8, 6, -2],\n [-4, -8, -6, 2],\n [-2, -4, -3, 1],\n [-6, -12, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 19, 19, -6],\n [16, 7, -26, -6],\n [-12, -4, 10, 2],\n [-12, -4, 10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 9, 12, 6],\n [-4, -12, -16, -8],\n [2, 6, 8, 4],\n [-2, -6, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -12, 16, 2],\n [5, 19, -28, -13],\n [-4, -6, 4, 16],\n [-7, -17, 20, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -28, -8, -16],\n [5, 10, 4, 6],\n [0, 25, 6, 14],\n [-3, -21, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 10, -9, 16],\n [-3, 5, -1, 4],\n [-21, 5, 13, -12],\n [-21, 2, 15, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-4, -3, -3, -3],\n [-4, -3, -3, -3],\n [4, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -12, -12, -12],\n [4, -2, -8, -2],\n [-6, 3, 12, 3],\n [-7, 1, 13, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 9, 6, 3],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -9, -9, -9],\n [4, -12, -12, -12],\n [-2, 6, 6, 6],\n [-4, 12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 6, 12, -9],\n [0, 8, 16, -12],\n [0, -4, -8, 6],\n [0, -4, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 21, 2, 11],\n [5, -5, -3, 0],\n [14, -4, -11, 5],\n [16, 8, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, -1, 3],\n [12, -5, -11, 0],\n [-8, 2, 7, 1],\n [20, 1, -16, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 12, 6, -9],\n [-6, -4, 0, 0],\n [-10, -12, -8, 7],\n [-17, -10, -17, 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[[-13, 6, -8, 9],\n [2, 8, -6, -8],\n [-1, -11, 11, 5],\n [5, 9, -11, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -3, -9, -9],\n [9, 3, 9, 9],\n [12, 4, 12, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -6, -10, 14],\n [0, 3, 9, -6],\n [0, 10, 14, -24],\n [-16, -3, -1, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [12, -4, 12, -4],\n [12, -4, 12, -4],\n [-9, 3, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -2, 1, -13],\n [6, 3, 11, -16],\n [0, 19, 18, 4],\n [14, -5, -5, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 10, 19, 13],\n [12, -14, -24, 0],\n [4, 2, 2, -10],\n [8, -12, -20, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -9, -24, 9],\n [0, -8, 2, -6],\n [0, -12, 3, -9],\n [0, -8, -28, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -3, 0, 17],\n [-2, -2, 0, 1],\n [1, 14, 0, -3],\n [-2, -19, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -4, 8, 8],\n [2, -20, 0, 10],\n [-1, -25, -6, 29],\n [0, -7, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -8, -4, -2],\n [6, -8, -4, -2],\n [6, -8, -4, -2],\n [-12, 16, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -1, 17, -11],\n [-1, 2, -7, 2],\n [12, 26, 6, -10],\n [-4, -2, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 12, 9, 9],\n [-3, -4, -3, -3],\n [0, 0, 0, 0],\n [-3, -4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 0, 2, 5],\n [-12, 28, -12, -16],\n [6, -14, 6, 8],\n [-2, 3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -5, -11, 31],\n [-28, 29, 11, 1],\n [-12, 8, 5, -10],\n [8, -8, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 3, -19, 10],\n [3, 5, 22, -8],\n [1, -1, -3, -3],\n [-12, -5, -1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 20, 0, 15],\n [-6, 16, -11, 12],\n [6, 0, -15, 0],\n [6, -8, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -7, -11, -5],\n [-10, -20, -19, -12],\n [-3, -13, -11, -7],\n [-16, 12, 0, 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[[-7, 14, -36, 12],\n [15, 10, 4, 4],\n [13, 18, -4, 8],\n [8, 10, 12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 10, -22, -4],\n [16, 14, -20, -6],\n [14, 0, 12, 13],\n [7, 7, -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[[-2, 6, 16, 6],\n [1, 5, 2, 9],\n [-9, -6, 2, -20],\n [-5, -3, -17, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -8, 6, -18],\n [6, -18, -5, -21],\n [9, -11, -3, -15],\n [16, -8, 10, -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[[-20, 19, 13, -10],\n [7, 9, 6, -6],\n [12, 2, 2, -4],\n [-10, -13, -1, -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, 7, -16, 11],\n [-3, 3, -9, 7],\n [-14, 10, 5, 14],\n [0, 6, 17, 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 4x4 matrix:\n[[3, -6, -21, 15],\n [-4, 15, 0, -2],\n [0, 2, -8, -5],\n [-7, 20, 25, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -1, -1, -6],\n [2, 7, -18, -3],\n [2, 7, -18, -3],\n [6, 6, -19, -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[[4, -8, -6, -4],\n [-6, 12, 9, 6],\n [8, -16, -12, -8],\n [8, -16, -12, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, 3, -5],\n [12, -5, -9, -5],\n [-4, 5, 3, 15],\n [0, 3, 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[[2, 8, -4, 0],\n [2, 8, -4, 0],\n [2, 8, -4, 0],\n [-4, -16, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -3, 2, 0],\n [2, -6, 4, 0],\n [-4, 12, -8, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -5, -9, -4],\n [3, 4, 2, -4],\n [-9, 0, -12, -2],\n [3, -14, 8, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [-3, 4, -3, -1],\n [6, -8, 6, 2],\n [-12, 16, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, 7, 19, -20],\n [1, -13, -16, 20],\n [-9, 7, 1, -4],\n [6, 12, 21, -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[[10, -1, 4, -8],\n [8, -5, 2, -10],\n [14, 0, 6, -10],\n [4, 15, 6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, 8, 14, 14],\n [-14, -17, -14, -17],\n [-8, 1, 10, 7],\n [9, -6, -6, -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[[-3, -9, -9, 0],\n [-1, -3, -3, -10],\n [-1, -3, -3, 8],\n [-2, -6, -6, 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[[2, 12, -4, 14],\n [0, 4, 0, 5],\n [10, 12, -20, 10],\n [-2, -16, 4, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 0, 2, 1],\n [-3, 0, -6, -3],\n [-1, 0, -2, -1],\n [-4, 0, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [16, 12, 16, 8],\n [8, 6, 8, 4],\n [-12, -9, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 1, 4, 4],\n [14, 7, -13, -14],\n [8, 16, -15, -2],\n [2, 11, -7, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -9, -5, -10],\n [16, -16, -19, 14],\n [16, 4, -4, 24],\n [16, -24, -25, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, -6, 0],\n [-6, 0, -6, 0],\n [6, 0, 6, 0],\n [3, 0, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -2, -6, -6],\n [8, -10, 17, 7],\n [-12, 2, 9, 10],\n [-4, 8, 2, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 0, 4, -7],\n [-6, -11, 5, 5],\n [18, 5, -11, 13],\n [-8, 4, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -9, -12, -3],\n [1, -3, -4, -1],\n [4, -12, -16, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 4, 16, 4],\n [6, -2, -8, -2],\n [6, -2, -8, -2],\n [12, -4, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, 6, -13, 0],\n [-24, -5, -4, -9],\n [9, -11, 15, -5],\n [-4, 8, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [12, 8, 0, 12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -8, 16, -4],\n [4, 9, 8, -8],\n [4, -21, 8, 1],\n [-16, 8, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 11, 11, -16],\n [12, -8, 1, 10],\n [8, -9, -14, 14],\n [-16, 12, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -10, 14, -10],\n [-4, 1, -8, 0],\n [4, 15, -8, 2],\n [26, 12, -10, 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, 2, -2, 6],\n [8, 6, -9, -3],\n [4, 9, -9, -13],\n [8, 10, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-9, -12, 12, 9],\n [12, 16, -16, -12],\n [6, 8, -8, -6],\n [6, 8, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 0, 4, -6],\n [-5, 17, -3, 21],\n [2, -4, 4, 0],\n [-10, -8, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 12, -16, 8],\n [8, -6, 8, -4],\n [-4, 3, -4, 2],\n [-8, 6, -8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 26, 4, 8],\n [-3, -10, 4, 8],\n [12, -12, 12, -16],\n [3, 0, 18, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, 12, -16],\n [-14, 4, -6, 12],\n [-3, 0, -3, 4],\n [4, 4, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -4, -6, 2],\n [6, -4, -6, 2],\n [-15, -2, -3, -11],\n [-9, -6, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 6, 14, 8],\n [-8, 5, 10, 5],\n [-8, 2, -2, -4],\n [-12, 7, 13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 12, -6, -12],\n [9, -12, 6, 12],\n [-9, 12, -6, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 0, -11, -1],\n [-3, 1, -13, -29],\n [19, 7, 4, 2],\n [-24, -7, -9, 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 4x4 matrix:\n[[-3, 0, 0, 3],\n [6, 0, 0, -6],\n [-12, 0, 0, 12],\n [-6, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 12, -9, -3],\n [-2, 8, -6, -2],\n [-1, 4, -3, -1],\n [3, -12, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -1, -6, 1],\n [8, 4, -16, 4],\n [-6, -11, 4, -3],\n [10, 9, -16, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 4, 4, 0],\n [4, 1, 1, 0],\n [8, 2, 2, 0],\n [-16, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 14, -18, 8],\n [-8, -12, 12, -12],\n [10, -7, 15, 5],\n [20, 8, 0, 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[[0, 0, 0, -3],\n [-8, 7, 5, 11],\n [-11, 16, 9, 20],\n [10, -8, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -9, -4, -11],\n [2, 18, -8, 20],\n [3, -3, 28, 0],\n [0, -12, 16, -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 4x4 matrix:\n[[-1, -10, -7, -19],\n [9, -1, -2, -24],\n [-9, -6, -3, 9],\n [-3, -9, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -2, -3, -13],\n [12, -6, -9, -12],\n [12, -8, -12, -13],\n [8, -8, -12, -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[[11, 6, 15, -1],\n [17, 15, 24, -4],\n [7, 7, 10, -2],\n [-7, 0, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -10, -6, -8],\n [1, -4, 0, -1],\n [7, -1, 9, 8],\n [-6, 6, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -15, -20, 8],\n [-6, -9, -12, 6],\n [-11, -3, -4, 8],\n [-4, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 15, -6, -3],\n [-1, 2, -2, -1],\n [1, -14, 2, 1],\n [1, -8, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -4, -12, -4],\n [-4, 0, -8, -4],\n [0, 0, 0, 0],\n [-8, -4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 10, -14, 6],\n [-5, -7, 5, 3],\n [-8, 7, 1, -12],\n [-19, -11, 13, -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[[1, -3, -22, -10],\n [3, 1, -1, 5],\n [11, 3, -8, 9],\n [9, 1, -16, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -6, -8, 8],\n [12, 12, 16, -16],\n [0, 0, 0, 0],\n [9, 9, 12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -3, -9, -3],\n [16, -4, -12, -4],\n [8, -2, -6, -2],\n [12, -3, -9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 12, -8, 4],\n [-6, 9, -6, 3],\n [-6, 9, -6, 3],\n [-2, 3, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [8, 6, -4, -4],\n [-12, -9, 6, 6],\n [12, 9, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, -8, -16],\n [15, -8, -6, 2],\n [-2, 12, 7, -14],\n [3, 4, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, 16, 8, -22],\n [4, -16, -8, 8],\n [13, -4, -2, 10],\n [16, -16, -8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 8, 4, 3],\n [9, -3, 3, 3],\n [-5, -7, -9, -11],\n [-13, 12, 0, -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 4x4 matrix:\n[[-15, 3, -12, -9],\n [-7, -3, -10, -9],\n [-4, -8, -12, -12],\n [-6, 10, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-2, 0, -1, -4],\n [-4, 0, -2, -8],\n [-4, 0, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -6, 9, -4],\n [14, 2, -10, -2],\n [-6, -6, 4, -6],\n [8, 7, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 0, -12, -3],\n [8, 0, -8, -2],\n [12, 0, -12, -3],\n [-16, 0, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -8, -4, 8],\n [0, 4, 2, -4],\n [0, 8, 4, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -7, 5, -1],\n [8, -12, 16, -10],\n [-2, -12, -10, 19],\n [4, 28, 12, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 2, 5, -14],\n [9, -24, -2, -8],\n [-4, 14, 1, 6],\n [-7, -13, 4, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 8, 12, 16],\n [12, 6, 9, 12],\n [-12, -6, -9, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -1, -8, -12],\n [-16, -4, 16, 0],\n [-7, -2, 22, 14],\n [-8, -3, 26, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -9, 12, 9],\n [2, 4, -6, -6],\n [1, -1, 0, -3],\n [-1, -14, 15, 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[[3, -8, 1, -3],\n [-1, 4, -3, -1],\n [-5, 16, -7, 1],\n [-4, 16, -12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 16, -16, -16],\n [4, -8, 8, 8],\n [2, -4, 4, 4],\n [4, -8, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -6, -4, -6],\n [8, 6, 4, 6],\n [-8, -6, -4, -6],\n [4, 3, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 4, 4, 3],\n [2, -8, -8, -6],\n [0, 0, 0, 0],\n [-2, 8, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 8, 32, -4],\n [15, 3, -13, -21],\n [-6, 0, -4, 10],\n [6, 12, 2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -6, 7, 10],\n [-16, 10, -13, 10],\n [-1, 1, -2, 4],\n [20, -12, 15, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-29, 20, 6, 3],\n [4, -6, 10, 6],\n [-29, 20, 6, 3],\n [-2, 17, 9, -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[[-13, -7, 3, 12],\n [-1, 6, 6, -2],\n [19, 18, 0, -22],\n [10, 9, -2, -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[[9, 4, -15, 6],\n [-19, -17, 8, 24],\n [1, 4, 16, -5],\n [0, -3, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 1, 8, -4],\n [-3, 1, 8, -6],\n [-18, 22, 8, 24],\n [-5, -1, 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 4x4 matrix:\n[[10, 5, -12, 7],\n [-2, 13, 8, 7],\n [8, 8, -8, 8],\n [2, 17, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 3, 1, -4],\n [-17, 21, 7, -4],\n [4, -7, 11, 12],\n [-10, 10, 10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -11, 12, 13],\n [3, 1, 12, 9],\n [0, -6, 9, 9],\n [0, 6, -9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -12, 8, -2],\n [4, 8, -8, 16],\n [10, 20, -14, 7],\n [6, 12, -10, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-19, 4, -10, 15],\n [20, 12, 12, -4],\n [-20, -12, -12, 4],\n [7, -20, 2, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -2, 23, -8],\n [-6, 1, 30, -11],\n [10, -10, 11, -19],\n [17, -10, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, -2, -6, -4],\n [1, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 4, 4, 12],\n [0, -2, 4, -6],\n [0, 1, 2, 3],\n [0, 2, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -9, 0, 9],\n [-4, -3, 0, 3],\n [16, 12, 0, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 8, 2, 12],\n [-28, -8, 1, 6],\n [19, 3, -2, -10],\n [3, 11, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 0, 12, 2],\n [-10, 8, -8, -11],\n [1, -12, 9, 12],\n [-7, -12, 24, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 2, 2, -8],\n [12, -4, -4, 16],\n [-3, 1, 1, -4],\n [-9, 3, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -11, -11, -4],\n [15, 15, -1, -12],\n [-16, -16, 4, 16],\n [-4, -4, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -8, -8, 16],\n [-11, 6, -2, -4],\n [-1, 5, 3, -8],\n [-20, 16, 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[[12, 2, 16, -6],\n [3, 3, 9, 1],\n [-6, 2, -2, 6],\n [12, 2, 16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 16, 0, 8],\n [8, -16, 0, -8],\n [8, -16, 0, -8],\n [-4, 8, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -11, 3, 14],\n [8, -13, 5, 18],\n [-10, 8, -4, -12],\n [-12, -8, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-26, 15, 17, -4],\n [-8, -2, 10, -16],\n [0, 15, 2, 3],\n [20, -7, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -12, 0, -6],\n [0, -4, 0, -2],\n [0, -8, 0, -4],\n [0, 12, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, 16, 6, -20],\n [3, -4, 0, 2],\n [-25, 12, 8, -22],\n [9, -12, 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[[-12, 12, 20, 10],\n [0, 0, 0, 0],\n [3, -6, -11, -1],\n [-12, 8, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 16, -4, 16],\n [-1, 1, -1, 4],\n [4, -4, 1, -4],\n [-13, 13, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -8, 8, -6],\n [-3, 4, -4, 3],\n [-9, 12, -12, 9],\n [3, -4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -4, 0, -6],\n [6, -6, 0, -9],\n [-4, 4, 0, 6],\n [-2, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -15, -4, 13],\n [10, -6, -16, 7],\n [-18, -9, 20, 5],\n [12, -9, -20, 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 4x4 matrix:\n[[-4, -16, 12, -12],\n [-4, -16, 12, -12],\n [-4, -16, 12, -12],\n [-2, -8, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 0, -22, 10],\n [9, -8, 11, 6],\n [-10, 4, 29, -20],\n [0, 2, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -4, 2, 6],\n [3, -6, 3, 9],\n [-2, 4, -2, -6],\n [-3, 6, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -2, 4, 10],\n [-12, 10, 10, 1],\n [4, -1, -8, -12],\n [0, -2, 4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 2, 4, -2],\n [-8, -4, -8, 4],\n [-8, -4, -8, 4],\n [8, 4, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 2, 3, -7],\n [-5, -5, 9, -10],\n [2, -1, 0, 1],\n [-4, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 8, 16, 8],\n [-1, 2, 4, 2],\n [4, -8, -16, -8],\n [-3, 6, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 1, 0, 0],\n [-6, 2, 0, 0],\n [-6, 2, 0, 0],\n [9, -3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 16, 12, -1],\n [-2, -4, 0, 4],\n [-1, -18, -16, -2],\n [3, 10, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -4, 11, 2],\n [-12, 4, 7, -4],\n [4, -16, -8, -4],\n [-12, 0, 12, -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 4x4 matrix:\n[[-12, 17, -10, 17],\n [-19, 14, -9, 8],\n [8, -10, 6, -10],\n [7, 8, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 20, 6, -10],\n [2, 4, 12, -14],\n [2, 4, 12, -14],\n [16, 20, 6, -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[[1, -2, 17, -5],\n [-1, -4, 2, -1],\n [1, 4, 1, 10],\n [-5, -12, -16, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, 21, -6, 27],\n [5, -1, -11, -5],\n [26, 26, -21, 32],\n [-22, -26, 14, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-24, 5, -1, -2],\n [-15, 10, 6, -10],\n [15, 8, -5, 4],\n [-9, -9, -4, 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[[8, 8, 8, 0],\n [-16, -16, -16, 0],\n [-16, -16, -16, 0],\n [16, 16, 16, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -6, -9, 12],\n [-16, 8, 12, -16],\n [12, -6, -9, 12],\n [8, -4, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[22, 25, -4, 1],\n [4, 8, 1, 14],\n [-4, -2, 2, 10],\n [-6, -3, 3, 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[[16, 12, 12, 8],\n [-4, -3, -3, -2],\n [0, 0, 0, 0],\n [-4, -3, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -2, -3, -4],\n [-8, 12, -12, -6],\n [-4, 10, -6, -1],\n [10, -12, 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 4x4 matrix:\n[[1, -1, 4, -1],\n [4, -4, 16, -4],\n [1, -1, 4, -1],\n [-2, 2, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -4, -4, -4],\n [0, 0, 0, 0],\n [3, 4, 4, 4],\n [-3, -4, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -15, 2, 12],\n [7, -7, 4, 12],\n [31, -3, 2, 21],\n [-2, -5, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -1, -2, 1],\n [12, -3, -6, 3],\n [-4, 1, 2, -1],\n [12, -3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -6, -3, -6],\n [-4, -4, -2, -4],\n [-2, -2, -1, -2],\n [-2, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -7, -8, 6],\n [-4, 18, -10, -20],\n [21, -1, 19, 6],\n [0, 5, 1, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 0, -4, -4],\n [5, 6, -14, -4],\n [3, 3, -5, 0],\n [1, 3, -13, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -6, -2, 0],\n [2, 6, 2, 0],\n [-4, -12, -4, 0],\n [1, 3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -15, -9, 2],\n [-4, -6, -5, 5],\n [-4, 15, 9, -2],\n [-16, 18, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, -2, 8, -2],\n [4, 2, -8, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 9, 9, -3],\n [4, -6, -6, 2],\n [0, 0, 0, 0],\n [2, -3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -14, -27, -5],\n [-18, -6, -18, -6],\n [-2, 2, 1, -1],\n [20, -4, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -4, -4, -1],\n [-12, 13, 0, -26],\n [-12, 6, -12, -6],\n [0, -3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -5, -8, -18],\n [4, 4, 4, -8],\n [-10, -9, 6, 22],\n [-10, -18, 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[[2, -1, -3, 2],\n [0, 0, 0, 0],\n [-6, 3, 9, -6],\n [6, -3, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 8, -4, 0],\n [16, 16, -8, 0],\n [-8, -8, 4, 0],\n [12, 12, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 0, -14, -8],\n [-2, 1, 2, 1],\n [1, 7, -8, -9],\n [-6, 5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 28, -20, 5],\n [-19, -28, 22, -9],\n [-12, -24, 16, -2],\n [18, 24, -20, 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[[-9, 7, 2, -7],\n [-1, -16, 6, -8],\n [26, -36, 8, 3],\n [-6, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -9, -6, -3],\n [0, 11, 6, 8],\n [1, -2, -3, 4],\n [-11, -11, -9, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 6, 21, 3],\n [-5, 10, -3, 15],\n [-6, 10, 21, 8],\n [19, 10, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 12, -16, 5],\n [7, -20, 1, -12],\n [-11, 4, -17, 0],\n [9, -28, 0, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 20, 2, 6],\n [-12, 2, -5, -3],\n [4, -24, -5, -9],\n [-20, 8, -7, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 9, -9, 3],\n [16, -12, 12, -4],\n [0, 0, 0, 0],\n [-4, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -18, 12, -5],\n [3, -6, 2, 1],\n [9, -13, 3, 7],\n [-1, -3, 3, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -3, 6, 12],\n [12, -3, 6, 12],\n [4, -1, 2, 4],\n [-8, 2, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-6, 6, 0, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 2, -3, -1],\n [-4, 8, -12, -4],\n [3, -6, 9, 3],\n [-3, 6, -9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -7, -4, 13],\n [1, 10, -14, 2],\n [-4, 9, -6, 6],\n [-6, -7, 20, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -6, -3, -9],\n [-3, 6, 3, 9],\n [-1, 2, 1, 3],\n [-1, 2, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 3, 6, 9],\n [5, -13, -8, -3],\n [-8, 10, 2, -6],\n [12, -12, 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[[-10, -16, -18, 8],\n [12, 12, 12, 6],\n [-2, 4, 2, 6],\n [0, 12, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 11, -1, -4],\n [0, 11, 19, -9],\n [8, -12, 12, 4],\n [-4, 8, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 15, 20, -13],\n [-1, -9, -9, -6],\n [-3, 6, 1, -15],\n [-1, 3, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, -2, 1],\n [-6, 6, 6, -3],\n [2, -2, -2, 1],\n [2, -2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -16, -12, -16],\n [8, -8, -6, -8],\n [0, 0, 0, 0],\n [-16, 16, 12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -4, -12, -5],\n [-2, -4, 4, 7],\n [2, -4, -4, 1],\n [6, 1, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 24, 6, 2],\n [18, -22, -8, -3],\n [-30, 36, 6, -16],\n [14, -6, -20, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -8, -12, -4],\n [12, -8, -12, -4],\n [-3, 2, 3, 1],\n [-9, 6, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 0, -32, -4],\n [-18, -4, -28, -7],\n [-4, -12, -4, -11],\n [4, 32, 0, 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[[12, 12, 12, 9],\n [4, 4, 4, 3],\n [-4, -4, -4, -3],\n [-12, -12, -12, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -3, 18, 1],\n [12, 2, -10, 4],\n [24, 3, -18, 11],\n [-21, -2, 10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -1, 3, 7],\n [4, -4, 4, 16],\n [9, -9, -27, -16],\n [-2, 2, 16, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, -1, 1],\n [-8, 0, 2, -2],\n [0, 0, 0, 0],\n [-4, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 24, -6, 14],\n [12, -8, 18, -2],\n [14, -16, 6, -9],\n [-10, 4, -21, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [8, -2, 6, 6],\n [-4, 1, -3, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -8, 7, 4],\n [0, 2, -2, 0],\n [0, -6, 3, 12],\n [0, 8, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -8, -8, 12],\n [-9, 12, 3, -6],\n [28, -16, 8, -8],\n [-20, 16, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 1, -9, 11],\n [6, -6, 12, 4],\n [-6, 4, -6, -6],\n [3, -4, 9, 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[[3, -2, -2, 2],\n [0, 0, 0, 0],\n [-9, 6, 6, -6],\n [-9, 6, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, -1, 9, 32],\n [-9, 12, -3, -4],\n [18, -4, 1, -12],\n [16, 7, -3, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -8, 4, -2],\n [6, 6, 9, 15],\n [12, -3, 15, 6],\n [4, -27, 11, -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[[-3, -6, 6, -9],\n [3, 6, -6, 9],\n [-3, -6, 6, -9],\n [-3, -6, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -8, -3, -9],\n [-20, 0, 20, 28],\n [-2, 4, 4, 8],\n [-12, 4, 14, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -8, -12, -4],\n [-12, -8, -12, -4],\n [6, 4, 6, 2],\n [12, 8, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 7, -20, 4],\n [0, 0, 0, 0],\n [-22, -9, 4, -16],\n [10, 5, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 4, 2, 16],\n [-6, -9, -3, -6],\n [1, -4, -1, 4],\n [-3, -10, -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[[-13, 12, 12, -12],\n [3, -3, -6, 7],\n [14, 5, -14, 11],\n [9, 17, -14, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -15, 12, 16],\n [-2, -6, 8, 8],\n [7, 9, -16, -14],\n [5, -9, 4, 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[[16, 0, -8, -4],\n [8, 0, -4, -2],\n [-4, 0, 2, 1],\n [12, 0, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -3, -1, -4],\n [-2, -6, -3, -8],\n [12, 0, -3, 0],\n [14, 6, 0, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -12, 9, 4],\n [6, -4, 3, -8],\n [-18, 16, -12, 24],\n [-3, -8, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, 8, -12],\n [9, 0, 6, -9],\n [-9, 0, -6, 9],\n [-12, 0, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -12, 0, -3],\n [0, 14, -6, -6],\n [0, 14, -6, -6],\n [-12, -2, -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[[0, -4, 8, 0],\n [0, 6, -12, 0],\n [0, -2, 4, 0],\n [0, -4, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, -12, -12],\n [8, 8, -8, -8],\n [4, 4, -4, -4],\n [-12, -12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 3, 0, -3],\n [-8, 4, 0, -4],\n [-4, 2, 0, -2],\n [-6, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 12, 16, 16],\n [0, 0, 0, 0],\n [4, -3, -4, -4],\n [-4, 3, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -4, -6, 8],\n [2, 4, 6, -8],\n [-4, -8, -12, 16],\n [2, 4, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -11, -2, -2],\n [16, -1, -14, -6],\n [4, -4, -10, -12],\n [17, -7, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, 6, 8],\n [-11, -1, 16, 14],\n [8, 0, -12, -16],\n [-9, -1, 13, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 0, -7, 16],\n [14, 10, -25, -15],\n [-24, 15, 3, -9],\n [22, -25, 16, 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[[-4, -2, 8, 8],\n [12, 9, 16, -6],\n [-18, 0, 16, 6],\n [-4, -14, -12, 20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -15, -12, -6],\n [0, -6, -6, -6],\n [-12, 5, 9, 17],\n [-9, -9, -6, 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[[-4, -3, 3, 3],\n [-4, -3, 3, 3],\n [4, 3, -3, -3],\n [-8, -6, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 6, 16, 14],\n [-8, 2, -2, 4],\n [-8, -12, -14, -20],\n [-12, -3, -21, -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[[8, 5, 0, -3],\n [-7, -4, 3, 3],\n [-15, -9, 3, 6],\n [3, 2, 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[[-22, -11, 14, -16],\n [0, -4, 4, 8],\n [1, 4, 0, 2],\n [10, 13, -8, 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[[12, -6, -6, -12],\n [-6, -2, 15, -2],\n [21, -13, -9, -7],\n [-9, 1, 14, -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 4x4 matrix:\n[[-4, -8, -20, 16],\n [-19, 12, -10, 16],\n [-16, 18, 5, 4],\n [6, -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[[-1, 4, -4, 4],\n [-8, -23, 28, 12],\n [-1, 20, -19, 12],\n [-3, -8, 18, 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[[-7, -14, 4, 14],\n [2, -11, 1, -4],\n [-26, -16, 4, 27],\n [-22, -11, 1, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 2, -8, -4],\n [-4, -2, 8, 4],\n [2, 1, -4, -2],\n [4, 2, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -16, -12, 8],\n [-6, 8, 2, -1],\n [24, -32, -8, 4],\n [2, 4, -9, 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[[-21, -6, 8, 0],\n [6, -4, 7, -15],\n [29, 0, -25, 15],\n [33, -1, -25, 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[[-2, 4, 24, 12],\n [-6, -16, -3, -7],\n [12, -4, -4, -2],\n [10, -8, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -3, 0, -3],\n [0, 0, 0, 0],\n [-4, 6, 0, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -4, 4, -3],\n [9, -12, 12, -9],\n [-9, 12, -12, 9],\n [-3, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 6, 8, 0],\n [9, -4, 3, 10],\n [0, -8, 6, -10],\n [-21, 17, -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 4x4 matrix:\n[[-12, -12, -16, 16],\n [3, 3, 4, -4],\n [-12, -12, -16, 16],\n [-3, -3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -15, -12, -3],\n [-9, -15, -24, -12],\n [13, -3, 0, -24],\n [-2, 9, 12, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -4, -6, 10],\n [-24, 0, -1, 11],\n [-18, 4, -3, 13],\n [4, 0, 1, -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[[0, 0, -1, 1],\n [0, 0, 2, -2],\n [0, 0, -2, 2],\n [0, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 3, -1, 2],\n [-2, -12, 6, 0],\n [-18, -10, 4, -4],\n [-3, 10, -6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, -2, 1],\n [0, 0, 0, 0],\n [0, 0, -6, 3],\n [0, 0, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 0, 3, -1],\n [-8, 0, -6, 2],\n [-4, 0, -3, 1],\n [-16, 0, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -3, -4, 1],\n [-12, 12, 16, -4],\n [-3, 3, 4, -1],\n [-3, 3, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, 4, 16],\n [1, 0, 1, 4],\n [2, 0, 2, 8],\n [-1, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -22, -10, -4],\n [0, 0, 3, 10],\n [-6, -12, -3, 6],\n [-4, -8, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 16, -16, 8],\n [-8, -3, 3, 0],\n [-4, -14, 14, -10],\n [-16, -11, 11, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -20, 8, -6],\n [0, -12, -21, 3],\n [-8, -21, -6, -4],\n [-24, 5, 3, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, 19, 16, -1],\n [3, -11, -12, 17],\n [15, -29, -23, 4],\n [16, -26, -21, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 16, -7, 7],\n [-5, 12, 1, 9],\n [5, -8, -9, -11],\n [-2, 12, -14, 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 4x4 matrix:\n[[12, 12, -3, 6],\n [20, 4, -7, 8],\n [-20, -4, 7, -8],\n [-12, -12, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -19, -2, 2],\n [28, -12, 22, 14],\n [7, -18, -14, -1],\n [16, -14, 15, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 15, 10, 4],\n [15, 12, 19, -25],\n [-3, -21, -19, 7],\n [-4, -24, -24, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -9, -3, -6],\n [-7, -9, 1, -2],\n [-6, 0, 6, 6],\n [-3, -3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 9, -11, 7],\n [-12, 5, 5, -17],\n [-13, 15, -14, 15],\n [-5, -1, 6, -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[[8, 16, -8, -1],\n [-15, 33, 29, 29],\n [-4, 5, 3, 7],\n [16, -8, 0, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -6, 11, -4],\n [0, 3, -15, 6],\n [-10, -19, 0, 2],\n [0, -4, 20, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -8, 10, 8],\n [31, 22, -7, 9],\n [5, 2, -11, 1],\n [2, 2, 7, 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[[4, 0, -16, -20],\n [-12, 13, -17, -18],\n [-8, 4, 12, 16],\n [-12, 13, -17, -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[[-9, 12, -4, -2],\n [24, -32, 8, 8],\n [12, -16, 0, 8],\n [24, -32, 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[[9, 0, -6, 9],\n [3, 0, -2, 3],\n [-12, 0, 8, -12],\n [-12, 0, 8, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -4, -8, 16],\n [-2, -1, -2, 4],\n [4, 2, 4, -8],\n [2, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -7, -2, 4],\n [1, -17, 0, 10],\n [-2, -11, 9, 7],\n [6, 8, -22, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -16, -6, 0],\n [-4, -16, -16, 8],\n [-4, -2, -7, 5],\n [-8, 24, 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[[-3, 4, 2, 4],\n [9, -12, -6, -12],\n [3, -4, -2, -4],\n [6, -8, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 3, 0, -3],\n [8, 2, 0, -2],\n [8, 2, 0, -2],\n [12, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 6, -4, -4],\n [10, -24, -3, -22],\n [14, -24, -1, -18],\n [-2, -15, -6, -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[[2, -17, 1, 5],\n [10, 10, 2, -11],\n [14, 6, 14, -1],\n [8, -21, 11, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 6, -4, -14],\n [4, 0, -12, -8],\n [-1, -6, -5, 8],\n [-3, -12, -7, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, -11, 10, 5],\n [16, 16, 6, 17],\n [44, -5, 16, 19],\n [-8, -1, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -6, -4, 6],\n [0, 12, 8, -12],\n [0, 9, 6, -9],\n [0, -3, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 2, 4, 4],\n [12, 8, 16, 16],\n [-12, -8, -16, -16],\n [6, 4, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 24, 24, -2],\n [2, 3, -6, -1],\n [23, -30, -24, 1],\n [12, -11, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 4, -4, 3],\n [0, 0, 0, 0],\n [2, -4, 4, -3],\n [4, -8, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 4, -4, 6],\n [-1, -2, 2, -3],\n [-1, -2, 2, -3],\n [1, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 15, 13, -11],\n [6, -12, -9, 13],\n [-16, 24, 20, -20],\n [-10, 18, 14, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -9, -3, 9],\n [2, 3, 1, -3],\n [-8, -12, -4, 12],\n [-8, -12, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -16, 8, 4],\n [2, -4, 2, 1],\n [2, -4, 2, 1],\n [6, -12, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 13, 1, -10],\n [12, -15, -5, 14],\n [16, 5, -15, 2],\n [11, 19, 7, -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[[-2, 2, 11, 7],\n [4, 10, -15, -5],\n [0, 4, 10, 6],\n [1, 8, 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[[-4, 5, 10, 9],\n [4, -2, -12, -6],\n [0, 6, -4, 6],\n [4, 4, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -6, -4, -2],\n [-8, -2, -3, 4],\n [-6, 4, 0, 1],\n [20, 7, 4, -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, -1, -4, 1],\n [-12, 0, -14, 2],\n [3, -3, 2, 1],\n [3, 7, 7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -8, 0, 0],\n [-4, 8, 0, 0],\n [2, -4, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -6, -22, 18],\n [6, 2, 29, -22],\n [5, 3, 11, -9],\n [14, 13, -9, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 2, 8, 4],\n [-6, 2, 8, 4],\n [-3, 1, 4, 2],\n [9, -3, -12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 10, -10, 14],\n [-16, 0, -5, 8],\n [-8, 8, -6, 8],\n [-4, 20, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 12, 8, -4],\n [8, -12, -8, 4],\n [-6, 9, 6, -3],\n [-8, 12, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, -16, -4, -6],\n [15, 18, 6, 24],\n [-14, -21, -6, -20],\n [28, 13, 4, 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[[-1, -3, -1, 0],\n [-1, -3, -1, 0],\n [4, 12, 4, 0],\n [-2, -6, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 0, 12, 9],\n [-4, 0, 16, 12],\n [1, -6, 2, -1],\n [-3, 12, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -20, -16, -17],\n [-6, 11, -7, 17],\n [8, -25, -36, -13],\n [4, -19, -22, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -6, -9, 9],\n [-16, 11, 15, -14],\n [-14, -11, 12, -18],\n [0, 9, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -4, 8, -16],\n [6, 3, -6, 12],\n [2, 1, -2, 4],\n [-4, -2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 4, 0, -2],\n [3, 2, 0, -1],\n [12, 8, 0, -4],\n [9, 6, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 1, -3, 3],\n [0, 2, -6, 6],\n [0, -2, 6, -6],\n [0, 3, -9, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -4, -6, -10],\n [9, 0, -13, -13],\n [7, -5, -7, -6],\n [-1, 15, -13, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 12, 5, -4],\n [-11, -3, -11, 14],\n [20, 16, 5, -4],\n [2, 0, 16, -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[[-16, 8, -19, -15],\n [-12, -12, -9, 3],\n [5, -13, 9, 13],\n [8, -16, 13, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -4, -16, -8],\n [4, -4, -16, -8],\n [-3, 3, 12, 6],\n [-2, 2, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 16, -10, 18],\n [-11, -3, -6, 1],\n [-1, -18, 9, -19],\n [20, -4, 16, -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[[0, 0, 8, -2],\n [0, 0, 8, -2],\n [0, 0, 12, -3],\n [0, 0, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -6, -2, 1],\n [6, -4, -8, 8],\n [-6, 4, 8, -8],\n [0, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, 1, 0, 3],\n [12, -3, 0, -9],\n [-4, 1, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 16, -4, -4],\n [1, -4, 1, 1],\n [-2, 8, -2, -2],\n [4, -16, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -4, -6, -2],\n [0, 0, 0, 0],\n [3, 2, 3, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 19, 0, 5],\n [-7, -8, 3, -13],\n [19, -16, -7, 21],\n [-8, 5, 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[[2, 4, 0, -4],\n [-1, -2, 0, 2],\n [-1, -2, 0, 2],\n [3, 6, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 12, -8, -4],\n [8, -6, 4, 2],\n [2, -5, 2, -3],\n [-5, 9, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, -10, 7, 20],\n [15, -14, -4, 10],\n [-31, 22, -4, -26],\n [2, -2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -2, -2, -4],\n [-10, -1, 11, 10],\n [-4, -4, 8, 4],\n [10, 1, -11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 1, 14, 13],\n [-20, -34, 8, -22],\n [-9, -23, 18, -7],\n [9, 23, -14, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, 16, -4],\n [0, 0, 0, 0],\n [-2, -4, -8, 2],\n [2, 4, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 0, -8, -13],\n [3, 18, -36, 1],\n [13, -11, 8, -16],\n [20, -5, -8, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -2, 2, 3],\n [0, 2, -2, -3],\n [0, -8, 8, 12],\n [0, 6, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 6, -12, 9],\n [-16, -12, 0, -12],\n [4, 24, 12, 25],\n [2, 12, -20, 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 4x4 matrix:\n[[8, -6, 6, 0],\n [-4, 1, -13, 16],\n [8, -4, 16, -16],\n [8, -8, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 16, 9, 20],\n [0, 5, -12, 0],\n [2, 14, 3, 20],\n [6, 11, -18, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, -19, -14, -7],\n [1, 2, 9, 4],\n [5, 5, 1, 2],\n [-2, 4, 17, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -12, -8, -4],\n [-3, -9, -6, -3],\n [-2, -6, -4, -2],\n [-3, -9, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 3, 12, -6],\n [-8, 4, 16, -8],\n [-2, 1, 4, -2],\n [-2, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 16, -11, -1],\n [16, 16, 12, 0],\n [-4, 16, 14, -5],\n [-8, 8, 24, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -4, -8, 4],\n [0, 0, 0, 0],\n [12, 3, 6, -3],\n [-8, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 18, 0, -13],\n [-3, -6, -6, 5],\n [6, 6, 15, -6],\n [5, 8, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 5, 3, -8],\n [9, 0, 24, -29],\n [12, 4, 12, 0],\n [1, 2, 0, -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 4x4 matrix:\n[[-3, -1, -4, 4],\n [3, 1, 4, -4],\n [-9, 6, -21, 21],\n [-3, 2, -7, 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[[-14, 8, -16, -18],\n [-20, 12, -16, -28],\n [-12, 7, -12, -16],\n [1, 14, -19, -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 4x4 matrix:\n[[8, 2, -8, -8],\n [12, 3, -12, -12],\n [8, 2, -8, -8],\n [-12, -3, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -2, 2, 4],\n [8, -1, 2, 5],\n [-8, -5, 2, 1],\n [0, -6, 4, 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 4x4 matrix:\n[[-6, 2, -2, 4],\n [6, -2, 2, -4],\n [9, -3, 3, -6],\n [9, -3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -10, -6, -8],\n [-2, 6, -2, 2],\n [-10, 10, 2, 6],\n [14, -12, -4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [9, 6, 3, -9],\n [-12, -8, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -4, -4, 8],\n [16, 1, 5, -5],\n [12, -12, 8, 9],\n [4, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 12, 6, -6],\n [-8, -16, -8, 8],\n [4, 8, 4, -4],\n [-8, -16, -8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-25, 4, -18, -7],\n [25, -10, 12, 4],\n [-19, 5, -9, 13],\n [19, -3, 11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 0, 4, -4],\n [10, -3, 3, -2],\n [-12, 18, 14, -20],\n [-7, 3, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -6, -3, 0],\n [-4, 0, -6, -6],\n [-6, 0, -4, -4],\n [12, -8, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 0, -8, -16],\n [0, 0, 0, 0],\n [4, 0, -4, -8],\n [6, 0, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 5, -5, 5],\n [-23, 8, -6, -6],\n [-2, 2, 6, -9],\n [-12, 2, 10, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -4, -8, 8],\n [-6, 6, 12, -12],\n [4, -4, -8, 8],\n [6, -6, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 16, -8, 4],\n [6, -12, 6, -3],\n [-8, 16, -8, 4],\n [-8, 16, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -4, 12, 4],\n [2, -4, -16, 0],\n [-6, -3, 9, 3],\n [-8, -9, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 6, -5, 7],\n [-4, 12, 4, 4],\n [0, 3, -6, 6],\n [-4, 12, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, 1, 13, -1],\n [-16, 4, 16, 8],\n [1, -5, -1, -3],\n [1, 13, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -7, 10, -9],\n [-14, -9, -4, 16],\n [-6, 9, 6, 21],\n [-18, -12, 10, -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, -16, 5, 13],\n [-3, 0, 3, -9],\n [-3, 0, 3, -9],\n [-2, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 15, -8, -15],\n [-7, 15, -8, -15],\n [-3, 9, -6, -12],\n [-14, 18, -4, -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[[10, -11, -5, 8],\n [10, -4, -5, 12],\n [10, -4, -5, 12],\n [14, 0, -7, 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, -16, -14, -4],\n [-8, 0, 13, 30],\n [10, 4, -1, -14],\n [-4, 12, 11, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [8, -6, 8, -6],\n [22, -6, 20, -10],\n [-6, -6, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 14, -20, 4],\n [-8, -1, -14, 8],\n [4, 11, -22, 4],\n [20, 17, 14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -4, -3, 0],\n [-6, 20, 7, 8],\n [4, -12, -5, -4],\n [-9, 20, 13, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [6, -9, 3, 0],\n [-8, 12, -4, 0],\n [-6, 9, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 2, 6, 3],\n [21, 6, 12, 3],\n [1, -6, -8, 1],\n [-6, -4, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 3, 6],\n [0, 0, -2, -4],\n [0, 0, 0, 0],\n [0, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, 7, -10, 4],\n [7, 13, 5, -14],\n [-13, -15, 3, 10],\n [-2, 4, 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 4x4 matrix:\n[[14, -3, 11, 17],\n [-4, 0, -2, -4],\n [-2, 3, -5, -5],\n [-6, -5, -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[[22, 4, 12, 1],\n [-2, 8, 12, 9],\n [4, 21, 20, -7],\n [16, 18, 28, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -2, 4, -8],\n [-8, 4, -8, 16],\n [0, 0, 0, 0],\n [8, -4, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -8, 18, -15],\n [-8, -6, -14, 15],\n [6, 5, 8, -9],\n [4, 0, 22, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -3, 2, -11],\n [0, 9, -2, 5],\n [9, 5, -10, 10],\n [5, 0, -4, 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 4x4 matrix:\n[[-9, 13, -8, -7],\n [0, 6, -3, 1],\n [-14, 21, -12, -14],\n [-19, 14, -13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 7, -9, 5],\n [16, -1, 0, -11],\n [12, 0, -1, -8],\n [-4, 4, -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[[-16, -16, -4, -16],\n [8, -8, -4, -4],\n [8, 24, 8, 20],\n [-8, -24, -8, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 8],\n [0, 0, 0, 4],\n [0, 0, 0, -6],\n [0, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 3, 1, 2],\n [0, 0, 0, 0],\n [-2, 6, 2, 4],\n [9, 9, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 20, -25, -3],\n [-9, 4, 3, -7],\n [1, 10, -9, 17],\n [1, 2, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 2, -6, -6],\n [24, 3, 3, 12],\n [0, -3, 5, 2],\n [-20, -1, -5, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 4, -28, -28],\n [-4, 11, 13, 13],\n [8, -4, 10, 10],\n [16, -12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 6, 6, -4],\n [0, 0, 0, 0],\n [-3, 3, 3, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -3, 12, 11],\n [-9, -17, 5, -10],\n [3, 9, -5, 2],\n [9, 10, 4, 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[[0, -9, 0, 3],\n [0, -6, 0, 2],\n [0, -3, 0, 1],\n [0, 6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 12, -6, -6],\n [0, 4, -2, -2],\n [0, -8, 4, 4],\n [0, -12, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, 1, -4],\n [1, -16, 5, -14],\n [3, 2, 0, -2],\n [-8, -12, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -8, -2, 4],\n [12, 16, 4, -8],\n [-12, -16, -4, 8],\n [-3, -4, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, 8, -8],\n [0, 0, 0, 0],\n [0, -2, -8, 8],\n [0, 1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 0, 12, 0],\n [1, 0, -4, 0],\n [0, 0, 0, 0],\n [2, 0, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -13, -1, 9],\n [-12, -16, -4, 8],\n [8, 10, 3, -7],\n [-18, -2, -11, -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[[-3, 0, 6, -5],\n [-1, -12, -18, 21],\n [13, 16, -2, -9],\n [5, 