{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-5, -13, 0, 26],\n [-5, -3, -5, 12],\n [1, 7, -2, -10],\n [-15, -11, -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[[-20, 2, 2, 8],\n [14, -3, -2, -3],\n [0, -8, -3, 13],\n [-20, -6, -1, 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, 3, -9, 0],\n [-10, 2, -21, -10],\n [-14, -8, 3, -14],\n [-16, -7, -3, -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[[16, 10, 8, -1],\n [2, -16, 8, 17],\n [1, -11, -6, 3],\n [28, -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[[19, 21, 31, 22],\n [-14, -14, -26, -12],\n [-4, 5, -1, 18],\n [-25, -19, -25, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 21, -13, 0],\n [-5, 14, 2, 0],\n [6, -20, -6, -3],\n [8, -19, 15, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, -6, -13, 3],\n [-4, -2, -8, 4],\n [1, 5, 9, -1],\n [-17, 5, -13, 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, 8, 22, 0],\n [-13, -13, -6, 0],\n [-5, -5, -18, 0],\n [9, 9, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -2, 9, -18],\n [-17, 4, 11, -34],\n [10, -10, 9, -2],\n [-13, 4, -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[[-9, 8, 5, 8],\n [-11, 16, -1, 12],\n [-3, 12, -9, 6],\n [16, -8, -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[[-13, 3, 7, -7],\n [5, -3, -4, 10],\n [-19, 1, 2, -12],\n [-14, -7, -12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -4, 2, 8],\n [3, -1, 0, 8],\n [-6, 4, -2, -8],\n [9, -8, 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[[14, 13, -1, 8],\n [-5, 14, -12, -12],\n [2, -13, 17, 4],\n [17, -10, 28, 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[[-15, -21, -3, 9],\n [11, 14, 0, -2],\n [-10, -7, 9, -17],\n [20, 20, -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[[19, 25, 22, 24],\n [-4, 4, 0, 10],\n [7, 13, 10, 15],\n [-5, -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[[-2, -3, -3, -2],\n [4, -24, -4, -12],\n [-17, -3, -18, -5],\n [-8, -12, -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[[17, -8, -8, 8],\n [19, -8, -16, 0],\n [-8, 6, -13, -25],\n [-17, 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[[-5, -8, -10, 8],\n [5, -6, 5, -9],\n [-12, -15, 8, -1],\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[[9, 0, -21, -3],\n [-3, -6, 2, -4],\n [-3, -12, -3, -9],\n [-4, 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[[-11, -15, -8, -5],\n [-14, 16, -16, 2],\n [3, 11, 2, 5],\n [4, 23, 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[[-1, 19, -14, -4],\n [-3, 9, -12, -6],\n [20, -1, 2, 16],\n [-7, -5, 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, 9, 4, 10],\n [4, 0, 1, -2],\n [4, -8, -3, -10],\n [2, 1, 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[[-4, 4, -4, 8],\n [2, 2, -2, 8],\n [2, 2, 8, -12],\n [-10, -18, -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[[3, 9, 14, 5],\n [-6, -10, -18, -4],\n [1, -6, -9, 1],\n [-11, 2, -10, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-2, 2, -8, 28],\n [-17, 1, -21, 10],\n [4, 8, -2, 0],\n [-12, 10, -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[[-19, -10, -1, 14],\n [-9, 6, 9, 6],\n [5, -9, -10, -3],\n [-16, 5, 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, -20, 12, 8],\n [3, 7, 1, -10],\n [6, 8, 2, -16],\n [-9, 26, -15, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -1, -5, 0],\n [16, -12, 4, 0],\n [-16, 11, -1, 0],\n [0, 1, -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[[13, -12, -6, 10],\n [2, -12, -22, 10],\n [-4, 6, 6, 2],\n [-3, 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[[-6, -4, -18, -6],\n [-7, 3, 15, -12],\n [-2, 21, 3, 23],\n [0, 13, 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[[11, 1, -8, 14],\n [14, -5, -4, 13],\n [22, 2, -16, 28],\n [-5, -20, 16, -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, 10, 6, -4],\n [-18, 18, 0, 0],\n [3, -2, -3, 2],\n [-18, 20, -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, -4, -8, -4],\n [14, -3, 2, -1],\n [-19, 4, -4, 1],\n [-7, 1, -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[[-12, -7, 13, -8],\n [0, 2, 4, -2],\n [9, 10, -13, 8],\n [9, -1, -18, 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, -5, -2, 3],\n [0, 9, -3, -3],\n [-3, -13, 8, 3],\n [3, -11, 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, 3, 12, 3],\n [12, -4, 12, 0],\n [4, -2, -1, -1],\n [-7, 3, -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, 0, -8, 6],\n [4, 16, -8, 16],\n [5, -12, -10, 0],\n [7, -4, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -14, 12, 16],\n [2, -4, 6, 8],\n [-2, -6, 6, 8],\n [-2, -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[[3, 12, 12, -13],\n [9, 13, 6, 0],\n [6, -13, -16, 7],\n [9, 10, 11, -27]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-7, -14, -7, 11],\n [-5, -10, -5, 5],\n [6, 12, 6, -13],\n [6, 12, 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[[-5, 1, 1, -5],\n [-7, 6, 1, -10],\n [4, 8, 2, -8],\n [13, -4, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-8, -8, -12, 0],\n [-2, 12, -10, 14],\n [2, 12, -2, 10],\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[[-20, -3, -13, 0],\n [6, -1, 13, -7],\n [-8, 8, -8, 0],\n [-40, -4, -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[[9, -5, 6, 11],\n [-4, -13, -23, -7],\n [6, -11, -15, 7],\n [2, -2, 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[[2, -10, 12, 5],\n [-22, 15, 5, -27],\n [-4, 8, -3, -4],\n [-10, 7, 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[[-1, 1, 0, 3],\n [1, -1, 0, -3],\n [4, -2, 0, -2],\n [1, 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[[2, -3, 3, -4],\n [-8, -16, 24, -20],\n [12, -4, 0, -6],\n [6, -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[[-3, -8, 14, -9],\n [-14, 18, -7, 1],\n [3, -12, 16, -5],\n [4, -8, -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[[-14, 7, -18, -12],\n [-10, 1, -14, -12],\n [-12, 4, -16, -12],\n [8, -5, 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[[3, -6, 8, 4],\n [3, -2, 2, 4],\n [12, 16, -28, 16],\n [0, 8, -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[[4, 0, 9, -4],\n [6, 12, 1, 6],\n [-10, -22, -2, -12],\n [8, 2, 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[[12, -15, 8, 1],\n [-12, 18, -10, 1],\n [-16, 13, -6, -6],\n [4, -13, 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, 3, 0, 12],\n [-8, 1, 10, 4],\n [-4, 3, 0, 12],\n [0, -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[[0, 10, -6, -8],\n [-12, -10, 6, -16],\n [-6, 7, -3, -20],\n [0, 0, -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[[-8, -8, 8, 2],\n [2, -2, -12, 7],\n [-4, -14, -12, 20],\n [-26, -22, 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[[-7, -6, -3, 0],\n [2, 9, -9, -3],\n [1, -2, 1, 16],\n [6, 0, 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[[4, -3, -11, -5],\n [-8, -1, -6, -4],\n [-12, 0, -3, -3],\n [-8, -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[[-3, -7, 10, -8],\n [6, 2, -12, -10],\n [15, -4, -24, -10],\n [3, -5, -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, -8, 0, 6],\n [-9, 24, 0, 6],\n [-16, 28, -3, 1],\n [-7, 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[[16, 8, 19, 1],\n [8, 10, 11, -1],\n [16, -12, 14, 6],\n [-12, 19, -8, -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, 0, -4, 10],\n [-17, 10, 2, 10],\n [4, 8, 6, -3],\n [-4, -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[[-5, 9, 8, -7],\n [8, -4, -3, 13],\n [4, 16, -6, 12],\n [0, -12, 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[[2, 6, -8, -4],\n [0, 4, -22, 0],\n [0, -2, 11, 0],\n [6, 12, 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[[-2, 9, 3, 12],\n [4, -12, -2, -16],\n [-6, -12, -17, -16],\n [2, 9, 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, 12, 0, -12],\n [-17, 7, 8, -17],\n [-7, 2, 4, -7],\n [18, -3, -12, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, 18, 9, -4],\n [10, -8, -14, 4],\n [9, 17, 5, -3],\n [4, -1, -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[[17, -13, 28, 3],\n [-14, 10, -16, -8],\n [6, 7, -8, -5],\n [17, -16, 16, 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[[0, -2, 2, 8],\n [12, -7, 7, -14],\n [10, -9, 9, 1],\n [-6, 5, -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[[-11, 20, 23, -3],\n [-2, 7, 5, 2],\n [2, 8, 2, 6],\n [5, -6, -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[[-8, -12, -8, -12],\n [6, 9, 6, 9],\n [-8, -8, -2, -5],\n [10, -1, -14, -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, 2, -5, 2],\n [-3, -5, -4, 6],\n [5, 7, 8, -10],\n [2, 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[[11, 8, 9, 9],\n [18, 6, 21, 18],\n [-4, 11, -15, -12],\n [-20, -13, -18, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-13, -9, -23, 12],\n [28, -4, 24, 24],\n [-20, 2, -19, -14],\n [-19, 10, -18, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 16, 0, -16],\n [8, 0, 12, -8],\n [-6, 0, -9, 6],\n [2, 8, -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, -2, -3, -3],\n [-6, -7, 3, 6],\n [6, 6, 0, -2],\n [3, 0, 9, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, -10, 7, 17],\n [13, -11, -13, 11],\n [-7, 14, 0, -20],\n [7, -21, 4, 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[[-10, -10, 14, -13],\n [24, 8, -19, 14],\n [26, 2, -10, 5],\n [-24, 2, 20, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, -12, 12, 3],\n [7, -4, 25, -10],\n [-3, 8, -15, 19],\n [-6, 0, -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[[-6, 4, 16, -2],\n [-7, 1, 12, -2],\n [-7, -10, -8, -1],\n [-8, 9, 28, -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, 12, -12],\n [0, 4, 0, 4],\n [-12, 3, -12, 6],\n [-8, 8, -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[[-1, -4, -1, 3],\n [4, 12, 6, -12],\n [2, 12, 0, -6],\n [-3, 16, -17, 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, 16, 5, -6],\n [-3, 5, 9, -5],\n [2, 0, 14, -10],\n [4, -35, 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[[6, 0, -5, 2],\n [12, -6, 0, -14],\n [2, 14, 3, -4],\n [-2, 10, 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[[14, -20, 8, -12],\n [-9, 14, -18, 2],\n [11, -18, 4, -10],\n [-14, -4, -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[[-8, 5, 15, -4],\n [3, -2, -4, 2],\n [3, -2, -4, 2],\n [-13, 9, 13, -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, 9, 20, 20],\n [-6, -1, 22, 17],\n [-6, 2, -18, -8],\n [2, -3, -22, -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, 2, 13, -2],\n [2, 4, 2, -4],\n [0, -2, 2, 2],\n [-6, -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[[4, -16, 12, 16],\n [0, 0, 0, 0],\n [10, 17, -15, 4],\n [6, 14, -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[[12, 4, -22, 9],\n [12, 4, -18, 3],\n [9, 3, -12, 0],\n [-3, -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[[5, 8, 3, -4],\n [-7, -12, 3, -4],\n [7, 12, -3, 4],\n [5, 8, 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[[0, -2, -2, -2],\n [-5, -2, -6, 13],\n [8, -9, 24, -14],\n [2, -3, 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[[-13, -33, 27, -11],\n [16, 21, -13, 3],\n [-3, -15, 13, -1],\n [13, 6, 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[[-24, 10, -6, 14],\n [4, -2, 3, -4],\n [-16, 5, 6, 1],\n [28, -10, -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[[0, -14, 6, -6],\n [-2, 18, -9, 8],\n [-10, 22, -16, 10],\n [13, 10, 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[[26, -17, 11, 16],\n [2, -4, 10, -2],\n [9, -8, 6, -2],\n [-19, 13, -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[[6, 6, -3, -3],\n [0, 20, -6, -14],\n [-7, 8, -1, -7],\n [-6, 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[[-3, 2, 5, 0],\n [-7, 10, -7, 0],\n [-2, 4, -6, 0],\n [-3, 6, -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[[7, -6, 4, -15],\n [-1, 0, 0, 3],\n [0, 6, -8, -6],\n [2, -6, 8, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-11, -19, -2, 4],\n [1, 3, -3, -8],\n [-7, -13, 1, 8],\n [-10, -18, 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[[-14, -4, 6, -12],\n [-11, -6, 9, -10],\n [12, -8, 12, 8],\n [-14, -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, 4, 9, -6],\n [0, 4, -3, 2],\n [-12, 22, 8, 0],\n [-10, 13, 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, 6, -8, -6],\n [-4, 2, -20, 6],\n [-3, 9, -25, -3],\n [-1, -10, 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[[-14, 16, -6, -4],\n [-19, 6, -6, -14],\n [-1, 14, 6, 14],\n [8, -4, 15, 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, -19, -12, 4],\n [12, 0, -9, 22],\n [0, 8, 6, -4],\n [-12, -28, -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[[3, -4, -5, -2],\n [-12, 8, 4, -24],\n [12, 1, 14, 25],\n [-6, 3, 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[[-18, -2, 22, -7],\n [0, -2, 4, 11],\n [-12, -20, 10, 14],\n [4, 2, -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, -13, -18, -17],\n [11, 25, 9, 1],\n [3, -18, -4, -15],\n [25, -4, -25, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[0, -2, -2, -3],\n [10, -2, -12, 12],\n [8, -2, -10, 9],\n [10, -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[[-20, 1, 3, -18],\n [8, 1, 15, 4],\n [-8, -1, -19, -2],\n [20, 2, 18, 18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, 18, -12, 14],\n [10, -4, -4, -2],\n [14, -8, -8, 2],\n [-11, 17, -10, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 19, 0, 0],\n [25, 6, 36, -2],\n [-13, 6, -10, -12],\n [3, -9, 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[[-3, 2, -3, -2],\n [-8, 4, -12, -3],\n [3, -2, 3, 2],\n [1, 2, 9, -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, 0, 0, -16],\n [-12, 3, 4, -13],\n [8, -12, -16, 12],\n [16, 3, 4, 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, 7, -8, -23],\n [0, -22, 8, 8],\n [-8, -24, 0, -20],\n [5, -5, 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, 6, 6, -4],\n [-2, -2, 6, -8],\n [6, -6, -18, 18],\n [1, 9, -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[[-4, 8, 3, 6],\n [4, -8, -3, -6],\n [-1, 6, 0, 4],\n [8, 0, -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[[-3, 9, 2, 20],\n [-4, 6, 8, -16],\n [2, 2, -6, 24],\n [6, -12, -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[[2, 2, 9, -4],\n [4, -4, 1, -2],\n [6, -10, -7, 0],\n [4, -4, 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[[-16, 8, -24, 32],\n [13, -11, 21, -26],\n [-13, 11, -19, 22],\n [8, 14, -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, 1, 0, 0],\n [-12, 0, -3, -6],\n [2, -1, 2, 4],\n [0, 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[[3, -16, -5, 6],\n [-6, -10, -2, -12],\n [3, -16, -5, 6],\n [-5, -13, -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[[2, 8, 4, 0],\n [-21, -4, -16, 14],\n [9, 0, 4, -4],\n [8, -4, 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, -7, -6, -4],\n [1, 1, 3, 0],\n [1, -1, 12, -4],\n [5, 11, -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[[16, 12, 5, -16],\n [-16, -32, 0, -4],\n [-4, 0, -2, 7],\n [4, 20, -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[[12, -4, 2, 3],\n [-20, 8, -2, -4],\n [24, -12, 0, 3],\n [16, -12, -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[[-2, 2, -6, 0],\n [-19, 3, 6, 9],\n [12, 2, -12, -6],\n [9, 5, -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[[2, -1, -20, 4],\n [1, 10, 18, -5],\n [-3, -15, 14, -3],\n [7, 19, -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[[-12, 12, 0, 3],\n [-3, 3, 1, -3],\n [-17, 16, 2, 5],\n [4, -5, -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[[-2, 7, 12, 8],\n [3, -6, -12, -9],\n [3, -9, -16, -11],\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[[-6, -9, 9, 3],\n [-6, -10, 11, 1],\n [20, 11, 20, 12],\n [-2, 0, -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[[0, 16, 4, 8],\n [16, 10, 12, -10],\n [-16, -4, -14, 16],\n [12, -12, -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[[-10, -2, -12, 14],\n [-7, 4, -5, -2],\n [5, 1, 8, -3],\n [-1, 7, 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[[-6, -9, -3, -7],\n [-9, -7, -4, -16],\n [-24, -9, 11, -9],\n [15, 17, -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[[-12, 3, 6, 0],\n [-12, 5, -6, 8],\n [-20, 6, 4, 4],\n [12, -6, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 11, -9, -10],\n [-9, -15, 9, 18],\n [-6, -14, 12, 12],\n [-12, -20, 12, 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[[-15, -12, 10, -10],\n [4, 4, -2, 2],\n [-14, -8, 12, -12],\n [-5, 4, 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[[15, -19, -18, -25],\n [-2, -3, -5, 4],\n [-10, 14, 8, 30],\n [19, -5, -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[[-26, 1, 23, -17],\n [3, 12, 6, 0],\n [23, 2, -20, 14],\n [-14, -11, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 0, -2, 4],\n [-9, 6, -6, 6],\n [-3, -14, 6, 2],\n [6, 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[[8, 20, -10, 4],\n [8, 0, 10, 9],\n [16, 4, 16, 17],\n [4, -10, 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[[-6, 18, -16, 13],\n [-20, -9, 16, -6],\n [-4, 3, 0, 2],\n [2, -17, 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, 24, -22, 8],\n [5, 4, -6, 6],\n [13, -16, 13, -2],\n [8, -20, 19, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, 5, -8, 4],\n [-10, -4, -20, -8],\n [-6, 21, 6, 24],\n [-1, -16, -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[[4, -18, -20, 4],\n [36, 13, 10, 6],\n [30, 8, -2, 0],\n [0, -19, -17, 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, 19, 16, 2],\n [6, -16, -13, -2],\n [14, 5, 9, 8],\n [-2, 8, 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, 16, -2, 4],\n [0, -1, 2, -4],\n [-8, 10, 0, 0],\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[[12, 16, 17, -25],\n [12, 9, 3, 3],\n [0, -3, -6, 12],\n [12, 15, 15, -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, 6, -3, -33],\n [0, 2, 5, 12],\n [0, 3, 2, -7],\n [0, -1, -7, -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[[10, -7, 7, 26],\n [18, -17, 11, 10],\n [-8, 9, -18, -6],\n [-16, 13, -4, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[8, -18, -2, 11],\n [-15, -30, -18, 12],\n [-12, -32, -16, 15],\n [1, -18, -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, 8, -8, 4],\n [-5, -20, 5, -10],\n [3, -12, -3, -6],\n [8, -2, -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[[-4, -6, 4, 4],\n [6, 9, -6, -6],\n [0, -9, 4, 4],\n [-9, -9, 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[[-2, 0, 2, -2],\n [-9, -4, 3, 3],\n [-14, -8, 2, 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": "Find the rank of the matrix:\n[[9, -12, 0, 12],\n [6, -8, 6, 4],\n [12, -16, -6, 20],\n [9, -12, 3, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -6, -4, -14],\n [-3, -10, 8, 11],\n [12, 17, 5, 11],\n [19, -22, 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[[8, 