10, -8, -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 4x4 matrix:\n[[-19, -1, 6, 24],\n [11, -1, -6, -18],\n [2, -2, -4, -8],\n [-13, -7, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -9, 8, -25],\n [-3, -5, -8, 1],\n [-9, -9, 5, -22],\n [12, 4, -8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -18, 12, -12],\n [15, 21, -6, 4],\n [-3, 18, 6, -3],\n [19, 12, -14, 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[[-1, 6, 2, -3],\n [0, -4, -4, 10],\n [2, -6, -4, 18],\n [-2, 7, 2, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -4, -8, -4],\n [7, -2, -12, -18],\n [-1, 2, 6, 6],\n [-6, 4, 16, 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[[16, -4, 0, -4],\n [-16, 4, 0, 4],\n [4, -1, 0, -1],\n [4, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [8, -8, 0, -8],\n [16, -16, 0, -16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 0, 30, 8],\n [-4, -3, -15, 2],\n [5, -5, -25, -6],\n [3, 17, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -4, 4, 1],\n [-3, -12, 12, 3],\n [-4, -16, 16, 4],\n [-3, -12, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -10, 0, 6],\n [2, -10, -13, -1],\n [12, 4, 6, 6],\n [3, -7, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -8, 5, -2],\n [-17, -10, -11, 15],\n [5, -12, -3, 2],\n [-9, -8, -9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -1, 2, 0],\n [0, 0, 0, 0],\n [0, -4, 8, 0],\n [0, 1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 2, 6, 13],\n [20, 12, 3, -10],\n [-8, -12, -12, -14],\n [12, 14, 12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -7, -9, 5],\n [9, -13, -2, -23],\n [1, 3, 5, 7],\n [4, 2, 6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -6, 2, -4],\n [-2, 3, -1, 2],\n [-2, 3, -1, 2],\n [-2, 3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 10, -12, -5],\n [-4, -6, 6, 6],\n [0, -10, 18, -10],\n [9, 11, -9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -6, -15, -7],\n [5, 0, -3, -7],\n [13, -12, -24, -20],\n [-7, -4, 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 4x4 matrix:\n[[9, 6, 6, 3],\n [9, 6, 6, 3],\n [-9, -6, -6, -3],\n [-12, -8, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -12, -8, -8],\n [-3, -3, -2, -2],\n [0, -3, -5, 7],\n [5, 3, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 12, 0, -3],\n [-12, 12, 0, -3],\n [8, -8, 0, 2],\n [4, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -26, 5, 21],\n [4, 7, -8, 0],\n [-8, -4, 10, -4],\n [24, -9, 1, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -8, 16, 8],\n [-3, 4, -10, -10],\n [1, -1, 3, 4],\n [-2, 1, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 10, -4, -24],\n [1, -5, 1, -4],\n [4, -4, 0, -16],\n [-3, -9, 3, 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[[0, 0, 4, 0],\n [0, 0, -1, 0],\n [0, 0, 1, 0],\n [0, 0, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -4, 8, 4],\n [8, 2, -4, -2],\n [-16, -4, 8, 4],\n [4, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 12, 0, 16],\n [-6, -9, 0, -12],\n [2, 3, 0, 4],\n [6, 9, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 22, -17, -16],\n [-32, 20, -18, 4],\n [-44, 14, -15, 16],\n [-4, 10, -13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -30, -28, -11],\n [10, -22, -20, -5],\n [15, -30, -27, -9],\n [-3, 12, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -12, 8, -8],\n [-3, -3, 2, -2],\n [0, 0, 0, 0],\n [3, 3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 12, 11, -10],\n [-12, 12, 17, -14],\n [4, -12, -11, 10],\n [-16, 3, 14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 9, 2, 7],\n [-1, -20, -3, -14],\n [-4, -19, -4, -18],\n [-8, -7, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-34, -3, 16, -2],\n [0, -8, 4, 5],\n [17, -7, -12, 5],\n [-3, -14, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [20, -24, 5, 13],\n [-6, 16, -14, -11],\n [-2, 8, 21, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 8, -4, -8],\n [-2, -8, 4, 8],\n [1, 4, -2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 9, -3, 11],\n [21, -7, 0, -14],\n [-24, 4, 0, 16],\n [7, 24, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 0, 16, 12],\n [3, 1, 4, 0],\n [0, -4, -4, 9],\n [11, 1, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 16, -8, -8],\n [-2, 4, -2, -2],\n [0, 0, 0, 0],\n [6, -12, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 4, 0, 10],\n [-10, -4, -4, -7],\n [-8, 0, 16, -12],\n [14, 4, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -9, 0, -3],\n [-20, -9, 4, -6],\n [-20, 3, 12, -8],\n [-24, -6, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -4, -1, -3],\n [-2, -8, -2, -6],\n [4, 16, 4, 12],\n [3, 12, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 0, -1, -12],\n [0, 8, -1, -29],\n [16, -18, -10, 20],\n [-6, 10, 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[[9, 9, 0, -12],\n [-3, 29, -24, -8],\n [15, -3, 6, -6],\n [1, 13, -14, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, -12, 6],\n [7, 6, -16, 10],\n [-8, 8, -16, 8],\n [6, 0, -8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -12, -8, 4],\n [-6, -9, -6, 3],\n [2, 3, 2, -1],\n [4, 6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 0, 0, -2],\n [0, 0, 0, 0],\n [6, 0, 0, 6],\n [-6, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 4, -10, 4],\n [0, 0, 0, 0],\n [-8, -2, 0, -7],\n [-18, -6, 4, -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[[0, 0, 0, 0],\n [4, -4, 1, -1],\n [-16, 16, -4, 4],\n [-4, 4, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, 3, -12, -15],\n [5, 0, -6, -3],\n [4, 8, 8, -20],\n [9, 3, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 16, -10, 15],\n [0, 24, -12, 22],\n [-4, -4, -2, -3],\n [24, 0, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 24, -3, -7],\n [-8, 6, -3, -1],\n [-6, -8, -1, 3],\n [-9, 13, -4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 9, 0, 12],\n [-2, -6, 0, -8],\n [-3, -9, 0, -12],\n [4, 12, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, 0, -6, 18],\n [-8, -2, -3, 15],\n [7, 1, 6, 6],\n [-3, 3, -3, -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[[-10, -3, -1, -4],\n [-22, 0, -10, -16],\n [-16, -24, 14, -4],\n [-18, 1, -7, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 2, -3, -4],\n [-12, 6, -6, -6],\n [-12, 5, -3, -1],\n [12, -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[[8, -8, -4, -8],\n [-17, 3, 4, 32],\n [-3, 9, 0, 0],\n [4, 0, -1, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -3, -12, 12],\n [-2, -1, -4, 4],\n [8, 4, 16, -16],\n [-4, -2, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -2, 5, -1],\n [-12, -18, 15, 21],\n [6, 14, -13, -15],\n [3, -8, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -9, 4, -22],\n [16, 12, 4, -8],\n [-8, 0, -4, 16],\n [-2, 3, -2, 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[[-4, -2, 6, 3],\n [8, 6, -14, -9],\n [16, 4, -20, -6],\n [-12, -2, 14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 1, 6, -6],\n [-12, 8, -3, 8],\n [-8, -8, -2, 8],\n [-11, -4, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -22, -20, -8],\n [-12, 16, 19, 16],\n [7, 0, 0, 7],\n [5, 26, 15, -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[[-2, 6, 12, 6],\n [3, 19, 10, -2],\n [2, -2, -8, -5],\n [-3, -19, -10, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-3, -3, 12, 6],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 3, -6, 8],\n [1, 3, -4, 10],\n [-2, 3, 2, -14],\n [3, -6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -10, 1, -2],\n [8, -8, -2, 8],\n [2, 10, -1, 2],\n [-4, -20, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 3, -8, -3],\n [6, -9, -3, 0],\n [-8, 6, -10, -4],\n [0, -3, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -8, -3, -21],\n [4, -20, -4, -28],\n [-7, 14, 9, 13],\n [-7, -13, 3, -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[[2, -16, -6, 4],\n [1, 15, 8, -4],\n [0, 28, 16, -16],\n [-4, -17, -13, 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, 0, 12, 3],\n [0, -3, 28, 10],\n [0, 4, -32, -12],\n [0, 2, 8, 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[[11, -9, -8, 4],\n [2, -8, -1, 8],\n [-1, -3, 1, 4],\n [2, -8, -1, 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[[17, 15, -10, 11],\n [-1, 6, 6, 4],\n [-14, -7, 9, -6],\n [-14, 10, -24, -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[[0, 0, 0, 0],\n [12, -12, -8, -16],\n [3, -3, -2, -4],\n [-12, 12, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 4, 8, -16],\n [-8, 4, 8, -16],\n [-6, 3, 6, -12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -2, -8, -2],\n [-13, 3, 15, -4],\n [24, -10, -28, -8],\n [8, -3, -6, -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 4x4 matrix:\n[[-4, -4, -8, 4],\n [8, 8, 16, -8],\n [-4, -4, -8, 4],\n [6, 6, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 10, 14, 14],\n [-7, 2, -5, 4],\n [-5, -2, -3, -20],\n [-12, 8, -8, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -4, 4, 4],\n [6, 12, -12, -12],\n [-2, -4, 4, 4],\n [-4, -8, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -6, 10, 0],\n [-4, 9, -1, -12],\n [1, -5, -1, 8],\n [3, -15, -3, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 15, 8, -3],\n [0, -13, 2, 2],\n [12, -6, -2, -5],\n [16, -1, -14, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 4, 0, 3],\n [6, 21, 9, 3],\n [8, 20, 9, -4],\n [4, 3, 3, 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, -5, 2, -6],\n [10, 4, -4, 4],\n [-2, 7, 2, 10],\n [8, 11, -2, 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[[11, -5, 5, -10],\n [1, 3, 6, 11],\n [2, -3, 4, 0],\n [1, -7, -4, -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[[1, -10, 16, -2],\n [-7, 7, 5, 20],\n [-2, -4, 28, 16],\n [1, 5, 19, 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[[-1, 2, -2, 1],\n [7, 6, -16, -7],\n [7, 2, -10, -7],\n [3, -2, 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[[-8, 16, -12, 4],\n [6, -12, 9, -3],\n [8, -16, 12, -4],\n [-8, 16, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -16, 6, -8],\n [-23, -5, -6, -7],\n [-14, 14, -3, -2],\n [-13, 9, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 0, -6, -6],\n [13, -7, 17, 11],\n [5, 21, -18, 0],\n [2, 1, -4, -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, -17, 2, -5],\n [3, -3, -9, 6],\n [21, 12, -22, 21],\n [-5, 2, -22, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -8, 0, -6],\n [-3, 4, 0, 3],\n [3, -4, 0, -3],\n [-9, 12, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -4, 1, 7],\n [-1, 8, -3, 5],\n [11, -16, -3, -19],\n [9, 16, -1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 0, -14, -9],\n [-4, 9, 8, 0],\n [11, -16, -22, -5],\n [-9, 8, 18, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -23, -10, -4],\n [12, 15, -14, 16],\n [-12, -18, 16, -20],\n [6, 7, -14, 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[[-7, 12, -9, 9],\n [-15, -1, 5, -5],\n [0, -11, 10, -10],\n [-4, 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[[-4, 0, -6, 4],\n [6, 0, 9, -6],\n [8, 0, 12, -8],\n [8, 0, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 9, 6, 9],\n [-12, -9, -6, -9],\n [0, 0, 0, 0],\n [-8, -6, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 15, -12, 12],\n [-8, -17, 8, -15],\n [-16, -22, 16, -18],\n [-8, -14, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 12, -10, 0],\n [2, 0, 4, 3],\n [6, 0, 2, 7],\n [1, -2, -36, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, -3, -2],\n [-4, -4, -3, -2],\n [4, 4, 3, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -5, -12, -12],\n [-10, -10, -14, 19],\n [-12, -4, -16, 0],\n [-9, 1, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 10, -6, 2],\n [-9, -11, 0, -7],\n [10, 14, -4, 6],\n [-8, -12, 5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 8, 8, 0],\n [-1, 2, 2, 0],\n [-3, 6, 6, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 11, 14, -24],\n [-16, -12, -7, 7],\n [0, -8, -8, 12],\n [-4, 1, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -12, -16, 8],\n [-9, 9, 12, -6],\n [-3, 3, 4, -2],\n [-9, 9, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, -6, 0],\n [5, -4, -10, 11],\n [10, 5, -17, 1],\n [7, 7, -21, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 8, 4, 6],\n [9, -12, -6, -9],\n [6, -8, -4, -6],\n [-6, 8, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -7, 3, 10],\n [-2, -2, 3, 0],\n [4, 4, -3, -4],\n [3, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -4, 8, 0],\n [0, 0, 0, 0],\n [-2, 2, -4, 0],\n [6, -6, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [12, -4, 4, 8],\n [6, -2, 2, 4],\n [1, 5, 7, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 3, 19, 4],\n [8, -8, -6, -3],\n [2, -11, -24, 0],\n [4, 9, 29, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, 2, 4],\n [0, 4, 1, 2],\n [0, -8, -2, -4],\n [0, 4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, 9, -8, 4],\n [12, 28, 0, 0],\n [-6, 2, 6, -3],\n [4, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 2, -1, 4],\n [-14, -10, -1, -8],\n [12, 0, -2, 4],\n [-18, -18, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -8, 16, 20],\n [1, -8, -2, -1],\n [2, -24, 0, 4],\n [-3, 0, 18, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [4, -4, -6, -8],\n [8, -8, -12, -16],\n [-4, 4, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[22, -8, -14, -13],\n [-14, 4, -4, 13],\n [-4, -4, -14, 10],\n [-14, 28, 10, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -12, -3, 6],\n [-2, 8, 2, -4],\n [1, -4, -1, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -3, -1, 3],\n [-4, 6, 2, -6],\n [-2, 3, 1, -3],\n [-4, 6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -6, 0, 6],\n [-16, -12, 0, 12],\n [8, 6, 0, -6],\n [-16, -12, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 6, -15, 5],\n [9, 10, 9, -3],\n [2, 0, 12, -4],\n [6, 6, 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[[-3, 13, 13, 6],\n [3, -1, -1, 6],\n [-12, 4, 4, -24],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -22, -16, -16],\n [1, 0, 10, 12],\n [-12, -12, -16, -8],\n [-13, -10, -10, 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 4x4 matrix:\n[[1, 0, 2, -1],\n [-3, -1, 5, -3],\n [-11, -3, 11, -7],\n [15, 4, -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[[1, 1, 4, 4],\n [1, 1, 4, 4],\n [3, 3, 12, 12],\n [2, 2, 8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, -7, 18, 12],\n [17, -6, -15, -14],\n [10, -4, -4, -6],\n [-10, 0, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -2, -4, 8],\n [-6, 2, 4, -8],\n [9, -3, -6, 12],\n [-6, 2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 3, 9, 9],\n [-9, -3, -9, -9],\n [-12, -4, -12, -12],\n [3, 1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -12, -4, -16],\n [-6, 6, 2, 8],\n [12, -12, -4, -16],\n [3, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 13, 3, -12],\n [-13, -8, -2, 30],\n [-10, -5, -7, 16],\n [-13, 6, -16, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 1, 1, 6],\n [16, 0, -4, -4],\n [6, 2, -7, 3],\n [15, -1, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [0, -1, 3, 0],\n [0, -4, 12, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 12, -8, 11],\n [-4, -10, -6, -6],\n [-20, 22, -6, 18],\n [-8, 4, -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[[4, 9, -21, 0],\n [0, -1, -3, 4],\n [0, 3, 9, -12],\n [3, 7, -15, -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[[9, 9, 12, 9],\n [-9, -9, -12, -9],\n [-9, -9, -12, -9],\n [-6, -6, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -5, 1, 4],\n [-18, -14, 8, 8],\n [6, 3, -11, 4],\n [3, 6, 17, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 9, 10, -14],\n [7, -7, -8, 10],\n [8, -8, -10, 8],\n [0, 0, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, -6, 6],\n [9, 0, -9, 9],\n [6, 0, -6, 6],\n [-9, 0, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -3, 13, -4],\n [-2, 3, -9, 2],\n [1, 0, -19, 3],\n [-13, 9, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 4, 20, -15],\n [-9, 4, -22, 14],\n [-1, 4, 2, -2],\n [4, 4, -4, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [-4, -16, 8, 16],\n [-3, -12, 6, 12],\n [2, 8, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-26, -10, 4, 0],\n [-24, -6, -4, 17],\n [-2, -6, 4, 13],\n [7, -6, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 1, -2, -7],\n [5, 10, -7, -19],\n [-1, -7, -1, 4],\n [-9, 17, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -1, 3, 1],\n [1, -1, 3, 1],\n [2, -2, 6, 2],\n [-2, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -8, 12, 4],\n [-4, 24, -17, -13],\n [12, -18, 22, 16],\n [-10, -24, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -16, 15, -11],\n [8, -9, 7, -8],\n [-5, -11, 12, -6],\n [-19, -4, 5, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -4, -8, 2],\n [0, 0, 0, 0],\n [-9, 5, 12, -1],\n [-2, 2, 8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 4, -2, 1],\n [6, -8, 4, -2],\n [-6, 8, -4, 2],\n [-3, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 4, -4, 8],\n [-9, 3, -3, 6],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 14, 4, -16],\n [25, -9, 3, 0],\n [-32, 15, 8, -10],\n [-7, -7, 11, 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[[9, 0, 6, -9],\n [-3, 0, -2, 3],\n [-9, 0, -6, 9],\n [9, 0, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, 12, -16],\n [0, -6, -9, 12],\n [0, 6, 9, -12],\n [0, 2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -12, 34, 14],\n [-1, -8, -13, -18],\n [0, -16, 15, -5],\n [2, 4, -25, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -10, -16, 2],\n [13, 1, 16, -11],\n [-10, -10, -16, 2],\n [2, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -8, 12, -4],\n [15, -2, 5, -4],\n [8, -6, 7, -1],\n [-14, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -2, -10, 8],\n [0, 2, 10, -8],\n [0, 2, 10, -8],\n [-10, -3, -25, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, 0, -3],\n [0, 0, 0, 0],\n [6, -6, 0, -9],\n [4, -4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, 16, 6, 7],\n [1, 10, 8, 4],\n [-9, -5, -2, -11],\n [2, -12, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 13, 2, -9],\n [9, 5, -2, 0],\n [10, -10, -12, 4],\n [-1, 17, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -18, 7, -24],\n [33, -10, 5, -28],\n [-1, -5, 1, -4],\n [-20, 9, -4, 20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -5, -20, -9],\n [-6, 1, 7, 11],\n [-4, -6, -1, 0],\n [6, -13, -10, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -6, -9, -12],\n [6, 6, 9, 12],\n [0, 0, 0, 0],\n [-2, -2, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 2, -1, -1],\n [3, -6, 3, 3],\n [4, -8, 4, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -3, 5, -8],\n [10, 6, -7, 15],\n [12, 5, 2, -1],\n [-4, -1, -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[[-16, -16, -8, -16],\n [-12, -12, -6, -12],\n [-4, -4, -2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[15, -26, 5, 15],\n [-4, 22, -12, -13],\n [10, 6, -14, -3],\n [18, -4, -10, -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[[-11, 2, 7, 13],\n [-1, 7, 2, 8],\n [-9, -2, 5, 7],\n [-1, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, -3, -3],\n [4, 4, 1, 1],\n [16, 16, 4, 4],\n [-16, -16, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 8, -6, 8],\n [-3, 4, -3, 4],\n [6, -8, 6, -8],\n [12, -16, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 16, -12, 8],\n [4, -4, 3, -2],\n [12, -12, 9, -6],\n [16, -16, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -14, -5, -8],\n [-8, -1, 2, 1],\n [12, -15, -6, -9],\n [3, -1, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [8, 0, 8, 6],\n [-16, 0, -16, -12],\n [-12, 0, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[14, 13, 7, -10],\n [-12, 1, 9, 14],\n [16, -2, -13, -19],\n [-18, -14, -6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, -14, -5, -2],\n [16, 0, 6, -6],\n [-9, -10, -4, -1],\n [9, -6, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -13, 12, -3],\n [21, -27, 16, 11],\n [9, -11, 4, 11],\n [-15, 15, -2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, -4, -4],\n [11, 3, -1, -8],\n [1, 6, 5, -9],\n [2, 3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 2, -8, -6],\n [-4, 4, -16, -12],\n [-4, 4, -16, -12],\n [1, -1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -9, 5, 2],\n [-6, 8, -4, 2],\n [6, 2, -2, -8],\n [0, 15, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 6, 11, -1],\n [13, 22, 7, -7],\n [-4, -6, -1, 2],\n [7, 8, -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[[5, -6, -9, 2],\n [-4, 16, 3, 4],\n [-11, 10, 21, -6],\n [-2, -12, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 23, -18, -11],\n [6, -12, 20, 25],\n [-4, 6, -11, -10],\n [5, -5, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 2, -8, -4],\n [16, -4, 16, 8],\n [-12, 3, -12, -6],\n [-4, 1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -3, 6, -3],\n [-2, -1, 2, -1],\n [0, 0, 0, 0],\n [2, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -6, -2],\n [2, -2, -3, -1],\n [10, 8, 6, 7],\n [-10, -8, -6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 14, -22, 25],\n [-8, 12, -25, 22],\n [-11, -10, -8, -13],\n [1, -14, 15, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -18, -4, 8],\n [17, -24, 3, 8],\n [-5, 30, 0, -17],\n [-6, -21, -19, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, -3, 16, 15],\n [-8, 6, -4, -2],\n [-10, 12, 4, 8],\n [4, -12, -16, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 9, -12, -9],\n [-9, 9, -12, -9],\n [2, 12, 5, -19],\n [0, -6, -1, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 9, -15, 4],\n [-2, -7, 25, -2],\n [4, -6, -6, -4],\n [2, -3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 4, 22, -12],\n [0, -4, 8, -8],\n [20, 24, 12, 8],\n [-2, -8, 10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -3, -3, 1],\n [16, 12, 12, -4],\n [4, 3, 3, -1],\n [16, 12, 12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -2, 4, -1],\n [2, -4, 8, -2],\n [-4, 8, -16, 4],\n [3, -6, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 9, 3, -12],\n [-3, -9, -3, 12],\n [-2, -6, -2, 8],\n [-1, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -16, 14, -20],\n [6, 0, -9, 2],\n [-24, -24, 12, -28],\n [-12, -18, 0, -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[[8, 0, 3, 3],\n [25, -9, 4, -7],\n [27, -5, 8, -5],\n [12, -10, -2, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 4, 0, 1],\n [2, -7, 10, -8],\n [-14, 6, -22, 20],\n [5, -1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, 4, 21, 4],\n [-5, 17, -12, 17],\n [-4, -12, 16, -12],\n [-2, -7, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 7, 23, 1],\n [-9, -7, -3, -5],\n [0, 1, 14, 1],\n [-12, -12, -28, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -6, 0, 4],\n [-8, 12, 0, -8],\n [4, -6, 0, 4],\n [-8, 12, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -4, -2, 0],\n [3, -2, -1, 0],\n [-6, 4, 2, 0],\n [9, -6, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 11, 6, -13],\n [-16, 16, -12, -20],\n [14, -11, 14, 9],\n [-6, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -17, -7, -23],\n [-6, -16, 16, -16],\n [-15, -5, 18, -6],\n [8, -17, 12, -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[[13, -5, -12, -8],\n [-13, 5, 12, 8],\n [16, -6, -14, -10],\n [-7, 2, 3, 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[[6, 6, 3, -6],\n [-2, -2, -1, 2],\n [0, 0, 0, 0],\n [-8, -8, -4, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 13, 10, -7],\n [-3, -3, 2, -7],\n [-2, -8, 16, 5],\n [-3, 9, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 6, -12, 6],\n [0, 0, 0, 0],\n [-4, -2, 4, -2],\n [12, 6, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -6, 2, 4],\n [13, -5, 7, -2],\n [6, -6, 2, 4],\n [7, -5, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 5, 5, 8],\n [-9, 11, -5, 0],\n [-16, 12, 8, 14],\n [-2, 3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 2, 11, -5],\n [8, -4, 3, 15],\n [6, 2, 11, -5],\n [11, -1, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -6, 6, -6],\n [-24, 4, 4, -4],\n [20, 0, -6, 6],\n [4, 11, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 26, -4, -12],\n [2, -25, 2, -2],\n [1, 22, 7, 11],\n [1, 3, 0, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 15, 12, 12],\n [1, -6, -3, -12],\n [-6, 8, 6, 8],\n [-12, 9, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 20, 8, -16],\n [9, 14, 14, -16],\n [-6, -11, 4, 4],\n [1, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 12, -9, 12],\n [-12, 12, -9, 12],\n [12, -12, 9, -12],\n [-8, 8, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, -1, -4],\n [0, 0, 0, 0],\n [-16, -16, -4, -16],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 6, 8, 13],\n [6, -6, -8, 8],\n [18, 0, 0, 21],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -12, 12, -6],\n [-16, 14, -11, -11],\n [13, 13, -6, 2],\n [-1, -27, 23, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -3, 9, -12],\n [-8, 4, -12, 16],\n [8, -4, 12, -16],\n [-8, 4, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, 8, -6, 14],\n [17, -5, 17, -5],\n [-7, 7, 1, 16],\n [2, -3, -3, 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 4x4 matrix:\n[[0, -11, 2, 5],\n [0, 4, -2, 2],\n [0, -8, 3, -1],\n [0, -12, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 4, -9, -1],\n [8, -2, 8, 4],\n [-16, 4, -12, -4],\n [-12, 3, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [2, 0, 8, 4],\n [1, 0, 4, 2],\n [2, 0, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 0, 11, -9],\n [18, -10, -10, 26],\n [2, -1, -12, 10],\n [23, -7, -3, 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[[6, 2, 2, 10],\n [10, -11, 15, 29],\n [4, 26, -2, -2],\n [-11, 6, -16, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 9, 12, 6],\n [-15, -10, -14, -5],\n [-3, 7, 8, 8],\n [-6, 14, 16, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 4, 24, 1],\n [-9, 3, 30, -3],\n [-17, 20, 2, -15],\n [-2, 31, 16, 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 4x4 matrix:\n[[0, 4, 6, 4],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, -6, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 4, -3, 0],\n [-6, 8, -6, 0],\n [-9, 12, -9, 0],\n [3, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -17, 16, 7],\n [-16, 8, 8, -4],\n [5, 4, -20, 1],\n [20, 3, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -6, 0, 0],\n [2, -6, 0, 0],\n [-3, 9, 0, 0],\n [-2, 6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 0, -4, -12],\n [-11, 3, 0, 16],\n [3, -9, 15, -3],\n [-9, 3, -1, 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 4x4 matrix:\n[[0, -1, -2, 4],\n [4, -9, -8, 10],\n [-2, 3, 1, 1],\n [-8, 15, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 8, -19, 1],\n [17, -13, -11, -9],\n [6, -4, 11, -5],\n [13, 0, -15, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -4, -12, -3],\n [-25, 8, 18, -9],\n [24, -7, -14, 10],\n [-22, 5, 8, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[28, -14, 13, 1],\n [28, -14, 16, 0],\n [22, -11, 12, -4],\n [4, -2, 9, -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[[16, -4, -4, 8],\n [8, 0, 0, 0],\n [4, -7, -7, 14],\n [-8, 6, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -21, 21, -24],\n [1, -17, 18, -20],\n [-2, -16, 19, -20],\n [7, 1, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -12, -28, 8],\n [-9, 18, 7, 5],\n [3, -3, 6, -5],\n [3, -15, -24, 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[[12, 16, 4, 8],\n [2, 9, 4, 3],\n [-20, -23, -10, -13],\n [7, 8, -1, 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[[12, 2, -12, 8],\n [3, 3, -3, -3],\n [19, 8, -3, -13],\n [-14, -2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -9, -10, -7],\n [-9, 15, 14, 5],\n [-3, 15, 18, 15],\n [3, -9, -10, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [8, -2, -4, 0],\n [16, -4, -8, 0],\n [-12, 3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -2, 11, 21],\n [-16, -6, -16, -11],\n [-15, -11, -15, 0],\n [9, 3, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -14, 6, -14],\n [-12, 6, 6, -6],\n [-24, 16, -4, 12],\n [-28, 18, -2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -9, -12, -12],\n [0, 9, 12, 12],\n [0, -6, -8, -8],\n [0, 6, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 23, 8, 8],\n [4, 24, 9, 4],\n [8, -20, 20, 16],\n [0, -5, -10, -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[[-8, 1, 11, -6],\n [-6, -4, -7, 10],\n [-5, 1, 18, -22],\n [-14, 6, 10, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 4, -8, 4],\n [-31, 3, -21, 13],\n [-15, -14, -7, 4],\n [-17, -5, -10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 0, 2, 2],\n [4, 0, 4, 4],\n [2, 0, 2, 2],\n [6, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[18, -30, -15, 3],\n [8, -14, -10, 20],\n [-4, -8, -2, -32],\n [4, -10, -4, -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[[-1, -4, 3, 0],\n [-4, -16, 12, 0],\n [-3, -12, 9, 0],\n [-3, -12, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -1, -4, 6],\n [7, -12, 13, -15],\n [-10, 10, -8, 22],\n [-7, 15, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -6, 9, -7],\n [-19, 0, -4, 0],\n [4, -20, -14, 22],\n [21, 16, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 11, 2, -13],\n [-4, -5, -2, 3],\n [0, 2, 2, 2],\n [-8, -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[[3, -12, -3, 12],\n [-5, 24, 11, -28],\n [-33, 2, -8, -4],\n [18, 8, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, -2, 10, 16],\n [-28, -4, -28, 8],\n [-13, -3, -13, 10],\n [6, -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[[-9, 0, -3, 9],\n [6, 0, 2, -6],\n [-12, 0, -4, 12],\n [-6, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -8, -4, 16],\n [-4, 2, 1, -4],\n [-12, 6, 3, -12],\n [16, -8, -4, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 12, 3, 6],\n [-15, -12, -6, -12],\n [11, -4, 2, 4],\n [6, -8, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 7, 12, -16],\n [0, 0, 0, 0],\n [-7, 7, 10, -4],\n [-5, 3, 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[[6, -12, -20, 8],\n [3, 3, 4, 2],\n [12, -6, -12, 12],\n [-1, -13, -20, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 28, 28, -8],\n [2, -8, -10, 1],\n [-6, 18, 24, 0],\n [0, 6, 14, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 12, 7, -10],\n [6, 2, 14, -4],\n [6, 6, 9, -6],\n [1, 3, -1, -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[[9, 0, 0, 12],\n [9, 0, 0, 12],\n [-9, 0, 0, -12],\n [3, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -12, 6, 6],\n [-6, -12, 6, 6],\n [6, 12, -6, -6],\n [8, 16, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 1, 14, -3],\n [5, -12, -2, 12],\n [9, -25, -6, 27],\n [5, -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[[-1, -5, -5, 3],\n [-12, -20, 0, -4],\n [-2, -2, 2, -2],\n [0, -4, -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 4x4 matrix:\n[[2, 6, -8, 0],\n [2, 6, -8, 0],\n [2, 6, -8, 0],\n [-1, -3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 3, 0, -6],\n [0, 4, 0, -8],\n [0, 0, 0, 0],\n [0, -4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -3, -6, 12],\n [20, 10, -12, -8],\n [0, 0, 0, 0],\n [-3, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 8, 2, -12],\n [-6, 3, -1, -8],\n [-12, 16, 8, -16],\n [-3, 3, 1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[26, 20, -10, -34],\n [15, 4, -17, -13],\n [9, 11, -3, -13],\n [-13, 7, 9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -6, -7, -4],\n [-4, -3, -3, -17],\n [12, 8, 12, -14],\n [-6, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, -12, -6, -8],\n [-11, 8, 6, 0],\n [9, -7, -9, 10],\n [0, 1, 9, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 8, -2, 4],\n [0, 12, -3, 6],\n [0, -8, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -5, 8, 16],\n [-6, 22, -10, 8],\n [8, -16, 4, -16],\n [1, 13, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-31, -24, -28, 18],\n [8, 20, 0, -4],\n [9, 10, 4, 0],\n [-16, -13, -12, 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[[-9, 0, -9, -12],\n [0, 0, 0, 0],\n [-6, 0, -6, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -15, 19, 14],\n [8, 8, 8, 8],\n [-28, 21, -16, 19],\n [32, 4, 2, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -16, -12, -12],\n [0, -16, -12, -12],\n [0, 0, 0, 0],\n [0, -16, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 14, -5, -8],\n [-12, 24, -12, -8],\n [-4, 4, 2, -8],\n [6, -12, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 4, 16, -12],\n [5, 5, -4, 3],\n [-10, 0, 16, -12],\n [2, -1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, 12, -9],\n [0, 2, 4, -3],\n [0, -4, -8, 6],\n [0, -8, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 2, -19, -4],\n [5, -3, 6, -4],\n [-4, 16, 7, 0],\n [22, -10, -4, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 0, -19, -5],\n [12, 0, -17, -5],\n [-12, 0, 25, 7],\n [-16, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -9, 9, 6],\n [-4, 3, -3, -2],\n [12, -9, 9, 6],\n [-12, 9, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 6, -4, 8],\n [-7, -6, -16, 20],\n [2, 8, 8, -8],\n [-6, 9, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 12, -4, -8],\n [12, -2, -10, -3],\n [4, -3, -3, 1],\n [-14, 4, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -3, 0, 4],\n [-4, -6, 0, 8],\n [-8, -12, 0, 16],\n [-2, -3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 8, -16, 16],\n [12, -6, 12, -12],\n [-4, 2, -4, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -28, 24, -8],\n [4, -13, 9, -13],\n [-8, -6, 6, 2],\n [16, 20, -18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -1, 2, -2],\n [6, 3, -6, 6],\n [-4, -2, 4, -4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-4, -4, 4, 3],\n [12, 12, -12, -9],\n [8, 8, -8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 2, -4, -4],\n [4, -4, 8, 8],\n [0, 0, 0, 0],\n [1, -1, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -1, 8, -6],\n [6, -3, 12, 0],\n [-2, 5, -2, -10],\n [14, 1, 2, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 4, 12, 0],\n [-6, -2, -6, 0],\n [-3, -1, -3, 0],\n [6, 2, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -10, 15, -4],\n [-20, 16, -24, 8],\n [-8, 6, -9, 4],\n [-9, 6, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -1, -1, 17],\n [-4, -5, 5, -17],\n [2, 10, -7, 4],\n [-20, 6, -4, 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[[-16, -8, -16, 0],\n [4, 2, 4, 0],\n [8, 4, 8, 0],\n [-16, -8, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, -12, -6],\n [-10, 12, 10, -4],\n [10, -4, -10, -2],\n [2, 12, -2, -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[[-2, -21, -9, 10],\n [22, -3, -3, 28],\n [7, 10, 3, 1],\n [-3, -18, -15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -2, -11, -11],\n [-18, 2, -13, -19],\n [-11, 4, -6, -13],\n [-14, -4, -14, -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[[32, -40, -34, -10],\n [10, -6, 0, -16],\n [6, -10, -12, 0],\n [10, -14, -13, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, 16, -8],\n [-12, 0, 16, -8],\n [-3, 0, 4, -2],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 2, 4, -8],\n [-3, -3, -6, 12],\n [-1, -1, -2, 4],\n [2, 2, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -6, -6, -9],\n [2, -4, -4, -6],\n [-4, -1, -7, 12],\n [-2, 1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 3, -3, 1],\n [8, -12, 12, -4],\n [8, -12, 12, -4],\n [-6, 9, -9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 8, 13, 3],\n [12, 16, -4, -4],\n [20, 0, -6, -2],\n [16, 0, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 13, 4, -15],\n [2, -5, 18, -16],\n [-2, -3, 15, -13],\n [-12, -8, 0, 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 4x4 matrix:\n[[-4, 7, -11, 7],\n [6, -3, 9, -8],\n [-2, -15, -3, -4],\n [-2, -13, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -10, -14, 14],\n [3, -1, 1, -3],\n [2, 1, 5, -8],\n [13, -11, -13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -2, 3, -2],\n [-8, 8, -12, 8],\n [-4, 4, -6, 4],\n [2, -2, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 10, 0, 8],\n [-20, -19, 1, -14],\n [-18, -15, 0, -12],\n [2, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, -4, -2],\n [6, 0, -4, -2],\n [-1, -2, 0, -1],\n [-11, 2, 8, 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[[8, -6, 33, 21],\n [-8, 6, 9, 14],\n [-13, 1, -7, 4],\n [2, -4, 25, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 5, 2, 10],\n [0, -16, -2, 10],\n [13, -16, -6, -1],\n [14, -28, -7, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 0, -3, -7],\n [5, 10, 11, -7],\n [-4, 1, -1, -2],\n [8, -8, 8, 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[[-16, 19, 10, 2],\n [-10, 11, 14, -8],\n [2, -8, -8, 0],\n [-1, -3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [3, 0, -12, 9],\n [-1, 0, 4, -3],\n [-3, 0, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 24, 3, -3],\n [3, 14, -7, -17],\n [14, -12, -5, -3],\n [31, -14, 14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -12, 0, -12],\n [-8, -8, 0, -8],\n [12, 12, 0, 12],\n [-16, -16, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -8, 6, -8],\n [-6, -4, -6, 8],\n [-12, 8, -12, 16],\n [-12, 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[[-14, 12, -8, 8],\n [11, -8, 6, -8],\n [-10, 15, -7, -2],\n [11, -8, 6, -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 4x4 matrix:\n[[-2, 2, 2, 0],\n [-6, 6, 6, 0],\n [0, 0, 0, 0],\n [-6, 6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -7, -5, 19],\n [-8, 5, 1, 7],\n [2, 1, 1, -5],\n [-7, 19, 9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 8, -4, 12],\n [-4, 6, -4, -1],\n [-4, -4, 4, 14],\n [6, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 1, 3, 0],\n [0, 0, 0, 0],\n [-12, -4, -12, 0],\n [-6, -2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -3, -3, -6],\n [0, 5, -7, -14],\n [1, -4, 5, 10],\n [9, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, 3, -11],\n [12, 8, 3, 5],\n [-4, -5, 6, -18],\n [12, 9, 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[[12, -5, 7, 13],\n [0, 12, -6, -6],\n [-4, 3, -3, -5],\n [4, 1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, 5, -10, 23],\n [0, -14, -4, -8],\n [-4, -12, -1, -22],\n [-3, -11, -1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 12, 0, -12],\n [0, -4, 0, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -10, 0, 7],\n [-2, 5, 8, -14],\n [2, 3, 0, -3],\n [2, -5, -8, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 3, -4, 8],\n [19, -6, 10, 4],\n [-5, 19, -22, -28],\n [10, 4, -4, 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[[12, 6, -8, -4],\n [18, 3, -20, 2],\n [6, -3, -12, 6],\n [-4, 5, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 4, 0, -4],\n [0, 0, 0, 0],\n [1, -7, -6, -2],\n [-4, -20, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 12, 8, -16],\n [4, 6, 4, -8],\n [8, 12, 8, -16],\n [8, 12, 8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -6, -8, -2],\n [-2, -4, 0, 12],\n [-3, -1, 2, 8],\n [-3, 9, 6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 26, 14, -8],\n [0, 0, 15, -18],\n [-16, 0, 0, 24],\n [-8, -19, -1, -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[[3, -2, 1, 5],\n [-1, -3, 3, -3],\n [-3, -2, 0, -4],\n [12, -13, -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[[-4, 0, -2, 2],\n [-13, 2, -7, 14],\n [3, -2, 1, -22],\n [6, -8, 6, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -6, -6, 3],\n [0, 6, 6, -3],\n [0, 8, 8, -4],\n [0, 8, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 24, 12, 12],\n [8, -3, 6, 6],\n [8, -3, 6, 6],\n [-6, -9, -7, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 9, 3, -18],\n [-12, 16, -4, -4],\n [6, -8, 2, 2],\n [-7, 5, -2, 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 4x4 matrix:\n[[16, -8, 4, 12],\n [4, -2, 1, 3],\n [-12, 6, -3, -9],\n [-16, 8, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 16, 4, -12],\n [1, 4, 1, -3],\n [-3, -12, -3, 9],\n [-1, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -2, 2, 8],\n [6, -3, 3, 12],\n [8, -4, 4, 16],\n [4, -2, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -1, -4, 4],\n [-3, 9, 6, 3],\n [1, -28, -6, 11],\n [3, 4, -2, -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 4x4 matrix:\n[[-4, 3, 2, 0],\n [-12, 9, 6, 0],\n [4, -3, -2, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 12, 12, 6],\n [-2, -8, 0, 8],\n [5, 12, -4, -18],\n [4, 16, 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[[4, -8, -4, 6],\n [4, -8, -4, 6],\n [-6, 12, 6, -9],\n [4, -8, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [4, -2, -4, 8],\n [6, -3, -6, 12],\n [2, -1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, 8, -4, 12],\n [6, 4, -2, 6],\n [12, 8, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -4, -4, 16],\n [3, -1, -1, 4],\n [12, -4, -4, 16],\n [9, -3, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, -2, -6, 7],\n [5, -3, -4, 3],\n [12, 4, 0, 4],\n [2, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, -6, -6],\n [-12, -3, 9, 9],\n [4, 1, -3, -3],\n [-4, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 0, 10, 2],\n [-10, 2, -6, -6],\n [14, -2, 9, 6],\n [26, 10, 14, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -3, 6, -3],\n [0, 0, 0, 0],\n [3, 3, -6, 3],\n [-1, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 3, 15, -2],\n [3, 3, -3, -5],\n [-7, -2, 12, 5],\n [5, 1, -9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 1, 3, -2],\n [2, -2, -6, 4],\n [-3, 3, 9, -6],\n [4, -4, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -3, 0, -2],\n [6, 21, 8, 22],\n [2, 6, 2, 6],\n [-2, -3, 0, -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 4x4 matrix:\n[[-4, 12, 4, 0],\n [-4, 1, 3, -2],\n [2, -10, -4, -4],\n [14, 19, -3, 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[[-4, -6, 7, -2],\n [-2, -2, 1, -2],\n [-4, -4, 2, -4],\n [2, 2, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 1, 13, 1],\n [6, -15, 16, -5],\n [-8, -10, 22, -2],\n [5, -11, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -11, -5, -2],\n [0, 0, -13, -14],\n [13, -13, 0, 4],\n [5, -5, 6, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -6, -2, -8],\n [-12, -9, -3, -12],\n [-4, -3, -1, -4],\n [-8, -6, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 1, 3, 11],\n [-11, -1, -3, -9],\n [-18, 1, 3, -14],\n [25, 9, 27, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, 2, -20, -6],\n [-28, 9, -14, 3],\n [24, -14, -4, -18],\n [-32, 10, -20, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -1, 5, -3],\n [0, 0, 0, 0],\n [16, 0, 16, -8],\n [4, 0, 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[[-6, -9, 12, 1],\n [2, 13, -4, -17],\n [0, -15, 12, 3],\n [0, 8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-3, 1, 3, -2],\n [12, -4, -12, 8],\n [6, -2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 9, 7, 16],\n [9, 12, 3, 12],\n [1, -13, -2, -16],\n [6, -18, 0, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 12, 4, 8],\n [6, -9, -3, -6],\n [-2, 3, 1, 2],\n [-2, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -2, 6, 8],\n [0, 0, 0, 0],\n [12, -4, 12, 16],\n [9, -3, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 9, 6, 6],\n [0, -9, -6, -6],\n [0, 0, 0, 0],\n [0, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -22, -4, 8],\n [3, -4, -3, 1],\n [-3, 5, -15, -5],\n [14, -19, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -4, 2, -8],\n [3, -2, 1, -4],\n [3, -2, 1, -4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, 3, 3],\n [-4, 0, 3, 3],\n [-4, 0, 3, 3],\n [-8, 0, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -9, 3, 6],\n [-12, -3, 9, -14],\n [-4, 9, -7, 2],\n [12, -9, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -3, -1, 1],\n [0, 0, 0, 0],\n [6, -9, -3, 3],\n [-2, 3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[24, 16, 16, 24],\n [28, 17, 17, 28],\n [4, 1, 1, 4],\n [16, 10, 10, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 4, 3, 5],\n [-8, -4, -3, 0],\n [19, -28, -21, -25],\n [-15, 24, 18, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -6, 6, -2],\n [-4, 5, -8, 3],\n [-18, 0, -7, -7],\n [28, -2, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 6, -13, -5],\n [-4, 2, 14, 10],\n [-10, 2, 25, 17],\n [2, 5, 13, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 5, -3, -4],\n [-10, 18, -1, -13],\n [-13, 9, -4, -7],\n [12, -12, 3, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -16, -10, 14],\n [14, -5, 2, -5],\n [-8, 20, 0, 0],\n [6, -27, 10, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 3, 3, -3],\n [3, -3, -3, 3],\n [2, 7, 1, 5],\n [1, 5, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 9, 0, -8],\n [-14, 8, -3, -20],\n [-18, 8, -6, -22],\n [-1, -4, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 16, 24, -8],\n [-4, 0, 8, 0],\n [-1, 4, 4, -2],\n [-6, 16, 20, -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[[16, -16, 0, -4],\n [4, -4, 0, -1],\n [-12, 12, 0, 3],\n [-4, 4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 6, -12, 12],\n [0, -6, 12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -6, -4, 1],\n [28, -12, -12, 5],\n [4, 6, -12, 11],\n [12, -3, -8, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, 3, 0],\n [-16, -16, -4, 0],\n [4, 4, 1, 0],\n [-16, -16, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 0, 10, -2],\n [0, 18, -8, -8],\n [20, 15, -16, 0],\n [12, -9, -4, 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 4x4 matrix:\n[[9, -3, 9, 12],\n [-12, 4, -12, -16],\n [-3, 1, -3, -4],\n [-9, 3, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, -6, 4],\n [-7, -3, -5, 7],\n [-2, 0, -3, 2],\n [-5, 9, -24, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 2, 3, 0],\n [1, 5, 0, -3],\n [24, 1, -21, -9],\n [13, 14, -9, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, -2, 8],\n [4, -2, 2, -8],\n [-8, 4, -4, 16],\n [2, -1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 12, 0, -9],\n [-6, -4, 4, -22],\n [25, 20, -3, 7],\n [36, 16, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 12, -18, 9],\n [6, -12, 20, -8],\n [-4, -8, 8, -8],\n [-2, -16, 20, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -1, -2, -1],\n [9, -3, -6, -3],\n [-6, 2, 4, 2],\n [12, -4, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 1, 3, -1],\n [9, -9, -3, 9],\n [-6, -2, 6, 6],\n [-12, 16, 14, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 16, 0, -16],\n [-3, 4, 0, -4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, -9, 0, -6],\n [6, 16, 7, -15],\n [-9, 11, 2, 0],\n [1, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -5, -8, -1],\n [-3, 4, -2, 2],\n [3, -6, -5, 3],\n [15, -1, 21, -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[[-1, 1, -1, -2],\n [-1, 1, -1, -2],\n [2, -2, 2, 4],\n [-3, 3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, 12, 12],\n [6, 8, -2, -10],\n [2, -2, -10, -8],\n [6, 4, -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[[0, 0, 0, 0],\n [12, -8, -12, 8],\n [6, -4, -6, 4],\n [-9, 6, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, -6, -6, -20],\n [-9, -9, -3, 12],\n [3, 3, 1, -4],\n [-9, -3, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -3, -20, 8],\n [0, 9, 6, 3],\n [3, 21, -4, 16],\n [-3, 3, 20, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -6, -2, 0],\n [0, 0, 0, 0],\n [-8, 6, 2, 0],\n [-8, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, -2, 8],\n [8, 8, -2, 8],\n [16, 16, -4, 16],\n [-16, -16, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 2, 8, 6],\n [-12, 4, 16, 12],\n [-12, 4, 16, 12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -14, -10, -10],\n [-2, -10, -5, -3],\n [-11, 8, 7, 4],\n [-21, -12, 6, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 8, 8, -12],\n [-12, -8, -8, 12],\n [9, 6, 6, -9],\n [12, 8, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -14, 0, 2],\n [-14, 14, 3, -4],\n [-10, 0, 1, 16],\n [26, -22, -7, 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[[-11, -10, -13, -8],\n [-2, 1, -2, 4],\n [3, 4, 8, 12],\n [-10, -3, -9, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 15, -15, 8],\n [20, -14, 6, -8],\n [4, -1, 21, -16],\n [-32, 20, -12, 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[[10, 19, 10, 12],\n [1, 4, 1, 0],\n [-6, -10, -6, -8],\n [4, -5, 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[[0, -12, 7, 2],\n [2, -20, 11, 1],\n [10, -16, 6, -9],\n [-4, 16, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 2, 0, 0],\n [-3, 2, 0, 0],\n [12, -8, 0, 0],\n [-6, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -1, 8, 7],\n [-5, -14, 2, 8],\n [-19, 2, -21, 1],\n [-9, -9, 1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 2, 2, 8],\n [0, 0, 0, 0],\n [-12, 4, 4, 16],\n [-6, 2, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -16, 0, 13],\n [24, 8, 10, -9],\n [-37, 10, -21, 2],\n [6, -16, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, -8, 0, -4],\n [4, 4, 0, 2],\n [8, 8, 0, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 2, -6, -4],\n [7, 6, -8, -8],\n [-18, -20, 0, 16],\n [8, 8, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 10, -4, -14],\n [2, -15, 1, 8],\n [1, -4, 0, 2],\n [0, -2, -7, -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[[-1, 2, -2, -4],\n [-9, -2, -8, -2],\n [15, 0, 15, 9],\n [-17, -6, -14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 4, 2, 4],\n [-18, -15, -19, 3],\n [11, 10, 18, -11],\n [-14, -7, -11, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 5, -23, 12],\n [-8, 0, 12, -3],\n [30, -13, -4, -12],\n [-34, 3, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 1, 0, 4],\n [0, 6, -3, 18],\n [3, -1, 1, -2],\n [-3, 7, -4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -8, 8, -8],\n [-2, -4, 4, -4],\n [2, 4, -4, 4],\n [4, 8, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -9, 3, 6],\n [-8, 12, -4, -8],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[26, 20, 8, 7],\n [-4, -4, -4, 1],\n [18, 12, 15, 6],\n [24, 16, 10, 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[[-1, 0, 1, 2],\n [-5, 10, 5, -2],\n [20, -34, -19, 3],\n [1, -4, -10, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -4, 0, -8],\n [10, -9, 16, 6],\n [4, 2, 0, 4],\n [17, -2, 12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -4, -25, -24],\n [12, -12, 9, 12],\n [-9, -12, -12, -9],\n [4, 24, 10, 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 4x4 matrix:\n[[2, -14, -4, -8],\n [8, 4, -10, 16],\n [14, -18, -20, 8],\n [-7, 9, 10, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 3, 0, 0],\n [-2, -11, 16, -8],\n [-12, 14, -24, 12],\n [6, 9, -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 4x4 matrix:\n[[1, 0, 3, -1],\n [2, 0, 6, -2],\n [-1, 0, -3, 1],\n [1, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -12, 12, -12],\n [6, 8, -14, 14],\n [6, -9, -2, 2],\n [8, -5, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -3, -3, -3],\n [16, -4, -4, -4],\n [-16, 4, 4, 4],\n [12, -3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 0, 7, -1],\n [-3, 0, 9, 3],\n [7, -8, 15, 11],\n [5, -4, 5, 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, 7, 6, 0],\n [12, -4, 8, 0],\n [-2, -10, -20, 0],\n [-8, -8, -24, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -3, -1, -1],\n [0, 0, 0, 0],\n [-4, -3, -1, -1],\n [16, 12, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -3, 2, 0],\n [-5, -1, 0, -12],\n [13, -3, 7, 20],\n [-2, 0, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 8, 15, 0],\n [-14, 2, -9, -17],\n [6, 1, 2, 5],\n [10, 3, 11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -12, 32, 10],\n [24, 12, 8, 30],\n [-15, -2, 17, -10],\n [-9, -6, 1, -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 4x4 matrix:\n[[2, 0, 0, 4],\n [-2, 0, 0, -4],\n [4, 0, 0, 8],\n [8, 0, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -2, 16, -12],\n [6, 8, -4, -6],\n [12, 16, -8, -12],\n [6, -5, 10, -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[[0, 0, 0, 0],\n [9, 0, 0, -9],\n [-12, 0, 0, 12],\n [-3, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [6, 3, 9, -9],\n [-6, -3, -9, 9],\n [-2, -1, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 5, 5, -2],\n [6, -19, -1, -3],\n [-18, 5, -3, 16],\n [6, -2, 0, -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 4x4 matrix:\n[[-12, -3, 3, 0],\n [-8, -6, -8, 6],\n [4, 16, 22, -18],\n [-11, 6, -8, -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, 3, -12, 6],\n [-6, 3, -12, 6],\n [-6, 3, -12, 6],\n [6, -3, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 12, -6, 3],\n [-2, 4, -2, 1],\n [-8, 16, -8, 4],\n [2, -4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 4, -2, -6],\n [6, -6, 3, 9],\n [8, -8, 4, 12],\n [6, -6, 3, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 15, -7, 2],\n [1, -6, -7, 2],\n [0, -4, 1, -1],\n [-1, 8, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, 10, -22],\n [0, -8, -6, -12],\n [-6, -12, -8, -7],\n [3, 11, 8, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, -10, 22],\n [-4, -4, 2, 1],\n [0, -2, 1, -2],\n [-4, 6, 7, 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[[-18, 15, 10, -5],\n [-12, 15, 8, -7],\n [6, -2, 22, -8],\n [14, -14, 10, 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[[-6, -7, -5, -10],\n [4, 9, 3, -13],\n [-24, -18, 12, 2],\n [-2, 0, 0, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -4, -16, 16],\n [16, 4, 16, -16],\n [16, 4, 16, -16],\n [16, 4, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[31, -1, 0, -13],\n [-10, 14, -4, 10],\n [11, -5, 6, -11],\n [8, 9, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -4, -3, 7],\n [-9, -4, 1, 3],\n [-9, 4, 5, -9],\n [-9, -6, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 3, -13, -12],\n [-8, 6, 10, 3],\n [-10, -3, 9, 9],\n [-10, -9, 7, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -4, -12, -4],\n [-4, -2, -6, -2],\n [0, 0, 0, 0],\n [-8, -4, -12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -12, 8, 0],\n [0, 0, 0, 0],\n [6, 6, -4, 0],\n [-12, -12, 8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -3, 13, 10],\n [0, 0, -8, -2],\n [-9, -3, 1, 7],\n [0, 0, 16, 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 4x4 matrix:\n[[4, 2, 7, -1],\n [-14, -14, 2, 0],\n [-1, 24, 18, -10],\n [14, 0, -9, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 9, -3],\n [0, 0, 3, -1],\n [0, 0, 0, 0],\n [0, 0, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 2, -6, -10],\n [-11, -1, 3, 7],\n [-8, 4, -12, -15],\n [-6, -2, 6, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[23, -12, -30, 6],\n [4, 8, 0, 28],\n [-6, -8, 0, 23],\n [-22, 3, 23, 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[[22, 5, 13, -25],\n [-8, -8, -14, 6],\n [4, 6, 10, -2],\n [14, 9, 17, -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[[-3, -6, -1, -2],\n [-12, -3, -18, -15],\n [9, 18, 3, 6],\n [-12, -12, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 0, 4, -4],\n [-4, 0, -8, 8],\n [4, 0, 8, -8],\n [6, 0, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 8, 4, -8],\n [9, -6, -3, 6],\n [3, -2, -1, 2],\n [12, -8, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 9, 18, 12],\n [-12, 1, 10, 0],\n [-16, 0, 12, -2],\n [12, 1, -8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -4, 2, -2],\n [0, 2, -1, 1],\n [0, 8, -4, 4],\n [0, -4, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, 0, 10, 0],\n [13, 0, 10, 0],\n [20, -4, 12, 0],\n [20, -4, 12, 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[[4, 2, 0, 10],\n [0, -1, 0, -4],\n [10, -1, 0, 1],\n [4, -1, 0, -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 4x4 matrix:\n[[-4, 11, 8, 2],\n [26, -9, 19, 14],\n [24, -6, 12, 8],\n [8, -18, 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[[-12, -14, -18, 3],\n [-6, -8, -10, 1],\n [-8, -2, -9, 7],\n [3, -11, 3, -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[[-6, -3, -15, 12],\n [13, 3, -13, 2],\n [-9, -4, -16, 14],\n [14, 4, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -4, 4, -1],\n [6, -12, 12, -3],\n [4, -8, 8, -2],\n [-4, 8, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[22, -17, 8, -14],\n [8, 13, -7, -2],\n [-24, -4, -8, 8],\n [4, 15, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[22, 19, -4, 32],\n [-17, -8, 6, -26],\n [24, 0, -8, 20],\n [16, -2, -8, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 3, -3, -3],\n [-4, 2, -2, -2],\n [2, -1, 1, 1],\n [-8, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -4, -1, 3],\n [4, 4, 1, -3],\n [0, 0, 0, 0],\n [16, 16, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, -9, -3],\n [-6, 6, 9, 3],\n [2, -2, -3, -1],\n [-6, 6, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -3, 0, -2],\n [7, -9, -1, -4],\n [19, -21, 0, -8],\n [-7, 3, 9, -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 4x4 matrix:\n[[4, -12, 0, -8],\n [1, -3, 0, -2],\n [-4, 12, 0, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -12, -14, -10],\n [10, 8, -1, 26],\n [2, 8, 7, 2],\n [0, 4, 2, 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[[-12, -12, -4, 12],\n [12, 12, 4, -12],\n [0, 0, 0, 0],\n [12, 12, 4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 8, -16, -8],\n [-4, 8, -16, -8],\n [4, -8, 16, 8],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -22, 10, 10],\n [-20, -24, -16, 26],\n [8, 9, 5, -10],\n [18, 29, -1, -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 4x4 matrix:\n[[8, 12, 4, -12],\n [0, 0, 16, 0],\n [-4, -6, 10, 6],\n [6, 9, 13, -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 4x4 matrix:\n[[0, -6, 0, -2],\n [10, -12, -5, -4],\n [4, 3, -2, 1],\n [-4, 9, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 1, 1, 6],\n [2, -2, -4, -6],\n [2, -1, -1, -6],\n [3, 4, 15, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, 6, -6],\n [6, -6, -6, 6],\n [8, -8, -8, 8],\n [-8, 8, 8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 2, 5, -4],\n [-1, 0, 1, 0],\n [2, 4, 4, -8],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -25, 22, 2],\n [-5, 0, 6, -4],\n [5, -11, 14, -2],\n [-5, -14, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 8, 12, 0],\n [-15, -18, -12, 0],\n [-7, -10, -4, 0],\n [8, 4, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 3, 3, 3],\n [-9, 3, 3, 3],\n [3, -1, -1, -1],\n [-9, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -14, -3, 3],\n [10, -14, 6, 8],\n [0, -2, -12, -6],\n [-10, 14, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -9, -3, 9],\n [4, 6, 2, -6],\n [-4, -6, -2, 6],\n [4, 6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -11, -2, 1],\n [-2, 6, 0, 2],\n [-2, 6, 0, 2],\n [4, -5, 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[[-4, 0, 4, 1],\n [3, 9, -3, 6],\n [1, -5, -1, -4],\n [4, 20, -4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 4, -14, -8],\n [-11, -5, 25, 12],\n [-3, 5, 5, -4],\n [11, 5, -25, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -1, -18, -12],\n [6, 11, 0, -6],\n [-18, -17, -12, 6],\n [-12, -9, -11, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -4, 13, -7],\n [0, -4, 4, -4],\n [-12, 0, 12, -4],\n [-6, 16, -10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 7, -7, 2],\n [-20, -1, 1, 1],\n [32, -8, 8, -4],\n [-20, 11, -11, 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 4x4 matrix:\n[[13, -7, -6, 8],\n [-8, 8, -6, -4],\n [-9, 11, -12, -4],\n [7, -5, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -1, 0, -22],\n [4, 6, 0, 0],\n [-8, 0, 0, -24],\n [4, 2, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -12, 4, -12],\n [0, 0, 0, 0],\n [-2, 3, -1, 3],\n [4, -6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 20, -10, 20],\n [-1, -14, 3, -18],\n [-2, 4, 2, 8],\n [5, 6, -7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 1, 0, -3],\n [-1, -9, 0, 6],\n [1, -7, 0, 6],\n [-4, 4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -7, -6, -28],\n [-17, -3, -11, -2],\n [-7, -7, 0, -36],\n [-26, -5, -16, -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 4x4 matrix:\n[[-13, -10, 4, -14],\n [-13, 14, 10, 4],\n [-1, -14, -16, -18],\n [-14, 0, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 4, -6, 4],\n [21, 4, -3, -7],\n [9, 8, -12, 1],\n [3, -2, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 14, 7, -12],\n [8, -6, 2, 3],\n [8, 2, 18, -9],\n [0, 4, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 20, 21, 10],\n [5, 13, 0, 12],\n [-13, -2, 12, -5],\n [14, -1, -12, 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, -4, -1, 2],\n [-6, -12, -3, 6],\n [8, 16, 4, -8],\n [-6, -12, -3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 4, -1, 4],\n [12, -16, 4, -16],\n [0, 0, 0, 0],\n [9, -12, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 6, 4, 8],\n [-22, -24, 2, -8],\n [-4, 4, 24, 28],\n [17, 16, -8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 8, -16, -20],\n [-4, -8, 10, 14],\n [2, 4, 2, 0],\n [-3, -6, 8, 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 4x4 matrix:\n[[-4, -16, 4, -28],\n [-2, 4, -13, 19],\n [-11, -16, -24, 0],\n [-2, -12, 7, -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[[0, 9, 6, -9],\n [0, -9, -6, 9],\n [0, -6, -4, 6],\n [0, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[21, -9, 6, 0],\n [-1, -3, 2, -6],\n [6, -6, 4, -6],\n [22, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, -8, -4, 10],\n [3, -5, -1, -5],\n [10, -13, -2, -13],\n [-7, -12, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, 6, -3, -9],\n [-11, 7, -6, -10],\n [17, 1, -8, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 2, 4, 4],\n [8, 2, 4, 4],\n [8, 2, 4, 4],\n [12, 3, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, -8, 4],\n [0, 4, -16, 8],\n [0, 2, -8, 4],\n [0, -2, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 9, 8, -10],\n [4, 4, 6, -16],\n [11, 8, -21, -2],\n [0, 1, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 5, 4, 18],\n [4, 4, -16, -12],\n [4, 4, -16, -12],\n [0, -1, 12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 3, 2, -4],\n [-12, -9, -6, 12],\n [-16, -12, -8, 16],\n [-12, -9, -6, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, 8, -10],\n [-4, 2, 4, -4],\n [14, 5, 2, -6],\n [-10, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -1, -3, -3],\n [-16, 4, 12, 12],\n [-8, 2, 6, 6],\n [8, -2, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [14, 7, 11, 15],\n [7, 2, 7, 3],\n [-16, -3, -27, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 0, 3, 1],\n [0, -2, -6, 12],\n [16, -2, -18, 8],\n [16, 2, -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[[-2, -14, -8, 0],\n [7, 25, 13, 4],\n [-4, 20, 14, -8],\n [1, -17, -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[[9, -12, -3, 9],\n [-12, 16, 4, -12],\n [3, -4, -1, 3],\n [9, -12, -3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -9, -12, -12],\n [16, 12, 16, 16],\n [8, 6, 8, 8],\n [8, 6, 8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 11, -2, 13],\n [4, 29, -14, 19],\n [2, -15, 6, -11],\n [-4, -12, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -6, -12, -3],\n [12, 8, 16, 4],\n [3, 2, 4, 1],\n [3, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -5, -6, -12],\n [8, 8, 7, 16],\n [-3, 0, 3, 9],\n [-8, 20, -28, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -1, -6, -4],\n [0, 5, -4, -6],\n [-1, 4, -7, -9],\n [-4, -24, -12, -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, -3, -1, 3],\n [21, -3, 9, 3],\n [-4, 16, -18, -16],\n [10, 14, -12, -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[[-14, 12, 8, -2],\n [3, -4, -3, 2],\n [1, 2, 2, -3],\n [13, -14, -10, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -8, 24, 16],\n [0, 1, -3, -3],\n [4, 5, -15, -11],\n [-8, -5, 15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -4, -6, -3],\n [-24, 0, 8, 0],\n [21, 4, -8, 3],\n [-24, 0, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -4, -4, 6],\n [6, 8, 8, -12],\n [1, 6, 6, -9],\n [-4, -6, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -4, -2, -6],\n [0, 0, 0, 0],\n [-2, -2, -1, -3],\n [-8, -8, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 12, -3, -6],\n [12, -16, 4, 8],\n [12, -16, 4, 8],\n [-12, 16, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 9, 7, -8],\n [10, 18, 18, -14],\n [9, 11, 5, -6],\n [-6, -12, -10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, 24, -4],\n [0, -15, 12, 5],\n [20, -12, 28, 8],\n [-3, -7, 23, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 1, -10, -5],\n [-8, -2, -8, -6],\n [-22, 5, -22, -9],\n [6, -2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -2, 4, -1],\n [5, 4, -5, 1],\n [1, -4, -1, 1],\n [-1, 4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -12, 4, -4],\n [-21, -9, 3, 15],\n [-16, -12, 4, 8],\n [-2, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 0, 6, -12],\n [1, 1, -5, 1],\n [-6, -2, 14, -10],\n [-4, 0, 4, -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[[-11, -10, 26, 2],\n [-5, -12, 16, -4],\n [10, -4, -4, 8],\n [-10, -10, 22, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-21, -17, 9, 12],\n [12, 11, -9, -12],\n [-3, -3, 3, 4],\n [18, 15, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -8, -6, 0],\n [0, 0, 0, 0],\n [0, 4, 3, 0],\n [0, -4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 12, 10, -5],\n [3, -2, 1, -1],\n [-16, 2, -16, 12],\n [-7, 18, 6, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -4, -6, -6],\n [20, 14, 18, -9],\n [-7, -10, 4, -9],\n [-4, -10, 6, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [9, -6, 9, 9],\n [3, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 6, -12, 3],\n [3, 2, -4, 1],\n [3, 2, -4, 1],\n [-12, -8, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -11, 0, 7],\n [16, -18, -4, 2],\n [-14, 13, -11, -5],\n [14, -11, 7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 16, 8, 4],\n [-15, 2, -4, 8],\n [-2, 12, 8, 0],\n [10, -16, -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[[0, 0, 0, 0],\n [0, -4, -8, 4],\n [0, 4, 8, -4],\n [0, -2, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 2, 2, 3],\n [-17, -20, 1, -9],\n [-12, -16, -4, -12],\n [-4, -8, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-2, 14, 6, 8],\n [2, -18, -8, -11],\n [6, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -4, -4, 17],\n [10, -12, 16, -12],\n [2, 12, -4, -15],\n [8, -16, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -3, 6, 0],\n [-3, 7, 5, -22],\n [-17, 11, 3, -5],\n [-3, 11, -1, -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[[2, -2, -4, 8],\n [8, 2, -12, 22],\n [-10, -10, 12, -20],\n [-7, -13, 6, -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 4x4 matrix:\n[[3, -2, -4, -4],\n [-12, 8, 16, 16],\n [9, -6, -12, -12],\n [-12, 8, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, 33, -17, 12],\n [-8, -4, -4, -24],\n [-8, 3, -7, -12],\n [15, -12, 3, 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[[-7, -18, -17, -8],\n [-13, -10, -16, -19],\n [-2, 0, -6, -4],\n [10, -8, -6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [3, -1, 2, -1],\n [-12, 4, -8, 4],\n [9, -3, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, 8, -20, -4],\n [-6, 0, -2, -6],\n [-3, 22, -9, 7],\n [20, -8, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -3, 9, 3],\n [3, 9, 11, 3],\n [-3, -20, -2, 1],\n [12, 14, 14, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, -22, 13, 17],\n [5, 5, -13, 3],\n [12, 20, -21, 13],\n [-10, 14, -5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 0, 4, -12],\n [-2, 0, 1, -3],\n [8, 0, -4, 12],\n [2, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 3, -9, 6],\n [-8, 20, 20, 16],\n [1, 0, -10, 3],\n [-1, 5, -5, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 10, 3, -4],\n [-10, -2, -4, 4],\n [-11, -7, 10, -2],\n [2, -14, -16, 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[[-6, 2, -4, 8],\n [-6, 2, -4, 8],\n [-6, 2, -4, 8],\n [12, -4, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -6, 0, -6],\n [10, -14, -12, -6],\n [2, 14, 6, 10],\n [-2, -2, 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[[-8, -7, 0, -11],\n [-1, -2, 4, -11],\n [7, -2, 12, -5],\n [-12, -2, -16, 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[[-8, -13, -1, 9],\n [-20, -16, 0, -34],\n [14, 10, -1, 14],\n [8, 13, 3, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -4, -4, -2],\n [-9, 6, 6, 3],\n [-12, 8, 8, 4],\n [3, -2, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -10, 17, 8],\n [-10, -12, -7, -6],\n [-12, 8, -14, -10],\n [-1, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, -3, 2],\n [-2, 0, -3, 2],\n [-8, 0, -12, 8],\n [2, 0, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, -4, -15, -4],\n [-14, 22, 12, 2],\n [-25, -4, 11, 12],\n [-16, -2, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -2, 4, 2],\n [8, -4, 8, 4],\n [-6, 3, -6, -3],\n [8, -4, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, 10, 9, -16],\n [-24, 4, -9, 3],\n [-1, 4, 15, -16],\n [1, -8, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, 0, 8],\n [-2, 8, 4, -10],\n [5, 12, 6, 1],\n [-3, -4, -2, -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, 4, 7, 0],\n [-2, 0, 6, -4],\n [2, -16, -18, 20],\n [4, 4, 5, 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 4x4 matrix:\n[[-3, 12, -6, 9],\n [2, -8, 4, -6],\n [1, -4, 2, -3],\n [3, -12, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 4, -8, -7],\n [0, 0, 0, 0],\n [0, -8, -8, -4],\n [8, 4, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[17, 6, -8, 12],\n [15, -15, -12, 12],\n [3, -21, -16, 12],\n [-6, -2, 7, -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[[-8, 6, -8, 8],\n [4, -3, 4, -4],\n [0, 0, 0, 0],\n [4, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-3, 2, 2, 2],\n [-12, 8, 8, 8],\n [9, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 4, 4, -2],\n [-9, 10, 12, -4],\n [20, -24, -32, 8],\n [4, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 19, 2, -2],\n [-3, 9, 26, 9],\n [-14, 22, 4, 1],\n [-6, -2, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -4, 8, 8],\n [13, 14, 2, 7],\n [-3, 6, -12, -12],\n [-6, -4, -4, -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[[9, 11, -3, -4],\n [-9, -17, 8, -4],\n [-12, 2, -6, 26],\n [-3, 0, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 0, 5, 18],\n [12, -3, 23, 14],\n [18, 3, 2, -1],\n [-3, -3, 3, -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[[-16, 8, -8, -4],\n [-3, -3, 3, 0],\n [-6, 6, -6, -2],\n [4, 4, -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[[-6, 12, 15, 0],\n [-8, 10, -4, 0],\n [8, -16, -20, 0],\n [4, -2, 14, 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 4x4 matrix:\n[[3, 0, 13, -12],\n [-9, -9, -12, 18],\n [6, 8, 2, -8],\n [-9, -12, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 18, -22, 6],\n [2, -5, 8, -20],\n [12, 0, 0, 3],\n [4, -12, 16, -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[[-11, 12, -6, -10],\n [-10, 16, -1, -11],\n [3, 4, 8, 8],\n [8, -8, 5, 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, -3, -3, 6],\n [4, -4, -4, 8],\n [-1, 1, 1, -2],\n [-3, 3, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -18, 3, 15],\n [-12, 18, -4, -17],\n [6, -22, 6, 16],\n [8, -8, 9, 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[[-4, 8, 8, 8],\n [1, -2, -2, -2],\n [3, -6, -6, -6],\n [2, -4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 21, -12, 9],\n [16, -20, 18, -14],\n [-16, 20, -18, 14],\n [-8, 17, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, 0, 4],\n [4, -8, 6, -4],\n [8, -1, 12, 2],\n [2, -7, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -5, -11, -14],\n [6, 3, -15, -6],\n [-6, -13, 5, -14],\n [6, 11, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -9, -12, -9],\n [2, 6, 8, 6],\n [-2, -6, -8, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 12, 7, -9],\n [0, 38, 12, -12],\n [17, -5, 11, -25],\n [5, 23, 7, -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 4x4 matrix:\n[[-2, 4, -4, 15],\n [2, -10, 1, -12],\n [-3, 8, -5, 16],\n [0, 4, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, 6, -8],\n [0, 4, 3, -4],\n [0, -4, -3, 4],\n [0, -4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -2, -3, -2],\n [-6, 4, 6, 4],\n [18, -21, -18, 6],\n [-9, 11, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 16, 8, -12],\n [5, 2, -5, -6],\n [-6, 12, 6, -9],\n [-4, 16, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -2, -3, 3],\n [8, -4, -6, 6],\n [-4, 2, 3, -3],\n [-12, 6, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -12, 0, 6],\n [4, -20, 20, 4],\n [9, 2, 16, -9],\n [-11, 7, 11, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -4, 13, 4],\n [4, 4, -4, -4],\n [17, 16, -19, -16],\n [-11, -12, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 4, -10, 16],\n [-15, -1, 7, -10],\n [15, -2, -1, 0],\n [11, -4, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -12, 12, -3],\n [-3, -12, 3, -6],\n [3, -12, -3, -8],\n [-4, 8, 4, 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 4x4 matrix:\n[[-4, 8, -8, 12],\n [1, -2, 2, -3],\n [4, -8, 8, -12],\n [-4, 8, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -16, -8, 0],\n [13, 13, 17, 9],\n [13, 13, 17, 9],\n [3, 12, 6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 1, 3, 8],\n [9, -3, -8, -28],\n [-12, 4, 18, 8],\n [-12, 4, 15, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 9, 12, -6],\n [16, 10, 15, -9],\n [-32, -12, 16, 16],\n [-20, -3, 7, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -20, 12, 4],\n [-5, -8, -3, 25],\n [11, -2, 6, -23],\n [-4, 0, -15, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -4, -3, -3],\n [16, 10, 18, 18],\n [24, 12, 24, 24],\n [14, 2, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[28, -24, -14, 8],\n [-32, 28, 16, -8],\n [0, 3, 0, 6],\n [-8, 10, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [6, -9, 3, -12],\n [-4, 6, -2, 8],\n [-6, 9, -3, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 2, 5, 10],\n [-12, 20, -6, 16],\n [6, 0, 8, 12],\n [-9, 16, -4, 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 4x4 matrix:\n[[-6, 12, 0, -3],\n [-4, 16, 8, -10],\n [8, -17, -1, 5],\n [6, -9, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 12, 6, -10],\n [-16, 22, 4, -15],\n [3, -4, -21, 14],\n [4, -16, -28, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [0, 2, 0, 4],\n [0, -4, 0, -8],\n [0, 4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 12, -8, -3],\n [-4, 24, -14, 6],\n [20, -8, 2, -18],\n [16, -12, 5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 16, -3, 4],\n [-24, -10, 12, 2],\n [24, -4, -6, -4],\n [-4, -25, 12, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -4, 4, -8],\n [0, -6, -15, -14],\n [-11, 3, 8, 17],\n [11, -3, 4, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 12, 8, 0],\n [3, 6, -9, -12],\n [11, -5, -12, -8],\n [5, -8, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -1, 1, 2],\n [-6, 3, 6, -9],\n [6, 3, -12, -3],\n [2, -4, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [6, -2, -2, -2],\n [9, -3, -3, -3],\n [3, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -5, -4, -5],\n [6, -5, 2, 7],\n [0, 6, -2, 2],\n [-3, -11, 13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 4, 18, -5],\n [12, -12, 8, -4],\n [4, -4, 14, -3],\n [0, 8, 10, 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[[-1, -3, -4, 2],\n [0, 0, 0, 0],\n [2, 6, 8, -4],\n [-4, -12, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, 8, 12, -9],\n [5, 16, 12, 15],\n [14, 14, 16, -2],\n [10, 11, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 9, -19, 9],\n [20, 12, -5, 3],\n [0, -17, 30, -16],\n [26, 2, 2, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -4, 16, -4],\n [0, 0, 0, 0],\n [-4, -1, 4, -1],\n [-4, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 14, -12, -2],\n [-2, -6, -2, 13],\n [-14, 8, -14, 11],\n [-8, 1, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -18, 18, -6],\n [14, -16, 20, -8],\n [-8, 8, -16, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -14, -12, 14],\n [-14, 0, 7, -12],\n [8, 21, 20, -18],\n [25, 15, 7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -16, 8, 8],\n [-9, -12, 6, 6],\n [9, 12, -6, -6],\n [-9, -12, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 6, 3, 6],\n [-4, -8, -4, -8],\n [4, 8, 4, 8],\n [-3, -6, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 12, 2, 3],\n [-8, -4, 10, -1],\n [6, 12, 6, 3],\n [0, 8, 12, 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 4x4 matrix:\n[[8, -6, -16, -5],\n [4, 2, -8, 5],\n [0, -6, 0, -9],\n [-6, 8, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 1, 4, -4],\n [3, -3, -12, 12],\n [4, -5, -17, 13],\n [-2, 3, 9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 2, 8, -8],\n [0, -3, -12, 12],\n [0, 1, 4, -4],\n [0, 1, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -2, -13, -1],\n [-15, -6, -15, -3],\n [7, 6, -1, 3],\n [-4, -8, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 8, 6, 10],\n [-4, 14, 13, 11],\n [2, -9, -9, -6],\n [24, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -12, 9, -3],\n [7, 0, 0, 3],\n [-8, -8, 6, -8],\n [-3, -24, 18, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -2, -8, -1],\n [-2, -2, -8, -4],\n [1, 5, 20, 8],\n [-5, 3, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 2, -8, 6],\n [12, 4, -16, 12],\n [-12, -4, 16, -12],\n [9, 3, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -12, 6, 12],\n [20, 0, -14, -4],\n [16, 17, -1, -1],\n [-15, -14, 12, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -8, 5, -4],\n [1, -16, 13, -12],\n [3, -12, 12, -12],\n [3, 0, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 4, 8, 2],\n [16, 8, 16, 4],\n [-16, -8, -16, -4],\n [12, 6, 12, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -4, 7, 11],\n [-1, -1, 4, 7],\n [-6, -5, 11, 18],\n [-18, -13, 7, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -28, -20, -25],\n [0, -8, 2, -13],\n [-6, -2, -9, 5],\n [-2, -12, -20, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -11, -1, -5],\n [2, 8, -8, 2],\n [-4, 10, -2, 4],\n [2, -18, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -12, 14, 8],\n [8, 12, -6, -12],\n [-3, 0, 5, 2],\n [-8, -8, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -8, 8, 12],\n [-1, -2, -1, 12],\n [9, 20, 3, 1],\n [-8, 5, 10, -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[[13, 13, 10, 7],\n [12, 12, -6, -6],\n [-8, -8, -18, -14],\n [-8, -8, 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[[2, -18, -26, -2],\n [9, 6, 18, -3],\n [-2, 14, 16, -7],\n [12, -4, 4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 8, 16, -16],\n [3, 6, 12, -12],\n [4, 8, 16, -16],\n [-4, -8, -16, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 4, -7, 0],\n [9, 12, -6, -6],\n [3, -4, -8, 6],\n [-9, 4, 18, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 1, -1, -4],\n [-7, 0, 1, 6],\n [5, 9, -2, 6],\n [-3, 3, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 4, -12, -8],\n [12, -6, 9, 7],\n [3, -5, -3, 0],\n [0, -6, -9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 1, -10, 12],\n [9, -5, 11, -12],\n [5, 1, 7, -4],\n [5, 4, 7, 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, -8, 8, 12],\n [12, 14, -14, -21],\n [3, 4, -4, -6],\n [12, 10, -10, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 14, 0, -3],\n [20, 0, 14, 12],\n [17, 2, 11, 9],\n [21, 6, 12, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -5, 0, -2],\n [9, -19, 18, -3],\n [7, -5, 6, -2],\n [-13, -8, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 0, 4, -8],\n [-8, 0, -4, 8],\n [12, 0, 6, -12],\n [-4, 0, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -12, -6, 13],\n [-1, -17, -26, 20],\n [12, 3, 26, -12],\n [4, -6, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 16, -12, -8],\n [0, 0, 0, 0],\n [-6, 8, -6, -4],\n [-12, 16, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -5, -4, -7],\n [-4, 0, -12, -16],\n [0, -8, 8, 8],\n [0, 8, -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[[12, -16, -12, -8],\n [-3, 4, 3, 2],\n [-3, 4, 3, 2],\n [6, -8, -6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -17, -28, 12],\n [-6, -3, -13, 28],\n [-6, 3, -9, 12],\n [0, 8, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 13, 8, -19],\n [-8, 13, 18, -7],\n [4, -9, -1, -6],\n [13, 4, -5, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -5, 8, 3],\n [-7, -5, 8, 3],\n [-11, -10, 4, 4],\n [-7, -5, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -11, -8, 2],\n [5, 0, -10, -14],\n [-4, 11, 8, -2],\n [-3, -3, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 0, -8, 0],\n [4, 0, -4, 0],\n [0, 0, 0, 0],\n [4, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -12, 9, 12],\n [0, 0, 0, 0],\n [-12, -12, 9, 12],\n [-12, -12, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 6, -9, 6],\n [-4, -4, 6, -4],\n [0, 0, 0, 0],\n [-6, -6, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -3, -12, -3],\n [12, 3, 12, 3],\n [8, 2, 8, 2],\n [-16, -4, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -10, 1, 21],\n [6, 5, 0, -3],\n [-6, -6, 3, 0],\n [14, 11, 0, -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[[4, -3, 6, 4],\n [-8, -2, 4, 8],\n [-12, -6, 12, 18],\n [8, 4, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -8, -12, 4],\n [3, -2, -3, 1],\n [0, 0, 0, 0],\n [-6, 4, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -2, -2, 2],\n [0, -8, 0, 0],\n [-20, 1, -5, 5],\n [16, 0, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -1, -3, -18],\n [21, 0, 4, 25],\n [18, -3, 3, 21],\n [-18, 3, -3, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-22, 0, 8, 12],\n [4, 30, -31, 2],\n [17, -2, -3, -8],\n [-10, 9, -5, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 9, 9, -12],\n [3, -3, -5, 6],\n [-6, 6, 10, -12],\n [3, 9, 3, -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[[16, -4, 12, 16],\n [12, 6, 14, 6],\n [-10, 16, 0, -19],\n [0, 9, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -5, 12],\n [9, -14, 2, -21],\n [-1, -2, 2, -3],\n [-5, 6, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 0, -8, 4],\n [-9, 0, 12, -6],\n [-3, 0, 4, -2],\n [9, 0, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 6, -8, -4],\n [6, -6, 8, 4],\n [-12, 12, -16, -8],\n [-9, 9, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [12, -16, -16, 12],\n [3, -4, -4, 3],\n [6, -8, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[34, 0, 2, -5],\n [10, -10, 8, -3],\n [2, -16, 10, 1],\n [16, 12, -4, -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[[1, -11, 2, 4],\n [6, 3, -2, 6],\n [-14, -1, -18, -22],\n [5, 5, 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 4x4 matrix:\n[[-4, 0, 5, 2],\n [-4, 0, 0, 2],\n [-6, 0, 5, 3],\n [-8, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -11, 11, -1],\n [8, -12, 12, -4],\n [4, -4, 4, -12],\n [0, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -4, -10, -8],\n [2, 0, 29, -10],\n [36, -2, 22, -2],\n [12, 16, 16, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -9, -5, 2],\n [0, 9, 3, -12],\n [0, -1, 12, -14],\n [6, -4, -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 4x4 matrix:\n[[-9, 4, -25, 9],\n [6, 1, 2, -6],\n [12, 3, 0, -12],\n [3, 3, -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[[4, 6, -2, 0],\n [0, 2, -4, 4],\n [6, 7, -5, 4],\n [12, 14, -10, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -2, 6, 0],\n [4, 6, -4, 8],\n [2, 3, -2, 4],\n [2, 14, -14, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 4, 2, -2],\n [-14, -20, -18, 10],\n [-16, -28, -24, 14],\n [-16, -16, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -6, -2, 4],\n [16, 4, 6, -6],\n [-12, 21, -5, -14],\n [0, 3, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 3, 6, 9],\n [-16, -4, -8, -12],\n [-12, -3, -6, -9],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -8, -2, -11],\n [13, 4, 10, 1],\n [8, 4, 16, 3],\n [-9, -2, 16, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 5, 6, -6],\n [0, 6, 4, -4],\n [9, -3, -6, 6],\n [6, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[17, 2, -16, 16],\n [-6, -4, 4, -11],\n [-10, 4, 12, -1],\n [4, 8, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -4, 0, -1],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [-4, 16, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 16, 12, -16],\n [1, -10, -3, 2],\n [-9, -1, 6, -11],\n [-16, 4, 12, -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 4x4 matrix:\n[[5, -3, -2, -9],\n [10, 8, -2, -4],\n [-7, -27, 2, -17],\n [18, 1, 5, -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, 4, -6, 2],\n [-10, 4, 1, 1],\n [2, 1, -5, 1],\n [4, -1, -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[[28, -13, -11, 20],\n [32, -16, -12, 24],\n [-4, 9, -2, -10],\n [0, -6, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 0, -4, -3],\n [8, 0, -16, -12],\n [0, 0, 0, 0],\n [-6, 0, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, 10, 11, 9],\n [-5, -2, -1, -3],\n [-6, -8, -11, -5],\n [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[[-10, -3, 14, -27],\n [-10, 7, -15, 23],\n [11, -2, 4, -3],\n [-16, 5, -12, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 2, -6, 9],\n [6, 10, 20, -4],\n [-9, -5, -16, 8],\n [-3, -10, -17, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 8, 0, -8],\n [6, -12, 0, 12],\n [4, -8, 0, 8],\n [8, -16, 0, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[17, -12, -12, 1],\n [-18, 14, -8, -14],\n [-13, 10, -6, -9],\n [6, -5, 11, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -7, 7, 10],\n [0, -8, 8, 8],\n [4, -1, 1, 2],\n [-20, 13, -13, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 32, 28, 24],\n [12, -9, 0, -12],\n [-3, -14, -16, 0],\n [-12, 16, 6, 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 4x4 matrix:\n[[9, -6, -9, -15],\n [-9, 5, 11, 16],\n [9, -7, -7, -14],\n [-6, 8, -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[[-5, 7, -8, 7],\n [4, -4, 0, -12],\n [6, -9, 12, -6],\n [-7, 10, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [2, 8, 8, -6],\n [-1, -4, -4, 3],\n [-2, -8, -8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 15, 16, 1],\n [0, -9, 5, 11],\n [8, 6, -2, 6],\n [-12, -9, 11, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -21, 12, 21],\n [-17, -21, 2, 6],\n [5, 11, -2, -14],\n [-9, -1, -18, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, 12, -14],\n [1, 10, -8, 12],\n [-22, -2, -10, -8],\n [8, 4, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 8, -6, -2],\n [4, -10, 6, 1],\n [9, -2, -5, -2],\n [-2, -4, -15, 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 4x4 matrix:\n[[-1, 12, 11, -16],\n [0, 3, 3, -3],\n [1, -12, -11, 16],\n [-2, -12, -14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 3, -1, 1],\n [12, -14, 2, -2],\n [10, -5, 3, -3],\n [-2, -1, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 4, -12, 4],\n [4, 4, -12, 4],\n [1, 1, -3, 1],\n [3, 3, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 3, -1, -2],\n [-12, 12, -4, -8],\n [-9, 9, -3, -6],\n [12, -12, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -5, 10, 2],\n [-12, -10, 16, -4],\n [-21, -4, 9, 4],\n [-16, 1, -4, 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 4x4 matrix:\n[[3, -6, 3, 25],\n [-1, 1, 0, -7],\n [-3, -9, 12, -5],\n [0, 6, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -1, 2, 4],\n [0, -2, 4, 8],\n [0, 2, -4, -8],\n [0, -2, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 4, -12, 14],\n [-4, -12, 24, 0],\n [7, 5, -18, 24],\n [14, 13, -27, 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 4x4 matrix:\n[[0, -12, -9, 3],\n [0, -8, -6, 2],\n [0, 8, 6, -2],\n [0, -12, -9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -9, -6, -12],\n [16, 12, 8, 16],\n [-8, -6, -4, -8],\n [-4, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, -15, -10, 3],\n [12, -12, -6, 0],\n [-9, 9, 22, -21],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -2, -2, -2],\n [4, -1, -11, 6],\n [19, 20, -5, 24],\n [3, -10, 25, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 7, -14, -14],\n [0, -6, 12, 3],\n [-3, -1, 2, -10],\n [-1, 3, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-8, -4, 0, -8],\n [4, 2, 0, 4],\n [-8, -4, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 4, 8, 0],\n [-6, 2, 4, 0],\n [9, -3, -6, 0],\n [-9, 3, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -12, 3, -9],\n [-3, 4, -1, 3],\n [-6, 8, -2, 6],\n [-6, 8, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -6, 6, -6],\n [2, -6, 7, -5],\n [-3, 2, 5, -3],\n [0, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -19, 7, 7],\n [-15, 17, 15, 7],\n [22, -20, -20, -10],\n [-30, 1, 19, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 3, 0, 0],\n [3, -1, 0, 0],\n [0, 0, 0, 0],\n [9, -3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 14, 12, 7],\n [5, 6, 2, 6],\n [-1, 4, 2, 2],\n [-14, -3, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, -2, -3, 1],\n [16, 8, 12, -4],\n [-4, -2, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [4, -6, 4, -4],\n [-6, 9, -6, 6],\n [-4, 6, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 12, 3, 15],\n [9, 6, -11, 10],\n [4, 16, 4, 20],\n [-2, -8, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -12, -18, 0],\n [-3, 12, 17, -4],\n [1, -2, -4, -6],\n [3, 4, 11, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, 6, -2],\n [4, -4, 3, 5],\n [-9, 3, 0, -9],\n [15, -13, 9, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -13, 3, 14],\n [-4, -12, -4, -4],\n [4, -8, 0, 4],\n [6, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -16, -8, -16],\n [2, -4, -2, -4],\n [8, -16, -8, -16],\n [-6, 12, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 2, 2, -1],\n [12, 6, 6, -3],\n [-12, -6, -6, 3],\n [4, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, -8, 4],\n [-6, 0, -12, 6],\n [-6, 0, -12, 6],\n [-8, 0, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -28, 16, -28],\n [-2, -10, 7, 4],\n [-6, 18, -21, 0],\n [-13, -20, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 16, -4, 4],\n [0, -4, 1, -1],\n [0, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 5, 11, -3],\n [-1, -4, -1, 3],\n [-16, 11, 19, -7],\n [0, -15, -7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 4, 16, 2],\n [0, 8, 0, -14],\n [-6, 1, 12, 5],\n [2, 13, -4, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -3, -6, -3],\n [16, -4, -8, -4],\n [8, -2, -4, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -6, 0, -6],\n [3, 6, 0, 6],\n [0, 0, 0, 0],\n [-2, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -10, -9, 11],\n [-1, 4, 3, -3],\n [-1, -24, -21, 25],\n [6, 4, 6, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -8, 6, 4],\n [4, -16, 12, 8],\n [3, -12, 9, 6],\n [2, -8, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -3, 4, -5],\n [-4, -9, 1, 1],\n [-10, -1, 8, -5],\n [6, -5, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 0, -8, 4],\n [2, 0, 4, -2],\n [4, 0, 8, -4],\n [-6, 0, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -2, 8, 0],\n [2, -2, 8, 0],\n [4, -4, 16, 0],\n [-3, 3, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 3, 0, -3],\n [4, -4, 0, 4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -7, 14, -1],\n [-26, 20, -23, 13],\n [25, -25, 21, -12],\n [-21, 18, -19, 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 4x4 matrix:\n[[6, -2, 0, 6],\n [-12, 4, 0, -12],\n [3, -1, 0, 3],\n [3, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 1, -14, -1],\n [3, 9, -3, 6],\n [-1, 10, -17, 5],\n [0, 1, -4, 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 4x4 matrix:\n[[6, 3, 1, 4],\n [10, 12, -10, 9],\n [-2, -12, -12, -15],\n [-14, -30, 6, -27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 6, 3, -6],\n [4, 3, -6, 2],\n [6, 0, -9, 6],\n [4, 0, -6, 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, -4, -8, 0],\n [0, -6, -12, 0],\n [0, 2, 4, 0],\n [0, 8, 16, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 2, -20, -4],\n [-10, -10, -2, 2],\n [5, 0, 17, 3],\n [-10, -5, -18, -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[[-8, -2, -2, -4],\n [-8, -2, -2, -4],\n [16, 4, 4, 8],\n [-8, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 2, 0, 3],\n [-6, 0, -2, -4],\n [10, -4, 4, 2],\n [6, 6, 1, 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 4x4 matrix:\n[[-9, 1, -5, -11],\n [0, 16, 24, 32],\n [0, 4, 2, 6],\n [0, 6, 7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -4, 3, 4],\n [-6, -8, 6, 8],\n [12, 16, -12, -16],\n [-9, -12, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 6, 14, -6],\n [4, -8, 8, 3],\n [12, 3, 12, 0],\n [12, 6, 12, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, -16, -8, -20],\n [-15, 0, 0, 15],\n [6, 16, 8, 0],\n [-22, 14, 4, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 2, -6, 8],\n [-12, -3, 9, -12],\n [-3, -9, 6, 12],\n [-4, -12, 8, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -16, -4, -3],\n [-16, -20, -8, -9],\n [14, 1, 7, 10],\n [6, -3, 3, 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[[-25, 1, -9, 30],\n [5, -9, 9, -6],\n [13, 20, -6, -24],\n [6, 5, -3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 4, -1, 2],\n [4, -4, 1, -2],\n [16, -16, 4, -8],\n [-4, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 6, 15, 0],\n [-22, -5, -18, 1],\n [0, -14, -2, -6],\n [-18, 1, -14, 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[[3, 6, 21, -14],\n [0, -3, -3, 2],\n [3, 0, 15, -10],\n [0, -12, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 19, -5, -4],\n [23, 25, -9, 1],\n [-8, -8, 4, 2],\n [-7, -9, 1, -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[[0, 0, 0, 0],\n [0, 0, -9, 12],\n [0, 0, -12, 16],\n [0, 0, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 2, 2, -4],\n [-4, -1, -1, 2],\n [12, 3, 3, -6],\n [8, 2, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, -26, 2],\n [13, 0, -10, 8],\n [-12, -5, -5, -1],\n [16, 0, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, -4, -3],\n [0, 0, 0, 0],\n [0, 2, 4, 3],\n [0, -8, -16, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 2, -4, 2],\n [8, -4, 8, -4],\n [4, -2, 4, -2],\n [-2, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -5, 11, 3],\n [12, -3, 1, -3],\n [-18, -23, 14, -12],\n [-9, -3, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -8, -16, 24],\n [-9, 6, 12, -18],\n [3, -3, -6, 6],\n [8, -6, -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[[1, -8, -10, -6],\n [3, 0, -1, -16],\n [1, -4, -4, -6],\n [-1, 3, -1, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -3, 6, 0],\n [-3, -11, 6, 4],\n [0, 4, -3, 10],\n [-20, -16, -3, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -16, 4, 16],\n [-4, -8, 2, 8],\n [-8, -16, 4, 16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [8, -4, 0, 16],\n [6, -3, 0, 12],\n [-6, 3, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 6, 7, -19],\n [-9, 10, 2, -12],\n [-17, 23, -7, -8],\n [15, -22, 7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 8, -8, 16],\n [-12, 6, -6, 12],\n [8, -4, 4, -8],\n [8, -4, 4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [3, -2, 0, -4],\n [0, 0, 0, 0],\n [3, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, -8, -12],\n [4, -1, -2, -1],\n [12, -3, 4, 12],\n [-12, 3, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 0, 17, -27],\n [-14, 6, -16, 6],\n [9, -18, 25, -15],\n [-3, -9, -1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, -1, 6, -12],\n [-12, -3, 3, -9],\n [-6, 2, 3, -3],\n [0, -7, -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[[0, 0, 0, 0],\n [12, -8, -4, 8],\n [3, -2, -1, 2],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 10, -5, -2],\n [-4, 8, -8, -3],\n [-6, 8, -5, 3],\n [5, -11, 11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 4, -6, -2],\n [-20, 2, -6, -10],\n [2, -3, 5, 3],\n [2, -3, 5, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -12, 16, -8],\n [0, 0, 0, 0],\n [-1, -3, 4, -2],\n [1, 3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[24, 12, -32, -8],\n [25, 9, 4, 8],\n [2, 0, 8, 4],\n [-15, -6, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -9, 6, -6],\n [16, -10, 11, -6],\n [-8, 14, -5, 10],\n [-21, 3, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-12, 8, 0, -4],\n [-12, 8, 0, -4],\n [9, -6, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -5, 3, 1],\n [13, -15, -12, -12],\n [-21, -21, 9, 0],\n [8, 12, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 4, -15, 5],\n [-10, 6, -5, -2],\n [11, 4, -8, 8],\n [-7, 4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, -6, -20, -20],\n [16, -16, -8, 15],\n [-12, 12, -8, 8],\n [-16, -8, -24, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, -12, 9, 21],\n [-14, -9, 8, 12],\n [2, 0, 1, -3],\n [-10, -9, 10, 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 4x4 matrix:\n[[-8, -12, -16, 16],\n [-14, -1, 12, -2],\n [16, 0, -16, 4],\n [22, 5, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -6, 0, -12],\n [6, -4, 0, -8],\n [-3, 2, 0, 4],\n [12, -8, 0, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 2, 10, 10],\n [-12, 14, -20, -10],\n [4, -10, 4, -2],\n [-4, 4, -7, -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 4x4 matrix:\n[[-4, 24, -4, -18],\n [0, 32, -12, -24],\n [14, -4, -16, 3],\n [-6, -20, 15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 8, -12, -28],\n [1, -4, 6, 20],\n [-3, -4, 6, 4],\n [-1, 2, -3, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-23, -3, 0, 11],\n [5, 8, -16, 6],\n [16, 18, 4, -2],\n [-5, -14, 11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 0, 14, 11],\n [-8, 0, 14, 6],\n [1, 0, -8, -7],\n [-12, 0, 6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 1, 11, 9],\n [-8, -3, 3, 7],\n [8, 3, 6, -1],\n [28, 14, -5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 16, 8, 8],\n [8, 4, 0, 2],\n [16, 8, 0, 4],\n [-4, -8, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 0, -7, 10],\n [-1, 11, 6, 5],\n [-16, -8, 4, -16],\n [27, -3, -12, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -9, 6, -1],\n [0, -9, 9, 12],\n [0, -11, 12, 19],\n [0, -6, 6, 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 4x4 matrix:\n[[0, 12, 0, -4],\n [0, 9, 0, -3],\n [0, 9, 0, -3],\n [0, 6, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 6, 0, 6],\n [0, 7, -4, 6],\n [0, -7, 12, -4],\n [0, 0, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -12, 5, -8],\n [-10, -24, -2, -4],\n [10, -8, 6, -8],\n [-3, 12, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 10, 6, -7],\n [16, 14, 18, 19],\n [-4, -8, -24, -4],\n [4, 6, 18, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -4, 0, 2],\n [-8, -13, -1, 4],\n [-2, -16, 4, 18],\n [4, 17, -3, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 11, 20, 5],\n [-2, -14, -8, 14],\n [0, 0, 0, 0],\n [-4, -6, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -4, -6, -8],\n [6, 0, 6, 0],\n [8, 10, 8, 10],\n [7, 11, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 6, 6, -4],\n [8, -8, -12, 8],\n [8, -8, -12, 8],\n [8, -5, -9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -4, 2, -1],\n [-6, 12, -6, 3],\n [-2, 4, -2, 1],\n [-6, 12, -6, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -5, -6, 8],\n [-12, 16, 8, -12],\n [15, 5, -8, 9],\n [3, -4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 8, -2, 0],\n [16, 8, 4, 8],\n [-12, 6, -11, 14],\n [10, 7, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 1, -8, -11],\n [4, 1, 20, 10],\n [8, 2, -8, -16],\n [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 4x4 matrix:\n[[21, 3, 0, -6],\n [-2, -11, 3, -8],\n [3, 4, -1, 2],\n [-4, 28, -8, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -18, -14, -3],\n [2, 11, 9, 3],\n [-4, -22, -18, -6],\n [4, 7, 13, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -3, -2, -1],\n [12, -9, -6, 2],\n [-4, 3, 2, -4],\n [-16, 12, 8, -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 4x4 matrix:\n[[-13, -9, 3, -15],\n [-13, 1, -9, 6],\n [-7, -11, 9, -21],\n [-19, -7, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -3, 0, -9],\n [0, -1, 0, -3],\n [0, -4, 0, -12],\n [0, -3, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, 0, -16],\n [-1, 1, 0, 4],\n [1, -1, 0, -4],\n [3, -3, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -8, 0, -20],\n [4, -4, -8, 8],\n [-7, 7, 2, 13],\n [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[[-16, -16, 8, 8],\n [-12, -12, 6, 6],\n [-16, -16, 8, 8],\n [-8, -8, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -9, 3, -9],\n [2, -6, 2, -6],\n [-2, 6, -2, 6],\n [-3, 9, -3, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 9, -24, -15],\n [8, 4, 16, 4],\n [-4, -14, 4, 10],\n [-4, -10, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 9, -6, 12],\n [0, 9, -6, 12],\n [0, 9, -6, 12],\n [0, 6, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -4, -4, 0],\n [6, -2, -2, 0],\n [-9, 3, 3, 0],\n [-12, 4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -8, 8, -8],\n [9, -6, 6, -6],\n [-9, 6, -6, 6],\n [12, -8, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 14, -4, -4],\n [20, -12, -17, -6],\n [-6, 18, 6, 0],\n [16, -12, -12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 2, -3, 6],\n [2, -4, 6, 0],\n [-5, 6, -9, -2],\n [11, -2, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-8, 12, -4, 0],\n [2, -3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -9, 15, 14],\n [3, -18, 22, 24],\n [10, 26, -22, -28],\n [-11, -9, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 0, -2, 6],\n [2, 0, 2, -6],\n [1, 0, 1, -3],\n [-2, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 7, 1, 1],\n [18, 6, 8, 12],\n [2, 10, -12, -24],\n [-14, -14, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 5, -6, 14],\n [-2, 11, -13, 17],\n [15, 6, 8, -6],\n [18, 4, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 6, 0],\n [0, -17, -13, 0],\n [-16, -28, -10, 0],\n [10, 3, -28, 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[[1, -19, 1, 7],\n [-3, -1, 5, -1],\n [7, 15, -13, -3],\n [4, 12, -4, -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[[-7, -14, -22, -20],\n [27, 1, 7, -7],\n [0, 6, 10, 10],\n [-2, -6, -12, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -6, 0, -3],\n [4, 8, 0, 4],\n [3, 6, 0, 3],\n [2, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[19, 10, -15, 2],\n [2, 2, -3, -5],\n [-13, -8, 12, 5],\n [-14, -8, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 0, 0, 4],\n [-2, 0, 0, -1],\n [-6, 0, 0, -3],\n [6, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 5, 2, 2],\n [0, -17, -10, -17],\n [8, -15, -14, -9],\n [-8, 14, 20, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 2, -8, 8],\n [-12, 7, -8, 16],\n [0, 0, 0, 0],\n [8, 0, 10, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 0, -6, 2],\n [-11, -8, 8, 4],\n [9, 0, 6, -2],\n [14, 2, -14, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -6, 0, 20],\n [-21, 12, 6, -8],\n [4, 18, 20, -14],\n [-15, 10, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -3, -6, 3],\n [-15, 12, 4, 2],\n [21, -32, 9, -19],\n [18, -13, 5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -15, -2, -8],\n [-4, -4, 9, -2],\n [12, 3, -9, 6],\n [3, -18, -16, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 4, -2],\n [8, -8, -8, -4],\n [-24, 24, -8, 12],\n [-4, 4, 0, 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[[-17, -13, -17, -2],\n [10, -2, 4, -8],\n [-8, -4, -7, 1],\n [12, 4, -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[[6, -14, 1, -21],\n [-12, 1, 6, 4],\n [-6, -17, -2, -18],\n [-8, -19, 1, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -5, -1, 8],\n [8, -1, -10, -11],\n [-3, 8, 3, -11],\n [-10, 10, 2, -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[[-11, 14, 3, 2],\n [6, -9, -3, -3],\n [1, 6, 7, 10],\n [5, -10, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-8, -12, -16, -8],\n [2, 3, 4, 2],\n [2, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, -6, -18, -10],\n [-4, -8, -10, -18],\n [3, 2, 1, 5],\n [-6, -4, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -1, 10, 4],\n [1, 12, -1, 1],\n [-6, -1, 17, 5],\n [1, 11, 2, 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[[24, 0, 3, 9],\n [-4, -10, -8, 6],\n [-24, -4, -6, -6],\n [28, -2, 2, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -16, 8, 0],\n [16, 12, -12, 16],\n [20, 8, -16, 32],\n [-15, -13, 11, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 8, 0, 16],\n [6, 4, 0, 8],\n [6, 4, 0, 8],\n [6, 4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, 8, -16],\n [-2, 1, 2, -4],\n [8, -4, -8, 16],\n [-2, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -8, -4, -6],\n [6, -12, -6, 0],\n [7, -4, -2, 2],\n [7, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -12, -12, 16],\n [0, 0, 0, 0],\n [0, 6, 6, -8],\n [0, 12, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 28, 0, 13],\n [3, 4, -10, 9],\n [3, -20, -13, 0],\n [0, 8, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 4, 3, 19],\n [18, 6, 6, 18],\n [17, -26, -1, 3],\n [1, -12, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 13, -9, 4],\n [-4, -3, 2, 0],\n [-12, -19, 14, -16],\n [2, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, 8, 4],\n [3, 0, 6, 3],\n [4, 0, 8, 4],\n [-1, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 9, -32, 2],\n [-3, -3, 12, -6],\n [-5, 11, -20, 2],\n [-8, 8, 12, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -4, -7, 1],\n [-2, -4, 21, -11],\n [15, 15, -19, 15],\n [-24, -18, -14, -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[[0, 4, 4, 4],\n [0, -2, -2, -2],\n [0, 6, 6, 6],\n [0, -6, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [16, 4, 0, -16],\n [-16, -4, 0, 16],\n [-16, -4, 0, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -1, -4, 2],\n [0, 20, 8, 16],\n [-16, -12, -12, 8],\n [8, 15, 15, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [-1, -2, 1, 2],\n [-4, -8, 4, 8],\n [-1, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 4, 0, 8],\n [0, 9, 6, 12],\n [3, 12, 12, 12],\n [-2, -8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -13, -14, 3],\n [-6, 16, -4, 20],\n [11, -8, -24, -2],\n [-15, 24, 24, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 1, 14, -9],\n [0, 0, 0, 0],\n [2, -2, -3, -2],\n [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 4x4 matrix:\n[[4, 12, -12, 4],\n [1, 3, -3, 1],\n [-2, -6, 6, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -4, 6, 8],\n [6, -4, 6, 8],\n [9, -6, 9, 12],\n [3, -2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -24, -24, 0],\n [-5, 2, 1, -3],\n [14, 20, 22, 6],\n [9, 21, 17, 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[[1, 0, 4, 0],\n [2, 0, 8, 0],\n [0, 0, 0, 0],\n [3, 0, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 3, -2, -1],\n [-6, 9, -6, -3],\n [2, -3, 2, 1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 1, -1, -10],\n [16, 4, -4, 0],\n [5, 1, -1, -2],\n [-12, -2, 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[[0, 0, -1, -1],\n [0, 0, -1, -1],\n [0, 0, 2, 2],\n [0, 0, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 6, 24, -7],\n [-5, -19, 3, 13],\n [-3, -10, -18, 5],\n [-2, -2, 13, -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[[-3, 3, 12, 12],\n [1, -1, -4, -4],\n [0, 0, 0, 0],\n [-4, 4, 16, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -3, 17, 12],\n [9, -7, 14, -8],\n [-10, -16, -3, -4],\n [-10, 4, -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[[9, -14, 1, -20],\n [-10, 12, 6, 8],\n [-15, 22, 1, 28],\n [4, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 10, 7, -13],\n [2, 2, 1, -4],\n [-1, 0, -2, -7],\n [-18, -14, -15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 0, -6, 2],\n [-4, 0, 3, -1],\n [8, 0, -6, 2],\n [4, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -8, 20, 8],\n [-8, -2, 12, 8],\n [8, -4, 3, -2],\n [-8, 10, -18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 8, 10, -18],\n [-10, -5, -3, 23],\n [12, 6, 2, -26],\n [12, 2, 2, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 14, -6, -6],\n [-6, 8, 4, -8],\n [-15, 15, 15, -15],\n [-13, 14, 13, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 3, -5, -2],\n [-2, 3, 4, -2],\n [0, 12, 4, -8],\n [14, 9, -18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -3, -6, 12],\n [0, -3, -6, 12],\n [0, -3, -6, 12],\n [0, 4, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -6, -8, 9],\n [-11, -8, -17, 3],\n [4, -10, -11, 12],\n [-9, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, -10, 4, -2],\n [-24, -15, 8, -9],\n [-1, 2, -2, 4],\n [3, 3, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 6, -12, 9],\n [-2, 3, 1, 0],\n [-14, 5, -17, 12],\n [-10, 3, -13, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -6, 0, -3],\n [-9, 6, 0, 3],\n [3, -2, 0, -1],\n [3, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -3, -2, 2],\n [-6, 1, -2, 2],\n [2, 13, 14, -14],\n [-2, -1, -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[[6, 0, -12, -12],\n [16, -8, -12, 12],\n [-16, 6, 17, -1],\n [-4, 0, 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[[9, -2, -1, 11],\n [0, 4, -7, 14],\n [-11, 6, -5, -1],\n [-2, 0, 1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -16, 0, -11],\n [24, 4, 20, 4],\n [0, 0, 0, 0],\n [-24, -4, -20, -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 4x4 matrix:\n[[23, 1, 4, 22],\n [2, 2, 24, -10],\n [-8, 0, 16, -12],\n [-1, 1, -20, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, 7, 10, -13],\n [7, -9, -5, 11],\n [-2, -6, 4, 2],\n [11, -7, -10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -4, 8, 1],\n [-3, 16, -16, 1],\n [-6, 10, -16, -2],\n [-9, 9, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 12, 16, -2],\n [-14, -4, -12, -6],\n [-7, -10, -16, -1],\n [-6, 4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, -4, 4],\n [0, 0, -4, -8],\n [1, 1, -3, -9],\n [2, 2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 9, -6, 3],\n [-9, 11, -10, 8],\n [15, -7, -6, 15],\n [6, -2, -4, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 7, 2, -2],\n [-8, 4, 0, 8],\n [-4, 6, 2, -4],\n [-10, 9, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 9, 3, -12],\n [6, -9, -3, 12],\n [6, -9, -3, 12],\n [-6, 9, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -13, -6, 5],\n [-16, 8, 15, -9],\n [-8, 18, -3, -1],\n [12, -17, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 5, 10, 8],\n [-1, 5, 6, 5],\n [-7, -6, -21, -7],\n [5, 12, 26, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [12, 0, -16, 0],\n [-12, 0, 16, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -16, -9, -7],\n [6, -17, -12, 8],\n [5, -13, -9, 5],\n [4, -9, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -4, -4, 14],\n [-18, -6, 18, 3],\n [15, 6, -14, -6],\n [-12, -4, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 17, 3, -20],\n [5, 4, -22, -2],\n [-6, 1, 28, 0],\n [10, -9, -22, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -15, -13, 8],\n [-9, 8, 0, -6],\n [-3, -1, -3, 0],\n [8, -1, 5, 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[[22, -6, 12, 2],\n [-19, -8, -29, 1],\n [12, -21, -15, 8],\n [-9, -10, -19, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [8, -2, -8, 4],\n [12, -3, -12, 6],\n [-4, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[29, 22, -19, -2],\n [-16, -15, -5, 3],\n [-7, -4, 12, 2],\n [-23, -17, 18, 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[[-12, 6, -6, 0],\n [16, -8, 8, 0],\n [8, -4, 4, 0],\n [4, -2, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -4, 10, 3],\n [2, 4, -7, -2],\n [8, 16, 11, 5],\n [2, 4, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 16, 16, -8],\n [-2, 4, 4, -2],\n [4, -8, -8, 4],\n [-6, 12, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, -12, -12],\n [-6, 0, 12, 12],\n [-8, 0, 16, 16],\n [-4, 0, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -10, -15, -1],\n [12, 6, -9, -3],\n [16, -10, -15, -1],\n [-16, -8, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-4, -12, -12, -12],\n [1, 3, 3, 3],\n [3, 9, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 7, 0, 2],\n [-1, 8, -3, -2],\n [-3, -2, 1, 4],\n [-14, 2, -22, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -3, 0, 0],\n [3, -3, 0, 0],\n [4, -20, 16, 16],\n [6, -6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 4, -1, -2],\n [6, -8, 2, 4],\n [3, -4, 1, 2],\n [6, -8, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-9, -12, -9, 0],\n [12, 16, 12, 0],\n [12, 16, 12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -1, 1, -2],\n [0, 0, 0, 0],\n [9, 3, -3, 6],\n [-3, -1, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 8, -20, 3],\n [22, 4, -26, -7],\n [7, -8, -16, -14],\n [25, 4, -30, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 12, 12, -4],\n [4, -3, -3, 1],\n [8, -6, -6, 2],\n [-8, 6, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 6, -6, -9],\n [-6, 6, -6, -9],\n [-6, 6, -6, -9],\n [-6, 6, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 12, -9, 0],\n [6, -4, 8, -20],\n [-4, 12, -10, 4],\n [7, -8, 11, -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 4x4 matrix:\n[[6, -12, -9, -13],\n [-10, -4, 7, -6],\n [-4, -10, 0, -11],\n [-8, -8, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -6, 2, 2],\n [0, 0, 0, 0],\n [-2, -6, 2, 2],\n [-2, -6, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 12, 15, 3],\n [9, -15, -7, -21],\n [4, -19, -16, -15],\n [8, 12, 15, 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 4x4 matrix:\n[[-12, 0, -9, 3],\n [0, 0, 4, -4],\n [4, 0, 9, -7],\n [-24, 0, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 8, 12, 0],\n [5, 1, 5, 1],\n [-5, -1, -5, -1],\n [-6, 6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 4, 8, 2],\n [-34, -15, -6, -19],\n [-14, -13, -2, -11],\n [2, -3, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 12, -12, 4],\n [6, -9, 9, -3],\n [4, -6, 6, -2],\n [6, -9, 9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, -4, 4],\n [0, 0, 0, 0],\n [4, 1, -2, 2],\n [12, 3, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -12, -6, -17],\n [17, 0, -18, -1],\n [6, 13, -1, 18],\n [7, 1, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -8, -2, -22],\n [-3, 11, -5, 13],\n [10, 5, -13, 1],\n [14, -1, -15, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-16, -16, -16, 16],\n [0, 0, 0, 0],\n [4, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 0, 4, -6],\n [-3, 0, 2, -3],\n [3, 0, -2, 3],\n [9, 0, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -16, 16, -12],\n [0, 16, -16, 12],\n [0, 4, -4, 3],\n [0, 16, -16, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -6, -12, -12],\n [0, 0, 0, 0],\n [12, 6, 12, 12],\n [-12, -6, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -16, 4, -4],\n [-3, -4, 1, -1],\n [3, 4, -1, 1],\n [9, 12, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 8, 8, -20],\n [6, -6, -9, 12],\n [-12, 4, 2, -12],\n [24, -8, -4, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -3, -4, -3],\n [-32, 20, 28, 24],\n [10, -1, -6, -15],\n [-16, 10, 15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -2, -2, -14],\n [1, -7, -6, -8],\n [4, 0, -10, 6],\n [20, -8, 10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -6, -12, 0],\n [-3, -2, -4, 0],\n [13, 5, 10, -1],\n [-4, 12, 24, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [8, -2, -6, 0],\n [0, 0, 0, 0],\n [12, -3, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, -8, 2, 0],\n [2, 4, -4, 0],\n [-20, -4, -2, 0],\n [11, 4, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 8, 20, -10],\n [-3, 6, 2, -13],\n [9, 27, 5, -8],\n [5, 2, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[23, 20, 17, 16],\n [-5, -4, -16, 12],\n [-20, -17, -14, -16],\n [6, 4, -2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [1, -2, -1, 2],\n [3, -6, -3, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [3, 12, 9, -12],\n [-3, -12, -9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -2, 4, 0],\n [9, -1, 5, 12],\n [-9, -6, 12, 0],\n [-20, -4, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -1, -15, 1],\n [-4, -2, -3, -4],\n [14, -8, 15, -7],\n [-6, -8, -11, -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[[9, 0, -3, 9],\n [-9, 0, 3, -9],\n [12, 0, -4, 12],\n [-3, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -4, -16, 7],\n [8, -32, 12, 0],\n [-8, 28, -8, -1],\n [-6, -4, 19, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 16, 16, 0],\n [0, 0, 0, 0],\n [2, -4, -4, 0],\n [-2, 4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -2, -2, 8],\n [4, 2, 2, -8],\n [-8, -4, -4, 16],\n [2, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -6, 16, 4],\n [24, 18, -9, 10],\n [14, 15, 0, 13],\n [-5, 3, 6, 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 4x4 matrix:\n[[-12, 9, -3, 3],\n [4, -3, 1, -1],\n [-4, 3, -1, 1],\n [8, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 24, 4, 8],\n [0, -9, -27, 21],\n [-5, 16, 23, -14],\n [-6, 0, 16, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -11, 10, -1],\n [-12, 16, -8, 6],\n [6, -1, 18, 10],\n [-2, 7, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 0, -4, -24],\n [-3, 1, -3, -17],\n [9, 7, 3, 25],\n [-7, -11, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -12, -16, 14],\n [-3, 16, 4, 3],\n [0, 0, 0, 0],\n [4, -20, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 9, 14, -9],\n [2, -12, -13, -5],\n [4, -6, -8, 2],\n [12, -6, -12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -4, 3, 6],\n [8, 8, -6, -12],\n [16, -12, 9, 4],\n [-4, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -12, 1, 15],\n [6, 18, -12, -8],\n [-12, 9, -6, 1],\n [16, -5, 1, 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 4x4 matrix:\n[[-12, 2, -4, -18],\n [-19, 10, -6, 4],\n [3, -2, 22, -12],\n [-8, 6, -20, 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[[-4, 6, 6, 2],\n [-2, 3, 3, 1],\n [6, -9, -9, -3],\n [2, -3, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, 4, 0],\n [12, 0, 4, 0],\n [-9, 0, -3, 0],\n [9, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -6, 16, 9],\n [4, -8, 18, 7],\n [6, -5, 13, 7],\n [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[[-2, -11, -12, 7],\n [-8, 5, 8, -7],\n [1, 9, 10, -6],\n [6, -2, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 4, -2, 10],\n [6, -2, 4, 0],\n [-6, -7, 11, 13],\n [18, -12, 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[[2, 11, -9, 7],\n [12, -14, 6, 2],\n [-2, -11, 9, -7],\n [24, 4, -12, 20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 1, 2, 4],\n [0, 4, 8, 16],\n [0, 0, 0, 0],\n [0, 3, 6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, -8, 4, -4],\n [0, -6, 3, -3],\n [0, 8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -4, 9, 12],\n [-24, 5, 1, -18],\n [-25, -3, 26, 10],\n [-5, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 3, 3, -9],\n [0, 0, 0, 0],\n [-8, -4, -4, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, -8, 2],\n [-12, 27, 0, -3],\n [-12, 7, 0, 1],\n [-2, -6, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -4, -8, 8],\n [0, 8, 16, -16],\n [0, -8, -16, 16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -12, 12, -8],\n [-2, -3, 3, -2],\n [-8, -12, 12, -8],\n [2, 3, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -1, 5, -5],\n [15, 7, -13, 2],\n [3, 1, -1, -1],\n [21, 9, -15, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 21, -12],\n [-4, 6, 13, -6],\n [0, 0, 14, -8],\n [-4, 6, -22, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -4, 2, 2],\n [10, 2, -9, -5],\n [4, 6, -15, -3],\n [6, -4, -28, -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[[-5, -10, 9, 0],\n [14, 4, 2, 12],\n [-4, 4, -4, 2],\n [19, 2, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, -10, -24, 23],\n [-8, -6, -9, 9],\n [-2, -16, 0, 1],\n [-11, 2, -18, 22]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [4, 3, -3, 0],\n [-8, -6, 6, 0],\n [12, 9, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 8, -2, 2],\n [9, -12, 3, -3],\n [-12, 16, -4, 4],\n [12, -16, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -6, 0, -6],\n [12, 9, 0, 9],\n [4, 3, 0, 3],\n [-8, -6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -8, 8, 4],\n [-1, 1, 2, -2],\n [9, 6, -8, -2],\n [2, 4, 0, -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 4x4 matrix:\n[[6, -3, 0, -3],\n [6, -3, 0, -3],\n [6, -3, 0, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -7, -16, 3],\n [36, -13, 3, 8],\n [6, 17, -16, -9],\n [3, -13, 21, 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 4x4 matrix:\n[[-17, 2, -4, 0],\n [1, 6, 14, -13],\n [3, -6, -12, 12],\n [-10, 4, 4, -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 4x4 matrix:\n[[-2, 4, 0, -8],\n [3, -7, -1, 8],\n [-3, 8, 2, -4],\n [-2, 5, 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[[-4, 4, 8, -12],\n [1, -1, -2, 3],\n [3, -3, -6, 9],\n [-1, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -15, -20, 9],\n [18, -12, 8, 18],\n [0, 0, 0, 0],\n [7, -13, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 12, 16, -12],\n [12, 0, -16, 16],\n [-2, -6, -6, 4],\n [-16, -12, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 0, 7, 2],\n [2, -4, 3, 2],\n [12, -12, 16, 8],\n [-4, 2, -5, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -16, -16, -1],\n [4, 10, 0, -7],\n [-18, 4, 16, 13],\n [13, -6, -13, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 1, 4, 3],\n [0, 1, 4, 3],\n [0, 4, 16, 12],\n [0, -4, -16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, 16, 4, 8],\n [-9, -9, -12, -6],\n [11, 7, 8, 16],\n [2, -10, -9, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 5, 18, 14],\n [2, -18, 2, 5],\n [18, 5, -6, -7],\n [-24, -20, 8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 14, 16, 12],\n [-13, 0, 4, -4],\n [-18, 2, 8, -4],\n [4, -12, -16, -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 4x4 matrix:\n[[15, -14, -11, 22],\n [-1, -6, 0, 4],\n [-6, -4, 5, 2],\n [5, 0, -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[[-2, 4, -3, -4],\n [-8, 16, -12, -16],\n [-2, 4, -3, -4],\n [-2, 4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[24, 4, -22, -1],\n [0, -2, -7, -19],\n [24, 12, -16, 20],\n [-8, -8, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-24, -24, -31, -12],\n [18, 31, 20, 9],\n [-24, -36, -28, -12],\n [-8, -16, 3, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 21, 11, 2],\n [-16, 9, 5, -8],\n [-12, 9, 7, 14],\n [-10, 12, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 14, 4, 1],\n [-15, 6, 12, 9],\n [-20, 8, 16, 12],\n [4, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[28, 5, 4, 5],\n [-12, 3, 12, -9],\n [16, 5, 8, 0],\n [-16, 1, 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[[17, 10, -9, 25],\n [7, 9, 1, 10],\n [-11, 6, 17, -16],\n [1, -7, -7, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -16, 12, -4],\n [-3, -12, 9, -3],\n [-3, -12, 9, -3],\n [2, 8, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 0, 4, -2],\n [-4, 0, -8, 4],\n [-4, 0, -8, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -6, 10, -2],\n [-9, -1, 11, -7],\n [-6, 3, 9, -9],\n [3, -7, -7, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 0, 12, 8],\n [-4, 0, -6, -4],\n [0, 0, 0, 0],\n [4, 0, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 4, -2, 0],\n [0, 0, 0, 0],\n [16, 16, -8, 0],\n [-8, -8, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 2, -8, 6],\n [4, 4, -16, 12],\n [-2, -2, 8, -6],\n [1, 1, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -4, 20, -8],\n [-20, -2, -14, 14],\n [0, 8, -24, 4],\n [28, 6, 10, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 13, -1, -16],\n [-6, -6, 6, 8],\n [-9, 9, 9, -10],\n [9, -9, -9, 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 4x4 matrix:\n[[-22, 14, -4, 18],\n [5, -5, -6, -7],\n [13, -6, 11, -7],\n [4, 2, 18, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 8, -8, 16],\n [-1, -4, 0, -5],\n [1, 4, 0, 5],\n [7, 16, 12, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 4, 4, 4],\n [-2, -4, -4, -4],\n [3, 6, 6, 6],\n [1, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -11, -13, 4],\n [0, 9, 7, 4],\n [11, 5, 10, -10],\n [-2, 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[[2, -3, 1, -3],\n [-6, 9, -3, 9],\n [2, -3, 1, -3],\n [2, -3, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -12, -12, 0],\n [2, -8, -8, 0],\n [1, -4, -4, 0],\n [-2, 8, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -14, 9, -2],\n [-7, -14, 12, -5],\n [-17, -12, 15, -9],\n [-14, -14, 15, -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, 1, 2, -4],\n [-4, -1, -2, 4],\n [8, 2, 4, -8],\n [-8, -2, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 2, 2, 6],\n [8, -2, -2, -6],\n [8, -2, -2, -6],\n [12, -3, -3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -3, -18, -2],\n [-7, -22, 0, 6],\n [0, 16, 18, -2],\n [-19, -6, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 4, 4, -24],\n [3, 7, -3, 6],\n [27, -1, -13, -2],\n [-32, 0, 23, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -4, 6, 2],\n [-5, -14, -15, -1],\n [11, 10, -6, -3],\n [2, -4, -12, -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 4x4 matrix:\n[[-24, -16, -4, -4],\n [0, -8, 4, -8],\n [18, 12, 3, 3],\n [2, -4, 3, -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[[4, -1, -2, 3],\n [16, -4, -8, 12],\n [-16, 4, 8, -12],\n [16, -4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 12, 8, 16],\n [-4, -1, 6, 2],\n [0, -2, 2, -1],\n [-4, -3, 8, 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[[-24, 12, 24, 12],\n [3, 9, -10, 2],\n [0, 9, -6, 3],\n [9, -6, -8, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 12, 6, 12],\n [3, -12, -6, -12],\n [-3, 12, 6, 12],\n [-4, 16, 8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 9, -14, -3],\n [-12, 0, -6, 9],\n [4, 6, -6, -7],\n [-8, 6, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, -20, -12, -4],\n [-23, -4, 2, 8],\n [17, 26, 18, 10],\n [-9, 4, 10, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 4, -8, 8],\n [8, -8, 16, -16],\n [-2, 2, -4, 4],\n [2, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -3, -12, 3],\n [6, -3, -12, 3],\n [8, -4, -16, 4],\n [-4, 2, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -18, 6, -14],\n [28, -12, 0, 4],\n [19, -15, 3, -5],\n [13, -1, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 2, 0, -7],\n [-7, 0, -8, 3],\n [6, -16, -8, 14],\n [-4, 12, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -4, 0, -4],\n [6, -2, 0, -2],\n [12, -4, 0, -4],\n [-9, 3, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-4, -2, 4, -4],\n [-12, -6, 12, -12],\n [-4, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -9, -21, 15],\n [-2, 5, 10, -6],\n [12, -6, -4, -4],\n [-2, 5, 10, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -2, -2, -2],\n [8, 2, 2, 2],\n [-4, -1, -1, -1],\n [12, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -2, 2, 4],\n [4, 14, 7, -7],\n [12, -3, 3, 6],\n [-8, 2, -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[[-10, -13, 1, -4],\n [10, 13, -1, 4],\n [6, 15, -3, 4],\n [-12, -21, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 4, 10, -5],\n [15, -17, 8, -15],\n [-14, 13, -2, 8],\n [1, -4, -20, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -14, -10, -8],\n [4, 4, -7, 4],\n [-10, -12, -18, -15],\n [0, -4, -11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 8, -8, 0],\n [0, 0, 0, 0],\n [6, -6, 6, 0],\n [2, -2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 17, -13, -13],\n [-4, 10, -2, -2],\n [-6, 10, -18, -18],\n [6, -15, 3, 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 4x4 matrix:\n[[1, -11, -10, -9],\n [-6, 11, -7, 18],\n [16, 4, 12, -12],\n [10, 10, 18, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 6, -2, 1],\n [-12, 37, -13, -7],\n [-10, 30, -8, -5],\n [9, -12, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -4, 0, -8],\n [8, -8, 0, -16],\n [-2, 2, 0, 4],\n [-4, 4, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -12, 0, 2],\n [31, 10, 21, -25],\n [0, 4, -5, -8],\n [-16, -13, -11, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [16, 0, -16, 4],\n [4, 0, -4, 1],\n [-12, 0, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -9, 9, -6],\n [0, 0, 0, 0],\n [0, 9, -9, 6],\n [0, -9, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 1, 0, 1],\n [-6, 2, 0, 2],\n [9, -3, 0, -3],\n [-12, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 10, 18, 3],\n [-4, 2, 5, -5],\n [-12, 6, 8, 13],\n [-12, 6, 10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -7, 9, -7],\n [0, -1, 1, -3],\n [-4, -4, 5, -5],\n [8, 8, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 6, 6, 9],\n [-8, -4, -4, -6],\n [12, 6, 6, 9],\n [16, 8, 8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -32, -24, 0],\n [-6, -12, -20, 3],\n [8, -20, 12, -15],\n [-14, 8, -16, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 5, 5, -3],\n [2, -2, -4, 4],\n [-2, 1, 2, 2],\n [4, 6, 2, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 4, -12, 0],\n [2, 1, -3, 0],\n [6, 3, -9, 0],\n [8, 4, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 4, -3, -10],\n [-4, -2, 3, 8],\n [-8, 0, 2, 4],\n [8, -2, 0, 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[[9, -12, -3, -9],\n [-8, 22, 6, 4],\n [-17, 0, -1, 25],\n [10, -19, -5, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -2, 12, -10],\n [-9, 1, -11, 7],\n [3, -2, -3, -4],\n [-12, 6, 4, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 12, 5, 5],\n [-1, -1, 3, -17],\n [-5, -3, 5, 9],\n [-9, -4, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [3, -1, -1, -1],\n [6, -2, -2, -2],\n [-6, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -4, -4, -16],\n [2, -1, -1, -4],\n [20, -16, 8, -16],\n [-2, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-24, -3, -15, 6],\n [-26, 2, -13, 1],\n [-6, 1, -5, 2],\n [-8, -1, -1, -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[[5, 2, -3, -4],\n [4, -12, 8, 16],\n [-8, 4, -6, 28],\n [9, -6, 3, 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[[-4, 0, 1, -4],\n [-4, 0, 1, -4],\n [-8, 0, 2, -8],\n [12, 0, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 5, -3, -13],\n [4, 0, -6, -6],\n [-3, -1, 3, 5],\n [8, 4, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 2, -8, 0],\n [-6, -3, 12, 0],\n [-2, -1, 4, 0],\n [2, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 18, -10, 5],\n [15, -12, 23, 28],\n [12, 12, 7, 2],\n [7, 2, 4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -12, 4, -4],\n [6, 6, -2, 2],\n [6, 6, -2, 2],\n [12, 12, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 4, -2, 4],\n [2, 4, -4, 0],\n [2, -4, 6, 4],\n [18, -4, 14, 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[[-2, -2, 4, 0],\n [-4, -4, 8, 0],\n [-1, -1, 2, 0],\n [-1, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -8, 4, -9],\n [5, 13, -2, -2],\n [11, 0, 1, -21],\n [-1, 22, -5, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -7, 14, 10],\n [-16, -14, 18, 14],\n [0, 9, -10, -18],\n [-8, -3, 14, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -5, -1, 6],\n [-15, -27, -5, 20],\n [-1, 4, 5, 0],\n [7, 7, 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[[8, 4, -7, 14],\n [16, -4, 1, 10],\n [12, -12, 12, -6],\n [4, -12, 14, -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[[-32, 4, -28, 20],\n [0, 7, 1, -3],\n [-12, -16, -13, 15],\n [-4, 25, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, -7, 7, -3],\n [-1, 9, 4, -15],\n [17, -2, -29, -6],\n [4, 1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-3, -3, 0, 3],\n [-4, -4, 0, 4],\n [-2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 19, 10, -15],\n [-2, 5, 0, 1],\n [-1, -23, -19, 8],\n [-1, 7, 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[[0, -8, -12, 4],\n [0, 6, 9, -3],\n [0, -4, -6, 2],\n [0, 6, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 16, -16, 12],\n [0, 0, 0, 0],\n [-6, -8, 8, -6],\n [-3, -4, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -16, -3, 4],\n [-6, 32, 15, 8],\n [-10, 6, 18, -7],\n [1, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 3, 3, 3],\n [0, -1, 5, 0],\n [0, 1, -11, -1],\n [0, 0, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 0, -3, 3],\n [0, 8, 16, 12],\n [0, -6, -12, -9],\n [0, -6, -12, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 12, -6, 12],\n [1, 4, -2, 4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -12, 0, 0],\n [-4, 4, 0, 0],\n [-16, 16, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, 4, 2, -12],\n [1, 2, 2, 8],\n [1, 3, 0, 2],\n [12, 10, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 6, 0, -9],\n [-6, 4, -8, -16],\n [3, 2, 4, 2],\n [6, 2, 8, 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, 8, -12, -12],\n [2, -2, 3, 3],\n [2, -2, 3, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, -8, 1, -1],\n [0, 0, 0, 0],\n [2, 18, 6, -6],\n [5, 17, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 2, 10, -8],\n [-17, 0, -18, 14],\n [-2, -14, 2, 0],\n [-8, -22, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -12, -6, -2],\n [-4, 7, 0, 2],\n [6, 9, 14, 0],\n [4, 5, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 18, 8, 8],\n [6, 12, 3, 9],\n [22, 4, -13, 25],\n [-8, -16, -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[[0, -3, 3, 3],\n [0, 4, -4, -4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 0, -4, 0],\n [-4, 0, 16, 0],\n [1, 0, -4, 0],\n [1, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -8, -6, 8],\n [-1, 4, -11, -4],\n [-1, -4, 25, 4],\n [13, -20, -1, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -28, -17, -14],\n [15, -13, -7, -24],\n [2, -14, -6, 0],\n [-14, 10, 5, 26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, 6, 4],\n [0, -6, -2, 8],\n [6, -6, -8, 4],\n [15, -6, -17, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, -8, -4],\n [0, 0, 0, 0],\n [0, -6, 12, 6],\n [0, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -4, 4, -3],\n [-12, 16, -16, 12],\n [-12, 16, -16, 12],\n [-12, 16, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -8, 20, -10],\n [7, 6, -19, 7],\n [-3, 3, 5, 5],\n [5, 0, -11, -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[[-8, -16, 12, -12],\n [-18, 0, -16, 8],\n [6, 10, 16, -18],\n [13, 16, 13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 0, 12, 0],\n [6, 0, -6, 0],\n [-12, 0, 12, 0],\n [9, 0, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 3, 2, 4],\n [4, -3, -2, -4],\n [-12, 9, 6, 12],\n [8, -6, -4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 12, 0, -8],\n [-3, 8, 5, 8],\n [6, 14, 2, -4],\n [-4, 4, 4, 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, 13, -4, 20],\n [0, 3, 12, -4],\n [10, 8, -8, 16],\n [-2, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -8, 2, 6],\n [0, 0, 0, 0],\n [4, 16, -4, -12],\n [4, 16, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 12, 8, 16],\n [-4, 6, 4, 8],\n [2, -3, -2, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 0, -3, -3],\n [0, 0, 0, 0],\n [9, 0, -9, -9],\n [-12, 0, 12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 4, 2, 3],\n [-16, 16, 8, 12],\n [-8, 8, 4, 6],\n [-4, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 6, -5, -14],\n [3, -2, -7, -6],\n [-12, -4, 12, 20],\n [0, -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[[-22, 12, -8, 2],\n [4, 3, -10, -10],\n [4, -3, 4, 3],\n [-20, 6, 0, 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[[-1, -16, 1, 16],\n [1, 16, -1, -16],\n [2, 4, -2, 3],\n [-7, -16, 7, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -4, -1, -4],\n [2, -4, -1, -4],\n [8, -16, -4, -16],\n [8, -16, -4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, 0, -9, 15],\n [11, 6, 5, -9],\n [-7, 3, -5, 8],\n [-5, 0, -3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -12, -8, 16],\n [0, 0, 0, 0],\n [9, -9, -6, 12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -4, 8, 4],\n [3, -1, 2, 1],\n [0, 0, 0, 0],\n [-9, 3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 2, -3, 2],\n [0, -4, 6, -4],\n [0, 2, -3, 2],\n [0, 4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 11, -9, -2],\n [-8, -28, 24, 0],\n [-12, -2, 0, 8],\n [-14, -9, 6, 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 4x4 matrix:\n[[-11, 16, 20, 5],\n [-6, 6, 12, 0],\n [-7, 5, 13, -2],\n [-6, 27, 9, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -20, -14, -8],\n [0, 6, 4, 1],\n [-15, -4, -1, 11],\n [0, 24, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 12, 18, -28],\n [-2, -3, -1, 0],\n [0, -6, -6, 8],\n [-8, 6, 14, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [-16, 16, -4, -4],\n [4, -4, 1, 1],\n [-12, 12, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 0, 8, -16],\n [-2, -8, -14, -16],\n [4, 0, -4, 8],\n [2, 6, 10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -5, -9, 2],\n [-11, 18, 13, -7],\n [4, -7, -12, 7],\n [7, -6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [-12, -4, 12, -8],\n [-3, -1, 3, -2],\n [-6, -2, 6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -6, 4, 0],\n [-2, 12, 2, 0],\n [-1, 6, 1, 0],\n [-3, -14, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, 2, 2],\n [-6, 0, 3, 3],\n [0, 0, 0, 0],\n [8, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -3, 6, 6],\n [-9, -3, 6, 6],\n [12, 4, -8, -8],\n [9, 3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -7, 3, 7],\n [8, 