0, -8, -16],\n [-8, -8, 8, -2],\n [5, -4, -5, -19],\n [-9, -12, 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[[4, -11, 2, 4],\n [0, 18, -11, 6],\n [8, -3, -4, 10],\n [8, 8, -11, 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, 24, 2, 25],\n [-12, -18, 16, -24],\n [28, -10, -20, -6],\n [4, 5, -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[[15, -5, 5, -2],\n [-10, 20, -10, 6],\n [-3, 21, -9, 6],\n [18, -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[[12, 0, -24, -4],\n [2, 10, 10, 9],\n [10, 10, 2, 4],\n [20, 14, -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[[-20, 2, -2, -12],\n [-6, 0, -4, -2],\n [-3, 3, 15, -9],\n [5, -2, -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[[-16, -12, 16, -16],\n [10, -5, 0, -2],\n [-3, 4, -2, 3],\n [-12, -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[[-8, 3, -14, 6],\n [2, -3, 8, -6],\n [10, -3, 16, -6],\n [-10, 1, -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[[2, -12, 8, 14],\n [-4, 10, -8, -18],\n [-17, -12, 4, -17],\n [5, -4, 6, 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, -10, 10, -4],\n [6, 3, -3, -15],\n [6, 3, -3, -15],\n [6, 15, -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[[1, 2, 1, 4],\n [7, 0, 11, 4],\n [-4, 6, -8, 8],\n [9, -3, 15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 8, 13, -16],\n [8, 0, 4, -4],\n [0, -10, -15, 12],\n [-8, 9, 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[[-3, 12, 6, 6],\n [6, 11, -7, -7],\n [-7, -7, 9, 9],\n [-1, -3, 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[[7, -1, 2, 1],\n [-1, -10, -14, 15],\n [-5, 8, 8, -12],\n [-8, -1, 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[[4, 3, -3, -2],\n [0, 3, -5, 2],\n [8, 6, -6, -4],\n [4, 6, -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[[-6, -5, 1, 5],\n [-15, 4, 11, -1],\n [3, -2, -4, -13],\n [-12, -2, 5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-4, -8, 0, -16],\n [-6, -8, -2, -12],\n [-2, -2, -1, -2],\n [2, -4, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, -6, 10, 17],\n [-7, 10, -6, -11],\n [3, -9, 3, 6],\n [-6, -4, -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, 24, 14, 0],\n [0, -32, -20, 4],\n [-9, 20, 11, 2],\n [-9, -20, -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[[16, 18, 16, 2],\n [-10, -7, -13, -16],\n [16, -18, 4, -4],\n [-2, 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[[-18, -16, -3, 11],\n [-2, 4, 4, -6],\n [0, -8, -6, 10],\n [0, -4, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 0, 6, 8],\n [-3, -1, 12, 18],\n [2, -1, -3, 3],\n [3, 1, -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[[3, -4, 4, 0],\n [9, -6, 4, 6],\n [6, -8, 8, 0],\n [12, 5, -12, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, -9, -10, 14],\n [-29, 0, -4, -28],\n [3, -9, -6, -6],\n [6, -13, -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[[7, 4, 18, -2],\n [16, -15, 16, -10],\n [6, -17, -4, 0],\n [-2, 16, 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[[-5, 3, 1, 9],\n [8, 0, -4, -20],\n [0, 6, -3, -7],\n [15, -21, 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[[16, 0, -14, -20],\n [-4, 8, -4, -6],\n [14, -14, -11, 3],\n [16, -2, -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[[4, 13, 12, 7],\n [-16, -7, -12, -1],\n [-4, 17, 12, 11],\n [20, 10, 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[[-2, -4, -20, 2],\n [20, -8, -4, 4],\n [-17, -8, 23, -11],\n [-12, 7, 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[[2, -4, -4, 3],\n [-1, -10, 5, -9],\n [7, -10, -15, 13],\n [1, 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[[-7, -30, -21, 20],\n [-12, 9, 17, -12],\n [-24, -9, 11, -3],\n [28, -6, -2, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-1, -3, 10, -6],\n [-4, 10, -4, 9],\n [0, 4, -8, 6],\n [0, 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[[7, 5, 7, 2],\n [-2, 2, -7, 16],\n [8, 16, -14, -4],\n [-9, -15, 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[[-9, -22, -12, 15],\n [-12, -10, -9, 12],\n [16, -14, -1, 4],\n [-7, -8, -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[[-7, -12, -7, -12],\n [-9, -29, -8, 10],\n [-8, -18, -10, 14],\n [12, 32, 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[[-2, 2, 8, 6],\n [-15, 12, 12, 6],\n [-12, 10, 16, 10],\n [7, -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[[8, 4, 0, -4],\n [-25, -18, -6, 13],\n [2, 1, 4, -5],\n [18, 15, 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[[16, -20, 0, 8],\n [3, 3, -18, 6],\n [12, -18, 8, 4],\n [-2, -2, 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[[16, 7, 12, -11],\n [8, 12, 5, -6],\n [-16, -16, -12, 8],\n [25, 28, 18, -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, 6, -12, -12],\n [-8, 14, 20, 8],\n [16, -18, -12, 0],\n [-2, 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[[10, -4, -4, -14],\n [0, 12, -3, -18],\n [4, -4, -1, -2],\n [-16, 16, 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[[-1, -1, 0, 4],\n [1, -3, 6, 4],\n [-3, -1, -3, 8],\n [4, -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[[7, -3, 4, -10],\n [7, -3, 4, -10],\n [-11, -2, 7, 6],\n [-3, -9, -16, 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, -12, 16, -18],\n [-6, 24, 0, 20],\n [-14, 13, 10, 2],\n [-12, 0, 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[[24, -4, -4, 4],\n [-4, -6, -14, -6],\n [18, 12, 18, 7],\n [14, 6, -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[[2, -2, 4, 6],\n [-9, 1, -6, 9],\n [5, -3, 7, 6],\n [1, -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[[13, -6, -3, -17],\n [-11, 14, -4, -8],\n [-6, 0, 3, 15],\n [1, -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[[-4, -2, 3, 2],\n [4, 2, -3, -2],\n [0, -2, 4, 6],\n [-8, -1, 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, 4, 12, -4],\n [-8, 2, 6, 0],\n [13, -13, -26, -1],\n [-9, 12, 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[[-14, -9, 10, -5],\n [6, 0, -12, -3],\n [0, 3, 6, 4],\n [8, 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[[7, -7, -9, -11],\n [-5, -1, -15, -8],\n [-35, 7, -3, 20],\n [19, -13, -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[[4, 13, -11, 0],\n [-5, 6, -7, -9],\n [3, -24, -1, 12],\n [-6, 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[[8, -22, -6, 19],\n [6, -14, 8, 13],\n [5, 4, 5, 0],\n [-4, -8, -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, -2, 10, 20],\n [-11, -11, -2, 20],\n [1, 17, 10, 4],\n [-14, -20, -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[[4, 8, 0, 10],\n [4, 8, -15, 0],\n [4, 8, -9, 4],\n [6, 12, 3, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 6, 8, -4],\n [-8, -3, -6, 2],\n [4, 8, 5, -1],\n [-2, -8, -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, -25, 0, 0],\n [6, 15, -5, 5],\n [-8, -19, 8, -8],\n [-2, -13, -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[[-1, 2, 0, -10],\n [7, 10, -6, -8],\n [-10, -12, 8, 4],\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[[2, 3, -3, 3],\n [-4, 6, -24, 18],\n [2, 3, -3, 3],\n [6, 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[[-12, -19, 4, 4],\n [-16, -22, 0, 4],\n [-6, -12, 6, 3],\n [-2, 6, -14, -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, 3, 16, 12],\n [20, -18, -31, -12],\n [12, 2, 13, 2],\n [6, -5, 17, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, -8, -4, -4],\n [3, 7, 8, -9],\n [0, 11, 9, -2],\n [-30, 5, -11, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-27, -25, -4, 10],\n [3, -6, -25, 13],\n [-2, -9, -15, 7],\n [-14, -5, -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[[-8, -11, 2, 10],\n [1, 11, 8, 7],\n [0, -7, -6, -6],\n [12, 20, 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[[-27, 7, 3, -14],\n [6, 7, 13, -1],\n [3, 4, -4, 9],\n [-10, 11, 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[[18, -2, -4, -6],\n [-6, -6, 8, -2],\n [6, -4, 2, -4],\n [-3, 17, -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[[-5, 7, 7, 10],\n [0, -9, 6, 0],\n [-1, -4, 5, 2],\n [4, -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, 6, 8, 6],\n [-11, 9, 28, 12],\n [-11, 9, 28, 12],\n [2, -3, 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[[-12, -4, 8, -8],\n [4, 13, -1, -4],\n [8, 12, -4, 0],\n [-12, 10, 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[[15, 6, 4, 16],\n [-19, 5, 2, -2],\n [13, 0, 0, 8],\n [13, -18, -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[[-11, 1, -13, -12],\n [-8, 0, -16, -8],\n [-14, 4, 8, -18],\n [-3, -1, -15, -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, 6, -9, -6],\n [4, 4, -26, -20],\n [8, 13, 3, 5],\n [-5, -5, -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[[-3, -14, 0, -5],\n [-17, -23, 10, -11],\n [15, 17, -6, 5],\n [19, 17, -14, 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, 4, -7, -10],\n [-2, -2, 6, 8],\n [0, 1, 2, 2],\n [-1, -1, 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[[2, 4, 4, -18],\n [5, 2, 6, -17],\n [-5, 5, -2, -12],\n [10, -6, 4, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-6, 4, -10, 3],\n [-6, -2, -4, 12],\n [4, -4, 8, 0],\n [10, -2, 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, -10, -6, -6],\n [32, -20, 12, 36],\n [-5, -2, -5, -6],\n [0, -4, -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[[11, 6, -1, 1],\n [-4, 6, -19, -2],\n [-23, 6, 0, -19],\n [-2, 6, 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[[18, 0, -3, -3],\n [15, -9, 2, -7],\n [24, 0, -4, -4],\n [9, -15, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 4, 13, 5],\n [1, 20, 15, -1],\n [11, 13, 14, 9],\n [-5, -7, -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[[3, -4, -9, -2],\n [-2, 0, -6, -4],\n [1, -2, -6, -2],\n [3, 0, 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[[-18, 6, -3, 3],\n [-16, 8, -4, 0],\n [-8, 4, -2, 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": "Find the rank of the matrix:\n[[19, 0, -8, -20],\n [13, -5, -7, -10],\n [6, 5, -7, -10],\n [2, -11, 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[[7, 4, 2, 10],\n [-4, 12, 0, 13],\n [14, -12, 12, -4],\n [6, -17, 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[[2, -6, 1, 2],\n [1, -3, -4, 19],\n [-1, 3, -4, 13],\n [-1, 3, 2, -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[[0, -6, -5, -7],\n [2, -3, 2, -4],\n [-4, 12, 1, 15],\n [2, -12, -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[[13, -4, -12, 13],\n [-16, 0, 8, -12],\n [20, 16, 12, 2],\n [8, 0, -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, -13, -12, 10],\n [4, 5, -13, 12],\n [-12, -24, 12, 0],\n [2, 1, -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[[-5, -5, -2, -1],\n [-23, -17, 15, -7],\n [-5, 9, 8, 7],\n [24, 30, 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[[14, -14, 10, -8],\n [-3, -14, -12, -12],\n [-12, -2, -14, -2],\n [8, 17, 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[[-23, -19, 15, 32],\n [7, -7, 15, -4],\n [-6, -1, -6, 4],\n [-4, -3, 33, 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, 12, 10, -8],\n [-1, -6, -2, 16],\n [-10, 12, 12, 0],\n [-6, 9, 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[[1, 0, 7, 4],\n [4, 3, -2, 4],\n [1, 2, -13, -4],\n [15, 11, -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[[10, -8, 4, -2],\n [0, 0, 0, 0],\n [-12, 3, -9, 3],\n [1, -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[[17, -11, -8, -18],\n [-21, -3, 25, -12],\n [8, -2, 16, -14],\n [-16, -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[[-7, 3, -6, 14],\n [3, 9, -6, 18],\n [7, 11, -3, 17],\n [11, 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[[0, 10, 12, -13],\n [0, 6, 4, -5],\n [0, 8, 8, -9],\n [0, -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[[20, 14, -6, 14],\n [10, -6, -28, 16],\n [-18, -11, 9, -14],\n [2, 16, -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, -4, 4, -4],\n [8, 10, -8, 0],\n [0, 2, -2, 2],\n [-12, -11, 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, -9, 9, -3],\n [-12, 1, -11, -1],\n [16, -22, 5, -9],\n [-16, 2, -25, -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, -13, 24, 11],\n [28, -12, 28, 12],\n [18, -5, 18, 7],\n [8, 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[[1, 7, 1, 10],\n [4, -2, -10, -2],\n [-3, -1, 1, -2],\n [4, 3, -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, -9, 17, -8],\n [4, -1, -25, 4],\n [4, -6, -4, 4],\n [8, -5, -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[[5, 2, -11, 0],\n [1, 10, 1, 8],\n [-8, -2, 18, 1],\n [7, 4, -15, 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, -11, -15, -3],\n [0, -14, -15, 0],\n [7, -2, 3, 7],\n [19, -25, -12, 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[[-2, 15, 8, 14],\n [1, -11, -6, -11],\n [-5, 6, 2, -1],\n [4, 5, 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[[-1, -10, -7, 12],\n [-12, -12, 0, -8],\n [10, 12, 1, 5],\n [8, 5, -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[[-14, -26, -28, 22],\n [6, 22, 23, -7],\n [-9, 21, 16, 11],\n [-6, -6, -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[[15, 3, 13, 2],\n [7, -9, 0, 7],\n [4, 12, 10, -6],\n [2, 6, 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[[8, 8, 13, -6],\n [-8, -8, -13, 6],\n [1, 6, 6, 3],\n [-4, 8, 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[[-9, -24, 21, 12],\n [15, 20, -19, -10],\n [-20, 0, 4, 0],\n [8, -12, 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[[-6, 0, 10, 9],\n [4, -12, 6, 12],\n [-14, -6, -17, -6],\n [-4, -8, -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[[12, 10, -8, 0],\n [8, -5, 19, 3],\n [-15, -2, -14, -9],\n [25, 8, 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, 9, -14, -5],\n [12, 8, -11, -1],\n [-24, 24, -14, -2],\n [16, 4, -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[[-13, 12, -12, 4],\n [7, 10, 6, -18],\n [15, -12, 18, -12],\n [17, -13, 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[[8, 10, -12, 0],\n [2, -5, 10, -6],\n [14, 12, -16, 2],\n [6, -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[[-1, 0, 2, 0],\n [-4, 0, 0, 6],\n [4, 0, -8, 0],\n [1, 0, -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[[-2, 22, -5, -19],\n [15, 20, 13, -25],\n [26, 4, 30, -18],\n [9, 22, 5, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[3, 6, -6, -3],\n [13, 14, 10, -9],\n [-16, -14, 0, 10],\n [14, 10, 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[[5, -15, 14, -12],\n [4, -1, -2, 8],\n [-6, 14, -12, 8],\n [-4, 11, -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[[6, 12, -20, -21],\n [0, 0, 0, 6],\n [15, -12, 6, 0],\n [16, -8, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 5, 5, 11],\n [3, 13, -1, 16],\n [-3, 9, -3, 9],\n [-8, -4, -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[[-2, 2, 5, 1],\n [-2, 2, 5, 1],\n [8, -17, -11, -4],\n [-2, 8, -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[[29, 4, 6, 2],\n [21, -12, 9, -18],\n [-1, -17, 1, -20],\n [5, -11, -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[[12, 12, 4, -2],\n [-24, -24, -8, 4],\n [-12, -12, -6, 5],\n [-12, -12, -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, 2, 4, -9],\n [12, 4, -12, 1],\n [-14, -2, 8, 2],\n [0, 0, -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[[-14, 6, 4, 8],\n [2, -6, 2, -15],\n [-2, 2, 0, 4],\n [-13, 9, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[20, 2, -4, -2],\n [5, -8, 1, -7],\n [-9, -5, 2, 1],\n [-25, 8, 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[[0, -7, -4, 7],\n [-3, -8, -14, 12],\n [9, -2, -14, 6],\n [3, 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[[21, 18, 8, -10],\n [1, -7, -4, -1],\n [3, 14, 16, 18],\n [-6, -3, -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[[8, -10, 0, 10],\n [18, -4, -5, 25],\n [-4, 11, -15, -20],\n [2, 9, -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[[1, 0, 5, -12],\n [19, -15, -10, 12],\n [0, 0, 0, 0],\n [-2, 2, 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[[-6, -4, 10, 11],\n [-1, 4, -2, 6],\n [4, 12, -2, -5],\n [-8, -8, 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[[20, 12, -32, 8],\n [7, 24, 6, 21],\n [9, 22, 10, 25],\n [6, 11, 16, 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[[-20, 12, 8, 6],\n [12, 0, -3, 0],\n [0, -8, -2, -4],\n [-4, -12, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-5, 18, -3, 14],\n [16, 7, -4, 13],\n [-4, 22, -4, 18],\n [-12, -10, 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, -11, -7, -12],\n [-14, -3, 15, 2],\n [28, 1, 1, 20],\n [-24, -5, -5, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-5, -4, 6, 6],\n [-22, -7, 19, 11],\n [-3, -10, 4, 12],\n [-24, -1, 21, 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, 1, -1, 4],\n [7, 10, -4, 3],\n [-8, 0, 8, -4],\n [17, 9, -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[[12, -4, -12, 8],\n [6, 2, -3, 8],\n [6, -2, -6, 4],\n [5, -3, -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[[8, 7, -8, -14],\n [12, -3, -3, -12],\n [12, 9, -5, -20],\n [-4, 13, -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[[8, -2, 0, 14],\n [32, 4, 23, -13],\n [20, 3, 9, 8],\n [-8, 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[[-19, 2, -5, -1],\n [-4, 12, -8, -6],\n [10, 0, 2, 0],\n [4, -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[[4, -6, -1, -16],\n [-6, 0, -8, -6],\n [9, -8, 10, -8],\n [-4, 4, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-9, 3, -19, -5],\n [-1, 3, -4, 0],\n [-6, 6, -15, -3],\n [-9, -37, 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[[-13, 9, -5, 6],\n [15, -8, 18, -10],\n [12, -5, 3, -8],\n [-11, 12, 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[[6, 2, -2, -18],\n [3, 11, 1, 12],\n [3, -3, -3, -24],\n [-12, -8, -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[[-16, 16, 8, 0],\n [-1, 11, 3, -10],\n [-10, 14, 6, -4],\n [-1, 9, -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[[31, -30, -15, -16],\n [-13, 10, 1, 12],\n [8, -5, 2, -10],\n [0, 5, 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[[-12, 16, -8, -4],\n [3, -2, 6, 7],\n [18, -20, 20, 18],\n [15, -18, 14, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, 4, -22, -15],\n [2, 0, 2, 1],\n [-4, -1, -2, 0],\n [-6, 1, -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[[-12, -32, -6, 6],\n [18, 40, 6, -11],\n [14, 24, 28, -6],\n [-13, -20, -26, 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 [-7, -3, -3, -5],\n [-4, 4, 4, 0],\n [-10, -2, -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, -2, 12, 10],\n [0, 6, -21, 0],\n [-1, -1, 12, 3],\n [15, 1, 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[[6, -20, 0, 16],\n [-30, -4, 6, 8],\n [4, -16, -16, 36],\n [-8, -24, 11, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, -9, 4, 4],\n [0, 