6, -13, -10],\n [-15, 5, 13, -4],\n [19, -6, -29, -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[[0, 0, 0, 0],\n [9, 12, -12, 12],\n [-9, -12, 12, -12],\n [-3, -4, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 1, 27, 18],\n [4, -12, 8, 28],\n [-13, 1, 5, -9],\n [2, 8, 6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -10, -16, 8],\n [-3, -16, -20, 1],\n [5, 12, 4, -2],\n [5, 24, 28, -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 4x4 matrix:\n[[-10, 12, 14, 10],\n [-6, -3, -2, 1],\n [-2, -9, -5, -3],\n [17, -3, -29, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 5, 0, 5],\n [-3, -11, 3, -17],\n [-4, -16, 8, -28],\n [2, -2, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 16, 8, 4],\n [-4, -8, -4, -2],\n [6, 12, 6, 3],\n [-4, -8, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -9, 3, 0],\n [-12, -9, 3, 0],\n [-16, -12, 4, 0],\n [-8, -6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -1, 3, -2],\n [24, 6, -2, 12],\n [-20, -5, 11, -10],\n [12, 3, -9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -10, 5, -6],\n [3, -12, 3, 0],\n [2, 13, -7, 9],\n [-1, 11, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-8, 16, -12, -8],\n [-8, 17, -14, -6],\n [6, -10, 5, 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[[16, -16, -8, 4],\n [-4, 16, 5, 8],\n [20, -16, -9, 8],\n [-20, 16, 9, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -19, 3, 16],\n [-12, 9, -9, 0],\n [2, -18, 6, 12],\n [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 4x4 matrix:\n[[4, 8, -16, -6],\n [0, 2, -6, -2],\n [6, 6, -6, -3],\n [-8, -4, -4, 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[[9, -2, -3, -1],\n [-19, -18, -3, 24],\n [36, 8, -4, -22],\n [-18, -12, 2, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 3, 9, 3],\n [4, 2, 6, 2],\n [8, 4, 12, 4],\n [4, 2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 4, -6, -18],\n [-2, 2, -4, -15],\n [2, 4, -2, 6],\n [-1, 4, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -6, 12, 6],\n [6, 4, -8, -4],\n [12, 8, -16, -8],\n [-9, -6, 12, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -10, -7, 2],\n [-3, 5, 5, -4],\n [12, 20, 28, -16],\n [-10, 1, 0, -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[[1, -3, 4, 0],\n [-4, 12, -16, 0],\n [3, -9, 12, 0],\n [2, -6, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -3, -5, -2],\n [-4, -6, 2, -8],\n [-20, 6, 16, 2],\n [20, -6, -16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, -2, 14, 11],\n [-18, 7, 22, 7],\n [6, 10, -7, 6],\n [7, -26, -11, -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 4x4 matrix:\n[[-13, 6, -12, -12],\n [17, 0, 12, 12],\n [13, -6, 12, 12],\n [-16, 10, -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[[-5, -15, 0, -9],\n [11, 6, 8, 6],\n [-5, -15, 0, -9],\n [-3, 13, -7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 12, 12, -12],\n [0, 16, 16, -16],\n [0, -4, -4, 4],\n [0, 16, 16, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -2, 3, -1],\n [-6, -1, 6, 1],\n [-7, 3, 17, 2],\n [-5, -6, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 10, 9, -3],\n [-10, -8, 0, 6],\n [-19, 6, 3, -3],\n [12, 0, -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[[8, 8, 9, -13],\n [2, 15, 5, -9],\n [4, 14, 12, -12],\n [4, -11, 2, 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[[-3, 2, 0, 0],\n [15, 4, -7, 0],\n [0, 6, -3, 0],\n [6, -4, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -16, 8, 4],\n [2, 0, 0, 0],\n [6, -16, 8, 4],\n [2, -4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -16, -4, 7],\n [21, 7, 12, -11],\n [5, -26, -3, 14],\n [1, -22, 11, 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[[-3, 2, 15, -5],\n [0, -3, -9, -6],\n [-4, 0, 12, -12],\n [2, 1, -3, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 7, 18, 11],\n [11, 11, 18, 1],\n [-9, -19, -18, 3],\n [-12, -22, -20, 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 4x4 matrix:\n[[12, -13, -20, 8],\n [-10, -5, 4, 25],\n [14, -11, -20, 1],\n [16, -9, -20, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 7, -1, -5],\n [-4, -26, -28, 4],\n [-26, 4, -1, 13],\n [-4, 3, 3, 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[[4, 12, 0, -8],\n [-10, -10, 8, 8],\n [2, 10, -4, -8],\n [-1, -13, -4, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 12, -8, -4],\n [16, 12, -8, -4],\n [0, 0, 0, 0],\n [16, 12, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 3, 0, 6],\n [0, -3, 0, -6],\n [0, 3, 0, 6],\n [0, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -3, -9, 3],\n [2, -1, -3, 1],\n [8, -4, -12, 4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 3, -5, -5],\n [13, -1, 25, 25],\n [-3, -1, -3, -3],\n [-6, -6, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 3, 0, -3],\n [-8, -2, 0, 2],\n [-16, -4, 0, 4],\n [4, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[19, 8, 10, 12],\n [11, 2, 6, 6],\n [-7, -24, -2, -12],\n [-5, -10, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, -25, 10, 21],\n [12, 1, -24, 10],\n [-9, -9, -6, 17],\n [-3, 8, 16, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 0, -1, 2],\n [0, 0, 0, 0],\n [-9, 0, -3, 6],\n [-3, 0, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 5, 3, 10],\n [20, -2, -7, -14],\n [-40, -6, 19, 22],\n [4, -2, 1, 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 4x4 matrix:\n[[9, 12, 9, -3],\n [-6, -8, -6, 2],\n [9, 12, 9, -3],\n [12, 16, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -2, -4, 4],\n [6, 2, 4, -4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 5, 2, -6],\n [0, -19, -2, 8],\n [4, 13, -3, 0],\n [-28, 28, -18, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 1, 0, -16],\n [9, -5, 4, 11],\n [-22, -3, -15, 2],\n [-13, 2, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 5, 12, 6],\n [28, -1, 4, -6],\n [-24, -5, -6, 3],\n [24, 0, 12, 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[[-1, -12, -10, 34],\n [12, 32, 13, -13],\n [-1, -10, -9, 23],\n [9, 24, 12, 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 4x4 matrix:\n[[-11, 4, 0, 2],\n [-23, 19, 9, -10],\n [11, 4, 6, -14],\n [10, -16, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 8, 10, 15],\n [-2, 6, 2, 14],\n [3, 0, 6, -3],\n [3, -2, 4, -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[[4, -4, -1, 2],\n [-12, 12, 3, -6],\n [8, -8, -2, 4],\n [16, -16, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -6, 6, -8],\n [5, 1, -1, -12],\n [10, 9, -9, -8],\n [5, 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[[1, -5, -2, -2],\n [-7, 17, 1, 3],\n [-24, 24, -8, -24],\n [-3, 3, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 0, -9, -9],\n [12, -18, 0, 0],\n [3, -12, -15, -15],\n [12, -24, -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[[4, -4, 16, 8],\n [2, -2, 8, 4],\n [1, -1, 4, 2],\n [4, -4, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 1, 2, -1],\n [5, -7, 1, 2],\n [-5, 7, -1, -2],\n [-21, 15, 3, -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[[3, 12, -9, -6],\n [6, 15, -3, -9],\n [5, 11, 0, -7],\n [6, 12, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -2, 3, 3],\n [-9, -6, 9, 9],\n [12, 8, -12, -12],\n [-3, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, -36, 20, -7],\n [7, -4, 12, 14],\n [-2, 16, -10, -6],\n [4, -4, 12, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -8, -2, -14],\n [-3, 11, 9, 6],\n [7, 15, 17, -8],\n [3, 17, 17, -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 4x4 matrix:\n[[14, -6, 12, 6],\n [-8, 4, 16, -10],\n [-13, 25, -4, -20],\n [11, -22, -17, 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[[6, 12, 9, -3],\n [0, 0, 0, 0],\n [6, 12, 9, -3],\n [4, 8, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 0, -8, -8],\n [6, 0, -12, -12],\n [-8, 0, 16, 16],\n [-6, 0, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -8, 12, -8],\n [-2, -4, 6, -4],\n [1, 2, -3, 2],\n [4, 8, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -3, 2, -3],\n [-12, -9, 6, -9],\n [-4, 10, 0, 18],\n [16, -1, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -14, -7, -1],\n [12, -18, 5, 13],\n [9, 20, 24, -1],\n [3, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -3, -6, 6],\n [9, -3, -6, 6],\n [-9, 3, 6, -6],\n [-12, 4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [12, -4, -8, 8],\n [-12, 4, 8, -8],\n [9, -3, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -3, 6, 6],\n [-3, -3, 6, 6],\n [1, 1, -2, -2],\n [3, 3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[18, 12, -6, -12],\n [-6, -2, -4, 6],\n [-15, -13, 14, 7],\n [18, 12, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -3, -3, 9],\n [-9, -7, 13, -4],\n [9, 11, -17, 2],\n [-3, 3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 9, -9, 6],\n [0, 0, 0, 0],\n [-8, 6, -6, 4],\n [-16, 12, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -4, -6, 10],\n [-12, 13, 12, -10],\n [4, 17, 12, -2],\n [-16, 4, 6, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -4, 10, -3],\n [1, -2, 6, -1],\n [4, -8, 8, -12],\n [0, 0, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 4, -12, -14],\n [4, 4, -4, 2],\n [-12, -16, 20, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [4, 4, -4, 4],\n [8, 8, -8, 8],\n [-4, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -8, -8, 0],\n [2, 4, 4, 0],\n [6, 12, 12, 0],\n [-4, -8, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 5, 2, 13],\n [-18, 8, 14, -24],\n [16, -4, 0, 12],\n [-13, 10, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 3, -12, -9],\n [4, 2, -8, -6],\n [-8, -4, 16, 12],\n [-6, -3, 12, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -6, 0, 14],\n [-1, -3, 0, -2],\n [7, -3, -12, 2],\n [-3, 9, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -2, -20, -9],\n [6, 17, 9, 2],\n [-12, -6, 24, 16],\n [-12, -4, 29, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 18, 18, -9],\n [18, -10, -10, 11],\n [7, -6, 12, -6],\n [-2, -13, -21, 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[[1, -17, 18, 2],\n [-11, -4, 0, -15],\n [14, -5, 10, 19],\n [1, -16, 16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -8, -8, -12],\n [0, 2, 2, 3],\n [0, 8, 8, 12],\n [0, -6, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -7, -6, 5],\n [-12, 6, -12, 6],\n [8, -16, -12, 8],\n [-32, 16, -12, 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[[-10, -1, 5, 4],\n [14, -2, -7, -6],\n [24, -9, -2, 2],\n [-24, 16, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -18, 14, -15],\n [11, 0, -18, 9],\n [9, 8, -14, 11],\n [2, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -1, 3, -3],\n [2, 1, -3, 3],\n [6, 3, -9, 9],\n [2, 1, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 8, -4, -8],\n [0, 0, 0, 0],\n [16, -8, 4, 8],\n [-8, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 6, 4, -6],\n [0, 0, 0, 0],\n [4, 3, 2, -3],\n [12, 9, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -5, -15, 15],\n [7, 17, 7, -15],\n [3, 4, 7, -9],\n [16, 30, 8, -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[[-1, -3, 0, 0],\n [1, 3, 0, 0],\n [1, 3, 0, 0],\n [-2, -6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 3, -1, -3],\n [6, 9, -3, -9],\n [-4, -6, 2, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -1, 7, 8],\n [28, 23, 14, 11],\n [16, 15, 20, 24],\n [5, 1, -11, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 6, -8, 4],\n [0, 4, -12, 2],\n [-1, 5, -10, 3],\n [11, -11, -6, 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[[7, -1, 25, -17],\n [-5, -1, -11, 7],\n [-17, -13, 1, -5],\n [-8, -10, 16, -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[[-6, 6, -9, 0],\n [-2, 2, -3, 0],\n [6, -6, 9, 0],\n [6, -6, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 6, -9, -9],\n [9, 0, -9, -18],\n [3, 6, -9, -9],\n [-4, 4, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, -8, -8, 1],\n [2, -2, -4, 1],\n [4, 5, 22, -7],\n [-4, 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[[-17, -2, -16, 7],\n [8, 0, 8, -2],\n [19, 6, 16, -13],\n [6, 4, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 0, -13, -9],\n [8, -2, 8, 6],\n [-12, 16, -12, -12],\n [5, 2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -12, -10, -8],\n [-1, 4, -3, -4],\n [-12, -7, -9, -9],\n [23, -2, 11, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 0, 32, 12],\n [12, -2, -16, -9],\n [8, 1, -20, -6],\n [-4, -3, 20, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, 6, -3],\n [-8, 0, -14, 3],\n [-8, 0, 6, 1],\n [4, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -7, 10, 12],\n [3, 5, -8, -15],\n [-6, -8, 12, 18],\n [-3, -6, 10, 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 4x4 matrix:\n[[-8, 12, 8, 4],\n [4, -6, -4, -2],\n [-4, 6, 4, 2],\n [6, -9, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -7, 0, 13],\n [-15, 5, 3, -17],\n [3, 7, -7, 5],\n [-3, -7, 7, -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[[-8, 0, 8, 16],\n [-2, 0, 2, 4],\n [-6, 0, 6, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 6, -6, 8],\n [-8, 6, -6, 8],\n [-12, 9, -9, 12],\n [16, -12, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 3, 4, 16],\n [12, -4, 16, 32],\n [-14, 8, -16, -24],\n [12, -9, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -4, 3, 6],\n [-5, -14, -7, 7],\n [-7, -4, 1, 8],\n [5, 12, 13, 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[[-14, -1, -15, -8],\n [-4, -3, -9, -10],\n [13, 3, 9, 7],\n [1, 4, -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[[-14, -12, -12, -2],\n [-29, 6, -2, 5],\n [7, -32, -26, -17],\n [-11, -20, -14, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -8, -10, 2],\n [-3, -8, -10, 2],\n [15, 16, 14, -10],\n [0, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -1, 2, 16],\n [16, 12, 15, -20],\n [-4, -9, 3, 0],\n [20, 15, 9, -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, 16, 8, 0],\n [12, 16, 8, 0],\n [0, 0, 0, 0],\n [-12, -16, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, 6, 2, -16],\n [0, -1, -12, -2],\n [-10, -3, 13, -6],\n [4, 10, 20, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 8, -14, -8],\n [9, -12, 9, 3],\n [0, -12, -3, -6],\n [-9, 0, -12, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -2, 0, -4],\n [5, -6, 0, -12],\n [2, 4, 0, 8],\n [2, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -9, 0, -6],\n [-2, -1, -2, 6],\n [4, 3, 3, -8],\n [4, 2, 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[[-6, 9, -12, 6],\n [-2, 3, -4, 2],\n [4, -6, 8, -4],\n [-4, 6, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -6, 0, 10],\n [-6, 14, -6, -18],\n [-6, 8, -15, 0],\n [-8, 14, -15, -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[[-14, 10, -16, 8],\n [-10, 20, -16, 24],\n [5, 24, -10, 32],\n [-8, 1, -10, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 0, -3, -12],\n [-6, -4, 0, 12],\n [5, 0, 2, -12],\n [0, -3, 0, -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 4x4 matrix:\n[[-1, 10, 25, 4],\n [-6, 14, 16, -16],\n [-4, -20, -2, -20],\n [4, 16, -12, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [4, 0, -2, 1],\n [-16, 0, 8, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -4, -11, 2],\n [2, -1, 10, 10],\n [17, 5, 19, 12],\n [10, 4, 11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -3, -6, -9],\n [8, 2, 4, 6],\n [12, 3, 6, 9],\n [12, 3, 6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -15, 18, 1],\n [0, 3, -3, 4],\n [-12, 9, -12, -9],\n [-12, 3, -6, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 6, -2, -8],\n [0, 0, 0, 0],\n [-9, -9, 3, 12],\n [-12, -12, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 3, -4, -15],\n [4, 5, -5, -21],\n [2, 7, -1, -15],\n [-2, -7, 1, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -12, -4, -4],\n [-1, -3, -1, -1],\n [-2, -6, -2, -2],\n [4, 12, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -4, 8, -8],\n [4, 2, -4, 4],\n [12, 6, -12, 12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -10, 0, 6],\n [6, -9, 12, -3],\n [-10, 7, 4, -7],\n [10, -13, 14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 3, -9, 0],\n [-8, 2, -6, 0],\n [12, -3, 9, 0],\n [-4, 1, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -7, 11, 21],\n [14, -7, 1, -19],\n [8, -6, 4, -2],\n [11, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 5, 8, -10],\n [8, 22, 0, -4],\n [-1, 1, 6, -7],\n [1, -1, -6, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 5, -6, 16],\n [5, 1, 10, -16],\n [5, 4, -9, 16],\n [-4, 4, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, -12, 12],\n [12, 0, 12, -12],\n [-8, 0, -8, 8],\n [16, 0, 16, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 8, -13, 4],\n [12, -9, 5, 6],\n [6, -1, -1, 10],\n [12, -5, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 3, -12, 11],\n [-7, 2, -8, 9],\n [-23, 9, -24, 26],\n [26, -18, 28, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-11, 1, 13, -17],\n [14, 2, -12, 16],\n [15, 7, -5, 9],\n [-17, -11, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 20, 22, 5],\n [-13, -10, -11, -9],\n [1, -12, -7, 3],\n [-15, -12, -15, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-17, -4, 10, 16],\n [10, 0, -6, -8],\n [0, 0, 0, 0],\n [-7, 16, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -12, 12, 6],\n [12, -16, 16, 8],\n [12, -16, 16, 8],\n [6, -8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 0, -8, -3],\n [4, -1, 2, 1],\n [-4, 19, -6, -7],\n [12, 6, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -20, 0, -5],\n [14, -8, 0, -2],\n [-12, 4, 0, 1],\n [5, -20, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 0, 0, -2],\n [11, 6, -6, -5],\n [7, 6, -6, -9],\n [2, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, -9, 6],\n [-8, -8, 6, -4],\n [4, 4, -3, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 16, -4, 16],\n [0, -4, 1, -4],\n [0, 16, -4, 16],\n [0, 4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 11, 2, -25],\n [0, -4, 8, 12],\n [0, 0, 0, 0],\n [-3, 5, -4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -2, -8, 8],\n [4, -3, -11, 8],\n [4, -1, -18, 14],\n [18, -1, -22, 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[[0, 0, 0, 0],\n [8, -2, -8, 0],\n [-4, 1, 4, 0],\n [16, -4, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -6, -3, -3],\n [-4, -8, -4, -4],\n [-3, -6, -3, -3],\n [-3, -6, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -8, -8, -16],\n [0, 2, -1, 7],\n [-5, -2, -14, 8],\n [-1, -8, 1, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 6, -2, -8],\n [21, 10, -3, -15],\n [6, 0, 2, -10],\n [-3, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 2, 4, -15],\n [-16, 4, -8, -14],\n [-1, 25, 5, -5],\n [4, 16, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -24, -6, 17],\n [0, -26, -4, 18],\n [7, 38, 7, -28],\n [13, 28, 2, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -21, 18, -12],\n [-6, 12, -9, 12],\n [-4, 6, -6, 0],\n [-2, 1, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, -12, 3, 3],\n [3, 4, -1, -1],\n [12, 16, -4, -4],\n [12, 16, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 28, -12, 32],\n [-12, -4, -12, -8],\n [8, 5, 7, 8],\n [-6, 5, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -3, -12, 3],\n [1, -1, -4, 1],\n [-2, 2, 8, -2],\n [2, -2, -8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 7, -4, 8],\n [-5, 4, -1, -1],\n [7, -7, 1, 5],\n [-15, 12, -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[[-2, -4, -4, -2],\n [4, 28, 18, -6],\n [15, 4, -3, 12],\n [3, 12, 9, 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[[-4, 0, 28, 20],\n [10, -28, 7, 6],\n [2, 0, -14, -10],\n [5, -16, 9, 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 4x4 matrix:\n[[15, -13, -12, 2],\n [-13, 15, 4, 10],\n [-5, 2, 8, -8],\n [19, -16, -16, 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 4x4 matrix:\n[[-11, 0, -13, 16],\n [-6, 0, 5, -12],\n [6, 0, 9, -12],\n [4, 0, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 1, -7, 10],\n [-10, 18, -10, 1],\n [-2, 10, 3, -9],\n [0, -12, -7, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 3, 4, -10],\n [0, -4, -16, 8],\n [6, 4, 12, -10],\n [-9, -2, -2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[28, -5, 2, -2],\n [-5, 5, 1, 1],\n [-5, -28, -18, -8],\n [16, -24, -7, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -4, -12, -8],\n [0, -1, -3, -2],\n [0, 1, 3, 2],\n [0, 2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 12, 0, -16],\n [1, -3, 0, 4],\n [-4, 12, 0, -16],\n [4, -12, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 16, 8, 16],\n [8, 16, 8, 16],\n [-6, -12, -6, -12],\n [-8, -16, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -2, 4, -4],\n [-4, -2, 4, -4],\n [-4, -2, 4, -4],\n [-12, -6, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 10, 10, 4],\n [-12, -10, 0, -8],\n [-4, -3, -1, -2],\n [-32, -20, -20, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-16, 4, 12, -16],\n [-8, 2, 6, -8],\n [-16, 4, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -20, -2, -5],\n [4, -4, -4, -1],\n [16, 32, -4, 8],\n [-8, -16, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 10, -2, 18],\n [6, -4, 2, -6],\n [2, -2, 0, -4],\n [6, -6, 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[[0, 12, 12, -9],\n [0, -16, -16, 12],\n [0, 12, 12, -9],\n [0, -16, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 16, 19, 5],\n [18, 4, -14, 10],\n [3, 19, 16, 9],\n [18, 14, -4, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 3, -3, 2],\n [3, 9, 0, 9],\n [25, -9, -21, -16],\n [-6, 6, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -6, -12, -9],\n [-28, -10, 4, 9],\n [-4, 14, 16, 9],\n [16, -2, -10, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -8, 0, -13],\n [-10, 6, 12, 12],\n [-4, -4, 0, -2],\n [10, 4, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 0, 4, 16],\n [-4, 0, 1, 4],\n [-8, 0, 2, 8],\n [4, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 8, 19, 8],\n [-8, 8, -15, -4],\n [9, 9, -2, 17],\n [-2, 10, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, 14, 8, -28],\n [15, -10, -10, 20],\n [6, -4, -3, 8],\n [-15, 10, 10, -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[[-1, 4, 8, 9],\n [3, 0, -4, -5],\n [4, -4, -12, -14],\n [-13, -8, 4, 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[[-5, 3, 12, -1],\n [4, 0, -12, 5],\n [4, -12, 0, -16],\n [3, -1, -8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -1, 1, -3],\n [6, -3, 3, -9],\n [-4, 2, -2, 6],\n [4, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [1, 4, -4, 2],\n [4, 16, -16, 8],\n [-4, -16, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 6, -2, 4],\n [12, -12, 4, -8],\n [-12, 12, -4, 8],\n [-6, 6, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -1, 4, -3],\n [13, 7, -12, 7],\n [11, 9, -4, -1],\n [-14, -10, 8, -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 4x4 matrix:\n[[8, -4, -5, -2],\n [22, 16, -15, -15],\n [12, -11, -5, 2],\n [12, 9, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[19, -2, 0, -6],\n [0, -3, 2, -10],\n [-5, 0, 9, 4],\n [5, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 2, -12, -4],\n [4, 7, -12, -18],\n [-12, 6, 3, -10],\n [-13, 3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 12, 12, -12],\n [6, 20, 8, -18],\n [9, 20, 2, -17],\n [9, -4, -22, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 0, 0, -14],\n [34, 8, -10, -4],\n [-19, -14, 8, -4],\n [9, -10, 1, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 0, -8, 16],\n [-8, 0, -8, 16],\n [-4, 0, -4, 8],\n [-6, 0, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 9, 15, -15],\n [6, -3, 3, -9],\n [-3, -9, -15, 15],\n [2, 13, 19, -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[[3, -12, 4, 2],\n [-1, 0, 16, 6],\n [-20, 11, -5, -5],\n [2, -9, 7, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 3, -10, 3],\n [9, -15, -10, 4],\n [-4, 4, 4, -6],\n [-1, 19, 0, 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[[6, 4, 0, -8],\n [12, 8, 0, -16],\n [3, 2, 0, -4],\n [-3, -2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -10, -7, 15],\n [-12, 6, 3, -12],\n [12, 6, 9, 3],\n [16, -4, 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 4x4 matrix:\n[[6, 6, 0, -3],\n [6, 6, 0, -3],\n [8, 8, 0, -4],\n [-2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 0, 2, 15],\n [-8, 0, -12, -10],\n [4, 0, 6, 5],\n [-8, 0, -14, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 0, -2, 8],\n [3, 0, 1, -4],\n [-6, 0, -2, 8],\n [9, 0, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [11, -10, 1, -1],\n [-4, 8, -8, -4],\n [-1, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, -1, 20, -16],\n [4, -4, 4, -10],\n [-11, 19, 12, -11],\n [-10, 18, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -13, -3, -2],\n [2, 12, 6, -4],\n [1, 1, 4, 0],\n [-10, -4, -16, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 2, -2, 0],\n [3, -1, 1, 0],\n [3, -1, 1, 0],\n [-9, 3, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, -16, -25, -4],\n [0, -3, 3, -10],\n [20, -20, -23, -7],\n [-17, 21, 24, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-17, -19, 6, 24],\n [6, -8, 17, -7],\n [11, 7, 3, -15],\n [12, 14, -5, -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[[6, 6, 2, -8],\n [-12, -12, -4, 16],\n [12, 12, 4, -16],\n [3, 3, 1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 13, -6, 0],\n [20, 16, -4, 0],\n [2, 3, 2, 0],\n [-2, -3, -2, 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 4x4 matrix:\n[[6, -2, -5, -1],\n [8, -3, -9, -1],\n [14, -4, -7, -3],\n [-8, 1, -5, 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 4x4 matrix:\n[[8, 16, 16, 12],\n [-2, -4, -4, -3],\n [-8, -16, -16, -12],\n [4, 8, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 16, -3, 8],\n [12, -8, 4, -4],\n [12, -20, 4, -10],\n [-12, 14, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 20, 0, 0],\n [-14, 11, -4, -8],\n [4, 2, 2, 4],\n [8, 4, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 12, -3, -9],\n [-2, -8, 2, 6],\n [4, 16, -4, -12],\n [-3, -12, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 0, -3, 1],\n [0, 0, 0, 0],\n [-4, 0, -12, 4],\n [2, 0, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-32, -24, -8, -8],\n [10, 3, -5, -1],\n [0, 8, 12, 5],\n [-12, -4, -12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -6, 6, -9],\n [16, -10, -6, -7],\n [9, -4, 8, -8],\n [12, -6, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [3, 0, 6, 3],\n [4, 0, 8, 4],\n [-4, 0, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 6, -9, -12],\n [-16, 8, -12, -16],\n [-16, 8, -12, -16],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 12, 16, -16],\n [16, -12, -16, 16],\n [-4, 3, 4, -4],\n [12, -9, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -6, -2, 9],\n [9, -6, 15, 6],\n [4, 8, 18, -10],\n [8, -24, -10, 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[[-13, 0, -5, 4],\n [4, 0, 10, -2],\n [-6, 0, 7, 1],\n [-3, 0, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 13, -17, 16],\n [11, -6, 0, -10],\n [1, 9, -15, 10],\n [2, 11, -19, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 12, -8, -12],\n [-6, -18, 10, 20],\n [9, 9, -6, -9],\n [-9, -3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, -8, -12],\n [4, 2, -4, -6],\n [2, 7, -6, -9],\n [4, 5, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 12, 6, -12],\n [-1, 4, 2, -4],\n [0, 0, 0, 0],\n [-1, 4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 9, 4, -11],\n [-8, 6, 4, -8],\n [-2, 15, -5, -11],\n [4, 19, 1, -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[[-9, 0, 9, 0],\n [-2, 2, 0, 6],\n [10, -1, -9, -3],\n [10, -4, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 16, 0, 16],\n [-6, 12, 0, 12],\n [-6, 12, 0, 12],\n [-6, 12, 0, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 6, 4, -6],\n [-7, 4, -7, -17],\n [9, -4, -23, -21],\n [9, -6, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -6, -1, -8],\n [-12, -6, 8, -20],\n [-9, 9, 15, -6],\n [-6, -9, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, -8, 8],\n [0, -4, 8, -8],\n [0, -8, 16, -16],\n [0, 2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, 16, -12],\n [1, -2, -28, 20],\n [-4, -6, 0, 4],\n [2, 1, -16, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, 2, 0, -6],\n [-2, 0, -24, -12],\n [3, 0, -14, -12],\n [-4, -14, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -12, 0, -15],\n [10, 1, -9, -7],\n [-20, -2, 18, 14],\n [14, 0, -12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 2, -1, -3],\n [8, -6, -11, -5],\n [9, -8, -18, -10],\n [16, -8, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 0, -9, 3],\n [-2, 0, 3, -1],\n [-2, 0, 3, -1],\n [8, 0, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, -13, 6, -3],\n [1, 5, -6, -19],\n [-2, -5, -2, -4],\n [-4, -13, 6, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 16, 14, -12],\n [-14, -6, -2, -10],\n [6, 6, 4, -2],\n [-6, -1, 0, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -12, -12, -6],\n [-6, 12, 12, 6],\n [8, -16, -16, -8],\n [-4, 8, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[7, -1, -7, 2],\n [-6, 8, -2, 2],\n [0, 7, -4, -11],\n [13, 10, -25, 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, -18, -3, -13],\n [-10, 11, -1, 9],\n [7, -16, -10, -10],\n [-4, -8, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -4, -22, -12],\n [-8, -11, -13, 2],\n [20, 11, -6, -16],\n [8, -4, -22, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -12, 16, 16],\n [2, -3, 4, 4],\n [2, -3, 4, 4],\n [-4, 6, -8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -8, 18, 4],\n [3, -1, 0, -1],\n [7, 6, -15, -4],\n [-2, -11, 21, 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[[-16, -16, 0, 12],\n [4, 4, 0, -15],\n [16, 16, 0, 4],\n [-16, -16, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 17, 12, -4],\n [-1, 8, 12, 8],\n [-3, 11, 23, 10],\n [3, 2, 16, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 4, 16, 12],\n [-3, 2, 11, 6],\n [1, -1, -7, -3],\n [-5, 1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -9, -9, -6],\n [-5, -5, 3, 8],\n [-1, -4, 0, 3],\n [9, 6, -6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 10, 16, 10],\n [0, -6, 0, -6],\n [3, 12, 12, 12],\n [5, 16, 20, 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 4x4 matrix:\n[[4, -10, 1, 7],\n [4, 2, 3, -3],\n [8, -2, 5, -1],\n [14, 10, 11, -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 4x4 matrix:\n[[-1, 0, -3, 1],\n [2, 0, 6, -2],\n [0, 0, 0, 0],\n [-2, 0, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -8, 16, -4],\n [-4, -8, 16, -4],\n [2, 4, -8, 2],\n [-1, -2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, 9, 10, -8],\n [-6, -9, -9, 12],\n [11, -2, -5, -1],\n [5, -6, -3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, -6, 13, -6],\n [0, -4, -3, 10],\n [6, 2, 9, -14],\n [14, -6, 13, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 12, -8, -10],\n [17, -10, 1, 4],\n [-22, 12, 10, 8],\n [-12, 8, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -1, 4, -2],\n [20, 1, -12, 2],\n [-20, -4, -12, -8],\n [-32, -4, 0, -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[[-9, 12, 9, -12],\n [-12, 16, 12, -16],\n [0, 0, 0, 0],\n [-9, 12, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -12, -3, 12],\n [-25, 12, -7, 22],\n [-10, -8, -2, 12],\n [12, 16, -4, -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[[1, 10, 10, -12],\n [2, -1, -1, 4],\n [-1, -4, -4, 4],\n [-1, 2, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, 18, -3, -9],\n [3, -10, -1, 11],\n [12, -14, 9, -8],\n [9, -14, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 2, 8, 8],\n [-4, -2, -8, -8],\n [-4, -2, -8, -8],\n [2, 1, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 0, 0, -16],\n [6, 0, 0, -12],\n [6, 0, 0, -12],\n [4, 0, 0, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 2, 6, -3],\n [2, -4, 12, 3],\n [-6, -6, 0, 9],\n [4, -2, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, 11, 4, -4],\n [-3, 5, 16, 14],\n [-17, -11, 8, 16],\n [-9, -3, 10, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 7, -11, 12],\n [4, 12, 0, 24],\n [7, 6, 21, 17],\n [7, -22, -7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 16, -4, -16],\n [-6, 8, -2, -8],\n [-3, 4, -1, -4],\n [9, -12, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 4, 0, 16],\n [4, 4, 0, 16],\n [-2, -2, 0, -8],\n [4, 4, 0, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -6, -7, 0],\n [-2, 3, 2, 1],\n [-2, 3, 2, 1],\n [2, -6, -7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [16, -4, 4, 8],\n [16, -4, 4, 8],\n [-4, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 8, 4, 36],\n [-11, -7, -8, -12],\n [27, 15, 22, 24],\n [13, 17, 20, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 24, -16, -8],\n [-8, 14, -10, -6],\n [10, -20, 14, 8],\n [8, -4, 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[[-24, 4, -4, 20],\n [-6, 3, -3, 3],\n [-4, 0, 0, 4],\n [12, -2, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 2, 12, 4],\n [7, -2, -16, -11],\n [-5, -3, 14, 5],\n [17, -32, 4, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, 12, -4],\n [12, 12, -12, 4],\n [6, 6, -6, 2],\n [-3, -3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 0, -2, -8],\n [30, 16, 10, -14],\n [-2, -4, -5, -6],\n [18, 4, 1, -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[[11, -8, 8, 11],\n [-3, 0, -12, -15],\n [7, -6, 1, 2],\n [11, -10, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -2, -4, -7],\n [-8, 1, 8, 13],\n [2, -1, 4, 4],\n [-6, -6, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -6, 9, -6],\n [4, 8, -12, 8],\n [4, 8, -12, 8],\n [-3, -6, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 10, 3, -14],\n [25, -10, 9, 2],\n [6, 6, 5, -8],\n [24, 6, 17, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -2, -14, 10],\n [10, 11, 14, 8],\n [0, -16, -4, -28],\n [8, 8, 11, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 6, -3, 0],\n [3, 2, 1, 0],\n [1, 4, -1, 0],\n [-4, -6, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 12, 9, -6],\n [0, 0, 0, 0],\n [4, 4, 3, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 7, -12, -10],\n [3, 8, -9, -14],\n [1, 10, 1, 2],\n [-1, -13, -7, 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[[-12, 0, 12, -9],\n [8, 0, -8, 6],\n [4, 0, -4, 3],\n [16, 0, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -6, 15, -12],\n [-21, 10, 6, -26],\n [2, -2, -3, 11],\n [2, 2, -12, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 8, -3, -3],\n [-12, 8, -4, -8],\n [0, 8, -1, 7],\n [1, -6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 8, -8, -4],\n [-4, -2, 2, 1],\n [-16, -8, 8, 4],\n [12, 6, -6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 12, 12, 3],\n [19, -12, 0, -7],\n [5, 12, 18, 1],\n [-5, -12, -18, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -9, 12, -22],\n [-2, -1, 9, -18],\n [9, -14, 3, 8],\n [-7, 25, -33, 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[[-12, 12, -12, 12],\n [16, -16, 16, -16],\n [8, -8, 8, -8],\n [-12, 12, -12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 2, 15, -13],\n [-17, 2, 11, 20],\n [2, -2, -2, -8],\n [1, -16, -14, -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[[6, 12, -15, 3],\n [6, 10, 13, -19],\n [-8, -14, -8, 18],\n [0, 10, 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[[0, -4, 1, 2],\n [18, 17, -30, 12],\n [12, 14, -26, 20],\n [12, -10, -8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[21, 6, -24, -15],\n [4, 4, 2, -20],\n [-5, 8, 5, -21],\n [-5, -2, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 0, 0, 12],\n [3, 8, -2, 0],\n [-20, -24, 16, -11],\n [14, 16, -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[[-3, -3, -1, -4],\n [9, 9, 3, 12],\n [6, 6, 2, 8],\n [-9, -9, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 14, 12, -7],\n [3, -6, -18, 12],\n [-1, 4, 2, -1],\n [1, 2, -14, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, 7, -15, 7],\n [1, -5, 1, -1],\n [-8, -14, 13, -7],\n [-12, 6, 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[[3, -4, 0, -2],\n [-6, 8, 0, 4],\n [-9, 12, 0, 6],\n [6, -8, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-18, 0, -6, -16],\n [18, -28, 14, 17],\n [4, -8, 5, 2],\n [-18, 12, -12, -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 4x4 matrix:\n[[-24, -6, 16, 2],\n [4, 3, -2, 0],\n [-20, -9, 12, 1],\n [16, 12, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-6, 8, 0, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -1, -4, -7],\n [-11, 3, -6, 1],\n [18, -2, 13, 9],\n [6, -2, -2, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 20, 14, -25],\n [22, -16, -4, 24],\n [-17, -26, -11, 5],\n [-15, -14, -5, -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[[9, -12, -6, -6],\n [12, -16, -8, -8],\n [9, -12, -6, -6],\n [9, -12, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -9, -6, -3],\n [0, -3, -2, -1],\n [0, -6, -4, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 0, 9, 6],\n [-8, 0, 12, 8],\n [-6, 0, 9, 6],\n [-6, 0, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -25, 2, 4],\n [-11, 5, -2, -8],\n [-4, 2, -12, 20],\n [-4, -6, 3, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 4, 4, 1],\n [0, 16, 16, 4],\n [0, 4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 18, 9, -3],\n [-24, 0, 12, -14],\n [24, 0, -12, 14],\n [-20, 14, 17, -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[[2, 6, -9, -18],\n [10, 12, -18, 0],\n [-2, -4, 6, 8],\n [-7, -6, 9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[11, 4, -3, 4],\n [13, 4, -3, 0],\n [6, -8, -5, 2],\n [-13, 12, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 8, 0, -6],\n [-12, -16, 0, 12],\n [-9, -12, 0, 9],\n [-9, -12, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -14, 0, 16],\n [-1, 7, -2, -5],\n [-12, 20, -8, -4],\n [10, -10, 6, -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[[-6, -8, 0, -6],\n [6, 8, 0, 6],\n [-12, -16, 0, -12],\n [3, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 10, 0, -14],\n [-7, -7, -1, -6],\n [-10, 8, 11, -4],\n [3, -9, -16, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -7, 11, -7],\n [0, 8, -10, 4],\n [-6, -1, -5, 13],\n [-6, -20, 21, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 0, -20, 6],\n [16, 0, 8, 7],\n [-7, 12, 23, 6],\n [25, -22, 7, -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[[2, 1, 1, -3],\n [8, 4, 4, -12],\n [6, 3, 3, -9],\n [8, 4, 4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 1, -3, -1],\n [-11, 5, -15, -7],\n [10, -4, 12, 6],\n [-16, 4, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-1, -1, 3, 1],\n [-4, -4, 12, 4],\n [-1, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 8, 16, 16],\n [0, 0, 0, 0],\n [0, -6, -12, -12],\n [0, -4, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 6, 2, 8],\n [-2, -18, 4, 10],\n [-5, -6, 4, 7],\n [-16, 12, 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[[-15, 8, -4, 11],\n [-7, 2, -2, 5],\n [9, -10, 2, -7],\n [9, -10, 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[[0, 0, 0, 0],\n [0, 0, 1, -3],\n [0, 0, 2, -6],\n [0, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 14, 6, 2],\n [8, 16, 8, 4],\n [6, 6, 2, 0],\n [-4, 10, 8, 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[[3, 7, -7, -1],\n [9, 3, -3, -12],\n [6, 10, -10, -4],\n [0, -8, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -9, 14, -8],\n [-6, -9, 0, 6],\n [3, 0, 6, -6],\n [6, 9, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 3, -19, -1],\n [2, -1, 5, 3],\n [-1, -12, 6, -1],\n [7, -6, 22, 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[[6, 12, -21, -6],\n [-6, 6, -3, 18],\n [-4, -11, 18, 2],\n [4, 2, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [3, -2, -9, 6],\n [5, -9, 0, -6],\n [1, -1, 17, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -2, 6, 10],\n [-1, 1, -3, -8],\n [-9, -4, 12, -7],\n [2, 0, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -3, 0, 0],\n [-2, -3, 0, 0],\n [-2, -3, 0, 0],\n [-6, -9, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-11, 16, 15, -5],\n [1, -4, -9, 17],\n [-13, 20, 21, -13],\n [2, -2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 7, -9, -4],\n [-6, 1, -2, -7],\n [-6, -14, 8, -2],\n [-6, 7, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 6, 3, -3],\n [-20, 12, 13, -13],\n [24, -6, -10, 10],\n [-16, 9, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 24, 7, 2],\n [25, 4, -1, -2],\n [-6, -11, -2, 9],\n [5, -2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 10, -4, -9],\n [-1, 12, -8, -9],\n [-32, -8, 0, 12],\n [6, 22, -9, -21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 7, -22, 10],\n [-11, 2, -10, 14],\n [-1, 2, -6, 2],\n [4, -3, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -5, 11, -11],\n [0, 4, -12, 12],\n [-2, 2, -8, 8],\n [0, -2, 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[[-4, 4, -6, -6],\n [16, -16, 16, 0],\n [-8, 8, -10, -6],\n [16, -16, 16, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 3, 6, -6],\n [4, 4, 8, -8],\n [4, 12, 24, -16],\n [-1, -5, -10, 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 4x4 matrix:\n[[-6, 4, 4, 6],\n [12, -8, -8, -12],\n [-6, 4, 4, 6],\n [12, -8, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -11, 11, 3],\n [-4, 2, -10, -2],\n [14, 7, 3, 1],\n [-10, 6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 0, -3, -9],\n [-6, 0, -2, -6],\n [-6, 0, -2, -6],\n [6, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 12, 10, -1],\n [0, -8, -5, -1],\n [-8, -24, -16, -2],\n [4, -12, -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[[0, -22, 9, -4],\n [21, 6, -12, 3],\n [-16, 8, 4, 0],\n [9, -10, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -1, 1, -2],\n [0, 0, 0, 0],\n [16, -4, 4, -8],\n [-16, 4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -3, -9, 6],\n [-3, -1, -3, 2],\n [3, 1, 3, -2],\n [12, 4, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, -9, -3, 19],\n [23, 0, 4, -14],\n [21, -6, 10, 0],\n [-8, 12, -6, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -1, 2, -3],\n [0, 3, 4, -9],\n [0, -7, -1, 6],\n [0, 5, 5, -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[[-10, 11, 8, 5],\n [1, 14, -5, 4],\n [-7, 20, 4, 7],\n [-1, 17, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 11, -15, -3],\n [-4, 0, -1, 2],\n [5, -3, 5, -1],\n [-4, 4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 18, 3, 12],\n [-12, 0, 6, 6],\n [-4, -2, 1, 0],\n [12, 18, 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[[15, 15, 11, -20],\n [9, 9, 6, -24],\n [5, 5, 4, 0],\n [19, 19, 15, -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[[9, 12, -12, 0],\n [4, 12, -8, -2],\n [-13, -4, 12, -4],\n [-16, -8, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -16, -12, 8],\n [-16, 16, 18, -20],\n [12, -20, 4, 0],\n [8, -8, -10, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 16, -12, -8],\n [13, -16, 12, 7],\n [1, 0, 0, -1],\n [-10, 12, -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[[-14, -6, 10, -4],\n [4, 6, -8, -2],\n [2, -12, 14, 10],\n [4, -24, 28, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 15, 4, 5],\n [-12, -12, -4, -4],\n [15, 18, 3, 6],\n [-2, -6, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 11, 3, -3],\n [-3, 3, 1, 3],\n [-13, 16, 5, 9],\n [-9, 6, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -22, 0, -5],\n [1, -6, 0, -1],\n [10, -12, 0, -10],\n [3, -2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -8, 0, 8],\n [16, 16, 0, -16],\n [-16, -16, 0, 16],\n [-12, -12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -1, 7, 11],\n [6, -20, 14, -4],\n [-3, -2, 5, 6],\n [-3, 4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 2, 6, 2],\n [-11, 3, 13, 5],\n [12, 0, -6, -3],\n [-7, 3, 11, 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 4x4 matrix:\n[[19, 12, 16, 16],\n [17, 12, 8, 16],\n [11, 9, -1, 12],\n [-12, -9, -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[[-9, -19, -18, 15],\n [0, 7, 6, -6],\n [3, 18, 16, -15],\n [3, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 4, 0, -4],\n [3, 3, 0, -3],\n [1, 1, 0, -1],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, -11, -13, -7],\n [-7, 17, 11, -1],\n [-11, -14, -2, -20],\n [14, -7, -21, 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[[-3, 2, 1, -4],\n [6, -4, -2, 8],\n [12, -8, -4, 16],\n [-3, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -2, -8, -8],\n [3, 3, 12, 12],\n [-4, -4, -16, -16],\n [-3, -3, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -5, -12, 0],\n [-13, 10, -13, -15],\n [-6, 5, -11, -10],\n [2, 4, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -6, 2, -1],\n [3, -6, -1, 5],\n [-7, 4, -1, 0],\n [-1, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -1, -3, 1],\n [-8, -4, -12, 4],\n [-4, -2, -6, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -8, 4, -8],\n [4, 16, -8, 16],\n [3, 12, -6, 12],\n [-2, -8, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-18, -5, -20, 2],\n [-14, 5, -20, -4],\n [0, -16, 8, 10],\n [-14, -3, -16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 16, -22, -12],\n [0, 2, 1, 0],\n [6, -10, 5, 4],\n [-9, 10, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 1, -14, -1],\n [-8, 4, -8, -4],\n [16, -8, 0, 8],\n [2, -1, -10, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -7, -8, 8],\n [12, 8, -8, 8],\n [10, 0, -20, 20],\n [6, 9, 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[[3, -3, 2, -4],\n [-9, 9, -6, 12],\n [9, -9, 6, -12],\n [12, -12, 8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 8, -8, 32],\n [0, -8, 8, -32],\n [12, 0, 12, -4],\n [-12, 7, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, -8, 0],\n [0, -8, 8, 0],\n [0, -12, 12, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -16, 16, 0],\n [3, 4, -4, 0],\n [-9, -12, 