6, -3, -2],\n [0, 18, -8, -8],\n [0, -15, 9, 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, 4, -2],\n [-5, -13, 13, 11],\n [8, 4, -4, 2],\n [-4, -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, -13, -9],\n [-7, 5, -18, -15],\n [2, -2, 8, 6],\n [8, -6, 22, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, -2, 3, -2],\n [-14, 20, -6, -8],\n [2, -4, 6, -4],\n [-13, 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[[-2, -2, -24, -24],\n [-3, 17, 4, 4],\n [3, -17, -4, -4],\n [3, -3, 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[[-6, 3, 12, 0],\n [0, 3, 4, 0],\n [-7, 2, 12, 0],\n [2, -7, -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, 6, -4, -4],\n [14, 2, -4, 0],\n [2, 5, -4, -3],\n [7, 12, -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[[-15, 16, -23, -17],\n [0, 16, -2, 6],\n [16, -16, 23, 19],\n [16, -10, 23, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-19, -5, 9, 6],\n [1, -4, -4, 0],\n [30, -13, -23, -2],\n [17, -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[[0, -4, -8, 32],\n [-15, 6, -18, 12],\n [-9, 7, -4, -20],\n [9, -2, 14, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, -2, -2, 23],\n [4, -8, -12, 16],\n [-3, -3, -6, 0],\n [-1, 2, 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[[-7, -7, -8, -7],\n [-20, -12, -16, -20],\n [4, 1, 2, 4],\n [12, 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[[12, 7, 8, -16],\n [-12, -12, -28, 16],\n [-12, -10, -20, 16],\n [0, -4, -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[[10, 6, -9, 6],\n [-13, 1, -10, -14],\n [-1, 11, 24, 6],\n [10, 6, -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[[-28, 15, 11, 8],\n [16, -8, -6, -4],\n [-16, 6, 5, 2],\n [8, 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[[-2, 0, 2, -1],\n [3, -3, -6, 4],\n [10, 12, 2, -5],\n [2, 0, -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, 0, 8, 2],\n [3, 4, 5, 2],\n [-4, -16, -12, -6],\n [-8, 0, -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[[-7, 3, -8, 17],\n [5, -3, 7, -13],\n [6, 0, 3, -12],\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[[-5, 8, 17, -11],\n [0, -10, -19, 1],\n [-12, 10, 11, -29],\n [8, 2, -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[[-2, -18, 26, -10],\n [14, -5, 2, 2],\n [11, 10, -17, 9],\n [2, -9, 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[[14, 2, 6, 10],\n [-14, -10, -2, -1],\n [24, 8, 8, 12],\n [-6, 6, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, 0, 6, -12],\n [5, 12, -2, -12],\n [10, 8, -14, 8],\n [6, 24, -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[[-3, -9, 12, -3],\n [7, -12, 16, -15],\n [1, -3, 4, -3],\n [11, -6, 8, -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, -16, 10, 10],\n [-14, 8, -12, -12],\n [-12, -2, -4, -10],\n [-17, -8, -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[[5, 7, 10, 6],\n [-4, -3, -7, -4],\n [13, 13, 24, 14],\n [-8, -6, -14, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 4x4 matrix:\n[[-12, 16, 8, 12],\n [2, 4, -13, -2],\n [-6, 16, -10, 6],\n [0, -4, 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[[12, -16, 4, 16],\n [-9, 11, -1, -10],\n [0, 1, -2, -2],\n [0, 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[[-5, -2, -1, -5],\n [8, -15, -25, -6],\n [-1, -3, -4, -3],\n [-8, 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[[16, 7, -6, -20],\n [3, -4, 22, -10],\n [9, -2, 31, -20],\n [-16, -2, -26, 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[[13, 6, -7, -8],\n [18, 5, -9, -7],\n [-5, 1, 2, -1],\n [14, -1, -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[[6, -6, 0, 8],\n [12, 20, 24, 0],\n [-3, -17, -15, 6],\n [-9, -15, -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[[1, -4, -3, 3],\n [0, -14, -10, 10],\n [-4, 16, 12, -12],\n [-2, -6, -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[[0, 0, 0, 0],\n [-4, 9, 13, 4],\n [4, 0, 8, -4],\n [-14, 6, -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[[0, 1, -1, -2],\n [0, -5, -7, 2],\n [0, 4, 2, -4],\n [0, 9, 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[[6, -1, 21, 13],\n [-9, 4, -3, 11],\n [18, 17, -6, -14],\n [6, 4, -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[[10, 2, 0, 10],\n [-12, 0, 6, 1],\n [24, -4, 3, 18],\n [8, 0, -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[[7, -6, 9, 7],\n [-12, 4, -4, 34],\n [-14, 10, -12, 3],\n [-15, 12, -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[[-12, 24, -4, -2],\n [-4, 20, -8, -14],\n [8, 14, 12, -16],\n [-8, -16, -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[[12, -12, 12, -4],\n [10, -8, 10, -5],\n [2, -4, 2, 1],\n [-2, 4, -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[[-13, -9, 6, -16],\n [-16, -12, 4, -20],\n [-12, -12, -12, -12],\n [-9, -7, 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[[19, 20, 10, -3],\n [-1, -5, 6, 12],\n [15, 3, 15, 10],\n [17, 1, -2, -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, -20, -4, -16],\n [0, 16, -16, 16],\n [9, 13, 5, 10],\n [-3, 9, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 3, -5, -2],\n [0, 8, -8, 0],\n [-4, -6, 0, -6],\n [-3, -22, 23, 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, 14, -20, -18],\n [0, -12, 18, 15],\n [0, 4, -6, -5],\n [-10, 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[[-4, 4, -6, -6],\n [-10, 6, -15, -3],\n [-8, 8, -12, -12],\n [-6, -2, -9, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 7, -14, -7],\n [-1, -2, -10, -4],\n [11, 4, 2, 14],\n [9, 3, -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[[-4, 0, 0, 1],\n [9, 3, 0, 0],\n [18, 6, 0, 0],\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[[-4, 0, 4, -2],\n [3, 10, 12, 4],\n [2, -8, -14, -1],\n [5, 6, 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, 13, 12, 12],\n [-2, -20, -2, 2],\n [1, 9, -2, -10],\n [11, -1, -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[[-12, -10, 6, -2],\n [-8, 15, -1, -13],\n [-18, -2, 6, -10],\n [-11, 6, 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[[-4, -7, -4, 14],\n [4, 3, 4, -6],\n [0, 4, 0, -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": "Find the rank of the matrix:\n[[9, 5, -2, -19],\n [12, 9, 9, -9],\n [9, 5, -2, -19],\n [7, 6, 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[[-3, 16, 0, 5],\n [0, -4, -6, 4],\n [1, 2, 11, -9],\n [4, -24, -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, 14, -12, -5],\n [-14, 0, 16, -12],\n [8, -4, -8, 10],\n [2, 20, -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[[0, -4, -8, 2],\n [8, 8, -24, -10],\n [0, -6, -12, 3],\n [2, -3, -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[[6, 10, 18, -4],\n [-3, -5, -9, 2],\n [-16, -18, -4, -16],\n [1, 1, -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[[2, -4, -1, -2],\n [-10, 14, 3, 5],\n [-16, 8, 0, -4],\n [12, -18, -4, -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, 12, -3, 3],\n [-15, 6, -3, -3],\n [16, 4, 0, 4],\n [10, 9, -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[[-12, 4, 2, 2],\n [-3, -2, 21, -9],\n [-21, 3, 10, -5],\n [-18, 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[[-10, 1, 4, 13],\n [7, 2, -1, -10],\n [17, 11, 7, -5],\n [-11, -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[[4, -17, 20, 19],\n [-18, -3, -4, 0],\n [-21, 3, -8, -6],\n [-11, -17, 24, 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[[-4, 4, 4, 0],\n [-7, 11, 3, 16],\n [0, -1, 1, -4],\n [3, -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[[16, -3, -1, -8],\n [4, 15, -25, 16],\n [-12, 11, -13, 16],\n [14, 0, -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[[-8, 0, 0, -12],\n [0, -4, 4, -6],\n [-4, -4, 4, -12],\n [-6, 0, 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[[13, -2, 15, -9],\n [4, -8, 12, 0],\n [5, 6, -1, -6],\n [0, 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[[-30, 22, 16, 22],\n [1, -4, 7, 10],\n [12, -9, -12, -12],\n [28, -20, 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[[9, -3, 3, 6],\n [-9, 8, -8, -4],\n [-3, 1, -1, -2],\n [-18, 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, 22, -2, -5],\n [-12, 8, 8, 0],\n [1, 6, 0, -2],\n [-1, -16, 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[[7, -15, -8, -5],\n [8, 0, -12, -10],\n [5, -21, -4, -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, 4, -12, 8],\n [2, -1, 3, -2],\n [2, -1, 3, -2],\n [-2, -11, -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[[-3, -6, 8, -2],\n [5, 12, -16, 8],\n [8, 8, -8, -4],\n [4, 0, 0, -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, 12, -12, 9],\n [17, 20, -20, 14],\n [-10, -26, 8, -2],\n [16, 17, -20, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 5, -5, 11],\n [-5, 1, -18, -8],\n [6, 4, -7, 7],\n [17, 11, -2, 23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 2, -24, -10],\n [-4, -10, -8, 6],\n [0, 8, 12, -3],\n [8, -8, -32, -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, 4, -8],\n [0, 4, 0, 8],\n [-8, -3, 8, -6],\n [-4, -1, 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, -6, 1, -10],\n [-2, 17, 3, -2],\n [-16, 14, 11, 2],\n [29, 4, 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, 2, -1, -2],\n [-25, -5, -4, 15],\n [-27, -9, -1, 11],\n [-18, -3, -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[[-14, 13, 2, 18],\n [29, -11, -17, -17],\n [1, 22, -13, 15],\n [-3, -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[[-18, -9, 6, 6],\n [6, 6, -3, 0],\n [18, 9, -6, -6],\n [12, 9, -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[[-9, -3, 6, 21],\n [-12, 2, 5, 16],\n [0, -6, 3, 12],\n [9, 3, -6, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 0, 21, -21],\n [-13, 12, -16, 19],\n [3, 12, 12, -9],\n [9, -28, 0, -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, -10, -6],\n [7, 9, -10, -3],\n [-13, -11, 22, 9],\n [-19, 22, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[0, -2, 4, -18],\n [-2, 0, -3, 5],\n [6, 2, 5, 3],\n [16, 6, 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[[-2, -6, -4, 8],\n [-10, -10, -10, 22],\n [12, 6, 9, -21],\n [-10, 0, -5, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, -10, 4, -14],\n [-22, 0, 3, -13],\n [16, -12, 0, 4],\n [4, 19, -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[[18, 14, -24, 18],\n [-12, -16, -13, 19],\n [16, 18, -3, 1],\n [-16, -19, -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[[-14, 20, 3, 2],\n [-4, 14, 16, 5],\n [5, -22, -14, 5],\n [-20, 16, 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[[-11, -3, -9, 4],\n [10, -22, -26, -24],\n [-3, 7, 32, 4],\n [9, -21, -29, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, 9, 1, -11],\n [-2, -3, -9, 1],\n [22, 21, -15, -9],\n [-12, -9, 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[[2, 1, 2, 1],\n [20, 13, -1, 13],\n [-16, -11, 5, -11],\n [-22, -15, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, 43, -45, -28, 8],\n [0, -8, 8, 5, -2],\n [0, 8, -8, -5, 2],\n [-25, -25, 15, 10, -20],\n [55, 15, 7, 3, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, -33, 6, -15, -18],\n [20, -2, -12, -22, -20],\n [-12, -30, 24, 18, 12],\n [-4, 3, 1, 4, 4],\n [16, 14, -18, -20, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[87, -12, -37, 7, 23],\n [28, 45, 54, -60, 16],\n [-8, 6, 39, -36, -17],\n [-3, 9, 10, -7, 3],\n [7, 21, 14, -5, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-32, 0, 14, -46, 16],\n [14, -29, -6, 28, -35],\n [-22, -48, 62, -16, -36],\n [0, 9, 8, 0, 7],\n [16, 58, -36, 5, 49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[38, -21, -6, -28, 36],\n [45, 10, -30, -55, 10],\n [23, 4, -18, -26, 7],\n [19, -28, 18, -7, 32],\n [20, -20, 0, -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[[8, -2, 0, -2, 2],\n [-22, 9, -3, 4, -5],\n [32, -36, 24, 4, 4],\n [-32, 36, -24, -4, -4],\n [24, -48, 36, 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, 14, 13, -17, 2],\n [7, -28, 53, 29, 7],\n [-6, 0, 22, -8, 6],\n [-6, 8, 22, -8, 2],\n [7, -12, -11, 13, -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[[9, 39, 39, 51, 3],\n [6, -43, -50, -55, -20],\n [-75, -10, -25, 40, 5],\n [-18, 33, 62, 19, 56],\n [51, 8, 1, -4, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, -12, -4, 4, 4],\n [-10, -2, 6, 2, 18],\n [20, 13, 6, -4, 0],\n [-40, -26, -12, 8, 0],\n [-5, -9, -13, 1, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, -28, -8, 40, 12],\n [4, 13, 5, -16, -9],\n [-1, -22, -5, 34, 6],\n [-6, 3, -3, -12, 9],\n [7, -11, 2, 26, -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, 30, 23, -11, -25],\n [12, 23, -18, -22, -20],\n [22, 29, 15, 3, -13],\n [-2, -11, -1, -18, -1],\n [-24, -12, 0, -21, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[26, -30, 6, -18, 2],\n [2, -36, 30, -18, 2],\n [-31, 7, -21, 35, -55],\n [-2, -46, 30, -14, -14],\n [-3, 45, -18, 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[[-16, 17, -12, 27, 2],\n [26, 5, -14, 23, -20],\n [13, -27, 19, -1, 3],\n [-23, 41, -29, 14, -3],\n [3, 6, -3, -33, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-7, -29, -4, 2, 29],\n [12, 15, -42, -42, -30],\n [-11, -1, -20, -19, -10],\n [35, 34, -10, -15, -32],\n [-31, -2, 50, 46, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-14, -10, -1, -42, 10],\n [6, -33, -12, 18, -25],\n [-2, -49, -16, -6, -25],\n [4, 35, 11, 12, 15],\n [-4, -8, -2, -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[[16, 42, -19, -36, 16],\n [15, 24, 14, 2, -18],\n [-11, 25, -4, -8, 15],\n [14, 10, -10, 59, -8],\n [22, 7, 15, 25, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, 36, -51, 35, 37],\n [48, 0, 12, -4, -46],\n [-44, -11, -17, -25, 36],\n [0, 32, -43, 31, 26],\n [-16, 46, -53, 57, 51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 5, 23, 21, 33],\n [-20, 11, 51, 45, 5],\n [-7, 2, -18, -39, -24],\n [-2, -1, -17, -9, -3],\n [-5, 3, 9, -12, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, -5, 6, 5, -10],\n [-72, 30, 54, 60, 24],\n [6, 20, -9, -5, 34],\n [-30, 5, 24, 25, -2],\n [6, -25, 0, -5, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[22, 5, 0, -60, -4],\n [-23, -20, 4, 25, 8],\n [-8, 29, -20, -15, -1],\n [13, -14, 13, -8, -1],\n [27, -15, -20, -18, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, 15, 3, -1, -3],\n [-10, 12, 15, 2, -12],\n [38, -13, 7, -17, 21],\n [-10, -18, -27, 8, 6],\n [-15, 26, 49, -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[[-4, 16, -20, -14, 12],\n [15, -42, 55, 38, -33],\n [-23, -34, 25, 21, -15],\n [13, 38, -35, -27, 21],\n [-17, 14, -25, -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[[-1, -9, 2, 21, 8],\n [9, -19, 32, 36, -22],\n [-11, 13, -34, -21, 32],\n [7, -5, 20, 6, -22],\n [-16, 28, -54, -51, 42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, 2, -41, -56, -6],\n [16, -5, -29, -16, -4],\n [-1, 20, -21, -12, -32],\n [19, -18, -17, -30, -27],\n [-25, 6, 36, 14, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[33, -12, 0, 17, 1],\n [20, 14, -15, -28, 2],\n [24, 6, 26, 26, 14],\n [-21, 5, -2, -34, -4],\n [-6, 15, -9, -22, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[27, 10, -6, 30, -7],\n [31, -2, 4, 22, 7],\n [-7, -18, 14, -22, 19],\n [-25, 10, -10, -10, -15],\n [-21, -2, 0, -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[[-17, -3, 6, -6, -40],\n [1, 8, 52, 21, 29],\n [10, -20, 20, -15, -10],\n [-15, 27, 30, 33, 24],\n [-5, -7, 30, -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[[-14, -2, 38, -22, -16],\n [28, 24, -36, 12, -4],\n [-33, -39, 21, 3, 24],\n [5, 5, -5, 1, -2],\n [-6, -18, -18, 18, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[4, -4, -4, -16, -24],\n [6, -13, -27, -38, -22],\n [-1, 2, 4, 6, 4],\n [-6, 11, 21, 34, 26],\n [0, 5, 15, 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[[24, -8, -1, -13, 23],\n [16, 0, -6, -30, 34],\n [30, -17, 12, 18, -12],\n [-6, 5, -19, -25, 47],\n [24, -6, -3, -21, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[5, 2, -6, 6, 1],\n [-29, 34, 42, 18, -7],\n [6, -28, -12, -28, 2],\n [-13, 10, 18, 2, -3],\n [30, -26, -42, -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[[-20, 15, -15, 10, 25],\n [10, 25, 0, 25, 0],\n [-30, -10, -15, -15, 25],\n [0, 39, -9, 36, 15],\n [-14, -22, -3, -23, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-5, 25, 18, 31, -28],\n [-7, -3, -7, 1, 22],\n [28, 20, 21, 26, -2],\n [-33, -9, -12, -15, -24],\n [-10, 7, 12, -5, -76]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, 35, 41, 24, -4],\n [-10, 38, -16, -10, -34],\n [9, -24, -27, -21, 5],\n [0, 10, -20, 6, -10],\n [8, -20, -8, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[34, -14, 25, 17, 5],\n [-48, -2, -13, -6, -3],\n [44, -40, 25, -18, 41],\n [3, -2, 27, -49, 2],\n [58, -2, 23, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, -15, 25, 30, 5],\n [8, 10, -20, -31, -9],\n [23, -15, 5, -36, -29],\n [16, -22, 20, -11, -21],\n [19, -13, 5, -29, -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[[1, 7, 9, -7, 36],\n [-12, 14, -20, -22, 32],\n [-25, -34, -27, -2, 12],\n [-1, 0, 9, -12, 52],\n [-2, 36, -12, -36, 50]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, -3, -13, 10, 6],\n [-14, -8, 22, -10, -6],\n [-7, -22, -48, 39, 36],\n [-2, 4, 32, -22, -16],\n [1, 16, 16, -15, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, -32, 72, -36, 25],\n [22, -12, 40, -14, 16],\n [4, -15, 23, -13, 12],\n [46, 7, 31, -7, 5],\n [-8, 9, -15, 13, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, -20, 11, 2, 11],\n [30, -17, 22, 5, 22],\n [-24, -8, -14, -4, -14],\n [-18, 27, -16, -3, -16],\n [24, -16, 18, 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 5x5 matrix:\n[[-9, -7, -14, 9, -6],\n [5, -17, -30, -18, -24],\n [-1, -17, -14, 16, -10],\n [-4, 2, 4, -19, 28],\n [4, -5, -5, 18, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-54, -14, 16, 37, -22],\n [18, 4, 12, -4, -2],\n [-1, 6, -30, -3, 33],\n [-24, -21, 24, 0, -59],\n [-15, -11, -22, 15, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-23, 3, -8, 13, -7],\n [-4, 22, -19, -9, 46],\n [-3, 22, 34, 1, 10],\n [-6, -5, 13, -11, 31],\n [-3, -33, 39, -9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -21, -24, 18, -15],\n [2, -21, -24, 18, -15],\n [24, -54, -72, 60, -18],\n [-25, 48, 66, -56, 12],\n [-24, 21, 36, -34, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[32, 1, 20, -13, -11],\n [12, 16, 20, 12, 4],\n [7, -24, -15, -29, -15],\n [3, -21, -15, -24, -12],\n [-19, 8, -5, 17, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, 4, 13, 2, 7],\n [13, -10, -5, -24, -4],\n [7, 2, -11, 0, -40],\n [18, -12, -13, -22, -3],\n [-7, -2, 11, 0, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 18, -2, 14, 14],\n [21, -21, 14, -3, -13],\n [21, -42, 7, -30, -32],\n [25, -51, 8, -37, -39],\n [-1, -3, -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[[27, -30, -39, 9, 8],\n [42, -48, -20, 43, 14],\n [-24, 30, 13, -29, -1],\n [15, 15, -34, -28, -42],\n [17, -32, -13, 31, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -28, -17, 18, 18],\n [-14, -28, -26, 2, 30],\n [21, 42, 30, -19, -33],\n [-12, -24, -12, 20, 12],\n [-6, -12, -24, -22, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-13, 21, -21, 15, -16],\n [-11, 46, -17, 3, 29],\n [-34, 32, -17, 32, -4],\n [-33, 38, -22, -10, -1],\n [46, -45, 29, -3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 6, 18, -24, 8],\n [21, -26, 30, 10, 34],\n [-63, -27, 103, -33, -22],\n [-90, -36, 49, -15, 14],\n [24, -9, -55, 5, 80]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-27, 34, 7, 28, 7],\n [-13, 16, 6, 8, 35],\n [-2, 13, 2, 10, -62],\n [40, -11, 17, -54, -6],\n [-45, 25, -11, 58, 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, 5, -10, 26, -7],\n [8, 10, 16, -20, -2],\n [-8, -30, 0, -36, 22],\n [-5, -15, -3, -12, 10],\n [2, 20, -10, 44, -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[[-48, 30, 54, 18, -6],\n [4, -14, 7, 1, 12],\n [-20, 19, 12, 0, -9],\n [20, 2, -53, -35, -12],\n [28, -24, -21, -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[[-30, -33, -31, 43, 23],\n [14, -26, -42, 12, 10],\n [5, 0, -22, -9, 10],\n [44, -18, -14, -2, -18],\n [-12, -12, 40, 32, -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[[-38, 12, -1, -13, -5],\n [-26, 10, 1, -9, -7],\n [16, -24, -16, 4, 28],\n [0, 22, 20, 0, -38],\n [22, -30, -19, 5, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -64, -6, -6, -28],\n [27, -14, -38, 6, 7],\n [4, 12, 3, 1, 5],\n [47, -14, -57, 17, 26],\n [-15, -43, -11, -6, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[27, 0, -24, 36, 51],\n [-18, -8, 20, -24, -32],\n [-31, -31, -15, 3, -26],\n [-14, -21, -29, 21, 1],\n [-34, -7, 49, -57, -69]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -1, -8, -33, -17],\n [-31, 29, 22, -63, -53],\n [-6, 28, 34, 8, 6],\n [41, -8, -9, 10, 31],\n [-13, 29, 22, -59, -39]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -17, 10, 16, 11],\n [-8, 32, -32, -26, -38],\n [-36, -3, -18, 9, -24],\n [-24, -9, -6, 12, -9],\n [36, 17, 6, -21, 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, 16, 12, -28, 4],\n [-20, -11, 4, -35, 34],\n [-18, -19, -2, -21, 32],\n [1, 9, 5, -8, -3],\n [14, -4, -10, 38, -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[[37, -5, -8, -14, 23],\n [-30, 24, -12, 24, -24],\n [-8, -10, 12, -4, -2],\n [24, 30, -36, 12, 6],\n [-18, -2, 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[[-27, -6, -51, -3, 6],\n [10, 1, 36, -5, 10],\n [-5, 0, -25, 5, -10],\n [-11, -4, 1, -9, 18],\n [-8, -2, -12, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-22, 13, -59, -17, 11],\n [-6, -16, 34, 45, -66],\n [20, 16, -20, -10, 26],\n [41, -17, 25, -10, 41],\n [-37, 19, -17, 15, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 27, -15, -20, 6],\n [-19, -18, 15, 20, -9],\n [-36, 18, 0, 0, -6],\n [29, 24, -21, -28, 13],\n [-3, -15, 9, 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[[-6, 0, 1, -11, -26],\n [0, -4, 2, 8, 20],\n [0, -8, 4, 16, 40],\n [42, 30, -22, 17, 32],\n [18, 16, -11, 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[[-9, -4, 65, 62, -24],\n [-49, -5, -18, -14, -15],\n [-9, -46, 11, 11, -3],\n [-11, 3, 32, 53, -22],\n [28, 30, -42, -11, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[23, -60, -36, 0, 8],\n [22, 5, 79, 55, -44],\n [10, 30, 61, 20, -30],\n [-27, 0, -41, -10, 26],\n [-14, -10, 7, 40, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, 6, 9, -5, -5],\n [3, 19, -12, -31, -46],\n [16, -9, -14, 6, 23],\n [-43, 8, 35, 0, 34],\n [16, -19, 1, 31, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, 2, 6, -13, 5],\n [28, 6, 31, -24, 12],\n [-57, 22, 24, -36, 37],\n [49, -56, -3, 28, -17],\n [-41, -6, -13, 0, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-49, 54, -25, 33, -18],\n [34, -41, 26, -12, 22],\n [4, -11, -20, 6, -74],\n [-7, -1, -17, 21, -64],\n [18, -24, 17, 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 5x5 matrix:\n[[6, -14, 23, -35, 38],\n [21, -23, -21, -30, 2],\n [1, -19, -38, -3, -29],\n [-90, -18, 9, 27, -21],\n [48, 8, -44, -4, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[34, -44, -25, -12, -29],\n [24, -28, -23, 3, -22],\n [22, -20, -31, 24, -23],\n [14, -8, -28, 33, -17],\n [-18, 28, 5, 24, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-14, 10, 22, 8, 10],\n [61, 34, -5, -22, 22],\n [-12, 22, 36, 8, 18],\n [-14, -16, -18, 11, 1],\n [21, 27, 7, 2, 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[[0, 6, 15, -15, -12],\n [-5, 6, 6, -2, 0],\n [30, -42, -51, 27, 12],\n [-15, 16, 13, -1, 4],\n [-15, 16, 13, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, 26, 32, -38, 35],\n [-12, 12, 4, -16, 10],\n [4, -4, -34, 10, -22],\n [-18, 18, -8, -22, 7],\n [20, -20, -16, 28, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-21, -56, 39, 0, -30],\n [44, 59, -1, 66, 20],\n [-7, -25, 21, 6, -15],\n [23, 57, -36, 6, 30],\n [33, 57, -6, 54, 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[[60, 66, -56, 18, 20],\n [-36, -9, 0, -18, -72],\n [15, -6, 9, -3, 15],\n [-40, -21, 12, -18, -60],\n [25, 45, -41, 15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, -60, -33, -42, 13],\n [-19, -64, -39, -55, -7],\n [-43, 6, -17, -17, -24],\n [-19, 34, 3, 19, 6],\n [-9, -30, -13, -31, -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, 11, 11, -7, -5],\n [-16, 13, -6, 9, 20],\n [4, -8, 14, -4, -6],\n [-2, 19, 3, -3, 3],\n [0, -22, 1, 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[[35, -33, -12, -7, -13],\n [24, -10, 18, 19, -23],\n [26, -26, -12, -8, -8],\n [-6, -30, -72, -66, 42],\n [-34, 12, -30, -31, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[10, 31, 1, 17, -13],\n [14, -57, -7, -53, 57],\n [-10, -28, -5, -10, 5],\n [2, 7, -7, 7, -11],\n [16, -31, -30, -27, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-63, 44, 18, -18, -55],\n [-49, 7, -4, -47, -14],\n [9, -2, 28, -9, 41],\n [12, -22, -44, 6, -18],\n [16, 5, 18, 17, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[24, 4, 16, 32, 8],\n [3, -5, -5, -1, 5],\n [27, -12, -3, 21, 21],\n [2, 4, 6, 6, -2],\n [9, -15, -15, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, -20, -9, 17, -6],\n [2, -10, 6, -16, 32],\n [-7, 5, 6, -13, 14],\n [-31, 35, 15, -28, 8],\n [-9, 15, 0, 3, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-32, -33, -19, 9, -6],\n [-6, -12, -21, -8, -5],\n [28, 29, 5, -17, 5],\n [-24, -41, 21, 45, -13],\n [20, 27, -41, -51, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-22, -20, 16, 15, -17],\n [20, 26, -23, 5, 32],\n [38, 27, -25, -45, 5],\n [8, 6, 13, -5, 30],\n [-14, -3, -14, 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[[6, 13, -13, -10, 4],\n [-22, -23, 12, -4, 22],\n [-64, -6, -9, 46, 36],\n [18, -53, 55, -18, -20],\n [-4, -32, 27, -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[[-28, 26, -20, 28, -21],\n [30, -38, -23, 10, -35],\n [-6, 13, -13, 8, -20],\n [-54, 58, 13, 10, 28],\n [30, -4, 23, -46, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, -34, -15, -4, -23],\n [9, 11, 8, 4, 0],\n [-39, 7, -11, 20, 14],\n [30, -22, -4, -32, -2],\n [-10, -26, -9, -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[[4, 7, -11, -3, -5],\n [1, -1, 27, 9, 19],\n [-20, 30, 58, -19, 26],\n [19, 22, 24, 17, 30],\n [-17, 0, 43, -7, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 39, -19, -15, -17],\n [1, -19, 33, 13, -19],\n [-28, 32, -16, 23, 18],\n [-14, 8, 40, 14, -42],\n [-25, 35, 11, 4, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[38, -36, -14, 18, 36],\n [-6, 8, 10, -10, -8],\n [12, -16, -20, 20, 16],\n [-2, 10, 28, -26, -10],\n [-4, 9, 19, -18, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, 0, 12, -10, -1],\n [48, -12, 0, 12, -42],\n [-30, 31, -24, -24, 5],\n [-31, 4, 6, -10, 25],\n [-31, 39, -18, -38, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[4, -24, -22, 12, 0],\n [30, -28, -2, 58, -8],\n [-3, 22, 23, -1, -4],\n [34, 12, 24, -26, 24],\n [28, 0, 14, 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 5x5 matrix:\n[[-3, -10, -4, -5, 14],\n [4, 25, -4, 9, -21],\n [2, 0, 8, 2, -8],\n [5, 20, 4, 9, -24],\n [-3, -5, -8, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, -67, -59, 6, -20],\n [-43, 3, -9, 66, 9],\n [-45, 42, -11, 30, -58],\n [20, 0, 9, -51, -3],\n [23, 18, 15, -12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -42, 8, -2, -38],\n [44, 14, -54, 15, 36],\n [-17, -14, 16, 25, 1],\n [8, 32, -8, -23, 13],\n [-22, 26, 26, -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[[13, 33, -7, -32, 36],\n [32, -18, 10, 8, 36],\n [50, -15, 4, -7, -9],\n [26, 21, -8, -31, -9],\n [-26, -26, 8, 34, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-34, 20, -3, -27, 10],\n [-45, 7, 22, -10, -2],\n [-31, 12, 5, 11, 10],\n [-61, 5, 34, 21, 6],\n [-4, 25, -24, 16, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-18, -51, 18, -22, 11],\n [9, 43, -2, 18, -2],\n [10, -8, 24, -52, -5],\n [12, 41, 2, 6, -4],\n [1, -8, -24, 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[[43, 22, -22, 16, 57],\n [46, -24, 12, 42, 66],\n [22, -28, -25, 28, -12],\n [2, -18, -10, 11, -30],\n [-7, -8, 1, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-28, 15, 6, -18, -38],\n [35, 15, -8, 32, 14],\n [-25, -21, 8, -20, -6],\n [-28, 23, -2, -37, -23],\n [33, -23, -8, 17, 53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 23, -6, -9, -2],\n [24, -27, -2, 2, 1],\n [-34, -2, -46, 37, -49],\n [3, -19, -10, -1, -5],\n [9, -28, -4, 11, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[17, -14, 12, 51, -9],\n [30, -35, -23, 62, -9],\n [36, 8, 4, 32, -72],\n [3, -50, -11, -1, 66],\n [35, -6, 33, 27, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[9, -9, 3, -51, -29],\n [-6, -1, 4, 6, -23],\n [7, -14, 12, -13, -38],\n [8, -14, -47, 64, -36],\n [-41, 33, 26, -33, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -9, -29, -17, 9],\n [22, -23, -5, 29, -21],\n [-31, -61, -22, 10, -10],\n [35, 7, -16, 12, -4],\n [28, -35, -19, 31, 25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, 5, -18, -35, -13],\n [20, 23, 48, 25, 29],\n [-40, 2, -18, 37, 14],\n [-5, 11, -34, -75, -28],\n [25, 30, 70, 15, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-51, 50, 56, -10, -32],\n [-21, 14, 20, -40, -44],\n [-27, 40, 42, 1, -18],\n [-17, 22, 24, -6, -16],\n [-28, 15, 18, 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[[11, 0, 3, -8, -7],\n [-13, 12, 17, -16, -13],\n [-3, -30, -45, 54, 39],\n [-17, 25, 25, -19, -4],\n [27, -14, -19, 14, 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[[37, -23, -6, -6, 3],\n [26, -26, 22, 0, 10],\n [-14, 10, 17, -52, -81],\n [0, -36, 3, 15, -27],\n [-3, -7, -8, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-29, -41, -55, -7, 22],\n [-20, -32, -10, -16, 4],\n [-17, -23, -40, -1, 16],\n [22, 30, 50, 2, -20],\n [-14, -18, -40, 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[[0, 12, 12, -12, 0],\n [-45, -33, 21, -21, -27],\n [20, 24, 0, 0, 12],\n [25, 17, -13, 13, 15],\n [-30, -18, 18, -18, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, 13, 1, -2, -1],\n [16, -19, -1, 3, 3],\n [8, 49, -5, -9, -33],\n [12, 54, -6, -10, -38],\n [-16, -20, 4, 4, 20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, -30, -18, 82, 38],\n [-1, 0, -6, -18, -12],\n [-3, 10, -26, 75, 11],\n [-8, 22, -27, 72, 6],\n [22, -10, 13, -63, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-27, 22, -38, 23, 10],\n [42, -42, 48, -18, 0],\n [42, -42, 48, -18, 0],\n [1, -6, -6, 11, 10],\n [-19, 16, -26, 15, 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, 11, -7, -8, 31],\n [-7, 15, 10, -11, 40],\n [-21, -9, -20, 15, -38],\n [-43, 6, -47, 7, 1],\n [-19, 7, -20, -1, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-36, 36, -2, 18, 12],\n [-6, 6, -43, -13, 2],\n [6, -6, -29, -14, -2],\n [-54, 54, 13, 33, 18],\n [-12, 12, 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[[25, -23, -50, 40, 29],\n [-5, -34, -38, 27, 41],\n [-2, 22, 47, -28, -63],\n [-24, 25, 46, -39, -20],\n [0, -35, -25, 25, 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[[27, -30, 9, 31, -31],\n [18, -5, 1, 14, -24],\n [3, -27, 18, 19, -1],\n [8, 44, -18, -16, -20],\n [-5, 66, -37, -41, -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, -8, 13, -23, 7],\n [-25, -16, 11, -5, 43],\n [-6, -5, 13, -27, -5],\n [6, 4, -20, 26, 21],\n [24, 14, -4, -18, -49]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, -6, 33, -16, 19],\n [-20, -24, -13, -10, -16],\n [-42, 10, 55, 24, 49],\n [10, -19, 32, -40, -6],\n [-19, -23, 3, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[1, 0, -28, -7, 12],\n [3, 0, -29, -6, 11],\n [3, 0, 4, 3, -4],\n [-10, 0, -6, -8, 10],\n [8, 0, -26, -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[[-9, -14, 16, 5, 9],\n [28, -4, -10, -48, 34],\n [-15, 11, -6, 18, -1],\n [-28, 6, -15, 20, -15],\n [-30, -42, 60, 36, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, -9, -6, 0, 14],\n [1, -15, -6, -3, 13],\n [-15, -20, 20, -25, -55],\n [-2, -19, -2, -8, 2],\n [-6, -29, 2, -16, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -19, 9, 0, -6],\n [31, -19, 17, -22, -36],\n [4, 7, 0, -13, -12],\n [39, -12, -3, -39, 0],\n [18, -7, -22, -15, 54]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[5, -20, 0, 5, -8],\n [3, 15, 0, 3, -21],\n [5, -30, 0, 5, -2],\n [-10, 20, 0, -10, 28],\n [2, -25, 0, 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[[17, -25, 59, -32, -5],\n [-4, 69, -52, 39, 35],\n [8, 2, 49, -18, 25],\n [2, -18, 58, -32, 2],\n [-67, 2, -46, 1, -35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -33, 1, 13, -19],\n [-17, -15, -6, 8, -66],\n [27, -27, 8, -11, 43],\n [-20, 24, -7, -10, -33],\n [7, 0, -2, 4, -23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[15, -10, 35, 40, -45],\n [38, 0, 24, -10, -12],\n [-18, -4, -18, -44, 18],\n [-18, -6, 9, 51, -27],\n [-11, -8, 16, 48, -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[[11, -14, -46, -26, 36],\n [-42, -25, -36, 30, -42],\n [-4, -29, -80, -31, 43],\n [42, -13, 28, -41, 25],\n [-12, -5, 4, 30, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 20, 20, 4, 4],\n [-3, -1, -28, 7, -20],\n [12, -22, -31, -2, -11],\n [15, -19, 8, -11, 16],\n [18, -20, 25, -16, 29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 16, -11, 1, 6],\n [15, -46, 6, 24, 49],\n [-12, 6, -10, -48, -52],\n [-20, 30, 5, -25, -55],\n [-7, -4, 5, -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[[-16, 37, 6, 78, 14],\n [23, -2, 39, -24, 5],\n [-1, -5, -37, -38, 9],\n [16, 12, -8, 40, 24],\n [-10, 33, 17, 14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-5, 13, 16, 20, -16],\n [4, -8, -8, -13, 9],\n [1, -17, 24, -20, 0],\n [41, 26, 57, -1, -43],\n [-21, -9, -18, 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[[11, -30, 2, -32, -8],\n [-34, 56, 12, 38, 19],\n [-3, -2, -21, 0, -30],\n [1, 22, 7, 32, 26],\n [30, -36, 10, -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[[-8, -4, 6, 34, -16],\n [9, -18, 27, -12, -17],\n [19, 21, 27, -1, 1],\n [26, 17, 60, 21, -22],\n [-3, 1, -24, -26, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-60, -54, 48, -48, -12],\n [-20, -4, 8, 12, -12],\n [-6, -11, 8, -16, 2],\n [54, 50, -44, 46, 10],\n [20, 11, -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[[-14, -4, -12, -29, 24],\n [42, -20, 40, 52, -64],\n [-16, -16, -28, -15, 24],\n [21, -26, 12, 28, -32],\n [36, -28, 36, 32, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[36, 0, -6, 6, -24],\n [-12, 9, -11, 5, 10],\n [-24, -18, 30, -18, 12],\n [4, -15, 21, -11, -6],\n [10, -6, 7, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[41, -3, -34, -18, -10],\n [0, -23, -1, -15, -22],\n [-15, 14, 13, 15, 16],\n [10, -17, -9, -15, -18],\n [49, 11, -40, -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, 4, 3, 7, -5],\n [-26, -5, -5, -13, 5],\n [4, 10, 0, -8, -20],\n [12, -18, 4, 28, 40],\n [8, -16, 3, 23, 35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[24, 0, -39, 21, -36],\n [-11, -10, 1, 1, -1],\n [-8, -16, -14, 10, -16],\n [-29, -22, 10, -2, 5],\n [30, 20, -15, 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[[9, -11, -18, -45, -24],\n [-34, 19, -5, 14, 14],\n [-70, 35, 15, 10, 10],\n [-18, 15, 23, 44, 23],\n [0, 7, 45, 54, 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[[-5, 4, 7, -14, 10],\n [-5, -30, -15, -20, -10],\n [14, 16, -2, 44, -12],\n [-13, -10, 5, -40, 14],\n [-8, -31, -13, -29, -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, -32, -16, 32, -10],\n [-20, -3, 6, 3, -25],\n [20, -21, -18, 21, 10],\n [-22, -17, 2, 17, -23],\n [-44, -23, 14, 23, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[34, -16, -44, -34, -46],\n [-14, -16, -6, 16, -11],\n [30, 12, -8, -38, 4],\n [7, 30, 26, -9, 33],\n [-18, -56, -24, -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[[0, -16, 14, 8, 16],\n [2, 13, -8, -7, -10],\n [28, 6, 42, -10, 36],\n [-10, -1, -16, 3, -14],\n [28, -10, 56, -2, 52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-40, -16, -32, 6, 8],\n [36, -6, 18, -10, -13],\n [-22, 8, 4, 10, -3],\n [21, -23, -25, -16, 11],\n [2, -18, -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[[6, -10, -8, -15, -22],\n [12, 22, -2, 5, 26],\n [-15, -26, 3, -5, -30],\n [-12, 2, 10, 15, 14],\n [-18, 0, 14, 20, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[12, -23, 16, -26, 41],\n [5, 45, -10, -5, -5],\n [3, -26, 4, 7, 8],\n [-1, -53, 12, 5, 13],\n [14, -31, 22, -36, 53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-40, -2, -21, 34, -13],\n [-10, -25, 60, -32, -20],\n [70, 3, -1, 2, 63],\n [16, 9, 23, -54, -18],\n [-24, 20, -4, -24, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 10, 8, -24, 20],\n [-4, -11, 11, 21, -22],\n [-20, -10, 25, 15, -20],\n [-16, 4, 12, -12, 8],\n [20, 1, -19, 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[[28, 84, 4, -16, -4],\n [-3, 48, -23, -14, -10],\n [-13, -2, -23, 11, -5],\n [35, 26, 41, 17, 13],\n [15, -9, -8, 13, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[7, -6, 9, -17, -27],\n [-4, 0, -6, 5, 6],\n [42, 12, 66, -36, -30],\n [0, 8, 2, 11, 22],\n [-16, 0, -24, 20, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -32, 18, 6, 30],\n [0, 43, -73, -75, 37],\n [59, 15, 49, 93, -65],\n [-31, 12, -51, -66, 41],\n [2, 21, -46, -54, 34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, 22, -10, 8, -16],\n [-14, 1, 8, 15, -24],\n [11, 28, 5, 18, -15],\n [-19, 15, -27, -35, 35],\n [41, -8, -13, -7, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 3, -26, 4, -35],\n [18, -18, -9, -38, -5],\n [-27, 17, 15, 