12, 0],\n [12, 16, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -2, -8, 4],\n [-3, 4, 9, 6],\n [-6, 2, 6, 0],\n [3, 8, 15, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[20, 8, -14, -11],\n [8, -6, 2, 19],\n [0, -3, 4, 16],\n [15, -13, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -4, 14, -12],\n [-11, 5, -11, -4],\n [-6, 0, -10, -4],\n [-17, 3, -10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 12, 6, -14],\n [-4, 3, -3, 3],\n [14, 0, 9, -13],\n [-6, 12, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 2, 4, -25],\n [-1, 2, -5, -18],\n [14, -14, 13, 7],\n [-10, -2, 30, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[17, 20, 18, -33],\n [15, 8, 13, -9],\n [-10, 0, -17, 4],\n [16, 11, 4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -2, -4, 2],\n [2, -2, -4, 2],\n [-2, 2, 4, -2],\n [6, -6, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, 6, -4, -10],\n [13, 8, -4, 7],\n [4, -10, -16, -1],\n [9, 18, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 16, -6, -3],\n [-9, 2, 3, 9],\n [-1, -4, 13, 13],\n [17, -18, 8, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -12, -3, -6],\n [16, 16, -4, 0],\n [4, 16, 2, 6],\n [-8, -8, 2, 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 4x4 matrix:\n[[10, 1, 5, 0],\n [2, -4, 4, 12],\n [8, -2, 6, 8],\n [-12, -4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 6, -2, -2],\n [-2, 2, 2, -4],\n [4, -2, -10, 14],\n [1, 2, -10, 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, -14, 5, -6],\n [-7, -8, 5, 3],\n [8, 10, -4, 3],\n [-16, -20, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, 2, 2],\n [10, -1, 1, 4],\n [-17, 2, -2, -7],\n [11, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [2, 3, -3, 2],\n [2, 3, -3, 2],\n [8, 12, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, 0, 8, -4],\n [-15, 6, 3, -6],\n [-13, 2, 5, -4],\n [12, 0, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, -8, -1, -7],\n [-8, 5, -14, 16],\n [-12, -12, 2, -10],\n [-12, -21, 16, -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[[-9, 4, -1, -7],\n [-10, 3, -6, -2],\n [-4, 10, 2, -3],\n [-9, 0, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 0, -2, 0],\n [-4, 0, 4, 0],\n [-4, 0, 4, 0],\n [-6, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 3, 0, 2],\n [10, -3, -16, 18],\n [-8, 6, 8, -6],\n [-8, 6, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -8, -16, 4],\n [8, 4, 8, -2],\n [-4, -2, -4, 1],\n [-16, -8, -16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, 0, -18, 12],\n [-12, -1, 14, -9],\n [-8, 6, 12, -10],\n [-16, 2, 20, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -8, -13, 13],\n [22, -14, 1, 4],\n [13, -17, 0, -8],\n [2, 6, -4, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, -8, 0, 5],\n [-2, 5, -5, -6],\n [0, 1, 7, -7],\n [4, 11, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 18, 24, -21],\n [-12, -21, -28, 24],\n [-3, -3, -4, 3],\n [6, -3, -4, 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[[16, -4, -8, 8],\n [-12, 3, 6, -6],\n [12, -3, -6, 6],\n [-12, 3, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 3, 2, -3],\n [0, -6, -4, 6],\n [0, -9, -6, 9],\n [0, 12, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 16, 4, -12],\n [-8, -16, -4, 12],\n [8, 16, 4, -12],\n [4, 8, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -11, 1, 4],\n [-9, 3, 0, 9],\n [-6, -1, 3, 3],\n [-24, 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[[0, 0, 0, 0],\n [-8, -16, -12, 12],\n [6, 12, 9, -9],\n [-6, -12, -9, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 17, 22, 1],\n [19, -7, 7, 21],\n [18, -24, -24, 8],\n [21, -9, 3, 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[[13, 12, 18, 12],\n [6, 14, 10, 3],\n [10, 20, 16, 6],\n [-7, 2, -8, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -8, 9, -7],\n [0, 14, 3, 1],\n [-10, 8, -9, 7],\n [18, 8, 21, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 4, 2, 8],\n [0, 4, 2, 8],\n [0, -2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, 2, -4],\n [2, 0, -2, 4],\n [4, 0, -4, 8],\n [3, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 13, -5, -7],\n [0, 21, -15, -9],\n [-8, 15, -9, -7],\n [-24, -4, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -2, -2, -10],\n [0, -2, -2, 2],\n [-6, -6, -6, 18],\n [-8, -2, -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 4x4 matrix:\n[[9, 7, -5, 2],\n [-14, -10, 9, -4],\n [-14, -10, 9, -4],\n [11, 5, -11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, -1, -4, 15],\n [-9, -9, -6, 3],\n [-17, -9, -10, 24],\n [11, -11, -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[[-4, -8, 6, -6],\n [-4, -8, 6, -6],\n [-4, -8, 6, -6],\n [-6, -12, 9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 5, -1, 9],\n [-9, -3, -7, -23],\n [12, 10, 7, 6],\n [0, 12, -8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 16, 16, 4],\n [0, 8, 8, 2],\n [0, 8, 8, 2],\n [0, 12, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -12, 1, 0],\n [0, -9, 3, 6],\n [12, 0, -12, -9],\n [32, -18, -16, -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 4x4 matrix:\n[[-4, -2, 0, 6],\n [6, -11, 2, 5],\n [14, -6, 1, 0],\n [8, -4, 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[[0, -28, 18, -3],\n [0, -14, 6, 6],\n [2, 9, -8, 5],\n [-32, -11, 13, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 12, 16, -8],\n [-2, -2, 8, -7],\n [-8, 2, -8, -8],\n [6, 0, 16, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[22, 12, 32, -28],\n [-6, 0, -16, 0],\n [-12, 2, -20, 20],\n [-4, 4, 0, 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, -3, 9, 9],\n [25, -6, 1, 12],\n [15, -4, -6, 3],\n [-1, -3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -8, 1, -2],\n [6, 8, -6, 12],\n [-3, 12, -3, 6],\n [-5, -4, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -3, -3, 3],\n [1, -1, -1, 1],\n [0, 0, 0, 0],\n [-2, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -6, 2, -2],\n [15, 9, 21, 15],\n [-2, -12, -4, -8],\n [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[[-2, -2, -6, 0],\n [2, 2, 6, 0],\n [-4, -4, -12, 0],\n [-3, -3, -9, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 10, 8, -12],\n [6, 1, 2, 4],\n [-9, 1, 0, -8],\n [-9, -16, -18, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -7, -9, 1],\n [9, -4, 6, 8],\n [3, 8, 6, -4],\n [-5, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 2, 4, 2],\n [-3, 1, 2, 1],\n [0, 0, 0, 0],\n [-12, 4, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 9, 12, 9],\n [-16, 12, 16, 12],\n [12, -9, -12, -9],\n [-4, 3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 16, 18, -18],\n [0, -4, -12, 7],\n [16, -16, 0, 12],\n [10, -12, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -10, 5, -6],\n [8, -8, 4, -24],\n [14, 4, -2, -12],\n [14, 16, -8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 9, 3, 3],\n [9, -9, -4, -6],\n [9, -9, -4, -6],\n [-9, 9, 4, 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[[2, -2, 0, -8],\n [4, -4, 0, -16],\n [-2, 2, 0, 8],\n [-3, 3, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 7, -1, 11],\n [-1, -10, 0, -17],\n [15, -12, 9, -15],\n [-6, -6, -2, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 6, -6, 0],\n [-6, -9, 21, 6],\n [-2, -3, 7, 2],\n [8, 3, -15, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 0, 17, -19],\n [7, -6, -2, -2],\n [-11, -5, 22, -22],\n [5, 1, -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[[2, 4, 2, 8],\n [2, 4, 2, -1],\n [3, 6, 3, 6],\n [-4, -8, -4, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 9, 16, 13],\n [11, 30, 13, 22],\n [-2, 4, 7, 4],\n [-12, -3, -12, -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[[-11, -1, -9, 1],\n [-1, -9, 10, 9],\n [3, 13, -13, -13],\n [-5, -3, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -3, 3, 4],\n [-14, -15, 12, 1],\n [15, 0, -6, -5],\n [-17, -4, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -9, 12, -5],\n [-21, 2, -8, -9],\n [14, -11, -10, 20],\n [5, -26, 0, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 18, -3, 12],\n [4, -8, 8, -12],\n [6, -16, 6, -14],\n [6, -20, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 12, 16, 2],\n [-9, 21, 28, 7],\n [10, 6, 8, -20],\n [2, 6, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -14, 16, -28],\n [28, 5, 17, 3],\n [-4, 5, -6, 6],\n [16, 12, 11, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, 3, 4, 10],\n [0, 15, -1, 13],\n [13, 5, 13, 14],\n [16, 5, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -8, 0, 8],\n [-12, 6, 0, -6],\n [-8, 4, 0, -4],\n [8, -4, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -20, 4, -2],\n [18, 18, 3, -3],\n [-20, -22, 0, 1],\n [8, 4, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -3, 8, 9],\n [0, -5, -10, -4],\n [20, 4, 24, 17],\n [8, 3, 20, 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 4x4 matrix:\n[[2, 7, -7, -4],\n [14, 12, -1, -7],\n [-4, -2, 0, -9],\n [-24, -13, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, -3, -3, -24],\n [22, -12, 7, 37],\n [16, 6, 1, 13],\n [-4, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 3, 4, -4],\n [15, -20, -23, -32],\n [-1, -5, -7, -12],\n [27, -16, -19, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 6, -3, 9],\n [0, 0, 2, 16],\n [-4, -8, 8, 28],\n [7, -4, 1, -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 4x4 matrix:\n[[-6, -6, -10, -4],\n [12, 12, 20, 2],\n [-6, -6, -18, 6],\n [-9, -9, -11, -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[[16, 6, 13, -12],\n [-18, -9, 3, 10],\n [16, 0, -4, 0],\n [2, 3, -4, -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 4x4 matrix:\n[[-10, -5, 10, 6],\n [15, 0, 0, 3],\n [-7, -4, 8, 5],\n [6, 2, -4, -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 4x4 matrix:\n[[0, 0, -12, -12],\n [0, 0, 8, 8],\n [0, 0, 4, 4],\n [0, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -4, 6, -2],\n [16, 8, -12, 4],\n [12, 6, -9, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -1, 4, 0],\n [16, -2, 14, -8],\n [-20, 3, -15, 4],\n [8, -3, -3, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -1, -2, -1],\n [-2, 2, 4, 2],\n [2, -2, -4, -2],\n [-2, 2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -28, -36, 12],\n [-5, 15, 9, 5],\n [-14, 18, 6, 14],\n [-4, 12, 28, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 16, 20, 5],\n [12, 10, 16, 7],\n [16, -1, 4, 6],\n [24, -9, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, -3, -14, -8],\n [4, -1, -1, 9],\n [-11, 3, -8, 0],\n [15, 6, 12, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -4, 3, 2],\n [9, -12, 9, 6],\n [-6, 8, -6, -4],\n [-9, 12, -9, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -9, -9, 9],\n [9, -9, -9, 9],\n [9, -9, -9, 9],\n [-9, 9, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -4, 8, 0],\n [-3, 1, -2, 0],\n [-9, 3, -6, 0],\n [-3, 1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -2, 3, 1],\n [9, -6, 9, 3],\n [-12, 8, -12, -4],\n [3, -2, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -6, 6, -8],\n [15, -3, 6, -4],\n [12, -12, 8, -16],\n [-9, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 2, -2, 4],\n [2, 2, -2, 4],\n [-3, -3, 3, -6],\n [4, 4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 4, -4, -8],\n [0, 0, 0, 0],\n [8, 4, -4, -8],\n [6, 3, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -12, -16, -4],\n [4, 12, 16, 4],\n [-1, -3, -4, -1],\n [4, 12, 16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 9, 6, 6],\n [0, 9, 6, 6],\n [0, 0, 0, 0],\n [0, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, -6, -4, -8],\n [9, -12, -27, 15],\n [8, 8, 8, 24],\n [-3, 10, 19, 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 4x4 matrix:\n[[-12, -11, 10, 6],\n [12, 4, 4, -20],\n [3, -2, 7, -11],\n [-12, -11, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 2, 2, 6],\n [-8, 2, 2, 6],\n [-12, 3, 3, 9],\n [-16, 4, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -7, -15, 20],\n [8, 3, -7, 16],\n [1, -5, -10, 10],\n [-3, -3, -9, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 6, 12, 12],\n [12, 8, 16, 16],\n [-3, -2, -4, -4],\n [3, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -24, 19, -1],\n [-1, -5, 3, -2],\n [4, -4, 9, 14],\n [-3, 9, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 1, 10, 6],\n [-10, -5, -1, -2],\n [5, 0, 7, 4],\n [15, 5, 8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 1, -4, -4],\n [4, 2, -4, -10],\n [-4, 2, -20, -2],\n [4, -2, 20, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 2, 4, -6],\n [4, -2, -4, 6],\n [-2, 1, 2, -3],\n [4, -2, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -6, -8, -4],\n [0, 0, 0, 0],\n [-12, 9, 12, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -24, 6, -14],\n [-2, 4, -5, 1],\n [-15, -12, -6, -10],\n [1, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, -7, 2, -8],\n [-4, -6, 2, -5],\n [4, 6, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 6, -7, -4],\n [3, -21, -2, -13],\n [30, 0, 22, 18],\n [9, -6, -1, -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[[8, -4, 12, 16],\n [-2, 1, -3, -4],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [12, -12, -12, 6],\n [10, -12, -6, 8],\n [-18, 10, 4, -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[[-6, -6, 4, 8],\n [0, 0, 0, 0],\n [-12, -12, 8, 16],\n [-3, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 10, 8, 16],\n [-6, -8, -8, -6],\n [1, 8, 16, 17],\n [-16, -16, 4, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -6, -8, -6],\n [2, -6, -8, -6],\n [3, -9, -12, -9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 5, 2, -8],\n [1, -5, -4, 12],\n [-2, -3, -1, 8],\n [6, 2, 6, -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[[-15, 8, 12, -17],\n [3, 4, 6, 11],\n [-7, 12, 22, 5],\n [-4, 9, 14, 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[[-9, 12, -9, -12],\n [6, -8, 6, 8],\n [9, -12, 9, 12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -4, -12, -16],\n [2, 16, -3, 1],\n [-17, 4, -2, -16],\n [4, -10, 17, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, -3],\n [0, 0, 0, 4],\n [0, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 0, -18, 0],\n [-16, 10, 16, 0],\n [4, 0, -9, 0],\n [-8, 0, 18, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 14, -14, 24],\n [-5, 7, -7, 12],\n [-1, -5, -11, -4],\n [8, -12, 10, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 9, 12, -24],\n [8, 0, -12, -10],\n [-11, -13, -16, 4],\n [7, 12, 22, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -6, -6, -1],\n [-1, 2, -2, 1],\n [14, 6, 5, 2],\n [-3, 0, 0, -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 4x4 matrix:\n[[1, -9, 10, -28],\n [16, 5, -12, -3],\n [9, 3, -6, -12],\n [0, 2, -4, 25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 10, 4, -2],\n [0, 20, 4, -12],\n [0, -3, -3, -3],\n [0, 5, 3, 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 4x4 matrix:\n[[-3, -3, 2, 4],\n [3, 3, -1, -8],\n [6, 6, -3, -12],\n [5, 5, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 6, -4, -8],\n [6, -9, 6, 12],\n [-2, 3, -2, -4],\n [4, -6, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 4, 12, -2],\n [5, -4, -12, 2],\n [-6, 0, 9, -6],\n [-9, -12, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, -4, 4, -3],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 4, -2, 1],\n [0, 16, -8, 4],\n [0, -4, 2, -1],\n [0, 8, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 9, 9, 3],\n [8, -24, -3, 5],\n [0, 0, 0, 0],\n [14, -6, 15, 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[[-6, -3, -5, 6],\n [24, 12, 20, -24],\n [-4, -2, -8, -3],\n [-6, -3, -5, 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, 8, -11, -4],\n [9, 4, -9, 4],\n [-9, -10, 3, 2],\n [9, 2, 9, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -3, 4, 0],\n [0, 0, 0, 0],\n [-6, -6, 8, 0],\n [-6, -6, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 9, -6, -12],\n [-14, 12, -2, 5],\n [6, -6, 2, 1],\n [8, -3, -4, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 18, 4, 3],\n [-26, -8, 20, -27],\n [7, -11, -22, 21],\n [2, 6, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [16, -8, -4, -4],\n [-8, 4, 2, 2],\n [12, -6, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 4, 12, 0],\n [-2, -2, -4, 2],\n [-4, 4, 0, -12],\n [-10, 2, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 3, 0, -6],\n [-20, 7, -8, -14],\n [-13, 9, -12, -10],\n [-11, 3, -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[[-12, -4, -8, 8],\n [3, 1, 2, -2],\n [-9, -3, -6, 6],\n [-12, -4, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 8, -6, 8],\n [1, -4, 3, -4],\n [0, 0, 0, 0],\n [1, -4, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 9, -7, -5],\n [-10, -5, -8, -4],\n [-5, 5, -3, 1],\n [2, 9, -16, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 8, 2, 4],\n [-12, -16, -16, 0],\n [-22, -8, 4, -8],\n [-1, -12, -18, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -9, -17, 10],\n [-17, 17, 13, -3],\n [-5, -25, -8, 22],\n [12, -8, -18, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 5, 8, -20],\n [18, -6, -2, -12],\n [-16, 5, 2, 16],\n [29, -1, 6, -23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -12, 3, 6],\n [2, -8, 2, 4],\n [-2, 8, -2, -4],\n [4, -16, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 13, -1, 9],\n [0, 16, 2, 12],\n [-2, -7, -17, -15],\n [-12, -10, -5, -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[[-18, -21, 17, 6],\n [-10, -12, 10, 2],\n [-1, 3, -6, 17],\n [-3, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -16, -16, 12],\n [2, 8, 8, -6],\n [16, -2, 18, -18],\n [2, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -22, -6, -18],\n [0, -8, -6, -6],\n [0, 0, 0, 0],\n [0, -12, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 16, -12, -12],\n [-9, 12, -9, -9],\n [12, -16, 12, 12],\n [3, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 3, 3, 2],\n [8, -12, -12, -8],\n [-2, 3, 3, 2],\n [-8, 12, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 3, 4, 0],\n [0, -6, -8, 0],\n [0, 0, 0, 0],\n [0, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -10, 14, 12],\n [-4, 4, -12, -8],\n [13, -13, 19, 16],\n [-2, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -3, 1, 1],\n [-4, -5, 3, 4],\n [-23, -8, 12, 7],\n [17, 7, -10, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[15, -12, 3, -1],\n [9, -12, -3, 1],\n [6, 0, 6, -2],\n [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[[0, 0, 0, 0],\n [6, 2, -8, -8],\n [-6, -2, 8, 8],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 12, 12, 12],\n [0, -9, -9, -9],\n [0, -12, -12, -12],\n [0, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, -16, 4, 16],\n [12, -6, 9, 6],\n [16, -28, -8, 28],\n [-4, 4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 9, 4, 0],\n [2, 1, 4, -8],\n [9, 13, -8, -6],\n [5, 7, -8, -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[[0, 10, 1, 15],\n [8, -4, 10, -18],\n [-2, -14, -4, -18],\n [16, 12, 22, -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 4x4 matrix:\n[[4, 6, 2, 6],\n [6, 9, 3, 9],\n [2, 3, 1, 3],\n [6, 9, 3, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 9, -12, -6],\n [-6, -12, -8, 9],\n [0, -12, -8, 12],\n [2, 18, 16, -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[[9, -8, 16, -5],\n [-9, -2, -11, 10],\n [9, -4, 14, -7],\n [6, 0, 8, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 12, 3, 12],\n [16, 16, 4, 16],\n [-8, -8, -2, -8],\n [-8, -8, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -14, -16, -5],\n [5, -10, -14, -7],\n [0, 20, 16, -2],\n [-2, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -3, -1, -1],\n [-18, 22, -2, 2],\n [4, -4, 1, 0],\n [-14, 18, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -12, 4, 0],\n [-4, -6, 2, 0],\n [-8, -12, 4, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -2, 2, -4],\n [-4, -12, 2, -8],\n [-20, -2, -4, 4],\n [-2, 4, -2, 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[[-3, -3, 0, 0],\n [-9, -9, 0, 0],\n [0, 0, 0, 0],\n [12, 12, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 4, 2, -1],\n [-10, 4, 10, -5],\n [-4, -2, -16, 8],\n [-19, -14, -14, 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 4x4 matrix:\n[[-6, 6, -9, -9],\n [12, -8, 4, 4],\n [8, -6, 5, 5],\n [2, -8, 24, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -6, -6, -6],\n [-5, 7, 1, 2],\n [-17, 24, 6, 9],\n [-7, 10, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 1, 0, 2],\n [3, 0, 2, 4],\n [-9, 0, -6, -12],\n [-12, 0, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 6, 14, -5],\n [1, 7, 14, -2],\n [-3, -3, 8, -8],\n [-1, -11, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -4, 3, 3],\n [-15, 8, -7, 9],\n [0, 0, 0, 0],\n [11, -7, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -12, 16, -8],\n [-12, 12, -16, 8],\n [3, -3, 4, -2],\n [-12, 12, -16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 6, 4, 2],\n [-12, 9, -4, 4],\n [-8, -8, -12, -2],\n [-8, -8, -12, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -2, -2, -13],\n [-3, 7, 3, 4],\n [0, 5, 3, 3],\n [-2, 0, 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[[2, -5, 6, -12],\n [12, -11, 10, 28],\n [-10, 7, -2, -28],\n [-6, 3, -2, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -2, -22, 10],\n [-15, -9, -24, 0],\n [-5, -1, -11, 5],\n [3, 9, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 2, 3, 3],\n [-4, 8, 12, 12],\n [3, -6, -9, -9],\n [4, -8, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -6, -16, -21],\n [-4, 8, -16, 0],\n [4, 6, 16, 21],\n [4, 2, 16, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -12, 8, 0],\n [9, -9, 6, 0],\n [-6, 6, -4, 0],\n [-6, 6, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, -6, -4],\n [0, 0, 9, 6],\n [0, 0, 9, 6],\n [0, 0, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 12, 0, 9],\n [-4, 16, 0, 12],\n [4, -16, 0, -12],\n [-1, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 16, 4, 8],\n [6, 8, 2, 4],\n [6, 8, 2, 4],\n [-6, -8, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, -16, 12],\n [0, 0, 16, -12],\n [0, 0, -4, 3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 24, -7, 15],\n [2, 9, -2, 0],\n [2, 1, 0, -2],\n [-4, 18, -5, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -1, -10, 5],\n [4, 24, 10, -5],\n [17, -20, -8, 4],\n [13, -17, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 6, -6, -3],\n [-8, -8, 8, 4],\n [2, 2, -2, -1],\n [6, 6, -6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 4, 2, -2],\n [4, 4, 2, -2],\n [8, 8, 4, -4],\n [-6, -6, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-32, -4, -4, 20],\n [28, 6, 19, 4],\n [24, 2, 10, -2],\n [4, 2, -10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 9, -3, 0],\n [6, -17, -9, -16],\n [-5, -1, 4, 4],\n [5, 14, -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[[17, 10, 22, 20],\n [4, -13, -1, -8],\n [-2, -14, -6, -11],\n [16, 4, 12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 5, -12, 1],\n [-8, -7, 12, -11],\n [-2, 1, 3, 11],\n [-6, -7, 9, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, 5, -3, 15],\n [-8, 4, 0, 6],\n [-10, 6, -2, 14],\n [-10, 4, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 2, 16, 14],\n [12, -11, -8, 3],\n [8, -12, -16, -4],\n [9, -10, -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 4x4 matrix:\n[[4, 0, -12, 16],\n [-3, 0, 9, -12],\n [-4, 0, 12, -16],\n [-2, 0, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, 11, 10, -10],\n [4, 8, 6, -8],\n [0, 12, 2, -16],\n [-1, 7, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 12, 6, -2],\n [-12, -16, -8, 16],\n [24, 24, 12, -4],\n [3, 2, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 12, -8, 24],\n [2, 0, 0, -7],\n [6, 16, -4, 9],\n [-2, 8, 12, 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 4x4 matrix:\n[[2, 2, -4, -3],\n [-6, -6, 12, 9],\n [-6, -6, 12, 9],\n [-6, -6, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 0, 0, 0],\n [8, 0, 0, 0],\n [16, 0, 0, 0],\n [8, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -8, 12, 4],\n [12, -8, 12, 4],\n [9, -6, 9, 3],\n [-9, 6, -9, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 2, -8, 6],\n [-9, -4, 16, -12],\n [-3, -2, 8, -6],\n [-12, 1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -9, 0, 20],\n [5, 12, -1, -28],\n [-13, 3, 14, 12],\n [-1, 3, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -7, 14, 6],\n [-4, -6, 0, -14],\n [-9, 4, -20, 1],\n [4, 0, 6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -16, -12, 4],\n [-4, -8, -6, 2],\n [2, 4, 3, -1],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -8, 8, 4],\n [3, -2, 2, 1],\n [-12, 8, -8, -4],\n [3, -2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 8, -4, -8],\n [12, -8, 4, 8],\n [-9, 6, -3, -6],\n [6, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 16, -12, -12],\n [3, 1, -12, 0],\n [4, -8, -9, 7],\n [2, 2, -9, -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[[0, 1, 0, -11],\n [-11, -1, -7, 8],\n [-10, 0, -5, 3],\n [-1, -1, -7, -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 4x4 matrix:\n[[0, 12, 12, -8],\n [0, -12, -12, 8],\n [0, 3, 3, -2],\n [0, -9, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, -15, 18, 14],\n [-16, -6, 12, 20],\n [8, 15, -14, -2],\n [-8, 3, 2, 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[[-8, 8, -6, -6],\n [0, 0, 2, -8],\n [4, -4, 5, -5],\n [8, -8, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 12, 0, 16],\n [-3, -9, 0, -12],\n [4, 12, 0, 16],\n [-4, -12, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, 4, 6, -5],\n [-9, 9, -10, -4],\n [-19, 3, 10, -8],\n [-13, 3, -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[[-2, -7, 16, 6],\n [-8, -10, -8, 12],\n [-18, 3, -3, 1],\n [-8, 14, -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 4x4 matrix:\n[[4, -12, 12, -16],\n [4, -12, 12, -16],\n [-4, 12, -12, 16],\n [-3, 9, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 12, -12, 4],\n [3, -7, 6, -1],\n [-2, 14, -18, 10],\n [-1, 11, -15, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -14, -4, -20],\n [3, -7, -6, -9],\n [-1, 7, 2, 10],\n [0, -4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -20, 8, -12],\n [1, -5, 2, -3],\n [18, -5, 1, 6],\n [28, -4, 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[[-4, 1, -4, -1],\n [-16, 4, -16, -4],\n [-4, 1, -4, -1],\n [8, -2, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -14, -16, 22],\n [-3, -5, -19, 19],\n [1, 5, -7, 3],\n [4, 2, 20, -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[[19, -23, 10, 8],\n [13, -14, 14, -8],\n [6, -6, 4, 8],\n [-17, 19, -12, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[11, 4, -1, 8],\n [3, 0, 0, 3],\n [3, 8, -2, -5],\n [-3, -8, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -3, -4, -12],\n [-2, -6, 0, 8],\n [-5, 0, 2, 8],\n [19, -3, -8, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -6, 3, -6],\n [-8, -8, 4, -8],\n [-2, -2, 1, -2],\n [-4, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 0, -24, 3],\n [-16, 0, -32, 4],\n [13, 0, 20, 8],\n [-9, 0, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 8, -1, 0],\n [24, 12, 3, -12],\n [16, 8, 2, -8],\n [-28, -15, -3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 0, -6, -2],\n [8, 0, -12, -4],\n [8, 0, -12, -4],\n [-6, 0, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -28, 12, 8],\n [-16, 24, -26, -10],\n [-12, -10, 10, 12],\n [-17, 5, 9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -4, -2, -15],\n [4, 6, -9, -18],\n [-7, -22, 3, 3],\n [7, 6, -17, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -2, 2, 4],\n [6, 6, -6, -12],\n [0, 0, 0, 0],\n [2, 2, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, -4, -4, -9],\n [0, -2, -8, -6],\n [-4, 1, -4, 1],\n [8, 3, 28, 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[[-19, 6, -22, 19],\n [-5, -12, 16, -10],\n [11, 22, -13, 2],\n [19, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 11, 10, 4],\n [5, -9, -5, -1],\n [10, -4, -10, -6],\n [-11, 10, 11, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -5, -20, -36],\n [-8, -4, -20, -40],\n [0, -12, 4, 4],\n [-5, 2, -13, -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[[-13, -10, 0, -7],\n [20, 3, -4, 15],\n [-2, -18, 16, 6],\n [-14, -4, 0, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -12, -8, -14],\n [-9, -10, 1, -7],\n [18, 28, 22, 30],\n [-4, -12, -14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 16, 28, -24],\n [-4, -16, -28, 24],\n [-24, 16, 0, -10],\n [4, 16, 28, -24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-17, -3, 6, 4],\n [-33, -3, 6, 12],\n [8, 4, -4, -10],\n [-12, 16, -20, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 4, 16, -4],\n [0, -4, -16, 4],\n [0, 4, 16, -4],\n [0, -3, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -5, 8, -1],\n [18, 15, -12, 9],\n [22, 16, -12, 10],\n [-16, -4, 0, -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 4x4 matrix:\n[[2, 0, -5, 1],\n [-4, -6, 4, -2],\n [-4, -6, 4, -2],\n [6, 12, -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, -8, -8, 8],\n [8, -8, -8, 8],\n [-4, 4, 4, -4],\n [-16, 16, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 1, -1, -4],\n [1, -1, 1, 4],\n [-3, 3, -3, -12],\n [-2, 2, -2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -14, -2, 8],\n [-12, -28, -4, 16],\n [-12, -28, -4, 16],\n [5, 9, -13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -8, 14, -1],\n [-22, 24, -15, 4],\n [-18, 44, -10, 4],\n [10, 0, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -16, 16, -4],\n [-11, -7, 5, 3],\n [-20, -16, 18, 10],\n [-7, 15, -12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, 20, 4, -9],\n [-8, 18, -4, -9],\n [8, -16, -8, 0],\n [13, 4, -4, -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[[-12, -8, 4, -9],\n [-3, 1, 4, 0],\n [9, 9, 0, 9],\n [-12, -12, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 2, 0, -10],\n [1, 5, 2, 12],\n [9, 4, -4, 10],\n [4, 7, 10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 1, -2, 2],\n [0, 4, -8, 8],\n [0, 4, -8, 8],\n [0, 4, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-10, 16, -8, -2],\n [-20, 8, 16, 14],\n [-25, 16, 12, 13],\n [-28, 16, 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[[-8, -7, 4, 9],\n [2, 8, -6, -6],\n [10, 10, -6, -12],\n [8, 12, -8, -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 4x4 matrix:\n[[0, 0, 12, -3],\n [0, 0, -16, 4],\n [0, 0, -12, 3],\n [-21, -14, -16, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 0, 8, 2],\n [8, 0, 16, 4],\n [-8, 0, -16, -4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 6, -3, 8],\n [-9, 6, 0, 12],\n [6, -8, -9, -28],\n [1, -6, -12, -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[[0, -3, 6, -3],\n [0, -8, 15, -20],\n [0, -5, 0, -5],\n [0, 3, -10, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 10, -9, 3],\n [8, 4, -2, -2],\n [-8, 8, -8, 4],\n [-2, -10, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -12, 4, 17],\n [4, -6, 2, 10],\n [-3, -9, 3, 12],\n [11, 6, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -1, 0, -4],\n [4, 8, -3, -7],\n [-12, 18, -5, 7],\n [4, -7, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -10, 10, 2],\n [2, 8, -7, -1],\n [0, -10, 10, 2],\n [-2, -13, 12, 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 4x4 matrix:\n[[-2, -1, -2, 2],\n [-6, -3, -6, 6],\n [-8, -4, -8, 8],\n [2, 1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -6, 2, 16],\n [-5, -8, 5, 28],\n [9, 11, 8, 4],\n [10, 14, 0, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -16, -32, 0],\n [0, 16, 24, 8],\n [0, 0, -16, 16],\n [0, 16, 20, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 5, 13, 18],\n [2, -18, 10, 4],\n [1, -1, 2, 4],\n [-1, 7, -8, -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[[2, 27, 14, -8],\n [-4, -18, -7, 3],\n [2, -29, -18, 12],\n [8, -24, -22, 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[[-10, -22, -8, -20],\n [-1, -13, -14, -8],\n [9, 0, -17, 7],\n [12, 12, -8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 7, 2, 5],\n [-14, -9, -4, -5],\n [-4, -3, -2, -1],\n [-12, -8, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 19, 5, -24],\n [-12, -1, -11, 35],\n [-16, -2, -14, 38],\n [-6, -9, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 4, 2, 0],\n [-12, 0, -2, 2],\n [-4, -20, -9, -1],\n [6, -24, -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[[6, 4, -2, 8],\n [6, 4, -2, 8],\n [-9, -6, 3, -12],\n [6, 4, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 23, 18, 23],\n [-10, -4, 21, 13],\n [2, -28, -18, -26],\n [-8, 22, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 3, 0, 1],\n [6, 6, 0, 2],\n [-3, -3, 0, -1],\n [3, 3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 4, 0, 8],\n [-8, -2, 0, -4],\n [16, 4, 0, 8],\n [-16, -4, 0, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 4, -2, 23],\n [-4, 7, -6, 14],\n [-1, 3, -8, 5],\n [-8, 12, -22, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -6, 4, 0],\n [-16, -12, 8, 0],\n [12, 9, -6, 0],\n [-8, -6, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 16, 4, 4],\n [3, -12, -3, -3],\n [2, -8, -2, -2],\n [1, -4, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [8, 6, 2, 6],\n [12, 9, 3, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 1, -3, -2],\n [4, -9, -6, -6],\n [-6, 1, -3, 7],\n [-4, 13, 5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -12, 12, 0],\n [0, 2, 4, -2],\n [0, 12, 16, -4],\n [-4, 0, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -3, 9, -12],\n [-4, -1, 3, -4],\n [-4, -1, 3, -4],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 20, -5, 14],\n [-10, -13, 9, -1],\n [-6, -9, 0, -6],\n [2, 3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 3, -1, -1],\n [16, 12, -4, -4],\n [12, 9, -3, -3],\n [12, 9, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, -15, 14, -13],\n [-18, 15, -11, 12],\n [-1, 3, -10, 5],\n [0, 3, -13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -4, -12, -8],\n [0, 1, 3, 2],\n [0, -4, -12, -8],\n [0, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -8, -6, 18],\n [-8, -4, -8, 20],\n [-8, 2, -6, 12],\n [8, -17, 1, 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 4x4 matrix:\n[[8, 0, 0, -8],\n [24, 6, -5, 3],\n [0, 8, 4, 28],\n [12, 2, -15, 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 4x4 matrix:\n[[11, 16, 18, -13],\n [7, 23, 18, -18],\n [11, 3, 10, -2],\n [9, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 16, 19, 13],\n [-2, -16, -23, -11],\n [-16, -2, -19, -1],\n [-17, 5, -13, 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 4x4 matrix:\n[[-16, -12, 0, -4],\n [4, -4, -4, 4],\n [-15, -6, 3, -6],\n [-9, -5, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 6, 20, 0],\n [-1, 3, 2, 4],\n [2, 0, 8, -4],\n [0, -3, -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[[-4, 6, -4, -8],\n [16, -16, 0, 8],\n [-4, 10, -12, -20],\n [-2, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, 27, 6, -12],\n [-3, 19, -1, -11],\n [10, 1, 5, 4],\n [0, -5, -7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -10, 8, 4],\n [4, 9, -7, -3],\n [-10, 2, 0, 4],\n [6, 3, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -2, -8, -6],\n [12, -3, -12, -9],\n [-16, 4, 16, 12],\n [12, -3, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -28, -8, 0],\n [13, -16, -8, -9],\n [13, 9, -2, -12],\n [-9, -12, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -3, 12, -12],\n [2, 2, -8, 8],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 12, -9, -9],\n [-3, -12, 9, 9],\n [2, 8, -6, -6],\n [4, 16, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 5, -4, -7],\n [28, -28, 20, 20],\n [-12, 16, -12, -16],\n [0, 7, -6, -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 4x4 matrix:\n[[-6, -4, 2, 2],\n [-10, -9, 7, 3],\n [1, -4, 7, -1],\n [3, 9, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -10, 12, 2],\n [-10, -13, 14, 7],\n [-8, 12, -8, -20],\n [-20, -12, 16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 17, -12, -1],\n [-4, -4, -23, 8],\n [12, -15, 2, 3],\n [-4, 4, 17, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -8, 4, 10],\n [-8, -19, -10, 1],\n [-6, -14, -8, 0],\n [0, 3, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -10, 12, -2],\n [0, 0, 0, 0],\n [-5, 1, 10, -3],\n [-1, 24, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -16, 0, 12],\n [1, -4, 0, 3],\n [1, -4, 0, 3],\n [3, -12, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, 3, 4, 19],\n [-16, 12, 16, 20],\n [-17, 9, 12, 25],\n [-3, 3, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 10, -4, 15],\n [-2, -3, -14, 27],\n [24, 6, 8, 21],\n [16, 10, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 5, 0, 1],\n [4, 18, -13, 15],\n [5, 9, -10, 7],\n [13, 0, 0, -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[[22, -14, 24, -6],\n [26, -15, 28, -9],\n [4, -18, 16, -6],\n [12, -3, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -8, -8, -6],\n [4, -4, 0, -3],\n [-2, 20, 18, 15],\n [-4, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -12, -12, -8],\n [-5, -6, -6, -4],\n [-12, -16, -8, -4],\n [2, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -3, -4, 10],\n [6, 6, 8, -8],\n [-16, -15, -20, 17],\n [17, 15, 20, -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[[4, -3, 3, 17],\n [10, -6, -6, 4],\n [-4, 1, 2, -9],\n [-1, 3, 0, 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 4x4 matrix:\n[[8, 4, -4, -16],\n [2, 1, -1, -4],\n [-4, -2, 2, 8],\n [-2, -1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 9, 17, 8],\n [-10, 4, 2, 8],\n [-8, 5, 5, 8],\n [14, -11, -13, -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[[-14, -4, 12, 0],\n [3, -12, 0, -12],\n [10, 5, -9, 2],\n [-11, -1, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 4, 4, 4],\n [2, 2, -1, 2],\n [15, -6, -11, -6],\n [-12, 0, 8, 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[[14, -2, -5, 5],\n [1, -10, 5, -5],\n [-7, 8, -1, 1],\n [1, 11, 5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, -8, 2, -4],\n [-18, 0, -5, -2],\n [-2, 8, -13, 14],\n [22, 0, -9, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 4, 8, -8],\n [0, 0, 0, 0],\n [16, -4, -8, 8],\n [8, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -2, 6, 3],\n [-2, 4, -4, 2],\n [-12, 4, 0, 6],\n [-8, 6, -4, 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[[-1, 4, 4, 0],\n [1, -4, -4, 0],\n [2, -8, -8, 0],\n [1, -4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -16, -8, 10],\n [6, 12, 14, -6],\n [-3, 14, -11, -2],\n [14, -13, 4, 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[[6, 9, -9, 12],\n [0, 0, 0, 0],\n [-2, -3, 3, -4],\n [-2, -3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 3, -3, 18],\n [16, 2, 10, -6],\n [-2, -1, -1, -3],\n [-11, -4, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -28, 8, -10],\n [9, -2, 14, -9],\n [-2, -20, -8, 6],\n [-1, 10, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 16, -4, 0],\n [-2, 8, -2, 0],\n [3, -12, 3, 0],\n [2, -8, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [1, -7, 8, 7],\n [1, -7, 8, 7],\n [-3, 9, -8, -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[[-7, -2, -13, -21],\n [7, -4, -17, -11],\n [6, 1, 7, 12],\n [-3, -8, -29, 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, 3, 6, 5],\n [-20, 4, 8, 4],\n [-7, 2, 4, 3],\n [-3, 3, 6, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -6, 6, 0],\n [6, 6, -6, 0],\n [-3, -3, 3, 0],\n [-6, -6, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 4, -8, -4],\n [8, 17, -13, 4],\n [-14, -5, 7, 2],\n [-13, -7, 8, 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[[22, 16, 4, 2],\n [3, 3, 3, -12],\n [12, 8, 0, 12],\n [5, 3, -1, 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 4x4 matrix:\n[[-13, 17, -12, 11],\n [8, -28, 0, 8],\n [12, 0, 16, 12],\n [5, -17, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 19, 12, -8],\n [13, -18, -4, 11],\n [0, 1, -20, -10],\n [2, -2, -16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, 10, -12, 0],\n [-4, 4, 3, -13],\n [-6, 6, -9, 3],\n [6, -6, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-13, -31, 12, -5],\n [-13, 1, -12, -6],\n [16, 21, -3, 5],\n [-3, -20, 9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -2, -4, -6],\n [12, -3, -6, -9],\n [0, 0, 0, 0],\n [-4, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 6, 12, -10],\n [4, 4, 0, -4],\n [0, -8, -12, 12],\n [0, -2, -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[[2, 1, -3, 2],\n [-2, -1, 3, -2],\n [4, 2, -6, 4],\n [8, 4, -12, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -11, -15, -5],\n [-3, -5, -9, -3],\n [3, 13, 21, 7],\n [-18, 2, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 0, -9, 0],\n [8, 0, 12, 0],\n [2, 0, 3, 0],\n [4, 0, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 1, 0, 4],\n [4, 10, 8, 8],\n [-2, -5, -4, -4],\n [6, -7, -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[[-12, 12, 4, -12],\n [-13, 5, 12, -7],\n [-11, -5, 8, 1],\n [19, 13, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -12, 4, 8],\n [9, -20, -3, 9],\n [-8, 10, 0, -4],\n [-2, 11, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -12, 0, 24],\n [8, -7, -4, 14],\n [-16, 5, 8, -10],\n [4, -2, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 10, -15, -7],\n [20, -4, 6, -8],\n [0, -12, 18, 6],\n [2, -4, 6, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -2, -4, 10],\n [16, 4, -4, 24],\n [4, 1, -1, 6],\n [3, -3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -15, -4, -14],\n [8, -6, -4, -8],\n [-9, 9, 3, 9],\n [-12, 15, 2, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 0, 3, 3],\n [8, 0, -2, -2],\n [16, 0, -4, -4],\n [16, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 0, 6, 0],\n [-4, -9, 9, -15],\n [11, 2, -9, 5],\n [14, -8, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 1, 1, -1],\n [-3, 3, 3, -3],\n [-4, 4, 4, -4],\n [-4, 4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, -3, -15, -25],\n [28, 0, -16, -28],\n [8, 6, -2, -6],\n [-4, -3, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -8, -10, -2],\n [2, -18, -16, 0],\n [14, 18, 8, -8],\n [-3, -11, -24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, -12, 4, 1],\n [-2, -20, 8, 2],\n [-2, 0, 8, 2],\n [-1, 0, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 2, 2, 6],\n [-9, -3, -3, -9],\n [3, 1, 1, 3],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 4, -7, 8],\n [4, 12, -11, -6],\n [-2, 12, -8, -15],\n [-8, -24, 22, 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[[-9, 0, -2, 5],\n [-7, -5, 4, -5],\n [3, -3, 4, -7],\n [7, -4, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -18, -6, 11],\n [-2, -1, -2, 4],\n [-8, -7, -8, 18],\n [-9, -16, -14, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 8, -2, -2],\n [16, 16, -4, -4],\n [-16, -16, 4, 4],\n [16, 16, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -9, -12, 6],\n [-6, -6, -8, 4],\n [6, 6, 8, -4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[15, 7, -7, -30],\n [-5, 17, 8, 1],\n [-13, 1, 7, 24],\n [-6, 8, 13, -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, -6, -7, -5],\n [-28, 0, 4, -4],\n [-2, -9, -7, -11],\n [15, -6, -7, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -8, -8, -11],\n [5, -8, 15, 10],\n [5, 4, 15, 15],\n [3, 13, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -6, 16, 24],\n [-13, -11, 18, 28],\n [14, 10, -16, -24],\n [4, -10, -18, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 11, -17, 7],\n [-6, -16, 4, 1],\n [-1, 11, -29, -6],\n [-9, 3, -21, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [-12, -9, 6, 9],\n [-12, -9, 6, 9],\n [16, 12, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-26, 6, -3, 9],\n [16, 1, -2, 3],\n [28, 1, 4, -3],\n [2, 1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -7, -9, -7],\n [11, -3, -8, -5],\n [10, 6, 8, 2],\n [15, 5, 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[[-3, 1, 1, 1],\n [12, -4, -4, -4],\n [9, -3, -3, -3],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 0, -8, 0],\n [4, 0, 16, 0],\n [3, 0, 12, 0],\n [2, 0, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 12, -9, -12],\n [-9, -5, 18, 14],\n [9, 1, -15, -10],\n [-12, -4, 22, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 4, 0, 8],\n [-4, -13, -2, -28],\n [-20, -10, 12, -8],\n [-22, -9, 14, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 10, 10, 18],\n [-4, 10, 10, 18],\n [10, -14, -22, -16],\n [0, 2, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 8, -8, 16],\n [20, 6, -10, 10],\n [12, 10, -6, 22],\n [8, -2, -8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 0, -7, -11],\n [-8, -12, -8, 8],\n [8, 15, 17, 1],\n [-4, -3, 5, 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 4x4 matrix:\n[[16, 12, -2, 12],\n [-3, -10, 7, -13],\n [9, 6, -15, 17],\n [-10, 14, 9, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, -11, -24, -18],\n [-30, 22, 4, -1],\n [-13, 13, 14, 8],\n [1, -3, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -2, 0, 9],\n [6, 4, 0, -8],\n [-4, -4, 0, 3],\n [4, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 6, 12, 12],\n [-9, -9, -18, -9],\n [-2, -5, -10, -6],\n [-10, 2, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 3, 1, -4],\n [-8, 12, 4, -16],\n [2, -3, -1, 4],\n [4, -6, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 3, -1, 0],\n [-9, -9, 3, 0],\n [12, 12, -4, 0],\n [6, 6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 8, -6, -4],\n [-6, -12, 9, 6],\n [-2, -4, 3, 2],\n [2, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, 5, 6, -15],\n [10, 4, 3, -9],\n [-1, 5, -3, 0],\n [-11, 1, -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[[16, -16, 0, 12],\n [4, -4, 0, 3],\n [0, 0, 0, 0],\n [-12, 12, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 0, 12, -9],\n [4, 0, 16, -12],\n [-1, 0, -4, 3],\n [-3, 0, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, 1, 2, 0],\n [-3, 1, 2, 0],\n [-6, 2, 4, 0],\n [3, -1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[22, -13, -12, 2],\n [-10, 0, -4, 5],\n [8, -7, -8, 3],\n [2, 7, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -12, -8, 12],\n [-2, -2, -12, 14],\n [-5, -6, -20, 24],\n [-4, -4, -24, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -9, 9, 3],\n [-7, 16, -9, -10],\n [2, -11, 9, 5],\n [-2, 11, -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[[-16, 16, -4, -4],\n [-12, 12, -3, -3],\n [4, -4, 1, 1],\n [12, -12, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 2, -6, -2],\n [-6, -2, 6, 2],\n [6, 2, -6, -2],\n [12, 4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -3, 0, -3],\n [-6, -3, -6, -6],\n [2, 1, 10, 6],\n [-8, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -11, 4, 1],\n [-7, 8, -7, -7],\n [-3, 9, -1, -4],\n [-13, 6, -9, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 10, -4, 1],\n [0, -16, 0, -4],\n [4, 14, 4, 5],\n [-4, 14, -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[[-9, -16, 3, 4],\n [-13, -14, -3, 23],\n [-9, -4, -8, 24],\n [4, 8, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -18, -6, 0],\n [6, -4, -6, 20],\n [33, -4, -27, -16],\n [15, -22, -19, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -10, -9, 8],\n [18, -20, -12, -1],\n [-18, 16, 12, -5],\n [-20, 12, 15, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -3, -3, -6],\n [0, 0, 0, 0],\n [-2, -1, -1, -2],\n [-4, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [4, 0, -4, -4],\n [4, 0, -4, -4],\n [16, 0, -16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -8, 8, -2],\n [3, 4, -4, 1],\n [6, 8, -8, 2],\n [9, 12, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -6, 4, -6],\n [6, 6, -4, 6],\n [9, 9, -6, 9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, -7, 20, 2],\n [-1, 13, 4, -14],\n [7, -10, 8, 8],\n [9, -9, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 2, -4, 0],\n [7, -12, -14, 8],\n [13, -6, 6, -12],\n [-4, 8, 7, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 5, 5, -1],\n [10, 2, -1, -4],\n [-4, -14, -8, 10],\n [-8, -6, -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[[-9, 0, -6, 0],\n [-13, -1, -9, -1],\n [4, 1, 3, 1],\n [-16, -4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -4, -9, -1],\n [7, 3, -11, 6],\n [-11, 6, 0, 2],\n [-10, 8, -7, 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[[3, -21, -5, 10],\n [-3, 12, 8, -7],\n [1, -3, -3, 2],\n [0, -6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -3, 12, -9],\n [0, 1, -4, 3],\n [0, 1, -4, 3],\n [0, 4, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -4, -15, 8],\n [12, -8, 24, 4],\n [9, 14, 3, -17],\n [-6, -16, 3, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -4, 0, -4],\n [12, -4, 0, -12],\n [4, -3, 0, -4],\n [-2, -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[[4, 8, 16, 16],\n [-4, -6, 2, 4],\n [-2, -1, 19, 22],\n [-1, -1, 5, 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 4x4 matrix:\n[[0, 3, -1, 26],\n [-6, -2, 10, -6],\n [-6, -2, -6, -10],\n [12, 4, -4, 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, -6, -12, -6],\n [-8, -3, 3, -3],\n [8, 2, -6, 2],\n [0, 2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -9, 9, -7],\n [1, 9, -9, 7],\n [10, 18, -12, 4],\n [-3, -15, 14, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 15, -5, -3],\n [8, -3, -17, -3],\n [-8, -9, 9, 3],\n [4, 4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[22, 18, 6, 2],\n [-9, -8, -5, -1],\n [4, 6, 12, -4],\n [-11, -10, -7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 8, 8, -8],\n [2, 4, 4, -4],\n [-2, -4, -4, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 4, -4, -1],\n [0, 0, 0, 0],\n [-1, -4, 4, 1],\n [4, 16, -16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -3, -12, -12],\n [-3, -3, -12, -12],\n [0, 0, 0, 0],\n [3, 3, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 6, 2, 2],\n [0, 0, 0, 0],\n [-3, 9, 3, 3],\n [-2, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -1, 2, -5],\n [10, 14, 0, -5],\n [-20, -14, 7, 8],\n [7, -15, 16, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -6, 13, -9],\n [0, 0, -8, 12],\n [1, 2, -3, 1],\n [4, 8, -10, 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[[-9, -9, 6, 3],\n [12, 12, -8, -4],\n [-3, -3, 2, 1],\n [-3, -3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -20, -2, 2],\n [-4, 2, 2, -2],\n [4, -2, -2, 2],\n [2, -5, 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[[0, -10, 10, -20],\n [-5, 5, -5, 0],\n [-5, 10, -10, 10],\n [-6, -2, 2, -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 4x4 matrix:\n[[1, -7, 3, -2],\n [8, 16, -12, 2],\n [-16, -8, 12, 2],\n [4, 8, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 8, 14, 12],\n [19, 28, 16, 20],\n [1, -8, -11, -10],\n [14, 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[[-11, -9, -28, 13],\n [-10, -16, -20, 19],\n [-2, -9, -18, 8],\n [-8, 0, -16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, -16, 4, -12],\n [2, -8, 0, 8],\n [4, 3, 4, 4],\n [4, -9, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, -4, -11, -5],\n [2, -8, -2, 2],\n [0, 10, 0, -4],\n [3, -12, -3, 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[[21, -3, -15, 18],\n [-2, -4, 4, 0],\n [8, -4, -4, 8],\n [-5, 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 4x4 matrix:\n[[-14, -10, -4, -12],\n [12, 10, -4, 8],\n [6, 7, -22, 4],\n [18, 13, 2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -8, -10, -12],\n [-10, -16, 7, 12],\n [-4, 0, 6, 8],\n [-4, -8, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 8, 8, 8],\n [0, 0, 0, 0],\n [-6, 6, 6, 6],\n [-6, 6, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[5, -6, 13, -13],\n [16, -6, 11, -14],\n [15, 6, 3, 3],\n [0, 2, -33, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -5, -9, -7],\n [16, 18, 17, 1],\n [-14, -17, -18, -4],\n [-2, 1, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 2, 4, -2],\n [-16, -4, -8, 4],\n [4, 1, 2, -1],\n [-8, -2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -4, -4, -16],\n [-6, -3, -3, -12],\n [4, 2, 2, 8],\n [-8, -4, -4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -2, -2, -4],\n [-5, -6, 5, 10],\n [1, 10, 8, -21],\n [10, -4, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -3, 17, 6],\n [14, 4, -4, -22],\n [3, -3, 21, 3],\n [13, 2, 6, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -4, 4, -2],\n [-9, -3, 12, -3],\n [-9, 8, 4, 2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, -4, 2, -12],\n [8, -12, -4, -10],\n [3, -15, -6, 0],\n [-5, -8, -19, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -2, -2, -3],\n [6, -6, -6, -9],\n [-4, 4, 4, 6],\n [-2, 2, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 5, 22, 6],\n [29, -7, 6, 24],\n [5, 13, -2, -6],\n [-7, -9, -22, 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[[11, -5, -3, -9],\n [6, -24, -4, -12],\n [17, 7, -3, -9],\n [0, -18, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 12, 10, 2],\n [0, 10, 7, -9],\n [6, -19, -9, 17],\n [-6, 7, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -3, -4, -2],\n [8, -6, -8, -4],\n [-12, 9, 12, 6],\n [-4, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 0, 0, 0],\n [0, -4, 6, -6],\n [0, -6, 9, -9],\n [0, 8, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [-2, 3, 4, -3],\n [-2, 3, 4, -3],\n [-6, 9, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 0, 3, 8],\n [-9, 8, -9, -16],\n [12, -16, 12, 16],\n [3, -5, 3, 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 4x4 matrix:\n[[3, 9, 12, 0],\n [-1, -3, -4, 0],\n [3, 9, 12, 0],\n [2, 6, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -12, 9, -12],\n [-4, -5, -6, 1],\n [-12, 24, -5, 16],\n [12, -6, 11, -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 4x4 matrix:\n[[2, -8, -6, 2],\n [2, -8, -6, 2],\n [-4, 16, 12, -4],\n [-1, 4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -22, 20, 1],\n [-8, 20, 2, -8],\n [0, 1, -5, 2],\n [-7, -3, -3, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-15, 7, -9, 5],\n [21, -15, -3, -7],\n [-3, 1, -3, 1],\n [9, -1, 15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 12, 16],\n [-9, 12, -15, -5],\n [-6, 8, -9, -2],\n [-9, 12, -18, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -1, 1, 2],\n [-2, -2, 2, 4],\n [0, 0, 4, -16],\n [3, 3, -7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, -22, -24, -21],\n [-3, 2, 9, 6],\n [-6, 12, 10, 14],\n [6, 4, 6, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, -2, 4, 0],\n [2, 19, -5, -22],\n [-11, 2, 7, -8],\n [4, -8, -4, 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[[11, 4, 13, 1],\n [-9, 2, -22, 11],\n [19, 8, 23, 9],\n [1, 8, -13, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 1, 8, -13],\n [17, -5, -11, 18],\n [-8, 7, 1, -3],\n [-2, 1, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-3, -1, -1, 1],\n [6, 0, 0, 3],\n [2, 4, 4, -9],\n [-6, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, 16, -14, -11],\n [7, 8, -15, -14],\n [-23, -16, 15, -2],\n [-10, -20, 1, -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[[-4, 8, 6, 6],\n [-2, 4, 3, 3],\n [0, 0, 0, 0],\n [-4, 8, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 3, 3, 6],\n [12, -12, -12, -24],\n [-9, 3, 9, 12],\n [0, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 0, 1, -11],\n [-13, 20, -1, 11],\n [11, -18, 2, -15],\n [4, 0, 1, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -12, -3, -6],\n [2, -8, -2, -4],\n [3, -12, -3, -6],\n [-1, 4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 11, -2, -10],\n [-10, 5, 12, 1],\n [-3, 4, 8, -3],\n [-6, 1, -10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 0, -3, -12],\n [-2, 0, 1, 4],\n [-4, 0, 2, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -9, 6, -8],\n [8, -4, 16, 0],\n [-22, -13, -8, -16],\n [-14, -5, -10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-16, 11, 7, 20],\n [-18, 12, 6, 24],\n [-12, -7, -22, -8],\n [-12, 3, -7, 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[[3, -12, -12, 12],\n [0, 0, 0, 0],\n [1, -4, -4, 4],\n [-2, 8, 8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -1, -2, -2],\n [-12, 3, 6, 6],\n [-4, 1, 2, 2],\n [-4, 1, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 15, 0, 5],\n [5, -5, 16, 9],\n [-8, -19, 14, 3],\n [-20, 14, 20, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 0, -6, -3],\n [12, 0, -6, -3],\n [-4, 0, 2, 1],\n [-12, 0, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -6, 0, -12],\n [0, 0, 0, 0],\n [2, 4, 0, 8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -2, 0, -3],\n [0, 0, 0, 0],\n [6, -4, 0, -6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 3, 13, 10],\n [-12, -1, 17, 18],\n [-16, 9, 19, 14],\n [-6, 1, 7, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 16, 0, 16],\n [0, 8, 0, 8],\n [0, -4, 0, -4],\n [0, -4, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 16, 4, 8],\n [-12, 8, 2, 4],\n [-22, 16, 4, 8],\n [-18, 12, 3, 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[[-9, 3, 6, -9],\n [6, -2, -4, 6],\n [-9, 3, 6, -9],\n [-12, 4, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -12, -6, 9],\n [-4, 0, 4, -6],\n [-16, 24, 4, -6],\n [-10, 8, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 4, -5, -10],\n [6, 8, 2, -4],\n [9, 4, 7, 6],\n [-3, -6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 3, 6, 0],\n [-3, -1, -2, 0],\n [6, 2, 4, 0],\n [-12, -4, -8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 16, -8, -8],\n [-4, -4, 2, 2],\n [8, 8, -4, -4],\n [12, 12, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 6, 15, -9],\n [-4, 10, -2, 18],\n [8, -13, -10, -8],\n [8, -13, -10, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 0, 11, 9],\n [3, 4, 9, 7],\n [0, 3, 4, 3],\n [-6, 7, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 3, 9, -9],\n [12, -3, -9, 9],\n [16, 4, 2, 8],\n [-12, -13, -19, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [3, -4, 1, -4],\n [-6, 8, -2, 8],\n [-3, 4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 13, -13, 8],\n [-8, -8, -4, 8],\n [-5, 0, -7, 7],\n [5, 15, -11, -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[[3, 9, -6, -3],\n [-2, -6, 4, 2],\n [-4, -12, 8, 4],\n [3, 9, -6, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -9, -9, 6],\n [-16, 12, 12, -8],\n [-4, 3, 3, -2],\n [16, -12, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 16, 8, 0],\n [12, 12, 6, 0],\n [-12, -12, -6, 0],\n [4, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -4, 19, 1],\n [8, 20, 4, -14],\n [0, 6, -12, -3],\n [-8, -24, 4, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -18, 7, 10],\n [-4, -2, -20, 6],\n [-12, -15, 3, 9],\n [8, 8, 12, -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[[-14, 6, 2, 4],\n [-22, 2, 3, 0],\n [16, 4, 5, 17],\n [2, 2, 9, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 1, 4, 2],\n [-3, -1, -4, -2],\n [-3, -1, -4, -2],\n [3, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 3, -5, -7],\n [9, 3, 23, -11],\n [-11, 3, 2, 22],\n [8, 8, 10, 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[[14, 3, -24, 2],\n [15, 6, -26, 5],\n [14, 3, -16, 18],\n [7, 21, -20, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 12, 19, -9],\n [17, -17, 1, -10],\n [-16, 10, -7, 11],\n [-11, 23, 13, 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[[8, -18, -1, -12],\n [6, -16, -2, -15],\n [-15, 4, 4, -20],\n [5, 10, -5, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, 19, 4, -13],\n [7, -7, -6, 31],\n [0, 14, 20, 4],\n [16, 8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 4, -15, -7],\n [-6, -3, 12, 6],\n [-14, 13, -16, 14],\n [10, -12, 9, -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 4x4 matrix:\n[[-6, 0, 4, -12],\n [4, 2, 4, 14],\n [1, -19, 8, -7],\n [1, 8, 8, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, -4, 20, 8],\n [24, 0, -22, -13],\n [10, 13, -2, -24],\n [-12, 8, 12, 26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -3, 2, -3],\n [8, -6, 4, -6],\n [-12, 9, -6, 9],\n [-4, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -9, -12, -6],\n [0, 0, 0, 0],\n [-4, 12, 16, 8],\n [-1, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 0, -1, -3],\n [1, 0, -1, -3],\n [2, 0, -2, -6],\n [2, 0, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-17, -13, 6, 4],\n [-18, -15, 1, 10],\n [-17, -13, 6, 4],\n [-13, -11, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -9, 3, 6],\n [-5, 8, 20, 9],\n [-6, -31, -36, -4],\n [-4, -16, -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[[0, -6, -8, 2],\n [0, -3, -4, 1],\n [0, 12, 16, -4],\n [0, -3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 1, 7, 11],\n [-1, 1, 7, 11],\n [-3, 3, 1, -7],\n [-3, 3, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 0, -16, -12],\n [-4, 0, -4, -3],\n [16, 0, 16, 12],\n [-12, 0, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 0, -9, 3],\n [4, 0, 2, 2],\n [0, 0, 0, 0],\n [-4, 0, 6, -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[[0, -8, -1, -18],\n [-3, -9, 0, -15],\n [-4, -4, 1, -2],\n [10, 14, -2, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -9, 12, 0],\n [1, -3, 4, 0],\n [-4, 12, -16, 0],\n [4, -12, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 4, 2, -6],\n [12, -6, -3, 9],\n [8, -4, -2, 6],\n [-12, 6, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 0, -10, -10],\n [4, 0, 18, 18],\n [-1, 0, 5, 5],\n [-8, 0, -17, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -4, 4, 2],\n [0, 0, 0, 0],\n [-4, -2, 2, 1],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 15, 10, -9],\n [-8, 1, -3, 6],\n [-24, -12, -14, 18],\n [-16, -4, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, -4, 8],\n [-5, 2, -5, -8],\n [-2, 2, -6, -6],\n [6, 3, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -6, -2, -2],\n [-27, -4, -4, -11],\n [-3, 7, 4, 5],\n [22, 8, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -12, -36, 0],\n [-24, -21, 0, 15],\n [18, 27, 15, 0],\n [18, 27, 11, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[10, 8, -10, 6],\n [21, -10, 0, 16],\n [-7, -14, 30, 20],\n [-14, 16, -6, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -4, 8, 6],\n [-4, -2, 4, 3],\n [-12, -6, 12, 9],\n [-4, -2, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 8, 12, 8],\n [6, -6, -9, -6],\n [4, -4, -6, -4],\n [-8, 8, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, -3, -12, -3],\n [6, 3, 12, 3],\n [6, 3, 12, 3],\n [6, 3, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -23, 10, 11],\n [0, -36, 16, 16],\n [6, -28, 12, 14],\n [20, 0, -16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -3, -1, 8],\n [-2, 10, 7, 10],\n [7, -1, 1, 16],\n [1, 1, 1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, 7, 11, 3],\n [-17, -29, 1, -1],\n [0, 3, -4, -1],\n [16, 16, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -12, 12, 0],\n [-14, -16, 11, 10],\n [-8, 0, -4, 8],\n [-4, -16, 16, 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, -3, -7, 9],\n [8, 3, -3, 12],\n [6, -1, -5, 8],\n [-2, 2, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -2, -12, 9],\n [-5, 6, 4, -4],\n [-6, 6, 8, -7],\n [-2, -6, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 9, 3, -6],\n [-10, 2, -4, 8],\n [-5, 18, -1, 2],\n [-2, -3, -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 4x4 matrix:\n[[1, -12, 5, -2],\n [10, 9, -8, 14],\n [-4, 4, 4, 8],\n [2, 16, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -11, -5, -13],\n [7, 0, -1, 0],\n [36, -2, -2, 2],\n [4, 7, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, 16, -4, 8],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, 8, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 3, 3, 3],\n [-12, 3, 3, 3],\n [4, -1, -1, -1],\n [4, -1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -6, 19, 1],\n [18, -2, 20, 8],\n [-4, 8, -16, 0],\n [-1, -8, 11, -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[[0, -4, 16, -4],\n [-16, -7, 8, -15],\n [0, -4, 16, -4],\n [16, 8, -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[[-8, 16, -4, 4],\n [4, -8, 2, -2],\n [-4, 8, -2, 2],\n [-2, 4, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -8, 6, -2],\n [-3, 12, -9, 3],\n [-1, 7, -5, -2],\n [0, -3, 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[[16, 12, 12, -8],\n [2, -11, -5, 2],\n [-16, -12, -12, 8],\n [14, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 12, -16, -12],\n [-8, -12, 16, 12],\n [4, 6, -8, -6],\n [-4, -6, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -10, -24, 12],\n [-11, 2, 5, 3],\n [-6, -1, -2, 2],\n [8, 0, -6, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, 0, 4, 20],\n [16, -6, -13, -11],\n [-1, -4, -7, 1],\n [-7, -14, -24, 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[[4, -16, 0, 12],\n [0, 0, 0, 0],\n [1, -4, 0, 3],\n [-2, 8, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 8, -6, 8],\n [-12, -16, 12, -16],\n [-3, -4, 3, -4],\n [-6, -8, 6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, 12, -3, -12],\n [0, 0, 0, 0],\n [6, 8, -2, -8],\n [-9, -12, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 3, -12, 9],\n [16, 4, -16, 12],\n [-12, -3, 12, -9],\n [-4, -1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -3, -4, -1],\n [-8, 12, 16, 4],\n [-4, 6, 8, 2],\n [4, -6, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, -2, -4, 11],\n [3, 7, -10, 0],\n [-9, -12, 18, -3],\n [3, -16, 15, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 4, 1, -1],\n [4, -8, -2, 2],\n [6, -12, -3, 3],\n [-6, 12, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 2, 3, 0],\n [-2, 4, -6, -8],\n [-8, 4, -24, -20],\n [-2, 0, -6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[24, -16, -4, -8],\n [-16, 8, 0, 12],\n [-6, -8, -11, -6],\n [-12, 8, 2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-2, -2, 4, 1],\n [-4, -4, 8, 2],\n [6, 6, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-8, 12, 8, -16],\n [-2, 3, 2, -4],\n [-6, 9, 6, -12],\n [-8, 12, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, 13, -19, -16],\n [-9, -2, 9, 12],\n [-11, -13, 11, 8],\n [9, 11, -11, -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[[-5, 0, 3, -11],\n [2, -1, 2, 21],\n [1, -7, 2, -7],\n [-10, -6, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, -8, 0, 8],\n [0, 0, -6, 6],\n [0, 0, 6, -6],\n [-8, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, -20, 0, -4],\n [6, -6, 0, 12],\n [-6, -6, 8, -4],\n [-26, -16, 10, -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[[3, -8, 0, -4],\n [2, 0, 0, 4],\n [6, -12, 0, -3],\n [-10, 28, 0, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 14, 25, 11],\n [8, 12, 2, 0],\n [0, 12, 30, 12],\n [12, 13, 28, 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[[-4, 0, 5, 2],\n [1, 2, -3, -3],\n [-7, 18, -7, -19],\n [-6, 20, -10, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 6, 2, -11],\n [-16, -12, -16, 16],\n [13, 9, 14, -11],\n [10, 6, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -12, 3, 9],\n [2, -4, 1, 3],\n [-8, 16, -4, -12],\n [-8, 16, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -10, 2, 1],\n [-18, 13, 3, -2],\n [1, -6, 9, 9],\n [0, 2, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -8, -10, 9],\n [8, 16, 16, -12],\n [-8, -16, -18, 15],\n [-3, -6, -5, 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[[1, -3, 6, 4],\n [-5, -2, 3, -8],\n [-1, -7, 9, -4],\n [16, -17, 27, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -10, -2, -8],\n [18, -1, 14, 20],\n [22, -10, 20, 12],\n [2, 6, 0, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [8, -13, 12, 16],\n [-12, 16, -14, -20],\n [-22, 6, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -6, -11, -6],\n [-4, -2, -4, -8],\n [-4, 8, 0, 3],\n [-16, 6, 4, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 2, -4, -4],\n [16, -8, 16, 16],\n [-4, 2, -4, -4],\n [4, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -2, 24, -4],\n [-10, -4, 17, -1],\n [24, -5, -16, -8],\n [7, 5, 4, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 19, -8, -8],\n [-15, 6, -11, 14],\n [18, 8, -3, -8],\n [0, -13, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, -9, 9, 4],\n [4, 7, -5, -2],\n [16, -7, 9, 4],\n [4, -3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 0, 12, 16],\n [4, 0, 12, 16],\n [2, 0, 6, 8],\n [-3, 0, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -6, -9, 6],\n [3, 7, 3, 1],\n [6, 6, 9, -3],\n [8, 6, 14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -5, 1, 7],\n [-1, -2, 2, 4],\n [-4, 4, 12, 4],\n [-2, 2, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, 10, -30, 22],\n [17, -12, 33, -24],\n [0, 12, 18, -20],\n [-6, 4, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 5, 5, -1],\n [2, -8, -8, 17],\n [-6, -6, -6, -1],\n [-2, 5, 5, -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 4x4 matrix:\n[[-4, 11, -4, 1],\n [19, -7, -3, -8],\n [-4, 10, -1, 9],\n [18, -5, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 16, -4, -4],\n [-6, 8, -2, -2],\n [3, -4, 1, 1],\n [6, -8, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 4, -7, 14],\n [-2, 0, -10, 12],\n [-8, 8, 16, -8],\n [-1, 0, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 6, 2, 4],\n [-1, -3, -1, -2],\n [-1, -3, -1, -2],\n [1, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 4, 3, 6],\n [-4, 8, 12, 0],\n [-7, 4, 3, 6],\n [11, -2, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 4, 2, -4],\n [-12, -8, -4, 8],\n [-6, -4, -2, 4],\n [6, 4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[15, 11, -9, -5],\n [15, 9, -15, -1],\n [10, -7, -13, -4],\n [3, -2, -9, 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 4x4 matrix:\n[[-9, 6, -12, 6],\n [9, -6, 12, -6],\n [-9, 6, -12, 6],\n [-3, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 0, 3, -3],\n [0, 0, 0, 0],\n [9, 0, 9, -9],\n [3, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -2, 0, 8],\n [6, 15, 9, 12],\n [4, -2, -2, -8],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -8, 4, -3],\n [8, 0, -16, 12],\n [10, 16, 4, -3],\n [9, 4, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[24, 21, 24, 13],\n [-1, 7, 13, 5],\n [-24, 0, 12, 4],\n [-4, -17, -26, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -2, -4, 6],\n [4, 2, 4, -6],\n [-6, -3, -6, 9],\n [-2, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, -12, 8, 8],\n [12, 14, 4, -4],\n [-6, -8, 8, 8],\n [-18, -20, 10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 0, -8, -12],\n [12, 0, 6, 9],\n [-4, 0, -2, -3],\n [4, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 0, -2, 1],\n [4, -7, -6, 10],\n [-6, -9, -4, 11],\n [-6, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, -8, -24, -4],\n [8, 10, 22, 3],\n [11, -16, -8, 2],\n [13, 4, 20, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-11, -24, 24, 8],\n [-8, -8, 10, -15],\n [5, 7, -5, 8],\n [2, -2, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -2, -4, 4],\n [-2, 1, 2, -2],\n [-6, 3, 6, -6],\n [4, -2, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -12, -4, 16],\n [11, 13, -15, -28],\n [10, 15, -13, -28],\n [10, 0, -28, -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[[-3, 9, 1, -21],\n [20, -8, -4, 12],\n [-4, 1, -5, 1],\n [16, -1, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, -11, 1, 5],\n [-2, 5, 4, -3],\n [12, 4, -8, 12],\n [6, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, -9, 19, 11],\n [21, 18, -10, -14],\n [-9, -9, 7, 11],\n [5, 17, 17, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, -9, -6, -9],\n [1, -3, -2, -3],\n [-3, 9, 6, 9],\n [1, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, -7, 12, -10],\n [10, -6, 12, -8],\n [3, -3, 0, -6],\n [-8, 5, -9, 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[[-3, 3, -4, -2],\n [0, -10, 8, -4],\n [-21, 6, -16, -20],\n [0, -15, 12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 4, 11, 13],\n [5, 12, 13, -11],\n [-14, -12, 1, 6],\n [0, 8, 14, -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[[0, 0, 0, 0],\n [-3, -3, -3, -12],\n [-1, -1, -1, -4],\n [-2, -2, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, -16, -4, 4],\n [18, -12, -7, -1],\n [-1, 4, -1, -3],\n [-21, 12, 9, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[8, 3, 1, -1],\n [4, 1, -1, 0],\n [-8, -2, 2, 0],\n [-4, 0, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -2, -6, 8],\n [-4, 4, 12, -16],\n [4, -4, -12, 16],\n [3, -3, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -9, 12, -6],\n [-3, -9, 12, -6],\n [4, 12, -16, 8],\n [-2, -6, 8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -12, 16, 4],\n [0, 0, 0, 0],\n [-16, 12, -16, -4],\n [16, -12, 16, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -12, -6, 4],\n [-12, -8, -13, 7],\n [0, -2, -11, 12],\n [-9, 14, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, -3, 11, 10],\n [13, -5, -3, 12],\n [-8, 2, -14, -14],\n [-22, -12, -2, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -6, -9, 11],\n [16, 6, 8, 0],\n [-10, -2, -3, -5],\n [11, 25, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -6, -9, -9],\n [12, -12, -15, -11],\n [-10, 10, 9, 1],\n [-7, 7, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -11, 6, 5],\n [-8, 17, -24, 7],\n [-5, 17, -17, 0],\n [-12, -20, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [-12, -4, -16, 8],\n [12, 4, 16, -8],\n [9, 3, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -12, 0, 0],\n [0, 6, 0, 0],\n [0, -6, 0, 0],\n [0, 9, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 20, 12, 12],\n [4, 12, 8, 8],\n [-7, -9, -5, -5],\n [-6, -10, -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[[-15, 7, -8, 9],\n [-9, 3, -1, 10],\n [4, 6, -11, -9],\n [4, -8, 10, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -19, 8, 10],\n [-5, 2, 0, 3],\n [1, 10, 8, -23],\n [-2, -29, 20, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -9, 11, -2],\n [-8, 2, -6, 4],\n [0, -15, 14, 1],\n [-13, 7, -12, 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[[0, -16, 12, 4],\n [12, -4, -12, 16],\n [6, 2, -22, 7],\n [12, -4, -28, 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[[-13, 3, 18, 13],\n [11, -9, 9, -11],\n [-6, 12, 2, 6],\n [-1, 3, 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[[-2, 4, -2, -1],\n [5, -19, -1, -8],\n [1, -5, -1, -3],\n [7, -11, 9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -4, 8, 0],\n [-4, 8, -16, 0],\n [2, -4, 8, 0],\n [-4, 7, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 12, 6, 18],\n [16, -8, 1, 3],\n [4, -11, -2, -6],\n [-12, 1, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -9, -6, 7],\n [0, 0, -3, -2],\n [14, -11, 1, 13],\n [-10, -5, 1, 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[[12, 9, 6, 3],\n [-2, 16, -22, -4],\n [6, -3, 12, 3],\n [2, -11, 16, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 4, 16, 12],\n [4, 4, 16, 12],\n [2, 2, 8, 6],\n [-3, -3, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -8, 15, 3],\n [-2, 20, 8, 0],\n [8, -4, -17, -5],\n [-2, 4, -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[[0, -9, -9, 6],\n [0, 9, 9, -6],\n [0, -9, -9, 6],\n [0, -9, -9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 18, 16, -8],\n [-14, -12, -14, 10],\n [4, -16, -12, 4],\n [6, 10, 10, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [-6, -5, 7, -6],\n [12, 11, -19, 12],\n [-16, -12, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -4, 16, -16],\n [16, 4, 0, 16],\n [8, 2, 6, 8],\n [16, 4, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -10, -8, 8],\n [-12, 1, -2, 9],\n [-6, 2, 0, 4],\n [-15, -1, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 16, -4, -4],\n [0, 0, 0, 0],\n [-12, 16, -4, -4],\n [-3, 4, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 0, 8, -2],\n [8, 0, 8, -2],\n [4, 0, 4, -1],\n [-12, 0, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[22, 0, -4, 9],\n [-16, -2, -4, -17],\n [-13, -13, -8, 1],\n [4, 18, 16, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 0, -6, -2],\n [0, 0, 0, 0],\n [2, 0, 3, 1],\n [-4, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 0, -1, -4],\n [-12, 0, -3, -12],\n [4, 0, 1, 4],\n [-4, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -1, 20, -6],\n [-3, 3, -12, 3],\n [23, 7, 9, -4],\n [-11, -5, 6, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 30, -6, -6],\n [-30, 2, -26, 14],\n [-7, 28, -10, 10],\n [-21, 0, -18, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -6, 0, -12],\n [-18, -18, 0, -9],\n [0, 4, 0, -10],\n [3, 2, 0, 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[[-1, -6, 6, -8],\n [-6, 0, -9, -12],\n [6, 0, 9, 12],\n [9, -2, 16, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [-8, -2, 4, 2],\n [16, 4, -8, -4],\n [-4, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[7, -7, -18, 1],\n [8, -8, -15, 2],\n [-4, 4, -12, -4],\n [7, -7, -18, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 0, -2, -6],\n [-10, -6, -2, 9],\n [-17, -14, -11, 2],\n [-18, -14, -10, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 0, 24, 20],\n [-4, 1, -10, -4],\n [5, 0, 0, 5],\n [14, -11, 20, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -10, -6, -3],\n [-21, 6, 0, 15],\n [3, -2, -12, 3],\n [4, 10, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, -13, -7, 4],\n [3, -17, -8, 5],\n [0, -7, 2, 1],\n [-1, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 0, 4, 4],\n [-4, 0, 4, 4],\n [-1, 0, 1, 1],\n [4, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 12, 12, 8],\n [-4, 12, 12, 8],\n [0, 0, 0, 0],\n [-4, 12, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 9, 12, 12],\n [4, 6, 8, 8],\n [0, 0, 0, 0],\n [8, 12, 16, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 4, 4, -12],\n [0, -4, -4, 12],\n [0, 0, 0, 0],\n [0, -3, -3, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, -10, 0, -6],\n [-3, 7, 1, 4],\n [-2, 6, -2, 4],\n [4, -28, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 16, 4, 11],\n [8, -6, 18, -8],\n [2, 28, 10, -20],\n [3, -3, -14, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-16, 12, 12, 0],\n [-16, -12, -12, 18],\n [-8, 2, 2, 3],\n [-4, -5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, -7, -10, 15],\n [13, -10, -10, -3],\n [6, -11, -4, 8],\n [-3, -7, -2, -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[[25, 19, 1, -26],\n [1, 7, 19, -2],\n [24, 19, 20, -22],\n [-18, -15, 12, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 12, 4, 14],\n [12, -8, -8, 4],\n [-5, 2, 4, -6],\n [-14, 12, 8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 10, 0, 2],\n [-1, 0, -20, -24],\n [-5, 2, 8, 12],\n [3, 10, -16, -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 4x4 matrix:\n[[-16, 11, -13, -18],\n [6, -5, -3, -2],\n [5, -3, 8, 10],\n [-13, 10, -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[[-2, 2, -4, -4],\n [2, -2, 4, 4],\n [2, -2, 4, 4],\n [-3, 3, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -9, 3, -9],\n [-4, 12, -4, 12],\n [4, -12, 4, -12],\n [-1, 3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 15, 9, 4],\n [20, 14, 10, 0],\n [0, 0, 0, 0],\n [20, 14, 10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, -4, 0, 0],\n [-8, -3, 5, 3],\n [6, 3, -15, -9],\n [-6, -5, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, -15, -6, 0],\n [-2, 16, 14, -15],\n [-16, 4, 17, 13],\n [-7, -9, -3, -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[[4, 0, 9, 3],\n [2, -5, 12, -1],\n [6, 5, 6, 7],\n [14, 13, 12, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -4, -16, -8],\n [2, -1, -4, -2],\n [-2, 1, 4, 2],\n [4, -2, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -1, -13, 0],\n [-17, -14, -11, 0],\n [-20, -20, -8, 0],\n [-8, -11, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -15, 6, -13],\n [0, 0, 0, 0],\n [2, 6, 0, 4],\n [16, -6, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -6, -12, -6],\n [2, 10, 14, 6],\n [0, 16, 20, 8],\n [-8, 24, 24, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 0, 3, -2],\n [12, 12, -9, -6],\n [-8, -3, 3, 1],\n [20, 10, -9, -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[[28, -24, -4, 12],\n [-28, 18, -2, -9],\n [-12, -4, -4, -4],\n [-21, 8, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 2, -4, 2],\n [1, 1, -2, 1],\n [-2, -2, 4, -2],\n [3, 3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -9, 9, -9],\n [3, -9, 9, -9],\n [3, -9, 9, -9],\n [-1, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 2, 8, 3],\n [16, 8, 9, -14],\n [-4, 4, 11, 0],\n [5, 4, 20, 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[[12, 5, 8, -12],\n [0, -3, -4, 0],\n [0, -3, -4, 0],\n [12, 11, 16, -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[[16, -14, -12, -4],\n [-14, 11, 11, 3],\n [14, -6, -13, -1],\n [-16, 14, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 1, 3, -3],\n [-6, 3, 9, -9],\n [-4, 8, 12, -9],\n [-4, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 0, 6, 4],\n [6, 0, 6, 4],\n [-3, 0, -3, -2],\n [6, 0, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 12, 0, -12],\n [0, 12, 0, -12],\n [0, -9, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -17, -21, -3],\n [11, -4, 0, -3],\n [0, 8, 14, 5],\n [1, -19, -15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, -10, 2, 16],\n [8, -15, -2, 20],\n [11, -1, -3, 12],\n [5, 9, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 4, 0, 4],\n [8, 4, 0, 4],\n [-16, -8, 0, -8],\n [12, 6, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 6, -5, -6],\n [3, 14, -3, -10],\n [-2, -6, 10, 18],\n [-3, -10, -5, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 1, 4, 1],\n [-3, -3, -12, -3],\n [-4, -4, -16, -4],\n [3, 3, 12, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -8, -4, -2],\n [4, 16, 8, 4],\n [-3, -12, -6, -3],\n [-3, -12, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 10, -13, -6],\n [-4, 4, 8, 0],\n [5, 13, -7, -6],\n [3, 9, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, -1, 3, 3],\n [-5, -1, -12, -5],\n [-19, 17, 9, -19],\n [-4, 12, 24, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 9, 3, -6],\n [4, -12, -4, 8],\n [2, -6, -2, 4],\n [-2, 6, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 4, -8, -12],\n [4, -5, 7, 18],\n [18, 3, -11, -4],\n [22, 1, -9, 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[[4, 16, -8, -8],\n [-1, -4, 2, 2],\n [-1, -4, 2, 2],\n [3, 12, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -12, 12, -6],\n [13, -18, 18, -4],\n [-18, 20, -20, -4],\n [-22, 20, -20, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -22, 16, 10],\n [4, -12, 10, 6],\n [3, -2, 4, 2],\n [12, 6, 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[[4, -2, 8, 6],\n [-3, -1, -7, -7],\n [2, 9, 8, 13],\n [0, 15, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 20, 18, 12],\n [-17, -12, 4, -3],\n [10, 12, 6, 6],\n [24, 26, 5, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -3, -3, 9],\n [0, 0, 0, 0],\n [-2, -2, -2, 6],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 1, 15, -9],\n [7, -1, 1, 0],\n [-3, 3, 2, -3],\n [16, 6, 0, -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, -3, 9, 9],\n [-3, 1, -3, -3],\n [-3, 1, -3, -3],\n [-12, 4, -12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -8, -8, 12],\n [-2, -4, -4, 6],\n [-1, -2, -2, 3],\n [4, 8, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 20, 17, 31],\n [26, -2, 2, 5],\n [-7, 18, 16, 7],\n [-3, -12, -9, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -7, 7, 10],\n [13, -4, -6, -10],\n [-5, 4, -2, -3],\n [13, 2, -12, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 2, 4, -4],\n [-6, -4, -8, 8],\n [3, 2, 4, -4],\n [12, 8, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 2, 2, -4],\n [4, 2, 2, -4],\n [6, 3, 3, -6],\n [-8, -4, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[9, -6, 6, -9],\n [9, -7, 10, -3],\n [9, -6, 6, -9],\n [-5, 4, -6, 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[[12, 3, -3, -12],\n [4, 6, -4, -10],\n [32, -12, 4, -8],\n [8, -8, 4, 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[[-4, 6, 12, -8],\n [7, -6, 3, 5],\n [-11, 9, -7, -7],\n [-8, 6, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 3, 1, -4],\n [-12, 9, 3, -12],\n [16, -12, -4, 16],\n [-8, 6, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 2, 7, -14],\n [-1, 15, -1, -22],\n [-3, -11, -6, 20],\n [3, -5, 8, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -28, -20, -32],\n [4, -4, 4, -8],\n [-2, 2, -2, 4],\n [4, -28, -20, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 4, -20, 10],\n [16, -20, -8, -26],\n [22, -20, 4, -10],\n [0, -12, -24, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -4, 8, 4],\n [-12, -3, 6, 3],\n [-4, -1, 2, 1],\n [-8, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 6, -3, 12],\n [8, 8, -4, 16],\n [-5, -11, 1, -20],\n [-14, -2, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -5, 4, -4],\n [14, -12, 10, -8],\n [-22, 8, -4, 10],\n [22, 2, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -11, -7, 3],\n [-4, 16, -4, -12],\n [8, -5, 11, 9],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -3, -6, -24],\n [8, 0, -4, -8],\n [-8, 1, 6, 16],\n [8, 1, -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[[0, 2, 8, -4],\n [0, 4, 16, -8],\n [0, 4, 16, -8],\n [0, 4, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, 4, 4, -7],\n [7, -1, -22, 9],\n [-14, 4, 10, -8],\n [-13, 4, 13, -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[[11, 3, 11, -15],\n [-19, -1, -5, 29],\n [-8, 6, -10, 26],\n [3, -2, 6, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -24, -4, -22],\n [5, 7, -3, -4],\n [-4, -2, 2, 4],\n [-13, 25, 3, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 6, -2, -8],\n [-8, -24, 28, -8],\n [4, 12, -14, 4],\n [-4, -12, 14, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 4, 8, 4],\n [-14, 2, 12, 20],\n [-12, 9, 10, -4],\n [-8, -11, -20, -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 4x4 matrix:\n[[11, -5, 13, 5],\n [-4, -2, -2, 2],\n [9, 15, -3, -15],\n [9, 15, -3, -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[[8, -4, -16, 0],\n [-8, 4, 16, 0],\n [-8, 4, 16, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -2, -10, 1],\n [2, 1, 6, 3],\n [3, 1, 7, -1],\n [-6, 4, -6, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -8, 12, -10],\n [-6, 4, 4, -2],\n [9, -17, -2, -2],\n [-6, -7, 8, -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[[-3, 3, -1, -4],\n [-1, 3, 2, -6],\n [-14, 9, -14, -14],\n [10, -6, 10, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -10, 4, 2],\n [-28, 25, 4, -8],\n [-20, 16, -12, -2],\n [-8, 9, 16, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -6, -6, -2],\n [-16, -12, -12, -4],\n [4, 3, 3, 1],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-9, -6, 5, 17],\n [-9, 0, 7, 25],\n [-6, 5, -4, -2],\n [6, -1, -5, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, -10, 22, 3],\n [4, -10, 26, -1],\n [-18, -18, 5, 19],\n [2, 10, -17, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -4, 8, 12],\n [12, -4, 8, 12],\n [6, -2, 4, 6],\n [12, -4, 8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 3, -1, -1],\n [-3, -9, 3, 3],\n [3, 9, -3, -3],\n [1, 3, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 0, -4, 6],\n [-2, 0, -4, 6],\n [0, 0, 0, 0],\n [-4, 0, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[16, 0, 12, -12],\n [-12, 0, -9, 9],\n [-16, 0, -12, 12],\n [-16, 0, -12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 12, -17, -3],\n [8, -8, -2, -8],\n [16, 8, -22, -10],\n [8, 16, -20, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 2, 14, -9],\n [-24, -4, -20, 24],\n [6, -5, 7, -5],\n [16, -8, 15, -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 4x4 matrix:\n[[8, -6, -10, 8],\n [-6, 2, 10, 4],\n [16, -12, -20, 16],\n [0, 3, -3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -4, 8, 3],\n [-21, -6, 0, -4],\n [19, 8, -12, -3],\n [8, -2, 20, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 11, 4, 18],\n [18, -9, -18, -12],\n [-2, 10, 2, 3],\n [-16, 2, 16, 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[[-3, -6, 12, 6],\n [0, 12, -3, -6],\n [4, 12, -17, -10],\n [-1, 14, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, -3, 9, 6],\n [1, 3, -3, 9],\n [7, 3, 6, 27],\n [15, 3, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-28, 8, 12, -28],\n [4, -16, -20, -4],\n [-13, 0, 1, -15],\n [28, -8, -12, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -16, -8, -8],\n [0, -12, -6, -6],\n [0, 0, 0, 0],\n [0, -16, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -1, -13, 20],\n [4, 12, 3, -2],\n [0, 8, -4, 8],\n [4, 0, 9, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[3, 10, -6, 4],\n [7, 10, -16, -14],\n [10, 36, -4, -21],\n [-3, 2, 13, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -9, 10, -5],\n [3, 1, 13, -5],\n [9, 16, -3, -10],\n [4, 12, -12, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [-6, 0, 2, -8],\n [-9, 0, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, 5, -4, -5],\n [-8, -3, 8, 0],\n [-17, -22, -16, 16],\n [2, 19, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -6, -2, -8],\n [0, 12, 4, 16],\n [0, -12, -4, -16],\n [0, -12, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, -4, -10, 2],\n [-6, 3, 7, -1],\n [3, 2, 0, 4],\n [-12, 8, 16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -2, 2, 2],\n [0, 1, -1, -1],\n [0, -2, 2, 2],\n [0, 1, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 25, 4, 15],\n [4, -8, -9, -15],\n [-2, 4, -12, -15],\n [-12, -12, 8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -3, 5, 2],\n [-13, -8, 14, 4],\n [-7, -5, 11, -2],\n [-12, -8, 16, 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[[17, 17, 5, -15],\n [-14, -14, -4, 12],\n [-9, -9, -3, 9],\n [-1, -1, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, 30, -16, -10],\n [3, 0, 9, -3],\n [22, 16, 16, -8],\n [4, 16, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -4, 2, -23],\n [-2, 4, -12, 10],\n [-3, 3, -11, 4],\n [-1, 3, -10, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, -8, -16, 20],\n [-12, -12, -12, 9],\n [8, 5, 4, -2],\n [-12, -15, -16, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -3, -9, -12],\n [-8, 4, 12, 16],\n [8, -4, -12, -16],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [9, 0, -3, 3],\n [-7, 8, 9, -11],\n [0, 12, 10, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 12, 20, -3],\n [-3, 4, 3, -3],\n [9, 6, -12, -5],\n [-18, -10, 9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, 12, -6, -10],\n [-3, -3, 9, 10],\n [2, -6, 10, 12],\n [5, 3, -11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 8, 13, 1],\n [-3, 4, -4, -4],\n [9, -12, 12, 12],\n [-1, -4, -10, -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[[3, 4, -2, -7],\n [12, -8, 4, -4],\n [3, -12, 6, 9],\n [20, -16, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -2, -9, 0],\n [-25, -7, 6, 15],\n [-3, 0, 15, 6],\n [18, 5, -5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, 3, -9],\n [8, 0, 2, -6],\n [-12, 0, -3, 9],\n [8, 0, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 12, -8, 6],\n [-17, -4, -16, -14],\n [-4, -8, 0, -8],\n [9, 0, 10, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[13, -5, 11, 1],\n [9, 6, 16, 16],\n [10, 2, 14, 13],\n [-10, 11, -3, 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 4x4 matrix:\n[[-17, -6, -16, 20],\n [0, 9, -10, 4],\n [12, 0, 16, -16],\n [4, -6, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -22, 4, 22],\n [14, -2, 2, -4],\n [-6, 22, -6, -20],\n [-8, -7, -2, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -11, 10, 4],\n [8, -2, -17, 