42, -2],\n [-18, 14, 19, 50, -9],\n [-13, -6, 5, -38, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-35, 0, 2, 22, -8],\n [-27, -29, 11, 42, 34],\n [-11, 42, -16, -34, -60],\n [-10, -5, -12, -12, 8],\n [-32, -20, 10, 40, 20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[26, 14, 1, 1, -4],\n [-46, -33, -57, -5, -42],\n [55, 44, -24, 10, -42],\n [-32, -22, 67, -3, 48],\n [-32, -28, 20, -6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[30, 29, -38, 14, -35],\n [-21, -27, 33, -27, 44],\n [-26, 8, -2, 53, -26],\n [26, 17, -25, 1, -27],\n [33, 43, -2, 26, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, -9, -48, -19, -4],\n [18, 5, 30, 13, 2],\n [-8, -12, -39, -7, -7],\n [-40, 20, 15, -25, 15],\n [4, 2, 9, 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[[17, -39, -10, 32, 7],\n [-25, -8, -19, 12, 24],\n [-25, 13, 10, -4, 68],\n [-53, -6, -11, 8, 19],\n [-32, 11, -1, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, 2, -8, -22, -12],\n [13, 5, -4, -17, -18],\n [-6, -4, 0, 6, 12],\n [-3, -13, -12, -9, 30],\n [15, -1, -12, -27, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-35, 60, -68, -1, 22],\n [-63, 21, -35, 10, 9],\n [-5, 40, -60, -21, -6],\n [-30, 66, -44, 19, 33],\n [-24, -30, 18, 10, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-22, 26, 14, -8, 8],\n [-20, 22, 10, -4, 6],\n [18, -9, 9, -18, 3],\n [-26, 7, -23, 38, -9],\n [-28, 2, -34, 52, -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[[10, -4, -8, 12, 8],\n [-15, 6, 12, -18, -12],\n [-44, 4, 0, -16, 8],\n [-11, 1, 0, -4, 2],\n [29, 2, 12, -2, -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, 39, -9, 24, 24],\n [8, 19, -4, 9, 9],\n [-28, -26, 5, -9, -9],\n [-44, -10, 1, 3, 3],\n [-20, -25, 5, -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[[-30, 32, -26, 44, -44],\n [25, -17, 65, -15, 32],\n [-9, 16, -16, 12, -3],\n [8, 9, 21, 17, -25],\n [-48, 32, -38, 45, -31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-29, 24, -5, -61, 56],\n [21, -24, -3, 21, -24],\n [10, -16, -6, -6, 0],\n [14, -16, -2, 14, -16],\n [-20, 16, -4, -44, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 0, -2, 4, 1],\n [-2, -16, -14, -4, -9],\n [-10, -20, -20, 0, -10],\n [-28, -20, -26, 12, -7],\n [-28, -20, -26, 12, -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, 3, 5, 6, 7],\n [-10, -15, 35, -5, 20],\n [36, 15, -29, -38, 3],\n [-15, -9, 18, 12, 3],\n [-28, -21, 31, 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[[-30, -86, 7, -6, 18],\n [-30, -75, 5, -5, 20],\n [-16, 53, -10, 9, 23],\n [-64, -37, 18, 23, 33],\n [-14, 41, -3, 11, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[50, 42, 12, 27, 30],\n [-25, -15, -15, -15, -25],\n [-19, -21, 3, -9, -3],\n [-18, -6, -18, -12, -26],\n [-16, -24, 12, -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[[19, -1, 7, -11, -15],\n [-15, -15, -93, 33, 33],\n [37, -6, -11, -12, -13],\n [3, -16, 21, 46, -41],\n [18, -5, 12, 5, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[17, 28, -19, 1, 6],\n [7, 18, -9, 15, 41],\n [-19, -2, 27, 7, -26],\n [31, 12, 53, 13, 44],\n [-16, 31, 56, 34, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -12, -17, -8, -2],\n [12, -24, -5, 23, -31],\n [-18, 43, 52, -14, 21],\n [45, 8, -10, 11, 15],\n [21, 10, 14, 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[[38, -27, 15, 11, 3],\n [17, -19, -18, 22, -16],\n [-25, 28, 25, -7, -1],\n [-61, 63, -35, 7, -29],\n [-8, -15, -2, 24, -26]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 0, 0, 20, 10],\n [4, 20, -12, -4, 0],\n [9, -15, 9, -9, -6],\n [26, -10, 6, -26, -14],\n [26, -10, 6, -26, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, 26, -20, 12, -22],\n [-14, 6, -8, -26, 0],\n [-18, -30, 24, -6, 24],\n [-16, -1, -2, -24, 5],\n [-16, -12, 8, -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 5x5 matrix:\n[[1, 11, -15, 3, -14],\n [-9, 16, -9, 7, -12],\n [-10, 33, -28, 54, 10],\n [33, 33, -13, 37, 22],\n [-4, -29, 10, -34, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[18, -45, 27, 3, -24],\n [-16, 33, -31, 9, 12],\n [18, -45, 27, 3, -24],\n [-2, 21, 13, -27, 24],\n [22, -51, 37, -3, -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[[-38, -6, 4, 2, -3],\n [3, -3, -5, -4, -13],\n [-59, -7, 5, -15, -84],\n [52, -1, -2, 13, 43],\n [63, -4, 5, 24, 59]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, 31, -9, -9, -1],\n [3, -12, -7, 23, -33],\n [-6, 31, -7, -39, 45],\n [-18, 6, -49, -17, 5],\n [-6, 28, -32, -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[[38, -60, -35, -21, -18],\n [30, 18, -47, -71, 24],\n [-28, -27, 9, 26, -32],\n [-12, 64, 2, 2, 12],\n [2, 31, -9, -28, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -12, 8, 24, 8],\n [6, 21, -15, -33, -11],\n [12, 12, -10, -6, -2],\n [42, 36, -31, -9, -3],\n [-18, -9, 9, -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[[20, -29, 35, -2, 45],\n [16, -5, -44, 82, -22],\n [-68, 46, 2, -28, -30],\n [13, -26, -12, 55, 3],\n [15, 4, -20, 60, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-26, 50, -38, -11, -31],\n [-12, -48, 8, 2, 9],\n [1, 7, -43, -10, -41],\n [46, 24, -36, -3, -39],\n [24, -51, 15, 12, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[61, 16, -17, 10, 35],\n [21, 0, 15, -30, -21],\n [-23, 12, -19, 40, 25],\n [29, 16, 3, -10, -3],\n [-5, 66, 8, 7, -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[[-14, -10, 2, -18, -10],\n [-27, -9, -11, 3, -17],\n [-2, -4, 4, -12, -2],\n [24, 12, 4, 12, 16],\n [-3, 3, -7, 15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-1, 2, 4, -37, 12],\n [24, 22, 5, -8, 17],\n [12, 15, 9, 6, 15],\n [19, 11, -6, 17, -4],\n [-41, -24, 13, 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[[-24, -12, 33, 36, -39],\n [12, 0, -9, -8, 11],\n [17, 13, -29, -33, 34],\n [32, 4, -29, -28, 35],\n [-34, -2, 28, 26, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, -17, 4, -6, -7],\n [-5, -1, 3, -34, 11],\n [12, 6, -2, 2, -4],\n [-41, -32, 11, -34, 12],\n [0, 1, -1, 11, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[41, -59, -32, -28, 51],\n [6, -3, 5, 6, 3],\n [4, 2, -2, 13, -3],\n [6, 6, -32, 30, -12],\n [31, -49, 8, -35, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[20, -4, -8, 16, 12],\n [30, -6, -12, 24, 18],\n [-22, 17, -5, -17, -15],\n [15, -3, -6, 12, 9],\n [14, -7, -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[[7, 9, 42, 9, -65],\n [24, -12, -6, 14, 21],\n [-3, -9, 6, 1, 5],\n [6, -6, -6, 21, -14],\n [-22, 18, -12, -1, -33]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[20, 22, -42, 24, 18],\n [-2, 11, -49, 6, 3],\n [-12, 21, -2, 21, 20],\n [6, -18, 1, -33, -75],\n [26, -35, -6, -27, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-34, 22, 40, 31, -11],\n [-48, 5, -8, 13, 5],\n [-46, -29, 16, 28, 31],\n [10, -39, -20, -22, 16],\n [-18, 20, 16, 47, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-13, 59, 3, -8, -24],\n [13, -5, -3, -4, 6],\n [-33, 48, 3, -6, -23],\n [12, 21, 3, 1, -8],\n [40, -59, -15, -13, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, -6, 26, 28, 4],\n [0, -18, 6, 12, -15],\n [30, -6, 42, 44, 10],\n [-30, 6, -42, -44, -10],\n [24, 0, 32, 32, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-59, -47, 6, 57, 5],\n [11, -5, 31, -7, -33],\n [44, 57, -39, -56, 32],\n [66, 68, -25, -76, 14],\n [-45, -54, 41, 51, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-38, 28, 7, -36, -15],\n [14, -19, -2, 15, -2],\n [42, 0, -24, 42, 0],\n [-23, 3, 17, -26, 15],\n [39, -6, -30, 45, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, 22, 4, -40, 8],\n [17, 18, 12, -34, 42],\n [-20, -36, -40, -14, -34],\n [-6, -16, -24, -10, -34],\n [-1, 0, 2, 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[[-19, -23, 16, -11, -3],\n [6, -39, 39, -3, 3],\n [41, 48, -22, 13, 59],\n [31, 8, -9, -6, 42],\n [6, -11, -35, -25, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, -26, 36, -13, -40],\n [8, -37, 44, -12, -45],\n [-17, 10, -14, -3, 27],\n [14, 27, -38, 7, 21],\n [-14, 49, -48, -25, 61]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-40, 51, 22, 16, 23],\n [-18, 29, 28, 28, 21],\n [-2, 18, 14, 20, -2],\n [30, -17, -8, 5, -30],\n [26, -40, -10, 37, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, -10, -9, 10, -4],\n [-56, -35, -18, 35, -33],\n [-75, -45, -35, 45, -30],\n [-12, -15, -20, 15, 4],\n [15, 15, -9, -15, 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[[2, 64, 8, -13, -62],\n [4, -47, -9, 10, 45],\n [-3, 37, 1, -12, -41],\n [-8, 62, 34, -14, -46],\n [-7, 22, -10, 4, -28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -19, -20, 3, -45],\n [-11, -17, -10, 14, 52],\n [-63, -23, -13, 15, -9],\n [43, 43, 1, -21, 54],\n [-13, 8, -14, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-15, -23, -8, -3, -3],\n [-21, -28, -19, 7, -6],\n [-34, -6, -37, 1, 17],\n [-14, -50, 5, -9, -17],\n [12, -17, 13, 10, -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[[45, 5, 11, -23, -41],\n [47, 7, 17, -23, -41],\n [-18, -2, 4, 5, 15],\n [35, 3, 37, -34, -38],\n [-40, -4, -39, 36, 42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 10, 9, -21, 19],\n [21, -11, -7, 2, -11],\n [-39, 29, -17, 6, 33],\n [-21, 8, 49, -39, 15],\n [27, -14, -51, 47, -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[[35, -3, 13, 22, 29],\n [45, -9, 53, -60, 7],\n [-20, -12, -29, 36, 21],\n [15, 9, 23, -30, -17],\n [50, 30, 30, 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[[-18, 17, -18, 37, -1],\n [-5, -41, 26, -2, -11],\n [14, 30, 20, -28, 34],\n [-20, 23, -17, 6, 11],\n [1, 2, -29, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-26, 0, -24, -13, 10],\n [29, 48, -9, 40, 14],\n [28, 20, -65, 13, 57],\n [-51, -24, 18, -24, -45],\n [22, 12, 3, 20, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-1, -9, 2, -5, -4],\n [-3, -13, 13, -15, -5],\n [1, -9, -11, 5, -5],\n [-4, 6, 29, -20, 5],\n [6, 16, -31, 30, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-1, 75, -37, 19, 8],\n [8, -39, -38, 7, -43],\n [-22, 63, 2, 7, 26],\n [-1, -45, -10, 7, -39],\n [8, -42, 25, -20, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, -23, 7, -25, 20],\n [8, 41, -7, 5, -46],\n [-10, 9, -1, 31, -2],\n [14, -3, -17, -9, 0],\n [-13, 12, 9, 23, -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[[1, -4, -9, 2, -23],\n [14, -10, -4, 19, 1],\n [18, -3, 8, 16, 25],\n [27, -16, -1, 35, 18],\n [-13, -17, -27, 7, -49]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-10, -20, -3, -33, -30],\n [-15, -11, 24, -2, -7],\n [5, 9, 0, 14, 13],\n [-15, -5, 33, 13, 5],\n [-20, -26, 15, -31, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-25, 31, 33, 28, -40],\n [-3, 12, -11, -12, -26],\n [-15, 19, 17, 16, -24],\n [-6, -19, -9, 2, 14],\n [-10, 34, 9, -18, -74]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-2, -8, -6, 8, -6],\n [25, 8, 15, 4, -1],\n [24, 27, 27, -18, 15],\n [-29, -1, -12, -14, 8],\n [-19, -7, -12, -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 5x5 matrix:\n[[-20, -36, 22, -18, -14],\n [21, 21, -9, 21, 15],\n [-39, -19, 1, -43, -30],\n [4, 0, 7, -3, -6],\n [27, 19, -7, 31, 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[[25, -44, -25, -7, 4],\n [29, 14, -4, -58, -17],\n [-22, -20, -28, 40, -6],\n [24, -16, -29, -33, -17],\n [26, -57, -14, 8, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-18, -42, 0, 30, 18],\n [24, 24, -20, -12, -24],\n [-36, -36, 30, 18, 36],\n [-33, -29, 30, 13, 33],\n [-39, -27, 40, 9, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-25, 13, 20, 0, -34],\n [9, 25, -27, -31, 30],\n [4, -12, -7, 1, 17],\n [-29, -16, 1, 27, -32],\n [14, 42, -14, -46, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[16, 0, 0, 4, -2],\n [-22, -17, 17, -31, 24],\n [10, 15, -15, 25, -20],\n [-6, -1, 1, -3, 2],\n [-32, -28, 28, -50, 39]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-12, 1, 40, -2, -13],\n [-32, 4, 40, 0, -12],\n [-52, 56, -19, 27, 80],\n [46, -57, 37, -31, -86],\n [-52, 69, -30, 52, 87]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-6, 10, 2, 10, -38],\n [2, -10, 0, -6, 28],\n [7, 25, -6, 3, -40],\n [-19, -25, 12, 9, 10],\n [-20, -30, 13, 8, 19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, 4, -24, -4, 4],\n [-18, -12, 36, 30, -30],\n [-3, -7, 36, 10, -10],\n [-27, -14, 30, 41, -41],\n [15, 10, -30, -25, 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[[25, -30, 8, 11, 11],\n [18, -18, 3, 9, 6],\n [16, -6, -5, 11, 0],\n [24, 6, -19, 21, -8],\n [6, -36, 24, -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[[9, 42, 33, -25, -14],\n [30, 0, 12, -60, -42],\n [15, 30, 27, -35, -22],\n [-17, 24, 10, 30, 23],\n [18, -6, 3, -35, -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, 35, 32, 4, -16],\n [-14, -30, 14, 9, 22],\n [-11, -5, 24, 8, 8],\n [-18, -30, 24, 12, 24],\n [-11, -5, 24, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[11, 13, 10, -20, 10],\n [3, 21, 18, -24, 18],\n [21, 3, 0, -15, 0],\n [-11, 3, 4, 3, 4],\n [20, -4, -6, -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[[12, 0, 7, 1, 2],\n [32, 16, 36, -20, 16],\n [0, -18, -14, 26, -2],\n [12, 12, -2, -18, -30],\n [44, -20, 15, 33, 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[[60, 90, 3, -32, 33],\n [-46, -12, -26, 6, 24],\n [15, 30, -29, -29, -24],\n [-24, -42, -17, 2, -45],\n [24, 48, -20, -28, 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, 54, 30, 41, -42],\n [-45, 9, -18, 47, -24],\n [-3, 51, 4, 53, -32],\n [33, 15, 40, -9, -20],\n [-48, -12, -32, 27, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-5, -9, 7, 8, -16],\n [-3, -15, -3, 12, 12],\n [-12, -32, 9, 27, -15],\n [-9, -17, 12, 15, -27],\n [9, 33, 0, -27, -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, 31, 0, -11, -13],\n [3, -3, 15, 18, -6],\n [3, 7, 27, 28, -16],\n [-2, 32, 26, 18, -26],\n [-4, 19, -2, -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[[-20, -30, -25, -35, -55],\n [-14, -20, -19, -25, -43],\n [-10, -16, -11, -17, -23],\n [-2, -6, 2, -2, 8],\n [-1, -1, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[97, 81, 24, 38, -7],\n [38, 47, 39, -18, 2],\n [4, -14, -12, 24, 0],\n [45, 38, 18, 14, -1],\n [43, 37, 3, -28, -19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[42, 3, -24, 34, 17],\n [-34, -23, -35, -15, -26],\n [40, 25, 16, 28, 57],\n [1, -6, 9, 7, 32],\n [-5, 9, 70, -10, 40]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, 4, -20, 31, 19],\n [8, -12, 16, -27, -2],\n [-8, -8, 0, -2, 12],\n [-22, -12, -8, 9, 28],\n [34, 24, 8, -6, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, 30, -23, 55, 81],\n [10, 29, 19, 21, 6],\n [12, 27, 32, 18, -3],\n [0, 11, 16, 14, 9],\n [21, 37, 0, 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 5x5 matrix:\n[[-24, 14, -30, 12, -48],\n [-2, 7, -22, -22, -11],\n [0, -7, -1, -22, 28],\n [24, 20, -15, -40, 31],\n [-36, -4, -16, 20, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[0, 0, 0, 0, 0],\n [-12, -17, 7, -19, 24],\n [-18, -30, 6, -36, 42],\n [15, 28, -2, 35, -39],\n [-9, 3, 21, 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 5x5 matrix:\n[[0, 24, 30, -9, -9],\n [-8, 0, 14, 7, 15],\n [6, 2, -8, -6, -12],\n [2, -34, -46, 11, 9],\n [-6, 14, 28, 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[[5, 20, -50, 25, 25],\n [-6, 12, -30, -6, 30],\n [4, -8, 20, 4, -20],\n [-11, -8, 20, -31, 5],\n [-5, -20, 50, -25, -25]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[14, -22, 22, 26, -12],\n [-20, 30, -40, -35, 0],\n [-4, 10, 16, -13, 48],\n [16, -28, 8, 34, -48],\n [6, -8, 18, 9, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-15, -1, -11, -42, -42],\n [-2, -15, -5, -25, -19],\n [7, 39, -15, 36, 10],\n [37, -16, -57, -7, -30],\n [10, 21, 25, 59, 59]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-36, -3, -1, -35, 44],\n [0, -3, 2, 5, 4],\n [-40, -30, 55, 1, 4],\n [-1, -4, 23, 12, 10],\n [4, -8, 4, 10, -32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, 30, 24, 3, -8],\n [-46, -26, 26, 29, -36],\n [-2, 40, 20, 16, 8],\n [21, -57, -42, -24, 4],\n [2, 17, 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[[30, 9, 21, 45, 42],\n [-8, -18, 23, -12, -6],\n [8, -6, 21, 12, 14],\n [-14, 3, -23, -21, -22],\n [-22, -3, -22, -33, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-33, 40, 42, -15, 16],\n [-39, 4, 17, -10, 22],\n [15, -48, -30, 6, 6],\n [-16, 17, -23, 12, -32],\n [33, -50, -17, 1, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-10, -29, 20, -9, -2],\n [-17, -9, -18, -14, -6],\n [-34, -49, 4, -29, -10],\n [-29, -50, 14, -25, -8],\n [8, 17, -8, 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[[-6, -28, -21, 45, 5],\n [12, -40, 6, 42, 2],\n [6, 28, 21, -45, -5],\n [6, -28, 0, 32, 2],\n [12, 24, 30, -46, -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, 32, -35, -22],\n [-16, -21, 33, -35, -45],\n [15, -3, -44, 51, 40],\n [-13, 8, 39, -47, -37],\n [-4, -12, 20, -14, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, 16, 19, 21, -32],\n [10, -23, -2, 15, -5],\n [-7, -26, -21, -12, 10],\n [2, -35, -10, 36, -32],\n [5, 50, 34, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[3, 42, -3, 8, 3],\n [-15, -42, 1, -26, 13],\n [33, -6, 6, 49, -45],\n [6, 12, 0, 10, -6],\n [30, -12, 6, 44, -42]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, -23, -24, -16, 0],\n [-12, -73, 30, 27, 77],\n [21, 17, 1, -22, -8],\n [6, 25, 4, -13, -36],\n [-37, -44, 23, 42, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -20, -24, -9, 3],\n [4, -14, 30, 21, -33],\n [-6, -23, 21, 18, -33],\n [-14, -11, -15, -6, 3],\n [20, 2, 42, 24, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -7, -22, -25, -15],\n [2, 7, -10, -59, -25],\n [1, 11, -9, -34, -23],\n [5, -25, -9, 8, 17],\n [-3, -34, 33, -4, 54]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, -22, -14, -19, -11],\n [18, -4, 2, 2, 8],\n [-30, -36, -22, -30, -16],\n [6, 20, 10, 14, 4],\n [-33, 2, -6, -7, -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[[-30, -23, -21, 16, 9],\n [-9, -24, -31, 1, -3],\n [-6, -1, 1, 4, 3],\n [-9, 12, 21, 9, 9],\n [30, 23, 21, -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 5x5 matrix:\n[[-24, -10, 31, -43, 3],\n [-18, -15, 22, -21, 21],\n [-22, -9, 32, -39, 5],\n [-8, 0, 18, -18, -2],\n [22, 39, 5, 0, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[9, 34, 18, 24, 10],\n [-42, -31, 22, -64, 6],\n [-7, -26, -14, 1, -22],\n [3, 39, 15, -13, 37],\n [-41, -16, 34, -33, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-29, -29, 7, -16, -6],\n [-22, 0, -1, -5, -15],\n [5, -21, 19, 4, 12],\n [-2, -2, -31, -25, 3],\n [10, -6, -47, -37, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-62, 68, -23, -26, 22],\n [55, -85, 7, 10, -74],\n [29, -29, 8, 48, -28],\n [-2, 5, 14, 0, 28],\n [12, 12, -7, 30, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[31, -4, -72, -34, 44],\n [14, 17, 87, 46, -55],\n [-39, -9, 66, 42, -24],\n [15, -19, 17, 29, 19],\n [29, -17, -8, -17, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, -22, -35, -9, 28],\n [24, -22, -49, 20, 40],\n [-3, -14, -26, -14, -12],\n [12, -7, -10, 8, 13],\n [38, -30, -19, -12, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[39, -6, -17, -33, 57],\n [-21, 69, 47, 27, -59],\n [-10, 30, 8, -16, -10],\n [-37, 42, 27, -21, -63],\n [-19, 15, 0, 36, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-24, -8, 20, 20, 16],\n [18, 31, -5, 5, 8],\n [30, -20, -37, -49, -44],\n [6, -23, -15, -25, -24],\n [-6, -22, -3, -11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-30, 22, 52, -52, 34],\n [2, -28, -11, 10, -2],\n [6, -72, -6, -18, 33],\n [-12, -4, 2, 32, -38],\n [0, 40, 3, -12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-18, 12, -8, -28, 2],\n [9, 3, -4, 10, -5],\n [-21, 8, -4, -30, 5],\n [9, 3, -4, 10, -5],\n [12, 25, -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[[-28, -30, 38, -16, 28],\n [16, 10, -11, 7, -1],\n [-22, -25, 32, -13, 25],\n [8, 0, 2, 2, 10],\n [24, 10, -9, 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[[-22, 13, -13, 5, 6],\n [41, -14, -11, -43, -8],\n [-52, 18, -14, 9, 17],\n [-49, 16, -3, 23, 14],\n [24, -11, -15, -46, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 1, -7, 10, 33],\n [-43, 12, 6, 10, 1],\n [-19, 16, -6, 2, 5],\n [-48, 15, 3, 18, 21],\n [53, -18, -8, -2, 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, 14, 9, -6, -5],\n [5, 19, -12, 4, -13],\n [-10, -16, -10, 4, 8],\n [0, 10, 5, 10, -15],\n [25, 10, 1, -42, 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[[-13, 6, -50, -11, 0],\n [-2, -26, 64, 26, 20],\n [8, 14, -4, -32, -44],\n [0, -15, 48, 2, -9],\n [9, 22, -34, -21, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[26, 23, -14, -5, -1],\n [-26, -23, 14, 5, 1],\n [-20, -5, 4, 3, 5],\n [-20, 10, -4, 2, 10],\n [-32, 4, 0, 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[[36, 12, -30, -36, -18],\n [26, 64, 55, 22, -55],\n [28, -3, -37, -39, -6],\n [-43, -39, 3, 53, 22],\n [-1, 27, 33, 11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[20, 12, -8, 6, 34],\n [8, -3, -11, -8, 24],\n [-24, -12, 12, -4, -44],\n [-12, 3, 15, 10, -34],\n [12, -3, -15, -10, 34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[3, 5, -1, 1, -1],\n [-15, 1, 25, 5, 1],\n [3, 18, 9, 6, -3],\n [4, 11, 2, 3, -2],\n [-26, -26, 22, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -6, 6, 18, 18],\n [-20, -10, 16, 24, 44],\n [16, 14, -20, -30, -46],\n [12, -19, 10, 54, 16],\n [2, -10, -2, 48, 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, 9, 3, 18, -18],\n [20, 42, -18, 20, -36],\n [-22, -39, 19, -14, 30],\n [16, -6, -10, -28, 24],\n [14, 33, -13, 18, -30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, -30, -18, -36, 12],\n [25, -25, -15, 6, 10],\n [0, 30, -45, 18, -45],\n [31, 30, -3, 42, -23],\n [28, 33, -39, 42, -44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 9, 11, 16, -11],\n [-12, 14, 6, 6, 14],\n [4, 14, 12, 11, 10],\n [10, -16, -1, 7, -42],\n [-18, 18, 15, 24, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[5, 2, -8, -3, 9],\n [-25, -28, -14, -39, 0],\n [0, 4, 12, 12, -10],\n [-20, -24, -16, -36, 4],\n [5, -4, -26, -21, 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, 12, -10, -9, 13],\n [11, -47, -42, -26, -21],\n [-22, 2, 32, 11, -9],\n [27, -10, -28, -47, 1],\n [-7, 56, 50, 8, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-25, 15, -17, -9, -15],\n [-8, 38, 9, 5, 16],\n [-20, 6, -1, -23, 10],\n [-30, 20, -12, -14, -7],\n [2, -26, 25, -24, 32]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-30, 9, -7, 3, 8],\n [-5, 17, 10, 0, 33],\n [20, 3, 59, 29, 33],\n [-11, -38, 17, -19, -26],\n [-27, 16, -93, -29, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-7, 0, 0, 8, -9],\n [7, -4, -2, -13, 4],\n [-13, -25, 19, -27, -2],\n [-36, -15, -39, 33, 29],\n [13, -2, -8, -15, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[52, -6, 4, -40, -36],\n [-4, 8, -18, -22, -12],\n [-10, 25, -20, -30, -30],\n [20, -55, 15, 35, 60],\n [42, -41, -16, -30, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-34, 24, 4, -74, -4],\n [24, -30, -5, 0, 42],\n [38, -66, -11, 76, 2],\n [34, -54, -9, 74, -2],\n [-16, -30, -5, 10, -46]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-40, -5, 32, -21, -11],\n [-10, 10, 3, -5, 1],\n [41, 1, 22, 18, 7],\n [-19, -23, -23, 31, 10],\n [9, 12, 5, -24, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-26, 26, -24, -2, -12],\n [-28, -8, 36, -8, -20],\n [3, 33, -51, 3, 15],\n [-6, 24, -51, 8, -11],\n [-19, -11, -22, 15, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, -25, -23, 29, -8],\n [70, -16, 19, 22, -53],\n [-31, -33, -6, 32, -2],\n [-25, -28, 15, 16, -1],\n [19, 19, 9, -16, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[52, 15, -29, -39, -18],\n [8, 20, -27, -14, 14],\n [-28, 5, -15, 5, -10],\n [-13, 8, -32, -13, -27],\n [-30, 22, -14, 14, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[8, -8, -16, 24, 16],\n [19, 16, -8, 42, -2],\n [-21, 0, 24, -54, -18],\n [-12, -30, -12, -18, 24],\n [2, 12, 8, 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 5x5 matrix:\n[[-14, -2, 44, 24, -48],\n [46, -50, -4, 10, 12],\n [-11, 49, 2, -31, -18],\n [3, -3, -30, -9, 36],\n [21, -16, -12, -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[[-21, -27, 31, -19, 9],\n [-41, -31, -1, -19, 61],\n [34, 38, -34, 26, -26],\n [20, 16, -2, 10, -28],\n [-1, -11, 29, -9, -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[[1, -36, 54, -19, -34],\n [8, -24, 36, -14, -26],\n [-2, -16, 24, -8, -14],\n [-41, -20, 30, -3, 0],\n [44, 0, 0, -8, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[13, 37, -27, 30, -40],\n [33, 9, -30, 21, -36],\n [-19, -19, 21, -42, 40],\n [38, -72, 7, 5, 8],\n [19, 34, -33, 9, -34]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[30, -12, -7, 55, -44],\n [-25, -1, -2, -28, 36],\n [38, 23, 1, 30, 0],\n [-19, 5, 10, -34, -3],\n [-33, -15, -9, -15, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, 30, -6, 30, -36],\n [-12, -32, -6, -28, 30],\n [0, -4, -24, 4, -12],\n [-4, -16, -34, -4, -6],\n [-4, -15, -28, -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[[9, -67, 3, 48, 31],\n [1, -8, -36, 29, -4],\n [-9, 25, 6, -32, -4],\n [29, 25, 29, 12, -36],\n [26, 3, 28, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, 7, 20, 14, -5],\n [-37, -4, 29, -9, -14],\n [-31, -28, -1, -3, -2],\n [42, 1, -29, 15, 15],\n [15, 8, 25, 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[[40, 0, 0, -5, 0],\n [-21, 16, -16, 59, 9],\n [10, 28, -28, -14, 8],\n [-42, 6, -6, 21, 3],\n [-10, 32, -32, -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[[2, -14, 13, 0, -6],\n [4, -22, -30, 8, -20],\n [-30, -29, 7, 10, -22],\n [-16, 14, 35, -5, 14],\n [0, 5, 13, -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[[-22, -21, -45, -9, 15],\n [15, -5, 25, 30, -25],\n [-13, -24, -30, 9, 0],\n [3, 16, 10, -15, 8],\n [6, 15, 15, -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[[43, -1, -16, 3, 38],\n [-31, -31, -9, -10, -36],\n [15, 28, -35, 7, -12],\n [-29, -29, 35, -12, -56],\n [-38, -30, -44, -10, -52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -26, 12, 4, 23],\n [0, 12, -21, 30, -21],\n [7, 9, -27, -8, -14],\n [2, 8, -4, -8, -6],\n [-9, -2, 14, 40, -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[[-27, 1, 28, 36, -17],\n [26, -6, -24, -40, 22],\n [8, -11, -2, -22, 17],\n [-23, -13, 32, 16, 1],\n [9, 28, -26, 18, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[1, 16, -10, 15, 17],\n [26, 0, -20, -10, -38],\n [-12, -10, 15, -5, 6],\n [-26, -26, 35, -15, 8],\n [30, 38, -45, 25, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-25, 20, -50, -25, -5],\n [6, 8, -4, -14, -2],\n [18, -24, 48, 33, 6],\n [14, -8, 24, 9, 2],\n [29, -20, 54, 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[[-8, -36, 48, 6, 17],\n [0, 0, 0, 0, 0],\n [-36, -14, -6, 27, -16],\n [-20, -6, -6, 15, -10],\n [24, 36, -36, -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[[29, 20, 28, 6, 26],\n [-18, -20, -45, 12, -60],\n [34, 24, 32, 12, 28],\n [44, 20, 32, -28, 34],\n [41, 24, 20, 26, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, 12, 6, -58, -8],\n [0, 0, -3, 43, 8],\n [2, 30, -3, -37, 2],\n [11, 45, -51, 11, 23],\n [1, -5, -5, -15, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, -11, 17, 40, 7],\n [3, -8, 35, -6, 28],\n [-16, -32, 8, -6, 8],\n [3, -7, 37, 43, 23],\n [-3, -5, -25, -1, -35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-7, -8, 7, 10, -14],\n [-9, 37, -6, -12, -8],\n [-10, -3, 12, 18, 2],\n [26, -24, -22, -12, 20],\n [-3, 56, 13, -40, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[1, 28, 12, 6, 61],\n [9, 21, 37, 33, 53],\n [-11, 20, -33, -48, 10],\n [-7, 38, 5, -12, 51],\n [-20, 9, -15, -9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, 2, 5, 11, 33],\n [19, 39, 23, 25, 33],\n [5, -7, 7, -38, 9],\n [15, 25, 10, 40, 40],\n [-12, -22, 9, -40, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, 27, -8, 3, 41],\n [39, 28, -7, -23, 51],\n [-45, -6, 12, 40, -28],\n [42, 31, 4, -25, 53],\n [-35, 10, 24, 29, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[54, 48, -6, 6, -3],\n [-18, -24, 18, -30, -27],\n [-4, 0, -20, 27, 11],\n [6, 2, 14, -20, -11],\n [10, 12, 6, -3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[7, 9, 33, 7, -6],\n [-12, -14, 34, 13, -19],\n [10, -52, 12, 19, -31],\n [31, -12, 14, 9, -10],\n [9, -43, -7, 11, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[3, 10, 7, 3, 7],\n [-18, 27, -24, -39, 9],\n [-1, -4, -16, -19, -2],\n [-1, 9, -1, -4, 0],\n [30, -16, 36, 48, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[38, -5, 6, 32, -10],\n [45, 7, -16, 63, -14],\n [17, -6, -24, -39, 22],\n [-37, 4, 13, -5, -5],\n [-39, 26, 0, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-8, 45, 18, -40, 20],\n [16, 25, 14, -20, 20],\n [22, 20, 13, -15, 20],\n [-2, -6, -3, 5, -4],\n [-36, 30, 6, -30, 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, -20, -30, 24],\n [-18, -8, 0, 20, -18],\n [-21, 9, -30, -15, 9],\n [-18, -8, 0, 20, -18],\n [1, -2, 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[[-7, 17, -13, 24, 21],\n [-1, -19, 2, 10, 19],\n [1, -16, 5, 11, 23],\n [7, -21, 15, -4, 11],\n [-13, 17, -25, -2, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[10, -14, 13, 29, 6],\n [23, -39, -2, 14, 9],\n [-44, 17, -7, -16, 15],\n [-1, 18, 37, 56, 0],\n [54, 24, 1, -17, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[12, 45, 0, 3, 34],\n [7, 32, 37, -23, 16],\n [28, 5, 22, 7, 2],\n [39, -14, -4, 14, -19],\n [-92, -30, 9, -3, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[16, 18, 10, -34, 28],\n [20, 17, -4, -15, 13],\n [-32, 3, 28, -37, 31],\n [-14, -13, -12, 31, -25],\n [26, 2, -31, 36, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[22, 16, -32, -34, 12],\n [-12, 42, -8, 48, 42],\n [0, -2, -15, 2, 28],\n [-13, -11, 18, -21, -42],\n [2, 17, -32, -4, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-13, -36, -9, 6, 8],\n [20, 17, 26, -31, -30],\n [25, -6, 21, -12, 10],\n [26, 6, 22, -14, 4],\n [-12, -18, -14, 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[[-30, 20, 10, 15, 0],\n [24, 2, -26, -9, -6],\n [12, 4, -16, -4, -4],\n [-6, 4, 2, 3, 0],\n [6, -28, 22, -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[[18, 66, -7, -13, -19],\n [-26, -24, 27, -15, 1],\n [17, 60, -4, -12, -17],\n [-27, 10, 41, -13, -22],\n [-26, -27, 11, -42, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[39, 50, -5, -12, 31],\n [-7, -10, -35, 36, 17],\n [9, 10, -55, 48, 41],\n [24, 31, 5, -15, 14],\n [2, 1, -55, 51, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -26, 6, -35, -45],\n [18, -12, 9, 3, 25],\n [45, -5, 15, -2, 30],\n [30, 0, 9, 3, 25],\n [-33, 7, -12, 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[[18, 1, -36, 8, 70],\n [-4, -15, -14, 16, 34],\n [40, -26, -12, 26, 0],\n [-18, 21, 24, -24, -42],\n [14, -2, -34, 10, 68]]\n\nPresent the 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, -47, 18, -22],\n [56, -22, 36, -40, -44],\n [41, -19, 18, -28, -35],\n [-27, 9, 20, -8, 29],\n [9, 9, 33, -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[[-41, 50, 14, 12, 10],\n [42, -49, -25, 15, -22],\n [-39, 42, 10, -4, 26],\n [30, -56, -12, -8, 26],\n [9, -12, 3, -23, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[11, -21, -10, -22, 6],\n [-25, 10, -7, 9, -36],\n [-21, -41, -16, -20, -20],\n [-32, 24, -2, 22, -42],\n [-67, -35, -20, 0, -68]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-26, -1, -2, -4, -6],\n [-6, 10, 20, 12, -24],\n [8, 12, 24, 16, -24],\n [5, -21, -42, -26, 48],\n [18, -11, -22, -12, 30]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-9, 14, 16, 17, -35],\n [-28, -21, 1, -6, 33],\n [-44, -25, 6, 49, 3],\n [-23, -33, -8, 1, 51],\n [-35, -6, -2, -27, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 4, -8, 20, -12],\n [-12, 9, -2, -3, 3],\n [-17, 18, 15, -19, -45],\n [-4, 22, -6, 20, -42],\n [-18, 27, 3, 0, -45]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, -5, -7, -8, 14],\n [-34, 45, 27, -12, -30],\n [-28, 7, 30, 3, 0],\n [2, 14, -25, 7, 14],\n [0, 4, 16, 4, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[2, 36, 10, -5, -31],\n [-7, -36, -21, 27, 34],\n [4, -12, -26, 34, 24],\n [2, -14, 17, -34, 3],\n [-2, 18, -13, 29, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-4, 9, 56, -37, 6],\n [62, 1, 4, 53, -16],\n [-5, 6, 22, -26, -3],\n [-24, -5, 16, -33, -20],\n [15, -3, -42, 33, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -24, 3, -24, 0],\n [-1, -21, 7, -22, -1],\n [0, 24, -3, 24, 0],\n [3, -17, -11, -14, 3],\n [-10, -2, 44, -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[[54, -2, -19, 45, -4],\n [-41, 4, 13, -27, -1],\n [2, -2, -9, 7, 10],\n [8, -28, -19, -24, 49],\n [12, 12, 6, 22, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-6, -1, 3, -2, 11],\n [-14, 7, 19, 2, 35],\n [-10, -11, -7, -10, 9],\n [-16, -19, -13, -17, 13],\n [-20, -22, -14, -20, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-43, -7, -2, 4, -22],\n [9, -22, -6, -19, 33],\n [-43, -23, 8, -28, 0],\n [3, -32, 2, -26, 37],\n [-2, 9, 1, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[5, -1, -19, -48, 15],\n [-33, 67, 11, 19, -12],\n [-18, 12, -54, -39, 18],\n [-8, -20, -32, 18, 3],\n [-20, 40, 20, 34, -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[[-31, 19, -12, 49, 29],\n [-22, 8, 28, 24, -18],\n [-32, -10, 64, 8, -80],\n [49, -16, 15, 8, 20],\n [-45, 3, 28, 6, -53]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, 4, 15, -19, 14],\n [-2, -6, -4, -24, -2],\n [9, -25, -14, 16, -27],\n [8, -21, 5, -22, -8],\n [-9, 0, -14, -35, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[6, 0, -32, 14, -6],\n [3, 3, -31, 10, -6],\n [3, 1, -21, 8, -4],\n [-6, 10, -18, -4, -4],\n [-3, 4, -4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-30, -20, -9, -17, 0],\n [-20, 17, 22, -9, -21],\n [-24, -4, 4, -14, -4],\n [-36, 6, 18, -30, 18],\n [6, 2, 1, -8, 38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[14, 22, 7, -22, -2],\n [-32, -22, -29, 53, 19],\n [20, -1, 50, -25, -41],\n [4, 9, -47, 24, 0],\n [22, 24, -6, 7, -34]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, -14, -1, 5, 29],\n [12, 0, -14, 29, -32],\n [7, -19, 28, 21, -33],\n [2, 24, -48, -1, 14],\n [1, 22, -43, -4, 17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[10, 12, 13, -8, -5],\n [36, -3, 48, -54, 11],\n [10, 39, 46, -32, 26],\n [-20, 2, -37, 38, -16],\n [-32, 23, -25, 32, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-73, 9, -1, -12, -61],\n [20, 49, 20, -11, 16],\n [-16, 18, 16, 5, 4],\n [46, 18, 34, 0, 22],\n [10, 75, 38, -32, -22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[12, 2, 11, 5, 12],\n [-43, -41, 43, -50, -22],\n [-54, 0, 15, -15, 15],\n [33, 60, -37, 67, 32],\n [-51, -51, 42, -63, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, -12, 12, 42, -12],\n [4, -6, -4, 16, -21],\n [-3, -2, -10, 1, -20],\n [12, -12, 0, 36, -30],\n [4, -2, 4, 8, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[13, -17, -3, 8, 24],\n [-25, 6, -22, 18, 8],\n [-8, 35, -12, 15, 25],\n [-8, 7, 17, -4, 14],\n [-8, 29, -51, 30, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[51, 25, 6, -15, 45],\n [65, 49, 8, -19, 53],\n [-35, 9, -15, 17, -31],\n [-5, -2, 23, -12, -18],\n [8, 17, 34, -21, -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, 10, 28, -48, -26],\n [-23, -38, -59, 3, -23],\n [8, 14, -13, 4, -21],\n [-17, -20, -6, -31, -18],\n [0, -18, -21, 60, 51]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-2, 20, -3, 39, 2],\n [-41, -20, 16, 40, -16],\n [-21, 26, 16, 46, -12],\n [15, 37, 8, 5, -18],\n [-3, -17, -10, -18, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, 56, -25, -7, -18],\n [36, -10, 29, 3, 4],\n [-20, 24, -14, -12, 4],\n [45, 16, -15, -39, 3],\n [-5, -55, 20, 4, 23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -23, -4, -35, 16],\n [-13, -2, 4, -14, -24],\n [18, -15, 4, 19, 20],\n [-7, 35, -8, -1, -16],\n [-3, -43, 8, -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[[12, 36, 24, 18, 6],\n [-27, 10, 57, 33, 3],\n [-22, -23, -10, -4, 11],\n [12, -9, 36, 0, -9],\n [31, 28, 35, 7, 23]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[6, -44, -7, -18, -49],\n [24, -1, 26, -3, -15],\n [52, 27, 30, -43, -27],\n [56, 25, 17, -2, -73],\n [-11, 3, -29, 26, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[38, 18, -23, 53, 8],\n [-22, 7, -34, 13, -6],\n [-25, 17, -18, 12, 43],\n [18, 4, -17, 30, -13],\n [19, -16, 19, -24, -41]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -7, 4, 12, 9],\n [-18, -12, 4, -18, 4],\n [-45, -45, 20, 0, 35],\n [-15, -14, 6, -3, 10],\n [3, 1, 0, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-3, 12, 9, 18, 3],\n [6, 24, 6, -4, 42],\n [6, 30, 9, 0, 48],\n [3, 0, -3, -10, 9],\n [6, -24, -18, -36, -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[[64, 8, 34, 48, 44],\n [29, 33, 31, 28, 34],\n [5, -4, 0, 2, 4],\n [-7, -26, -19, -18, 10],\n [11, -63, -29, -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[[-1, 6, 9, 1, 8],\n [-24, 24, 3, 43, 12],\n [-10, -4, 6, 30, -16],\n [-14, 20, -24, 12, 16],\n [9, -14, -6, -14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-1, 0, 24, -40, 22],\n [-14, 16, -21, 60, -33],\n [-6, -14, -58, 58, -8],\n [-16, -8, 33, -41, 11],\n [-27, -3, 54, -54, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-15, -16, 23, 30, 17],\n [75, 38, -10, -3, 20],\n [45, 38, -10, -21, -16],\n [45, 