4],\n [25, -1, -13, -16],\n [20, -4, 5, -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[[5, -4, -1, -11],\n [1, -4, -5, 5],\n [-4, 16, 20, -20],\n [5, -8, -7, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 1, -1, -4],\n [13, -2, 0, 13],\n [10, 6, -14, -4],\n [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[[-9, -9, -9, -3],\n [0, 0, 0, 0],\n [12, 12, 12, 4],\n [6, 6, 6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, 8, 16, -8],\n [-2, -6, -8, 10],\n [22, -6, -20, -2],\n [-18, 6, 18, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, 7, 4, -15],\n [2, -8, 14, -7],\n [-10, 22, -16, -10],\n [-4, 8, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 0, 0, 0],\n [0, -6, 2, -4],\n [0, -12, 4, -8],\n [0, 9, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -13, 15, 0],\n [-10, -13, 15, 0],\n [-8, 4, -12, -12],\n [12, 18, -22, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 2, 4, 13],\n [-14, 8, -12, 10],\n [20, -8, 8, -16],\n [9, -6, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 2, -3, -2],\n [0, -8, 12, 8],\n [0, -4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 2, -4],\n [0, 0, -4, 8],\n [0, 0, 4, -8],\n [0, 0, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, -8, -2, 10],\n [17, -4, -7, -13],\n [-2, -8, -5, 1],\n [12, -16, -14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -10, -2, -8],\n [-2, -4, 2, 2],\n [0, -6, 0, 0],\n [-5, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-12, 12, -4, 16],\n [12, -12, 4, -16],\n [3, -3, 1, -4],\n [-3, 3, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -1, 10, 16],\n [1, 0, -2, -4],\n [-17, 4, -6, 4],\n [3, 0, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 3, 2, -2],\n [-3, -3, -2, 2],\n [3, 3, 2, -2],\n [-6, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, 8, 6, 8],\n [2, -8, -6, -8],\n [-3, 12, 9, 12],\n [1, -4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -11, -10, -1],\n [-10, -13, -25, -4],\n [-2, 15, 1, -10],\n [-5, 11, -6, -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[[-8, -1, 4, -4],\n [0, 3, -12, 12],\n [0, 1, -4, 4],\n [2, 1, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 4, 12, 12],\n [3, 1, 3, 3],\n [6, 2, 6, 6],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 2, 13, 4],\n [-7, -3, -2, 1],\n [-6, 1, 9, 3],\n [-1, -4, -11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [1, -3, 0, 3],\n [2, -6, 0, 6],\n [-1, 3, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 13, -25, -3],\n [-2, -12, 10, 8],\n [-2, -15, 13, 5],\n [3, -19, 10, 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[[20, -13, -6, 8],\n [-14, -6, 10, 2],\n [0, 5, -8, 10],\n [-2, 21, -1, -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 4x4 matrix:\n[[6, -6, 6, 12],\n [-2, 2, -2, -4],\n [6, -6, 6, 12],\n [-8, 8, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-3, 12, 3, 9],\n [-4, 16, 4, 12],\n [-2, 8, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -2, -6, -6],\n [-6, -3, -9, -9],\n [1, 3, 4, 10],\n [12, -4, 8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -22, 12, 22],\n [-9, 2, 1, -3],\n [11, -5, 2, 1],\n [-13, 5, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -7, 14, 14],\n [8, -12, -9, 6],\n [6, -1, 8, -3],\n [-4, 0, -3, 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[[-1, -4, 4, -3],\n [2, 8, -8, 6],\n [3, 12, -12, 9],\n [-3, -12, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 6, 2, 4],\n [12, -12, -12, -8],\n [20, 0, -16, 0],\n [-12, -5, 9, 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[[10, -2, 0, -4],\n [16, -12, 4, -8],\n [2, -7, 3, -2],\n [-19, 6, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 3, 0, 3],\n [-4, 12, 0, 12],\n [2, -6, 0, -6],\n [4, -12, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 5, -6, -16],\n [4, -3, 4, 8],\n [0, 2, 0, -16],\n [-2, 0, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 3, 2, 2],\n [-9, 3, 10, -2],\n [-1, 4, 22, -3],\n [8, -2, -20, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 0, 10, 8],\n [3, -7, -4, -20],\n [1, 7, -6, 12],\n [-7, -9, 22, -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[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, 11, -18, 8],\n [-4, -14, -16, -12],\n [-8, -17, -14, -16],\n [-1, -12, -10, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, 28, 25, 15],\n [5, -4, -7, -3],\n [-2, 13, -5, 3],\n [7, -10, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 1, 5, 3],\n [-1, 4, 9, 6],\n [-5, 7, -8, -3],\n [-3, 5, -2, 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 4x4 matrix:\n[[0, -15, 11, -1],\n [-8, 3, 1, 5],\n [6, -21, 13, -5],\n [20, 0, -8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 3, 0, -1],\n [4, 3, -3, -1],\n [1, 12, 3, -4],\n [4, 15, 1, -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[[-20, 9, -4, -12],\n [13, 14, 3, 16],\n [-13, 11, 5, 4],\n [-1, -26, 2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -3, -4, -2],\n [20, 0, -5, -13],\n [8, -16, -18, -2],\n [-20, 10, 15, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -16, -4, 8],\n [-3, 9, 6, -4],\n [-3, 5, 5, -2],\n [-3, -11, 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 4x4 matrix:\n[[1, -15, -5, -6],\n [-19, 3, -17, 19],\n [13, -3, 12, -14],\n [-4, 20, 20, -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[[12, 6, -6, 0],\n [-16, -8, 8, 0],\n [12, 6, -6, 0],\n [8, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, 12, -20],\n [-14, -8, -16, 18],\n [14, 6, 12, -10],\n [6, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -12, 4, 4],\n [-6, 9, -3, -3],\n [-2, 3, -1, -1],\n [4, -6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-16, -5, -28, 0],\n [-2, -11, 7, 2],\n [5, 4, -10, 4],\n [-7, -5, -22, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 4, -3, -8],\n [2, -8, 6, -6],\n [16, 16, -12, -8],\n [0, -8, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, -6, 6, -15],\n [-2, 2, 0, 1],\n [8, -8, 8, -20],\n [2, -2, -6, 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 4x4 matrix:\n[[-12, 9, -6, 9],\n [12, 3, -12, 6],\n [8, 2, -8, 4],\n [-16, 12, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -4, 0, -12],\n [-18, 20, 6, -6],\n [-11, 12, 12, 0],\n [4, 2, -13, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -10, 6, -13],\n [0, 18, -18, -3],\n [-14, -10, 3, -24],\n [6, 0, 3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, -4, -3, 3],\n [-4, 8, 6, -6],\n [-2, 4, 3, -3],\n [-4, 8, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -15, 7, -5],\n [-15, 14, -2, 8],\n [-20, 11, 21, -1],\n [-16, 12, 16, -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 4x4 matrix:\n[[6, 10, -10, -6],\n [-8, -12, 12, 0],\n [-4, -4, 4, -12],\n [-1, 2, -2, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 12, -8, 16],\n [-5, 0, -7, 8],\n [2, -6, 4, -8],\n [1, 17, -2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -16, 2, -6],\n [5, 8, 9, 13],\n [-6, -20, 10, 0],\n [4, 16, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 2, -11, 5],\n [3, 0, -5, 2],\n [16, -14, -8, -1],\n [11, -10, -5, -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 4x4 matrix:\n[[-8, 6, -10, -10],\n [-6, 15, -11, 3],\n [-4, -3, -3, -11],\n [-4, 15, -9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[14, -6, 14, 5],\n [-10, -13, -10, 9],\n [-16, -1, -16, 0],\n [-4, 19, -4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, 4, -12, 16],\n [12, 3, -9, 12],\n [-12, -3, 9, -12],\n [8, 2, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -2, 13, -12],\n [-3, 2, 8, -14],\n [-8, -2, -10, 6],\n [-2, -6, -7, 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[[10, 19, -8, -1],\n [-22, -13, -2, -1],\n [-2, -5, 17, -8],\n [22, 13, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 12, -12, 4],\n [1, 3, -3, 1],\n [-2, -6, 6, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 4, 4, -1],\n [-2, -6, -6, -4],\n [4, -4, -4, 0],\n [-6, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[14, -8, -7, -18],\n [-2, -16, -19, -30],\n [-8, 4, 3, 6],\n [14, 6, 10, 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, 3, -11, -1],\n [11, 0, -9, -6],\n [15, -12, 7, -14],\n [-16, -21, 29, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, -4, 4, -9],\n [-6, 3, -6, -12],\n [3, -8, -8, 27],\n [-4, -15, -30, 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[[-3, -3, 0, 4],\n [9, 9, 0, -12],\n [0, 0, 0, 0],\n [12, 12, 0, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-23, -21, -10, -15],\n [-4, -12, 36, -4],\n [28, 36, -18, 28],\n [10, 10, 16, 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[[21, -18, 10, -6],\n [-13, 6, -9, -10],\n [12, -36, 17, -24],\n [-19, 32, -17, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, -2, -3, 1],\n [-1, -2, -3, 1],\n [-4, -8, -12, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -11, -11, -4],\n [0, 14, 14, 8],\n [8, 2, 2, -8],\n [-10, 1, 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[[-16, 0, 0, 8],\n [4, 0, 0, -2],\n [-16, 0, 0, 8],\n [-4, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -6, -9, 9],\n [-4, -2, -3, 3],\n [-16, -8, -12, 12],\n [-8, -4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, 0, -16, -8],\n [-6, 0, 8, 4],\n [-9, 0, 12, 6],\n [-12, 0, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 3, 0, -6],\n [-2, -1, 0, 2],\n [-2, -1, 0, 2],\n [2, 1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 5, -2, -4],\n [14, -7, 4, 3],\n [20, -7, 3, 8],\n [-14, 2, 1, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -15, -3, -18],\n [-12, -14, -18, 5],\n [8, 1, 7, -15],\n [-5, -3, -3, 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[[0, 0, 0, 0],\n [-3, 6, -9, -3],\n [-3, 6, -9, -3],\n [2, -4, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -2, 3, 3],\n [11, 10, -5, 1],\n [-10, 4, 4, 2],\n [-12, 8, 18, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 8, 0, 24],\n [-14, 28, -5, -5],\n [-6, 12, 7, 7],\n [7, 28, -12, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -14, -6, 1],\n [-4, -2, 0, 1],\n [5, 0, -2, -2],\n [-12, -16, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 8, -2, -10],\n [20, -4, 1, -10],\n [-4, 4, -1, -2],\n [12, -8, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -2, -8, -2],\n [4, -1, -4, -1],\n [-12, 3, 12, 3],\n [8, -2, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [12, 9, 3, -3],\n [-8, -6, -2, 2],\n [12, 9, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[2, 5, -16, -8],\n [0, 34, 1, -25],\n [-24, -14, -2, 26],\n [-10, 6, -12, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -4, 8, 2],\n [3, -6, 12, 3],\n [1, -2, 4, 1],\n [-2, 4, -8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, -8, 17, -16],\n [9, -6, 9, -7],\n [12, -8, 11, -8],\n [9, -6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, 8, 4, 0],\n [8, -16, -8, 0],\n [6, -12, -6, 0],\n [-8, 16, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 31, 7, -16],\n [6, -11, -2, 11],\n [-5, 6, 1, -7],\n [13, -14, 1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 9, -2, 14],\n [12, 6, 12, -3],\n [8, 6, 7, 6],\n [-4, -1, -7, 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[[26, 23, -21, 12],\n [29, 22, -11, 9],\n [14, 7, 1, -2],\n [4, 7, -9, 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[[-10, -24, -11, -16],\n [-10, -24, -11, -16],\n [20, 4, 6, -4],\n [20, 4, 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 4x4 matrix:\n[[-12, 0, -4, 4],\n [15, 2, 1, -1],\n [15, 4, -3, 3],\n [0, 3, -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[[-4, -6, -12, 24],\n [23, 1, 12, 2],\n [19, 6, 22, -14],\n [28, 4, 20, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, -12, -10, 20],\n [-12, 5, 3, 0],\n [9, 14, 20, -25],\n [8, -8, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[16, 16, 4, -4],\n [0, -16, -4, -20],\n [-12, -8, -2, 8],\n [0, 12, 3, 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[[6, 0, 3, 3],\n [-8, 0, -4, -4],\n [-6, 0, -3, -3],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -10, 4, -4],\n [0, 18, -6, 6],\n [-3, 6, 0, 0],\n [-8, 25, -7, 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 4x4 matrix:\n[[4, 2, -2, -2],\n [2, -1, -2, 8],\n [10, -12, -12, -2],\n [16, -12, -16, -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[[6, -2, 8, -2],\n [12, -4, 16, -4],\n [9, -3, 12, -3],\n [9, -3, 12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 0, 15, 13],\n [-8, -16, 16, 0],\n [-12, -16, 12, -12],\n [6, 16, -18, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, 3, -9],\n [-4, -6, 9, -5],\n [0, 9, -15, 12],\n [20, 9, -10, -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, 4, -4],\n [-2, -1, 4, -4],\n [-4, -2, 8, -8],\n [-8, -4, 16, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 4, -2, 10],\n [16, 16, -8, 12],\n [-4, -4, 2, -10],\n [-4, -4, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 0, -11, -2],\n [17, -11, 0, -6],\n [8, -2, 6, 0],\n [-12, 12, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -5, 11, -8],\n [-8, 20, 4, -12],\n [5, 1, -4, 3],\n [8, -20, -4, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [3, -3, 3, 3],\n [12, -12, 12, 12],\n [-9, 9, -9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, -10, 0, 12],\n [-9, -14, -7, -14],\n [-19, 0, -1, 10],\n [-18, -16, -8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 16, 13, -8],\n [4, -8, 6, -8],\n [6, 3, -21, 21],\n [14, -18, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -1, 6, 4],\n [8, 1, -6, -4],\n [-16, -5, 0, 8],\n [0, 1, 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[[-12, -12, 4, -6],\n [-4, -20, 0, -16],\n [18, 6, -28, -5],\n [0, 12, 4, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 2, 2, -5],\n [-4, -4, -4, 10],\n [0, -4, -2, 3],\n [-2, -10, -6, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-1, 8, 13, 2],\n [21, -3, -3, -12],\n [-25, 2, 1, 14],\n [-9, 6, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 1, 1, 0],\n [-12, -5, -5, 7],\n [26, 18, 18, -22],\n [19, 12, 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[[-6, -5, 3, -11],\n [0, -4, 0, -1],\n [0, -16, 0, -4],\n [2, -5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-25, -15, -27, 20],\n [1, 15, 18, 10],\n [17, -1, 12, -26],\n [-16, -2, -16, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-18, 18, -6, 0],\n [-10, 3, 6, -21],\n [-16, 18, -8, 6],\n [20, -21, 8, -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 4x4 matrix:\n[[-4, 0, -16, -12],\n [4, 0, 16, 12],\n [0, 0, 0, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 3, -9, 14],\n [-7, 21, 9, 2],\n [-4, 12, 12, -8],\n [-2, 6, -3, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[10, 16, -8, -11],\n [-4, -4, 2, 2],\n [6, 12, -6, -9],\n [-2, -6, 3, 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[[3, -2, 3, 1],\n [-1, 1, 0, -1],\n [16, -13, 9, 10],\n [1, 0, 3, -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[[-11, -17, -12, 20],\n [-18, 4, -6, 0],\n [18, -28, -12, 24],\n [15, -16, -12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 4, 10, -3],\n [26, 15, -3, -10],\n [8, -1, -7, 6],\n [-20, -8, 16, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 15, 0, 1],\n [-14, -6, -9, 2],\n [-14, -11, 1, -1],\n [8, 2, 8, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [-9, -3, -3, -3],\n [-6, -2, -2, -2],\n [3, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 12, -3, 12],\n [-14, 20, 3, 0],\n [2, -20, 1, -10],\n [8, -20, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[28, 18, 9, -10],\n [-8, 12, -4, -12],\n [-13, -18, -19, 23],\n [-2, -2, 14, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 16, -16, -16],\n [8, -16, 16, 16],\n [4, -8, 8, 8],\n [6, -12, 12, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -17, -17, -25],\n [-20, 9, 1, 0],\n [2, -20, -11, -12],\n [0, 8, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -6, 2, -2],\n [8, 0, 11, -11],\n [-4, 5, 2, -2],\n [12, -3, 12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, -2, -2, 2],\n [2, -2, -2, 2],\n [1, -1, -1, 1],\n [-3, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -8, -12, -8],\n [-8, 8, 12, 8],\n [-2, 2, 3, 2],\n [6, -6, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 6, 4, -6],\n [0, 0, 0, 0],\n [-9, 9, 6, -9],\n [-6, 6, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 9, -3, 0],\n [1, 3, -1, 0],\n [2, 6, -2, 0],\n [-3, -9, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-7, 17, -2, 1],\n [4, -8, -16, -16],\n [0, -12, 8, -16],\n [14, -26, -20, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -8, 8, 4],\n [1, -2, 2, 1],\n [0, 0, 0, 0],\n [1, -2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 0, 0, -2],\n [-2, 0, 0, -2],\n [1, 0, 0, 1],\n [4, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -22, 12, -9],\n [-6, 20, -9, 12],\n [-6, 4, -9, -12],\n [6, -8, 9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, -3, 1, -3],\n [-1, 3, -1, 3],\n [4, -12, 4, -12],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -11, 11, 11],\n [-11, -5, 8, 10],\n [21, 10, -21, -11],\n [2, 7, 5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -12, 6, -12],\n [8, -8, 4, -8],\n [-4, 4, -2, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -16, -12, -4],\n [0, 12, 9, 3],\n [0, -12, -9, -3],\n [0, 8, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[9, 10, 14, 3],\n [-9, 4, 20, 3],\n [9, 13, 7, 0],\n [-3, 8, 0, -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[[0, 12, -13, 20],\n [0, 20, 4, 24],\n [0, -2, -7, 0],\n [0, 0, 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[[1, -4, 10, 1],\n [2, -14, -6, 30],\n [-25, 22, -12, -21],\n [-9, 18, -8, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, 14, 4, 18],\n [-6, -2, -4, -6],\n [-4, -12, 8, -4],\n [12, 12, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -3, -12, 3],\n [-4, -2, -8, 2],\n [-8, -4, -16, 4],\n [2, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 8, -12, -24],\n [9, -5, 12, 13],\n [-4, 3, 0, -11],\n [13, 4, 21, 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[[3, 3, 9, -9],\n [-4, -4, -12, 12],\n [4, 4, 12, -12],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -12, -4, 16],\n [16, -12, -4, 16],\n [4, -3, -1, 4],\n [-16, 12, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -20, 16, -7],\n [10, 8, -12, 14],\n [7, 8, -10, 10],\n [-4, 4, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, -1, -17, -10],\n [-8, 3, 1, -5],\n [8, -4, -8, 2],\n [28, -11, -7, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, -25, 2, -8],\n [-11, 8, 19, 0],\n [18, -9, -3, -24],\n [-18, -18, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 11, 12, -3],\n [-4, -26, 2, 20],\n [8, 26, 6, -16],\n [7, 23, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, 0, -3],\n [-4, 4, 0, 3],\n [-12, 12, 0, 9],\n [8, -8, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[4, 6, -2, -7],\n [10, 6, -8, -10],\n [-12, -18, 6, 21],\n [-3, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 3, 1, 4],\n [0, 4, 4, 12],\n [-20, -7, 3, 4],\n [4, -5, -7, -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 4x4 matrix:\n[[-4, -2, 2, 8],\n [16, -4, 4, -12],\n [-8, -1, 1, 11],\n [20, 1, -1, -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[[-8, 1, -3, -7],\n [-6, 1, -13, 25],\n [2, 6, 12, -22],\n [-5, -7, -10, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, 3, -12, 13],\n [0, -10, 8, -14],\n [8, -12, 0, -8],\n [-24, 16, 16, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 0, -12, 15],\n [-1, -1, -9, 14],\n [0, 1, 13, -19],\n [11, 3, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -12, 0, 14],\n [0, -9, -10, 8],\n [0, 3, -18, -8],\n [0, 0, -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[[-13, -4, 8, -8],\n [-11, -14, 22, -16],\n [-2, 1, -3, 0],\n [-9, -9, 3, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 2, 6, -2],\n [-8, -2, -6, 2],\n [-4, -1, -3, 1],\n [8, 2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 0, -4, 2],\n [-12, 0, 12, -6],\n [-16, 0, 16, -8],\n [-4, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 16, 12, -16],\n [12, 16, 12, -16],\n [-3, -4, -3, 4],\n [6, 8, 6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, 4, 6, -5],\n [-6, 2, 3, 8],\n [-9, 6, 9, -3],\n [2, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 1, 11, 5],\n [-4, -13, 1, -11],\n [23, -3, -21, -12],\n [-12, 7, 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 4x4 matrix:\n[[-3, 0, -4, -1],\n [0, 0, 0, 0],\n [-12, 0, -16, -4],\n [9, 0, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -14, -15, -3],\n [4, -8, -12, -12],\n [-5, 6, 11, 15],\n [-1, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 2, 3, 0],\n [-4, 2, 3, 0],\n [16, -8, -12, 0],\n [-4, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 2, -4, 0],\n [12, 4, -8, 0],\n [12, 4, -8, 0],\n [3, 1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, 8, 1, 8],\n [8, -11, 11, -20],\n [-2, 4, -5, 8],\n [12, 1, -15, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[16, 8, -16, 0],\n [12, 6, -12, 0],\n [12, 6, -12, 0],\n [16, 8, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -8, -7, -5],\n [-11, 12, 9, 8],\n [3, 4, -7, 6],\n [-11, 12, 9, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -8, 12, 4],\n [-12, -6, -18, 9],\n [7, 16, 3, -14],\n [-10, -10, -12, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 2, -8, -6],\n [-12, 4, -16, -12],\n [6, -2, 8, 6],\n [-9, 3, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 18, -12, 0],\n [15, -15, 15, -3],\n [-16, 4, -16, 8],\n [12, -3, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 16, 12, -16],\n [-18, 8, 6, -4],\n [0, -4, -3, 5],\n [0, 4, 3, -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 4x4 matrix:\n[[-2, 6, -6, 6],\n [-3, 9, -9, 9],\n [2, -6, 6, -6],\n [4, -12, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, -14, -2, 2],\n [10, 9, -3, 6],\n [9, -15, -3, 24],\n [-7, 11, 2, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 8, -2, -7],\n [17, 4, 8, 1],\n [22, -4, 4, 4],\n [1, 20, 10, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 13, -6, -20],\n [-14, -20, 23, -4],\n [2, -14, -5, 20],\n [-10, -3, -7, -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[[1, -2, 0, -5],\n [-15, -6, -12, 19],\n [6, 6, 6, -2],\n [7, 16, -6, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 2, 10, -11],\n [-8, -4, -12, 6],\n [0, 0, 2, -5],\n [-10, -2, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, -2, 4],\n [-1, -19, -11, 2],\n [2, -7, -5, 2],\n [13, -8, -10, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-9, 5, -1, 7],\n [-24, 25, -11, 2],\n [-9, 12, -6, -3],\n [28, -28, 12, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 13, 5, 6],\n [10, -9, -2, -4],\n [2, -10, -4, -6],\n [-18, -8, -1, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, -11, -11, 4],\n [-7, -2, -1, -1],\n [-5, 4, 5, -3],\n [-20, 12, 20, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 2, -4, -6],\n [0, 0, 0, 0],\n [2, -1, 2, 3],\n [4, -2, 4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, -5, 16, 8],\n [22, 8, -4, -8],\n [30, 14, -6, -6],\n [-7, -9, 13, -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[[-10, 34, -16, 28],\n [-10, -18, 4, -12],\n [-14, -15, 3, -10],\n [11, -3, 9, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[1, 6, 10, 17],\n [-36, 12, -12, 4],\n [-7, 14, 12, 13],\n [12, -6, 0, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 6, 5, 6],\n [13, -4, -2, 4],\n [27, -8, 0, 0],\n [28, -16, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-6, -6, 12, -6],\n [-4, -4, 8, -4],\n [-2, -2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 5, -25, 6],\n [-10, -2, 24, -8],\n [-14, 2, 16, -8],\n [14, -8, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, -12, 4, 8],\n [-2, -6, 2, 4],\n [-1, -3, 1, 2],\n [3, 9, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[17, 11, 21, -2],\n [10, 9, 9, -2],\n [-6, 12, -8, 16],\n [-16, -8, -28, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-2, -6, -6, -4],\n [2, 6, 6, 4],\n [-3, -9, -9, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, 6, 9],\n [16, 0, 8, 12],\n [-12, 0, -6, -9],\n [-12, 0, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -8, -14, 16],\n [1, 1, 3, 0],\n [7, -8, -9, 12],\n [4, -5, -12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0],\n [3, 9, -6, 12],\n [0, 0, 0, 0],\n [-4, -12, 8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 7, -3, 12],\n [-8, -6, 12, 2],\n [-10, -6, 16, 6],\n [6, 11, -9, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 3, -12, -6],\n [-2, -1, 4, 2],\n [6, 3, -12, -6],\n [-2, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 4, 8, -8],\n [0, -4, -8, 8],\n [0, -2, -4, 4],\n [0, -4, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -4, -10, 14],\n [-9, 3, -6, 3],\n [-5, 5, 2, -7],\n [2, 1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 6, 12, -6],\n [-16, 8, 16, -8],\n [-4, 2, 4, -2],\n [-4, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, -8, -28, -4],\n [4, 4, 0, 4],\n [15, 11, 13, 12],\n [-11, -15, 19, -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[[10, 40, -2, -16],\n [2, -6, 9, 3],\n [11, 27, -6, -5],\n [0, -10, -7, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, 8, 0, -8],\n [6, -19, -12, 7],\n [4, 2, 8, 6],\n [-8, -4, -16, -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[[0, -8, -2, 0],\n [-3, 12, 6, -6],\n [1, 20, 4, 2],\n [2, 24, 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[[10, -2, 13, 5],\n [-2, 2, 13, 7],\n [38, -22, 8, 2],\n [24, -8, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 16, 7, -26],\n [-1, 3, 3, 0],\n [4, 19, 7, -28],\n [2, 2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -16, -19, -7],\n [12, -11, 4, -7],\n [-8, -12, -16, -9],\n [4, -21, -28, -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[[-4, -3, -3, 17],\n [-19, 23, 2, -2],\n [-4, 10, 4, -12],\n [8, -12, -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[[-15, 6, -11, 2],\n [18, -11, 7, -3],\n [9, -20, 1, -6],\n [-1, 14, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [-12, -4, -8, 12],\n [3, 1, 2, -3],\n [6, 2, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -10, 6, 2],\n [-14, 9, 7, -12],\n [8, 3, -1, 3],\n [5, 7, 17, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -6, -9, -12],\n [7, -2, -1, -4],\n [1, -2, -4, -4],\n [-3, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[28, -24, 3, 7],\n [-12, 9, 0, -12],\n [-32, 28, -4, -4],\n [32, -28, 4, 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[[3, 9, -9, 9],\n [-3, -9, 9, -9],\n [4, 12, -12, 12],\n [-4, -12, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 2, 4, 0],\n [8, -15, -2, 28],\n [26, -21, 7, 28],\n [17, -8, 10, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -11, 10, -12],\n [-5, -3, 0, 4],\n [5, -8, 10, -16],\n [-11, -11, 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[[0, -1, 16, -10],\n [-32, -4, -24, -10],\n [8, 18, 4, -3],\n [0, 2, -12, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 12, 0, 0],\n [8, 16, 0, 0],\n [-8, -16, 0, 0],\n [8, 16, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 2, 23, -11],\n [-29, -12, -18, 6],\n [-1, -12, 24, -15],\n [-7, 8, -22, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, -4, 8, 0],\n [8, -2, -4, 8],\n [4, -2, 4, 0],\n [-8, 0, 16, -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[[4, 20, -7, -8],\n [4, 8, -4, -8],\n [0, -12, 3, 0],\n [6, 4, -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[[-16, -10, 2, -16],\n [20, 17, -10, 20],\n [-20, -11, 0, -20],\n [8, 8, -6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, 14, 14, 1],\n [3, -8, -8, 1],\n [-9, 12, 12, -7],\n [3, 10, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -6, 8, -6],\n [2, -3, 4, -3],\n [4, -6, 8, -6],\n [8, -12, 16, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-25, -2, 18, 12],\n [29, 3, -22, -15],\n [4, 3, -6, 10],\n [-21, -4, 18, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, -3, 0, 14],\n [-12, -15, 11, -14],\n [6, 0, -6, 0],\n [-2, -3, -15, 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 4x4 matrix:\n[[12, 9, -12, -3],\n [5, 5, -7, -1],\n [-2, -4, 6, 0],\n [9, 8, -11, -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[[-2, -7, 2, -6],\n [5, -2, -10, -17],\n [-3, -12, -8, -11],\n [-2, -5, -14, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -6, -2, 6],\n [4, 3, 1, -3],\n [16, 12, 4, -12],\n [-16, -12, -4, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 8, 4, 11],\n [10, -18, 8, -11],\n [-6, 16, -2, 12],\n [-4, 26, 0, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-14, -6, 8, -13],\n [0, -12, 12, 6],\n [-14, -22, 24, -5],\n [-22, -18, 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[[-26, 2, -10, 9],\n [-22, -2, -6, 11],\n [-12, -6, 0, 9],\n [-16, 4, -8, -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[[-24, 14, 11, -10],\n [-10, 2, 0, -3],\n [4, -2, 1, 4],\n [-12, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, -2, -2, -2],\n [4, -8, -8, 6],\n [-10, -2, 7, -2],\n [14, -2, 7, 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[[-4, -10, 4, -4],\n [-8, -21, 3, -8],\n [22, 0, 18, 22],\n [4, -12, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -2, 13, 3],\n [9, 2, 8, -3],\n [-5, -6, 18, 9],\n [-9, -12, 27, 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[[12, -4, 8, -12],\n [6, -2, 4, -6],\n [0, 0, 0, 0],\n [12, -4, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[13, 10, 2, -1],\n [10, -6, -16, -12],\n [3, 10, 11, 6],\n [-6, -18, 21, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 0, -3, 0],\n [16, -16, -4, 16],\n [-10, 4, 7, 4],\n [-4, 16, 14, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, -5, -4, -4],\n [13, 2, 10, -1],\n [2, -22, 4, -6],\n [-8, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -9, -10, -1],\n [-3, -9, 12, 0],\n [-6, 0, 10, 1],\n [2, -12, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, -8, -4, -6],\n [22, 14, 14, 8],\n [12, 12, 6, 9],\n [2, -6, 4, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 1, 3, 1],\n [-12, -4, -12, -4],\n [12, 4, 12, 4],\n [-12, -4, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 12, 3, -12],\n [-17, -6, -13, -8],\n [25, 7, 19, 13],\n [-14, -3, -11, -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[[-1, -3, -2, -2],\n [-3, -9, -6, -6],\n [1, 3, 2, 2],\n [-2, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -6, 6, 3],\n [-1, -2, 2, 1],\n [0, 0, 0, 0],\n [-2, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 6, 5, -2],\n [8, 8, 6, -4],\n [-6, -7, -5, 4],\n [-4, -6, -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[[-19, 9, 2, 1],\n [3, -7, -13, 7],\n [16, -18, -14, 10],\n [19, -11, -4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, 1, 8, -10],\n [-3, 8, -3, -8],\n [0, 0, -7, 7],\n [8, -14, 2, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-12, 7, 5, 9],\n [14, -6, -4, -6],\n [-18, 13, 5, 6],\n [-8, 12, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 16, -12, 16],\n [3, 12, -9, 12],\n [1, 4, -3, 4],\n [-4, -16, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -6, -8, 14],\n [-6, -4, -6, 6],\n [13, 7, 11, -8],\n [-16, -4, -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[[16, 8, 8, -12],\n [12, 6, 6, -9],\n [0, 0, 0, 0],\n [-16, -8, -8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 8, -12, -4],\n [-6, 12, -8, -10],\n [-12, 14, -1, -15],\n [15, -16, -1, 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 4x4 matrix:\n[[-14, 8, -19, -4],\n [10, -16, -2, -6],\n [-24, 20, -20, 0],\n [-28, 5, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, -9, 18, 1],\n [0, -3, 6, -13],\n [15, 1, -2, -3],\n [-12, -3, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, -10, 20, -14],\n [-10, -4, 8, 12],\n [4, -22, 28, -1],\n [1, 11, -16, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -8, 16, 4],\n [2, -4, 8, 2],\n [-3, 6, -12, -3],\n [-1, 2, -4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 10, -6, -16],\n [-10, -5, 3, 8],\n [-1, -11, -6, 12],\n [-6, -6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 1, 4, -1],\n [3, 3, 12, -3],\n [2, 2, 8, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[12, 12, 0, -6],\n [0, 0, 0, 0],\n [4, 4, 0, -2],\n [4, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 6, 0, 2],\n [-6, 9, 0, 3],\n [4, -6, 0, -2],\n [-8, 12, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 6, 2, 4],\n [14, -13, 5, 2],\n [-19, 18, -8, -4],\n [9, -8, 2, 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[[3, 6, -12, 12],\n [0, 0, 0, 0],\n [3, 6, -12, 12],\n [-3, -6, 12, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -6, -11, 5],\n [-8, -17, 0, 11],\n [0, 5, -3, -4],\n [4, 5, 1, -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 4x4 matrix:\n[[0, 0, 0, 0],\n [0, -9, 6, 9],\n [0, 12, -8, -12],\n [0, -6, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-10, -12, 19, 3],\n [-5, 12, -3, 10],\n [2, 28, -3, 25],\n [0, 12, -23, -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[[-4, -4, 6, 8],\n [-10, -10, 4, -2],\n [-6, -6, 6, 6],\n [-12, -12, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 9, 12, 9],\n [0, 0, 0, 0],\n [0, -6, -8, -6],\n [0, 9, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-23, -3, -11, 22],\n [-8, 3, -11, 7],\n [10, 11, -15, 5],\n [3, 8, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-4, 16, -16, -12],\n [0, 0, 0, 0],\n [-2, 8, -8, -6],\n [2, -8, 8, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -6, -11, -13],\n [-3, 0, -23, -19],\n [9, 0, 5, 1],\n [-10, -8, -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[[-8, -10, -10, -6],\n [0, 22, 2, 6],\n [14, -5, 4, 5],\n [-6, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, 0, 6],\n [-12, 0, 0, -6],\n [-8, 0, 0, -4],\n [16, 0, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-8, 4, -8, -8],\n [-8, 4, -8, -8],\n [8, -4, 8, 8],\n [-4, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-15, -6, 11, 23],\n [-17, -8, -1, 17],\n [-11, -3, 12, 19],\n [-7, -9, 18, 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[[10, 12, 22, -4],\n [17, 7, 4, -2],\n [6, 5, 7, 0],\n [-8, -6, -2, -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[[-4, -16, -4, -16],\n [3, -1, 0, -5],\n [-17, -16, -5, 0],\n [-5, -7, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-20, 4, 0, 2],\n [-6, 4, 20, -5],\n [20, 4, 16, 0],\n [8, 4, 24, -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[[0, 3, 5, -18],\n [11, -5, -1, 8],\n [3, 0, 2, -6],\n [-3, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -8, 16, 8],\n [-6, 4, -8, -4],\n [9, -6, 12, 6],\n [-12, 8, -16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -12, 0, -8],\n [-2, 11, 0, 9],\n [8, 7, 0, -2],\n [-6, -15, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -8, 0, 2],\n [-2, 4, 0, -1],\n [2, -4, 0, 1],\n [6, -12, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 2, 3, -2],\n [-3, -6, -9, 6],\n [-3, -6, -9, 6],\n [-2, -4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 8, 8, 0],\n [2, -4, -4, 0],\n [-8, 16, 16, 0],\n [-6, 12, 12, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 1, 4, 3],\n [0, -4, -16, -12],\n [0, 1, 4, 3],\n [0, 4, 16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -10, -8, -10],\n [6, -4, -25, 5],\n [-8, 17, 17, 12],\n [6, -12, -2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 14, -4, 2],\n [7, -7, 0, 6],\n [-12, 12, -13, 3],\n [9, -9, 1, 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 4x4 matrix:\n[[0, 0, 0, 0],\n [-9, 6, 0, 3],\n [12, -8, 0, -4],\n [-6, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[7, -20, 3, 18],\n [0, 1, 3, -5],\n [-8, 5, 15, 7],\n [2, -12, 6, 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[[8, 12, -12, -4],\n [-4, -6, 6, 2],\n [8, 12, -12, -4],\n [4, 6, -6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 3, 5, 1],\n [16, -2, 11, 0],\n [-15, 4, -8, 4],\n [10, -7, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -1, 2, -1],\n [0, 0, 0, 0],\n [-3, -1, 2, -1],\n [12, 4, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 4, 0, 2],\n [-1, -6, -5, -3],\n [16, -4, 0, -2],\n [5, 10, 9, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 4, 1, 4],\n [-9, 10, -8, 2],\n [-7, 12, -11, 5],\n [-2, 12, -1, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -21, -4, -21],\n [-7, -8, -3, -8],\n [-8, -12, -4, -12],\n [-12, -13, 1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 20, 16, -20],\n [5, -1, -5, 4],\n [3, 12, 11, -13],\n [16, 4, -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[[-12, -19, -9, -7],\n [3, 1, -13, -3],\n [-10, -10, -14, -6],\n [-7, 6, 10, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -8, 3, 14],\n [16, 4, -12, 0],\n [-3, -2, 3, 2],\n [-5, -10, 9, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 0, 0, 0],\n [0, -1, -4, 4],\n [0, 0, 0, 0],\n [0, 2, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[2, 7, -5, -16],\n [0, -4, 6, 8],\n [-2, 5, -13, -8],\n [0, 8, -12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, 15, 7, -11],\n [1, -14, -10, -15],\n [-7, -12, 2, 19],\n [-2, -2, 0, -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 4x4 matrix:\n[[-1, 19, 22, 2],\n [5, -18, -26, 4],\n [-3, -9, -6, -6],\n [-17, 18, 14, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 10, 4, -23],\n [-16, 4, -9, -9],\n [12, 2, 4, -3],\n [4, 2, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 9, 6, 6],\n [0, 0, 0, 0],\n [-16, 12, 8, 8],\n [8, -6, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 9, 18, -9],\n [-4, 7, 16, -10],\n [1, -1, -2, 1],\n [4, 11, 20, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -24, -2, -8],\n [8, -24, -4, -4],\n [12, 8, -2, 3],\n [9, 11, 10, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, 6, -12, -6],\n [9, 6, -12, -6],\n [3, 2, -4, -2],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 2, 2, 4],\n [0, 0, 0, 0],\n [-12, -3, -3, -6],\n [-8, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -5, -1, -7],\n [7, -4, 8, 12],\n [-9, -2, -6, -14],\n [7, 1, 5, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[11, 4, 6, -7],\n [-6, -9, -6, -3],\n [2, 8, 4, 6],\n [-4, -6, -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 4x4 matrix:\n[[-1, -32, -1, 22],\n [-4, -40, 0, 24],\n [2, 14, 3, -5],\n [11, 22, -4, -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 4x4 matrix:\n[[-5, 6, -9, -10],\n [-10, 3, -7, -10],\n [4, 6, -6, -4],\n [-8, -12, 12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 1, -4, 4],\n [-8, -2, 8, -8],\n [-8, -2, -24, -8],\n [12, 3, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-4, 12, 0, 4],\n [0, 0, 0, 0],\n [-4, 12, 0, 4],\n [-4, 12, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-2, 6, 2, -8],\n [-9, 3, -15, 12],\n [2, -10, -6, 16],\n [1, -7, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, -3, 4, -1],\n [3, -3, 4, -1],\n [12, -12, 16, -4],\n [3, -3, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -10, 8, 0],\n [9, 11, 0, 16],\n [-9, -11, 0, -16],\n [6, 9, -5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 0, -3, 3],\n [6, 0, 3, -3],\n [0, 0, 0, 0],\n [2, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -1, -4, 3],\n [-4, 1, 4, -3],\n [-8, 7, 10, -9],\n [0, 10, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 9, 9, 3],\n [-2, -6, -6, -2],\n [-3, -9, -9, -3],\n [-4, -12, -12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -4, -16, -8],\n [3, 3, 12, 6],\n [2, 2, 8, 4],\n [3, 3, 12, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 1, 1, -4],\n [2, -2, -2, 8],\n [1, 1, 1, -4],\n [3, -1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 1, -7, 1],\n [6, -6, -6, 2],\n [-18, 18, 24, -7],\n [11, -11, -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[[4, 0, -12, 12],\n [1, 0, -3, 3],\n [3, 0, -9, 9],\n [-3, 0, 9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 8, -2, 10],\n [-5, 6, 6, 10],\n [-16, -10, 8, 16],\n [5, 14, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -8, 4, -4],\n [0, 0, 0, 0],\n [6, 6, -3, 3],\n [2, 2, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[32, 5, 28, 30],\n [9, 14, 10, 10],\n [12, -20, 8, 8],\n [-17, 9, -14, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, 20, 12, 0],\n [12, -9, -12, -6],\n [-8, 13, 10, 2],\n [10, -11, -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[[-3, -2, 6, 7],\n [12, -24, -8, 4],\n [-12, 8, 16, 12],\n [0, -8, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, 12, -12, -16],\n [13, -12, 14, 14],\n [-4, 3, -2, -5],\n [13, -12, 14, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, -1, -1, -4],\n [4, 2, 2, 8],\n [-4, -2, -2, -8],\n [-8, -4, -4, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 3, 6, 9],\n [-4, -4, -3, 0],\n [21, 9, 3, -9],\n [19, 15, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -2, -22, 11],\n [-6, 8, -2, 7],\n [-4, 12, -3, 13],\n [4, -6, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -3, -4, 4],\n [0, 0, 0, 0],\n [6, 6, 8, -8],\n [9, 9, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[4, 2, 2, 0],\n [6, 3, 3, 0],\n [8, 4, 4, 0],\n [2, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, 16, 17, -12],\n [-12, 0, 2, 0],\n [-8, 0, 0, 0],\n [-11, 8, 11, -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[[11, 21, -9, -21],\n [-4, -3, 11, 3],\n [-7, -15, 3, 15],\n [4, 12, 4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, 0, 9, -3],\n [4, 0, 3, -1],\n [0, 0, 0, 0],\n [-8, 0, -6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, 1, -4, 0],\n [-3, -1, 0, 4],\n [4, 0, 4, -4],\n [-5, -3, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 2, -3, -2],\n [0, -4, 6, 4],\n [0, 6, -9, -6],\n [0, 8, -12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -2, -6, -8],\n [-16, -4, 10, 28],\n [-5, 3, 1, -4],\n [-15, -3, 9, 24]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [4, 8, -16, 4],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-3, 8, 4, 0],\n [-6, -14, 8, 12],\n [9, 6, -12, -12],\n [12, 3, -16, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[8, 2, 6, 6],\n [12, 3, 9, 9],\n [-16, -4, -12, -12],\n [-4, -1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -20, 16, -24],\n [0, -3, 3, -6],\n [-3, 8, -5, 4],\n [4, -12, 8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, 17, 0, -18],\n [13, 11, -10, -14],\n [16, 12, -14, -16],\n [-16, -12, 14, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -4, -3, -4],\n [12, -12, -9, -12],\n [-16, 16, 12, 16],\n [12, -12, -9, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -9, -5, -13],\n [3, -29, -11, -36],\n [7, -19, -7, -20],\n [-3, 13, 5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -12, 9, 9],\n [5, -18, -9, -3],\n [24, 2, -9, -17],\n [2, -2, 12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[6, 12, 0, -9],\n [-4, -8, 0, 6],\n [8, 16, 0, -12],\n [6, 12, 0, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, 1, 3, 2],\n [-6, -7, -17, -10],\n [3, 3, 7, 4],\n [6, 3, 5, 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, 0, -24, 20],\n [-6, 6, -9, 3],\n [-8, -4, -12, 13],\n [12, 0, 18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -6, 2, -20],\n [-11, -8, 7, 8],\n [-4, -6, 2, 27],\n [13, 16, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, -7, -8, -4],\n [5, 7, 8, 4],\n [2, -6, -10, -16],\n [5, 11, 14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[12, -19, -2, -21],\n [8, -2, -4, -6],\n [-20, 6, 11, 11],\n [20, -6, -11, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-4, 1, 1, 4],\n [-16, 4, 4, 16],\n [8, -2, -2, -8],\n [-8, 2, 2, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 2, -1, -1],\n [0, -4, 2, 2],\n [0, 8, -4, -4],\n [0, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, -5, -2, -2],\n [-6, 3, 12, -6],\n [-6, 3, -12, 10],\n [-4, 2, 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[[8, -6, 0, -2],\n [-8, 6, 0, 2],\n [-8, 6, 0, 2],\n [8, -6, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -18, -9, 15],\n [9, -12, -9, 0],\n [-13, 7, 8, 9],\n [16, 5, -1, -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[[18, -3, 8, 13],\n [0, 12, -14, 20],\n [-16, 0, -4, -16],\n [14, 3, 0, 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[[4, -14, -14, 7],\n [0, 12, 12, -6],\n [8, -4, -4, 2],\n [0, 12, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 5, -16, 19],\n [-13, -5, 7, -3],\n [-21, -7, -1, 13],\n [-13, -2, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[16, -16, 0, 8],\n [8, -8, 0, 4],\n [-16, 12, -4, -4],\n [-12, 8, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, -2, -4, -2],\n [-3, -6, -12, -6],\n [3, 6, 12, 6],\n [-1, -2, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -16, 12, 6],\n [-13, 4, -16, -21],\n [10, -8, 16, 18],\n [-16, 0, -16, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -8, -10, -3],\n [-7, 2, -3, -1],\n [-15, -18, -18, -16],\n [19, 4, 15, 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[[2, 8, 8, 0],\n [-1, -4, -4, 0],\n [3, 12, 12, 0],\n [-4, -16, -16, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -16, 12, 25],\n [-2, 2, 0, -2],\n [9, -6, 9, 0],\n [-11, 9, -6, -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[[-1, 1, 8, -19],\n [13, -5, -2, 11],\n [0, 8, 10, -20],\n [20, 44, 12, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[6, 2, 2, -7],\n [-20, -10, -7, 24],\n [-24, -8, -8, 28],\n [10, 0, 3, -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[[0, 0, 0, 0],\n [0, 0, 0, 0],\n [2, -2, -8, 8],\n [-3, 3, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -6, -3, -6],\n [0, 4, 2, 4],\n [0, 8, 4, 8],\n [0, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -13, 14, -15],\n [1, -18, -5, -10],\n [-8, 44, 4, 28],\n [5, 1, 5, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, -10, -8, -24],\n [8, -1, 10, 4],\n [9, -5, -1, -11],\n [3, 10, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}