24, -9, -6, 9],\n [10, 32, -12, -38, -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[[-23, -35, 24, 16, -1],\n [24, 39, -34, -11, -3],\n [-4, 2, -7, 21, -20],\n [-15, -28, 12, -1, 16],\n [-2, 2, -17, 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[[-19, -36, -45, 20, -3],\n [15, 30, 37, -16, 2],\n [-19, 24, 11, 12, -17],\n [-16, -24, -32, 16, -4],\n [32, -12, 8, -24, 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[[25, -48, 32, 49, 15],\n [-14, 2, -28, 26, 41],\n [-13, 20, -25, -10, -1],\n [7, -8, 2, 9, -11],\n [15, -18, 12, 15, -18]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-26, 6, 5, -12, -3],\n [-8, -12, 0, -16, -14],\n [-8, 6, 2, 0, 3],\n [12, -36, -6, -24, -30],\n [-40, 12, 8, -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[[7, 15, -8, -24, -12],\n [-33, 27, 48, 0, -36],\n [-25, 17, 36, 4, -24],\n [-29, 22, 42, 2, -30],\n [21, -12, -30, -6, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[34, 33, -18, 24, 37],\n [13, 29, -46, 23, -41],\n [-15, 32, 34, 57, 20],\n [-21, -55, 19, -61, -2],\n [-10, -23, -23, -34, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-38, -18, 24, 19, -39],\n [-12, 24, -14, 30, -48],\n [-44, -30, 52, 13, -15],\n [12, -6, -15, -14, 9],\n [22, -36, 14, -48, 72]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[1, 47, -21, 6, -23],\n [26, -61, 20, -27, 37],\n [28, -56, -1, -48, 36],\n [16, -66, 16, -6, 42],\n [6, -21, -84, -3, 37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-16, 20, -32, 8, 16],\n [-29, -20, 5, 1, 29],\n [21, -20, 35, -9, -21],\n [11, 30, -27, 5, -11],\n [17, -15, 27, -7, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[22, 20, 0, -15, 59],\n [-2, 22, -28, 36, -14],\n [18, -14, -4, -32, -14],\n [-28, -10, 25, 15, -1],\n [-3, -21, 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, 44, -64, 26, -10],\n [-30, -15, -15, 24, 3],\n [2, -53, 33, -17, 0],\n [16, -15, -15, -2, -9],\n [-20, -12, -48, 34, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[31, 40, -12, 99, -41],\n [42, 44, -43, -4, 36],\n [-1, 11, 6, 38, 15],\n [35, 38, -25, 55, -15],\n [-42, -23, 35, -45, 62]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, 0, -10, 10, -5],\n [20, 12, -20, 4, -16],\n [-30, -18, 30, -6, 24],\n [20, 30, -38, -2, -34],\n [-10, -12, 16, 0, 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[[-29, 27, -1, -46, 0],\n [34, -12, -46, 12, 38],\n [28, -9, -40, 8, 33],\n [-26, 18, 14, -28, -12],\n [-25, 0, 55, 10, -45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-31, -30, 26, 18, -18],\n [-11, -5, 9, 11, -13],\n [3, 24, 12, 24, -44],\n [-25, 14, -18, 25, -8],\n [10, 25, 15, 20, -45]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-15, -10, -15, 30, -5],\n [16, 12, 18, -34, 12],\n [13, 8, 12, -25, 1],\n [14, 8, 12, -26, -2],\n [-16, -12, -18, 34, -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[[52, -67, -66, 85, -16],\n [1, -1, -4, -1, 8],\n [44, -38, -48, 44, 4],\n [18, -3, 6, 15, -44],\n [-16, -17, -2, 25, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, -20, 24, 8, 26],\n [-11, -10, -15, -31, 7],\n [17, 12, 5, -27, 0],\n [45, 30, 3, -13, -15],\n [-4, -23, 11, 41, 32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-28, 3, -25, -22, -4],\n [21, 13, 20, 19, -8],\n [-44, -4, -40, -36, 0],\n [30, 36, 30, 30, -24],\n [-14, 32, -10, -6, -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[[48, 27, -24, -15, 18],\n [6, -19, 7, -9, 16],\n [-22, 19, -39, -22, -39],\n [8, -10, 8, -4, 14],\n [32, 12, -41, -43, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-1, 0, -5, -4, 0],\n [1, -10, 50, 4, 25],\n [3, 10, -30, 12, -25],\n [1, 10, -40, 4, -25],\n [5, 12, -29, 20, -30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-40, 40, -38, -22, 4],\n [24, -16, 18, 10, 12],\n [28, -12, 17, 9, 26],\n [8, -22, 16, 10, -26],\n [4, -21, 14, 9, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-13, -11, 16, -7, 55],\n [-1, -5, -28, 35, 30],\n [-47, 27, 8, -9, 1],\n [25, -21, -17, 36, 38],\n [-30, 15, -34, 15, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-20, -16, -26, -38, 48],\n [21, 13, -8, 18, -62],\n [-3, -7, 35, 42, 8],\n [-8, -14, -15, 1, 8],\n [-15, -33, -60, -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[[30, -8, 18, 31, -30],\n [-30, 16, -18, -41, 42],\n [-15, 44, -27, 2, 12],\n [0, 28, -12, 10, 0],\n [-20, 16, -12, -34, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 1, -42, -10, 23],\n [-21, 7, -21, 29, 17],\n [-9, 13, -1, -43, 20],\n [46, -98, -34, -2, 16],\n [17, -5, -7, -29, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-42, 50, -9, 4, -26],\n [-6, -18, -15, -36, 42],\n [42, -39, 15, 12, 6],\n [8, 13, 14, 32, -36],\n [-22, 33, -1, 12, -26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -10, 5, -30, -25],\n [-14, -2, -21, 54, 13],\n [-28, -13, -21, 36, -10],\n [30, 18, 13, -6, 27],\n [26, 8, 29, -66, -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[[42, 28, 14, 0, -62],\n [-12, 1, 23, -27, -26],\n [30, 8, -26, 36, 14],\n [-12, -5, -8, -9, 31],\n [6, 12, 0, -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[[30, -18, 30, 24, 30],\n [5, -19, -20, 7, -25],\n [2, -14, -18, 4, -22],\n [11, 3, 26, 7, 29],\n [28, -20, 23, 23, 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[[7, 0, -12, 20, -11],\n [12, 45, -9, -33, -63],\n [23, 46, -20, -21, -63],\n [4, -24, 28, -26, 16],\n [35, 0, -32, 30, 29]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, -26, -30, 14, -26],\n [-12, 21, 34, -18, 13],\n [-1, -2, 55, -40, 2],\n [-15, 10, 13, -6, -2],\n [-11, -27, 5, -11, -35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[25, 0, 9, -36, 23],\n [-16, 0, -8, 20, -12],\n [-3, 0, -5, -1, 2],\n [17, 0, 19, -7, 0],\n [6, 0, 24, 21, -21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, 7, -24, 2, 21],\n [18, 11, -5, 4, -3],\n [8, 37, 6, -16, 17],\n [34, 6, -42, 12, 40],\n [9, -6, 11, 12, -33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-48, 6, 38, 26, -24],\n [-12, -12, 26, 20, 36],\n [8, -16, 12, -4, -8],\n [32, -28, 4, -18, -8],\n [-54, 18, 29, 34, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-10, -26, 1, 2, 23],\n [-4, -20, -2, -4, 2],\n [8, 4, -5, -10, -31],\n [8, 12, -3, -6, -25],\n [12, 60, 6, 12, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-24, -15, -18, 33, -15],\n [12, 8, 12, -16, 12],\n [-8, -5, -6, 11, -5],\n [0, 1, 6, 1, 9],\n [-12, -6, 0, 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[[-35, -4, 31, -26, -4],\n [-19, 4, 11, -10, -8],\n [-5, 2, 2, -2, -3],\n [-10, 22, -13, 8, -23],\n [44, 4, -38, 32, 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, -2, -27, 30, 11],\n [-24, 16, 31, -30, -3],\n [-18, 2, 12, -24, 16],\n [30, 6, -26, 48, -14],\n [9, -31, -6, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, 14, 16, 9, -2],\n [45, -20, 5, 0, 5],\n [13, 28, 45, 24, -3],\n [-20, -8, -24, -12, 0],\n [29, -34, -24, -15, 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, -30, -30, -30, 10],\n [-10, -32, -24, -28, 12],\n [-1, -17, -15, -16, 6],\n [-19, -1, 9, 4, 2],\n [24, -6, -18, -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[[-66, -43, -6, -21, -44],\n [30, 17, 4, 7, 20],\n [-12, -12, 1, -8, -8],\n [-18, -5, -5, 1, -12],\n [-48, -32, -4, -16, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[33, 24, 30, -14, -41],\n [17, 9, 22, -5, -24],\n [-17, -1, 10, -7, -8],\n [-15, 13, 22, -21, -28],\n [63, 2, 2, 22, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[15, -10, 39, 3, 7],\n [2, -10, 11, 3, 1],\n [-6, 4, -72, 4, -16],\n [46, -4, 28, 8, 4],\n [17, 7, 20, -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[[6, -10, -8, -24, -70],\n [24, 44, -25, -13, 21],\n [-19, 4, -39, 8, -40],\n [-53, -15, -32, 53, 22],\n [0, 22, -33, -8, -42]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[34, 24, 12, -14, -6],\n [14, 19, -9, 4, -10],\n [15, 35, -15, 15, -15],\n [22, 40, -12, 12, -16],\n [29, 25, 3, -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[[44, 6, -18, 10, 0],\n [-20, 16, 3, 17, 5],\n [11, 7, 1, 41, 8],\n [0, 41, 1, -33, 16],\n [-16, -13, 25, 23, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[38, -22, 26, -13, 6],\n [-17, 7, -15, 33, 9],\n [0, -6, 34, -4, 6],\n [-23, 25, -21, -39, -11],\n [5, -4, 14, 23, 28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[11, 2, -21, -3, 5],\n [1, 26, -63, -29, -2],\n [16, -28, 41, 32, -3],\n [-7, 1, 14, -4, 25],\n [11, -15, 25, 10, 48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[27, 37, -29, 28, -15],\n [36, 54, -17, 48, 7],\n [54, 42, -5, 12, 1],\n [54, 15, 6, -30, -9],\n [-60, -62, 20, -36, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-11, -37, -33, -11, 19],\n [2, -3, 3, 5, 4],\n [-10, -5, -17, 16, 55],\n [-23, -42, -13, -41, -53],\n [-1, -13, 15, -20, -56]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[17, 1, 16, 2, -6],\n [-27, 22, -15, -49, 19],\n [44, 8, -17, 22, -11],\n [13, -22, 35, 31, -15],\n [-42, -22, 3, 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[[-29, -10, 14, 50, -2],\n [-17, -9, 14, 31, 8],\n [8, 24, -20, -11, -25],\n [17, 58, -26, -9, -27],\n [7, -28, 2, -27, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, 6, 16, -5, -4],\n [40, 60, -15, -15, 30],\n [-4, -6, 19, -2, -10],\n [32, 48, -17, -11, 26],\n [-4, -6, 29, -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[[73, 6, -39, 23, -14],\n [18, -8, -19, 38, 53],\n [-46, -1, 27, -11, 7],\n [-19, 10, -3, 61, 38],\n [-11, -8, 7, -51, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[29, -14, 50, -3, 9],\n [22, 0, 8, -10, 2],\n [10, -9, 29, 2, 5],\n [15, -8, 28, -1, 5],\n [12, -13, 41, 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[[-18, 16, 3, -18, 19],\n [-5, -4, -14, 21, 21],\n [31, -5, -19, -22, -41],\n [0, -3, 2, 7, 1],\n [-10, 12, 2, -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[[2, -9, 6, 14, -39],\n [-5, -16, 27, -14, -4],\n [15, 24, 15, -6, -44],\n [6, 17, -30, 18, -1],\n [0, 15, -60, 30, 35]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 5, 18, -24, -22],\n [8, 28, -10, 6, -15],\n [-37, 2, 44, -31, 28],\n [-7, 19, 8, 43, 24],\n [17, -34, -46, 1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[6, 5, -7, 10, 3],\n [12, 10, 0, -8, -8],\n [-24, -20, 8, 0, 8],\n [24, 20, -12, 8, -4],\n [-24, -20, 24, -32, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-8, -4, 14, 5, -12],\n [10, 6, -2, -10, 4],\n [50, 17, -18, -12, -9],\n [-3, 0, 15, -3, -9],\n [26, 7, -8, -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[[-8, -1, -31, 14, 30],\n [32, -45, -21, -16, -14],\n [-8, -16, 11, -20, 24],\n [-2, -25, 33, 12, -2],\n [28, -44, -11, -36, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-38, -5, 8, -15, 11],\n [-3, 42, 19, -63, 29],\n [8, -47, -24, 38, -39],\n [9, 4, -37, 34, 33],\n [13, -35, -5, 3, -48]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[5, 2, -10, -3, 0],\n [-5, -2, 10, 3, 0],\n [7, 6, -10, -5, 8],\n [-6, -4, 10, 4, -4],\n [-28, -24, 40, 20, -32]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[8, -5, -7, -3, -9],\n [-23, -4, 7, 6, -24],\n [-26, -17, -1, 5, -61],\n [-10, -6, 0, 2, -22],\n [-3, -6, -3, 0, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[21, -12, 29, 2, -11],\n [11, 1, -24, -31, 9],\n [-19, -19, 35, 25, -48],\n [-26, -18, 46, 38, -36],\n [11, 14, -33, -28, 47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[18, 1, 30, -4, -58],\n [36, -29, 31, 53, -20],\n [20, -15, -15, 42, 49],\n [-48, 48, -44, -78, 26],\n [-15, 30, -5, -43, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 18, 15, 9, -9],\n [5, 36, -3, -26, -18],\n [1, -30, -13, 1, 15],\n [5, 30, -5, -25, -15],\n [-6, -54, 0, 33, 27]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 15, 30, -36, -12],\n [8, -18, -23, 28, 15],\n [28, -18, -62, 12, -26],\n [-44, 54, 43, -3, -14],\n [-26, 3, 71, -4, 51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 25, 15, 0, 5],\n [52, 24, 20, 42, -40],\n [-40, -36, -18, -14, 8],\n [-36, -27, -13, -17, 13],\n [4, -10, -13, 9, -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, 24, 32, 11, 0],\n [-19, 9, -5, -32, 0],\n [5, -5, 3, 11, -4],\n [-9, -11, 13, 3, -28],\n [0, -10, -16, -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[[25, 1, -8, 42, 29],\n [37, 26, -4, 0, 22],\n [-44, -7, -8, -20, -17],\n [-72, -14, -4, -46, -40],\n [-23, -54, 26, 25, -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[[0, -17, 15, 14, -8],\n [0, -17, 15, 14, -8],\n [27, 26, 30, 15, -38],\n [-6, -28, -1, 16, 30],\n [3, 10, -19, -3, 36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[21, 29, -31, -10, -22],\n [-30, -27, 21, 18, -6],\n [12, 37, -3, -6, 14],\n [38, 4, 0, -28, 49],\n [-48, -37, 27, 30, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[7, 25, 49, 24, -13],\n [0, 15, 42, 20, -12],\n [23, 11, -1, -16, 13],\n [53, 59, 31, 8, 5],\n [-6, -24, -12, -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[[-43, 35, -6, 1, 23],\n [29, -25, -4, 8, -27],\n [-57, 11, -25, 27, -24],\n [11, 9, 7, -9, -4],\n [2, -19, 3, 1, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-19, -10, 9, 19, 23],\n [16, -20, -16, -10, -16],\n [49, -27, -3, -15, -19],\n [-39, 18, 5, 15, 19],\n [46, -17, -10, -22, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-12, 14, 2, 28, -60],\n [-12, 2, -2, 12, -12],\n [18, 6, 6, -6, -18],\n [0, 12, 4, 16, -48],\n [-12, 8, 0, 20, -36]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, 34, 13, -1, 44],\n [-31, 44, -33, -15, -16],\n [22, 36, 50, 40, -4],\n [4, 24, 17, 10, 14],\n [-10, -22, -29, -1, -72]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[18, -27, 10, 35, -5],\n [-9, 0, -23, -13, -2],\n [-6, 7, -6, -11, 1],\n [15, 2, 41, 21, 4],\n [-6, -11, -30, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[36, -26, 19, -29, 5],\n [-28, 30, -8, 30, -13],\n [8, -38, -19, -23, 40],\n [-8, -4, -9, -19, -12],\n [8, -8, 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[[-32, -65, 2, -6, -15],\n [-6, 14, -46, -32, 18],\n [26, 17, 17, 57, -3],\n [21, -9, -21, -4, -18],\n [-42, 5, 10, -78, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-22, -14, 28, -7, 33],\n [8, 14, -24, 16, 16],\n [-32, 32, -28, -13, -35],\n [-18, 38, -14, -1, 33],\n [-4, 20, 28, -30, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 15, -36, -4, -8],\n [56, 10, -23, -8, -40],\n [55, -10, 12, 2, -28],\n [-32, -20, 2, 24, 24],\n [26, -20, 23, 16, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-20, 20, 14, 0, 46],\n [-8, 8, 20, -16, 44],\n [14, -14, 1, -12, -13],\n [-18, 18, 9, 4, 35],\n [-8, 8, 11, -6, 28]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-9, 25, 10, -14, 29],\n [48, -22, 37, 51, 3],\n [-49, -9, -33, -43, -44],\n [-5, 8, -18, -22, 36],\n [-51, 30, -47, -43, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[23, 11, -7, -6, 38],\n [9, -23, 11, 25, 13],\n [-31, -6, 21, -40, -57],\n [23, -26, 12, 5, 26],\n [6, -48, -4, 19, -19]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[21, 11, -19, -14, -19],\n [-34, -30, 44, 59, 51],\n [-18, -21, 16, 14, 17],\n [-14, 21, 10, 7, -7],\n [-24, -24, 38, 55, 52]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[2, -4, -19, 4, 14],\n [-10, -20, 15, 20, -30],\n [0, 12, 24, -12, -12],\n [10, 26, -3, -26, 24],\n [0, -4, -8, 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[[-58, 13, -47, -23, -13],\n [16, -28, 47, 16, 24],\n [28, -14, 54, -6, -10],\n [-22, -64, 0, 4, 50],\n [18, 85, 5, 9, -51]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-46, -48, -30, -25, -32],\n [2, 4, 4, -6, 0],\n [-8, -4, 8, 10, -4],\n [34, -24, -46, 27, 24],\n [14, 58, 44, 13, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-21, 21, -49, -17, 1],\n [-36, 25, 70, 4, 38],\n [19, -48, -59, -13, -21],\n [18, -37, -52, -10, -20],\n [-8, 60, 24, 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[[-4, -5, 4, 9, -1],\n [4, 1, -24, -22, 10],\n [12, 9, -24, -33, 9],\n [-20, 8, 26, 33, -13],\n [-20, 33, -44, -32, 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, -29, -22, 3, -6],\n [-8, 4, -4, 0, -9],\n [50, -20, -10, -30, 60],\n [6, -44, 2, 30, -9],\n [-5, 55, -10, -45, 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[[-40, -26, 15, 19, 34],\n [40, 28, -26, -18, -36],\n [-30, -18, 3, 15, 24],\n [-10, -12, 34, 2, 14],\n [-30, -24, 36, 12, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[24, 6, -6, -36, 12],\n [-14, -20, 20, 24, -10],\n [-27, -26, 26, 44, -17],\n [-20, 6, -6, 28, -8],\n [2, -16, 16, 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[[-13, 26, -6, -6, 22],\n [-22, 9, -8, 26, 33],\n [18, 31, -16, 2, -21],\n [-12, 29, -16, -8, 7],\n [-30, -71, 10, 21, 8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-10, -12, 8, 12, 6],\n [-20, -19, 16, 29, 13],\n [-30, -51, 24, 21, 15],\n [30, 46, -24, -26, -16],\n [0, 5, 0, 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[[-8, 9, -12, 37, 19],\n [20, -15, 2, -9, -31],\n [0, 24, -14, 74, 15],\n [-6, 30, 23, -17, 6],\n [0, -21, 10, -59, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[9, -5, -7, -28, 45],\n [-21, -8, -8, 2, 6],\n [-15, 7, -15, 5, -24],\n [-5, 29, -33, -40, 31],\n [46, -42, 34, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-22, -39, 8, -27, 42],\n [-12, -10, 10, -26, 6],\n [4, -6, -8, 18, 12],\n [-16, -32, 4, -16, 36],\n [8, 4, -8, 20, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[31, -33, -25, -78, -33],\n [-33, 11, 2, 30, -9],\n [-15, 27, -36, -34, 5],\n [5, 4, 19, -20, -43],\n [10, 8, -12, -16, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-34, -12, -4, -18, 11],\n [12, 19, -4, 15, -2],\n [-7, -22, -15, -34, 7],\n [35, 23, 23, 69, -1],\n [28, 14, 14, 68, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-27, -10, 4, 25, -31],\n [-4, 15, -44, 19, 8],\n [-50, 24, -14, 16, -10],\n [46, -17, 30, -33, 18],\n [30, -30, 25, -5, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-22, -6, 12, 22, 6],\n [-9, -5, -6, 13, -3],\n [14, 7, 6, -19, 3],\n [-4, 4, 24, -4, 12],\n [-11, 4, 36, 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, -42, 14, -16, 46],\n [18, -36, 7, -18, 32],\n [-24, 6, 12, 12, 6],\n [-8, 39, -16, 14, -41],\n [20, 15, 10, 10, -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[[36, -8, 7, 4, -32],\n [10, 4, 2, -36, 14],\n [10, -12, 25, 8, -14],\n [8, 6, -31, 27, -22],\n [-14, -2, 26, -35, 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[[16, 14, -20, 9, -19],\n [-14, 24, 0, 24, 6],\n [13, 33, -9, 26, -28],\n [-11, -37, 13, -30, 26],\n [-27, 27, 27, 29, 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[[-19, 1, 19, 11, 2],\n [26, 21, -9, -7, 8],\n [-1, -21, -15, -7, -10],\n [3, -12, -12, -6, -6],\n [-16, -11, 7, 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, 30, 0, 32, -10],\n [22, 12, -34, 23, -21],\n [10, 30, -10, 35, -15],\n [16, -15, -30, -7, -10],\n [-12, 9, 22, 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[[6, 21, 9, -5, 18],\n [2, -60, -6, 36, -18],\n [32, 21, 3, 3, 36],\n [-39, 6, 18, -10, -18],\n [11, 39, 2, -19, 21]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-18, 1, 7, -22, 12],\n [24, 18, -26, 24, 16],\n [-3, -28, 2, -20, -15],\n [-11, -26, 33, -53, -27],\n [18, 18, 78, -30, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[38, 25, -7, 36, 19],\n [-28, -3, 39, -49, -94],\n [4, 15, 28, -12, -63],\n [-11, -3, 16, -47, -60],\n [59, 36, -46, -24, 24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[29, 11, -11, 3, 19],\n [16, 21, -14, 11, -10],\n [27, 22, -18, 12, 0],\n [0, 29, -3, 3, -27],\n [50, 28, -28, 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 5x5 matrix:\n[[-28, -43, 4, -18, -8],\n [-32, -64, 25, -15, -24],\n [-3, 15, 24, 29, 3],\n [-4, -42, 21, -11, -28],\n [-3, 5, -20, -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[[-52, 34, -24, 28, 44],\n [7, 19, -18, -56, 8],\n [-9, -11, 14, -16, 17],\n [-21, 4, -2, 54, 5],\n [27, -4, -2, -2, -29]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-3, -13, -15, -6, 24],\n [-58, -12, -4, 56, -4],\n [42, 18, 16, 31, -52],\n [-34, -5, 4, -20, 24],\n [-13, -7, -31, 33, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[31, 27, -3, 4, 12],\n [-4, 7, 6, 28, -17],\n [-58, -59, -39, -5, 25],\n [12, -6, -55, 30, 21],\n [-1, 7, 5, 25, -17]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-34, -38, -6, -16, -30],\n [-20, -20, -8, -4, -16],\n [13, 21, -10, 21, 16],\n [12, 24, -18, 30, 18],\n [26, 22, 18, -4, 18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[18, -18, -18, -90, -66],\n [20, 25, 27, -9, -43],\n [14, -4, -49, -18, 3],\n [10, -15, -6, -63, -48],\n [14, 21, 33, -3, -37]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -5, 29, 17, 10],\n [1, -5, 18, 14, 5],\n [3, 6, -37, -21, -13],\n [-6, -3, 35, 15, 14],\n [-4, 11, -33, -29, -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, -37, -21, -5, 5],\n [-20, 1, 39, 40, 53],\n [-45, 0, -33, -6, -4],\n [-55, -19, 0, 26, 21],\n [-20, 31, 6, -3, -31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[12, -39, -2, -11, 17],\n [37, 3, -2, -28, -13],\n [25, -2, -20, -31, -26],\n [20, 11, -25, -37, -42],\n [104, -37, 9, -19, 40]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[13, -17, 13, -4, 12],\n [43, -60, 50, 11, 30],\n [-20, 31, -29, -25, -6],\n [-4, 2, 2, 22, -12],\n [17, -26, 24, 19, 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, 2, 27, 27, 3],\n [64, 65, 2, 27, -46],\n [10, 1, -1, 0, -31],\n [-11, -29, -13, -18, -1],\n [-37, -40, 22, 14, 44]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[16, -24, 6, 18, 12],\n [-8, -2, -3, 15, 0],\n [-13, 23, -18, -10, -4],\n [-32, 28, 18, -26, -32],\n [2, 6, -18, 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[[-31, 66, 37, -25, 8],\n [-40, 20, -18, -2, -42],\n [14, -51, -5, 43, -20],\n [10, -41, -60, -10, -45],\n [-25, -6, 13, 48, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-41, -39, -14, -43, 23],\n [7, -10, -12, 40, -31],\n [47, 27, 62, 10, 1],\n [22, -1, 54, -13, 12],\n [10, -14, 20, 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 5x5 matrix:\n[[-1, -31, 30, 9, 10],\n [-8, 4, -5, -12, 3],\n [9, -9, 10, 15, -2],\n [-42, -6, 0, -54, 24],\n [-7, -1, 0, -9, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[20, 42, -6, 4, -10],\n [-8, -56, -2, -16, 6],\n [6, -22, -4, -16, -22],\n [0, -11, -5, 6, 47],\n [26, 65, -7, 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[[21, -17, 21, 9, -3],\n [-11, -1, -27, -19, -5],\n [14, -30, -11, 10, 32],\n [17, -13, 21, 25, 23],\n [25, -45, -8, 17, 43]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-24, -4, -3, 20, 0],\n [-56, -20, 3, 36, -8],\n [-30, 7, -15, 37, 9],\n [-26, -11, 3, 15, -5],\n [0, -32, 30, -32, -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, 6, -13, -12, -6],\n [-6, -8, 12, 6, 8],\n [1, 16, -16, 3, -16],\n [1, -6, 5, -3, 6],\n [8, -4, -2, -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, 11, 42, -7, 16],\n [-15, 3, -40, 0, -10],\n [-12, 23, -4, -12, 17],\n [1, -1, -8, 4, -10],\n [-3, 9, -31, 0, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[31, -29, -25, 18, -20],\n [-2, -5, 8, 0, -9],\n [-19, 10, -23, -39, -3],\n [13, 0, -7, 15, 11],\n [34, -42, -28, 15, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-2, -26, -36, 38, -28],\n [16, 32, 30, -25, -12],\n [-36, -22, -6, 18, 68],\n [-27, -19, 4, 30, 46],\n [-7, -33, -15, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, -51, -24, -48, -10],\n [-11, 4, 22, -45, -20],\n [-31, 8, 29, 21, -26],\n [58, -8, 22, -12, -10],\n [-64, 13, -8, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-6, -18, 27, 6, -6],\n [7, 34, -49, -13, 15],\n [-17, -12, 24, -1, 7],\n [-2, -6, 9, 2, -2],\n [13, 26, -41, -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[[-3, 9, 11, 2, -10],\n [9, 18, 12, -24, -15],\n [-9, 12, 18, 12, -15],\n [9, -22, -28, -8, 25],\n [-9, 12, 18, 12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, 16, -34, 19, 3],\n [-34, 12, -28, -8, -14],\n [16, 23, -22, 22, -9],\n [5, 12, -24, 17, 0],\n [-22, 3, -24, 17, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[23, 20, -18, -11, -15],\n [19, 19, -22, -13, -10],\n [-13, 27, -12, -5, -28],\n [-13, 19, -33, -17, 1],\n [-21, 33, 1, 3, -47]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-45, -49, 29, 3, 4],\n [-27, -21, 6, -16, -10],\n [-48, -15, 24, -18, -6],\n [18, 30, 21, 53, 46],\n [21, 6, -51, 5, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-3, -72, 3, 15, 0],\n [45, -14, -13, 4, 4],\n [-24, -4, -15, -38, 14],\n [21, 43, -17, -36, 22],\n [40, 7, -54, -86, 50]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-21, 17, -26, -21, 29],\n [-6, 5, -8, -6, 11],\n [1, -2, 6, 1, -24],\n [-23, 17, -22, -23, 1],\n [30, -24, 36, 30, -36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-23, 24, 4, -5, 28],\n [23, -22, -38, 27, 20],\n [11, 1, 20, -28, -47],\n [-12, 20, 1, -4, 21],\n [10, 7, 8, -27, -31]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-6, 16, 30, 55, -38],\n [0, -6, 10, 15, -2],\n [1, -2, -24, 11, 6],\n [-57, 31, 41, 52, -5],\n [-50, -10, 18, 78, 30]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, 1, 25, -46, 13],\n [15, -6, 11, -11, 27],\n [10, -2, 5, -8, 4],\n [-22, 5, 3, -12, -13],\n [28, -2, 8, -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, -9, 0, 9],\n [10, -26, 1, -25, 37],\n [-10, 10, 12, -10, 0],\n [9, -27, -29, 20, 1],\n [-12, 2, 20, -30, 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[[-38, 15, -5, 11, -4],\n [14, 10, 18, -26, 28],\n [12, -19, 1, 1, -10],\n [31, -28, 16, -15, 2],\n [-2, 3, -5, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-28, -6, -30, 4, -8],\n [-26, 6, -36, 2, -4],\n [7, -12, 17, 1, -2],\n [26, 21, 17, -6, 12],\n [-24, 18, -42, 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[[-68, 13, 8, -11, -32],\n [20, 4, 32, 44, -25],\n [-33, 0, -43, -37, -6],\n [14, -38, 29, 13, 43],\n [11, -48, 15, 25, 19]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-42, -11, -20, 5, 6],\n [-40, 53, 5, 28, 16],\n [24, 29, 14, -21, -2],\n [41, 24, 15, -38, -18],\n [1, 13, 15, 44, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[60, 33, 15, 30, 21],\n [28, 10, 12, 8, 26],\n [-42, 3, -22, 8, -17],\n [24, -21, 23, -26, 23],\n [26, -10, 19, -14, 22]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[21, 21, -2, 23, -48],\n [-15, 12, 4, -6, 45],\n [-36, -45, -17, -43, 36],\n [3, 24, 12, 9, 4],\n [18, 24, 13, 20, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[42, 34, 18, -22, -36],\n [-57, 1, -38, 2, -4],\n [0, 51, 25, -24, -22],\n [27, -27, 8, 12, 16],\n [3, -17, 1, 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[[-14, 3, 15, -12, -9],\n [-3, -17, -37, 20, 19],\n [15, 16, 38, -22, -20],\n [-8, 6, 12, -6, -6],\n [-10, -14, -31, 17, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-56, -56, -55, -33, 4],\n [-44, -82, -38, 2, 60],\n [22, 40, 15, 58, -2],\n [-10, -16, -28, 17, 38],\n [30, 11, 46, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, 12, 2, 4, 6],\n [-2, 16, 14, 0, 2],\n [36, 16, -20, 16, 20],\n [-10, 42, 41, -2, 3],\n [40, 22, -19, 18, 23]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[15, 10, -67, -72, 10],\n [-13, 31, 1, -12, -45],\n [18, -37, -11, 5, 39],\n [26, -13, -40, -30, -13],\n [30, -29, 13, 37, -68]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-14, -35, -30, 17, -13],\n [-12, -10, -17, -19, 39],\n [-1, -3, 3, -5, 6],\n [0, 5, -8, 5, -3],\n [-14, -20, -16, -18, 36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-20, -38, 35, 6, 31],\n [2, 3, 16, 19, 29],\n [-3, 11, -16, -3, -20],\n [27, 37, -26, 0, -10],\n [-7, 42, 22, 65, 33]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-40, 20, -12, -34, 28],\n [-38, 12, -3, -26, 14],\n [-34, 16, -9, -28, 22],\n [-10, 0, 3, -4, -2],\n [8, -2, 0, 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[[28, -27, -3, 15, -1],\n [-24, 40, -16, -12, 4],\n [-6, -22, 28, -5, -1],\n [13, -6, 15, 10, -28],\n [17, -27, -30, 4, 46]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-25, 6, -2, -18, 30],\n [-1, 4, -6, 14, -33],\n [-32, 30, -30, -46, 4],\n [-4, 6, -15, -6, -20],\n [-1, 8, -1, 8, -20]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-3, 11, 15, -24, 31],\n [-13, -2, -27, 5, -33],\n [-7, 12, 10, 7, -5],\n [4, -22, 46, 6, -8],\n [4, 15, -3, 49, -28]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[0, -11, -19, 24, 12],\n [-37, 47, 50, 45, 5],\n [14, -20, -33, 7, 26],\n [12, 6, 0, -12, 36],\n [14, -28, -19, 37, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[0, -5, -14, -23, 33],\n [-45, -4, -30, -4, 0],\n [-48, -3, -21, 0, -12],\n [11, 7, -6, 35, -25],\n [-48, -5, -18, -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 5x5 matrix:\n[[-20, 13, 25, 3, -6],\n [-42, -24, -21, -3, 54],\n [-72, 11, 13, 3, 18],\n [18, -34, 19, -3, 54],\n [-2, 2, 54, 3, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-5, 2, 3, 4, 17],\n [-10, 10, 5, 20, 55],\n [-9, 12, 4, 24, 60],\n [-10, 4, 6, 8, 34],\n [-12, -12, 10, -24, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, 10, -3, 1, -10],\n [20, -16, -7, 31, 18],\n [24, -28, -9, 15, 20],\n [12, -5, 23, 11, 27],\n [8, -13, 2, -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[[4, -18, 5, 10, 21],\n [-14, 11, 2, 17, -15],\n [-6, -1, 3, 13, 0],\n [12, 10, -9, -34, -9],\n [-8, -4, 5, 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[[-19, -4, -38, 19, -14],\n [-9, 34, -18, 9, -36],\n [23, 6, 46, -23, 16],\n [2, 12, 4, -2, -8],\n [14, -48, 28, -14, 52]]\n\nPresent 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, -33, -7, 3, 3],\n [-10, 21, 7, 28, 17],\n [0, 2, 20, 5, 10],\n [-4, 11, -31, 19, -1],\n [15, -21, -32, -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[[7, -1, 10, -25, 6],\n [-5, 11, -6, 27, -2],\n [10, 5, 15, -30, 10],\n [18, 36, 30, -30, 24],\n [12, 15, 19, -28, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[68, -17, -55, -34, -16],\n [78, 6, -68, -20, 2],\n [66, -9, -63, 4, -28],\n [-1, 11, -11, 12, -13],\n [-45, 19, 43, 8, 35]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-17, 19, 0, 17, -12],\n [-19, -1, -14, 19, -20],\n [-27, 27, -2, 27, -20],\n [-1, 17, 10, 1, 4],\n [37, -8, 21, -37, 36]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-16, 3, 1, 13, -11],\n [32, -6, -2, -26, 22],\n [-7, 6, -8, 6, 3],\n [-14, 12, -16, 12, 6],\n [-25, 0, 10, 20, -25]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-45, 25, -10, -20, 35],\n [6, 9, -10, 6, -2],\n [39, -30, -10, 24, -29],\n [-42, 36, -24, -12, 30],\n [-33, 20, 18, -18, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[8, -2, 4, -8, 0],\n [0, -21, 10, -14, -14],\n [-19, 16, -23, 17, -2],\n [-7, 28, -19, 21, 14],\n [52, -28, 40, -54, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-2, 8, 2, -12, 12],\n [20, 18, 1, -27, 13],\n [-2, 8, 2, -12, 12],\n [-34, -4, 4, 6, 14],\n [22, 24, 2, -36, 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[[-44, 57, 13, 73, 9],\n [22, -29, 4, -28, -4],\n [23, -40, -3, -29, -2],\n [-20, -6, -33, 34, 9],\n [-17, 17, 10, 21, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-4, 25, -30, -33, 10],\n [0, 8, -12, -8, 2],\n [-20, -24, 66, -4, 4],\n [-2, -24, 39, 30, -11],\n [-16, 31, -24, -7, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[-32, -2, 6, -12, -23],\n [-44, -14, -40, -2, -30],\n [74, 14, 30, 12, 50],\n [16, 20, 72, -12, 12],\n [12, -10, -42, 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[[-14, -24, 12, -12, 26],\n [-8, -6, -9, -12, -25],\n [9, 10, -11, 20, -32],\n [6, 2, -2, 19, -10],\n [25, 44, 4, 4, 31]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-50, -21, 26, 58, 7],\n [4, -24, 8, 8, -8],\n [-9, -39, 10, 26, -11],\n [-51, 0, -4, 44, 8],\n [62, 3, -30, -62, -17]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[0, -10, -28, -4, 14],\n [30, 0, 33, 24, -24],\n [32, -14, -4, 20, -6],\n [26, -2, 23, 20, -18],\n [-14, 3, -7, -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[[-17, -17, 2, -19, 14],\n [-17, 17, 27, 7, 2],\n [22, -18, -32, -6, -4],\n [-28, -8, 18, -16, 16],\n [-42, -12, 27, -24, 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[[-18, 15, 7, -16, -14],\n [-43, -28, -43, -21, 35],\n [6, 9, 9, 4, -6],\n [8, -4, 4, 0, -8],\n [35, 38, 55, 5, -59]]\n\nPresent the 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, -6, -10],\n [-38, -27, 15, 14, 35],\n [8, 7, 0, 1, -10],\n [-30, -20, 15, 15, 25],\n [6, 14, 21, 27, -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[[-16, -3, 36, -16, 7],\n [8, 10, -11, 36, 14],\n [-21, -8, 31, -22, 5],\n [-25, -35, -11, -38, -24],\n [-19, -14, 37, -39, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-64, 51, 64, -26, 60],\n [-29, -12, -1, 7, 35],\n [34, 30, 9, 4, -38],\n [-42, 43, 50, -32, 41],\n [-12, -3, -1, 32, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-20, -11, -14, 12, -17],\n [-30, 47, 10, -30, -12],\n [-10, 44, 28, -26, -21],\n [15, -14, 2, 9, 3],\n [-25, 0, -10, 5, -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, -21, -42, -3, -21],\n [27, 28, -9, 20, -11],\n [-4, -12, -9, -7, -3],\n [-1, 20, 30, 9, 14],\n [-3, -17, 6, -22, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[14, -16, 2, -16, -18],\n [-7, -17, 17, -10, 8],\n [8, -2, -4, -4, -10],\n [-11, -16, 19, -8, 13],\n [10, -40, 22, -32, -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[[33, -6, 54, -21, 9],\n [24, 0, 36, -36, 24],\n [1, 2, 0, -11, 9],\n [-15, 10, -30, -25, 25],\n [28, -8, 48, -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, -5, 10, -6, -1],\n [0, 15, 0, -6, -9],\n [-24, 30, 30, -36, -30],\n [-16, 15, 20, -22, -17],\n [0, 30, 0, -12, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[4, -2, 16, 0, 21],\n [-10, 22, -34, -34, -19],\n [-30, -8, -26, 32, -41],\n [-42, 19, -64, 1, -42],\n [4, -16, 28, -2, -20]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-14, -10, -15, 6, 61],\n [-6, -13, -16, 3, 46],\n [15, 9, 6, -3, -37],\n [-31, -8, -3, 21, 35],\n [41, 0, 5, -30, -64]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[18, 4, -15, -17, -7],\n [-18, 8, 2, 46, -15],\n [-16, 4, 41, 7, 16],\n [20, -2, -6, -29, 5],\n [-8, -60, -45, 25, 21]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-14, -8, -2, -18, 8],\n [3, 8, -3, -7, 4],\n [24, 31, -6, 1, 2],\n [46, 42, -2, 32, -12],\n [56, 54, -4, 34, -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, 1, -16, -7, 58],\n [10, 4, -17, -1, 50],\n [8, -2, -6, 0, 24],\n [-10, 14, -5, -27, 14],\n [-19, 5, 12, 11, -60]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[10, -8, 24, 16, 20],\n [1, -12, -6, -4, 2],\n [0, 24, 18, 12, 0],\n [7, -20, 6, 4, 14],\n [8, -8, 18, 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[[13, -8, 32, -9, -8],\n [9, -12, 12, 0, 18],\n [22, -13, -58, -5, 7],\n [-19, 16, 1, 32, 50],\n [8, 29, 28, 13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the rank of the matrix:\n[[2, 1, 9, 32, 10],\n [-14, 11, 63, 26, 6],\n [-18, 5, 31, 33, -10],\n [15, -5, -37, -46, 9],\n [-27, 1, -19, 48, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-28, -38, -35, 13, 2],\n [-5, -6, 13, -24, 1],\n [6, -3, 10, 23, -40],\n [-49, -68, -25, 0, -11],\n [39, 52, -6, 13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[4, 6, 1, -2, 0],\n [-12, -18, -3, 6, 0],\n [-3, 17, 4, -23, -12],\n [3, 36, 9, -36, -16],\n [-11, -28, -4, 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 5x5 matrix:\n[[-28, -34, -42, 17, 45],\n [14, 62, 51, -9, -55],\n [-2, -28, -24, -18, 23],\n [30, 0, 15, -46, -20],\n [30, 22, 36, -15, -38]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-12, 9, 29, -6, 8],\n [-15, 42, 26, -28, 10],\n [-9, 6, 22, -4, 6],\n [9, -3, -23, 2, -6],\n [-15, 24, 32, -16, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-39, 39, 27, -9, 19],\n [-36, -15, 24, -58, -8],\n [-44, 29, -26, -30, 18],\n [17, 58, -31, 73, 29],\n [14, 13, 0, 28, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[-5, -12, -10, -4, 2],\n [-1, -45, 54, 14, 3],\n [9, -19, -8, 15, 33],\n [-6, -32, -18, -1, 16],\n [-23, -36, -20, -21, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[-20, 21, 0, 6, -23],\n [-15, 19, -5, 4, -22],\n [-25, 10, 25, 10, -5],\n [12, -10, -4, -4, 10],\n [5, -2, -5, -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[[-33, 27, 15, -5, 0],\n [14, -12, -5, 0, 2],\n [23, 15, -11, -12, 44],\n [1, 3, -2, 1, 2],\n [-16, 24, -12, 26, -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[[-34, 4, -32, 32, -4],\n [-6, -2, -18, 20, 10],\n [6, -15, -37, 8, 29],\n [-12, -9, -39, 12, 15],\n [4, 12, 36, -2, -18]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the rank of the following matrix:\n[[25, -17, -11, -1, -7],\n [23, -28, -26, -26, 17],\n [9, -15, -25, 21, 37],\n [20, -43, -43, -1, 10],\n [12, -16, -8, -4, -24]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the rank of the matrix:\n[[-6, 4, 18, -18, 7],\n [-2, -24, -26, 22, -13],\n [-25, -8, 32, -46, 2],\n [-57, -5, 48, -78, -14],\n [0, -9, 18, 8, 26]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the rank of matrix A where A =\n[[2, 8, -3, -4, -4],\n [-35, 16, 19, 3, -8],\n [34, 17, -18, -2, 3],\n [-23, 3, -5, -33, -31],\n [6, -2, 5, 16, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[6, -20, -14, -6, -14],\n [7, -10, -7, -6, -6],\n [20, 30, 36, -3, 35],\n [2, 0, 30, 18, 14],\n [16, 0, 0, -12, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-15, 27, -3, 18, -42],\n [-16, 26, 0, 21, 6],\n [-12, 28, -4, 16, -24],\n [20, -38, 2, -27, -2],\n [-5, 5, 1, 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[[13, 23, -24, 9, 23],\n [-8, -22, 21, -6, -22],\n [34, 0, -15, 20, 0],\n [-20, 30, -15, -10, 30],\n [38, -6, -12, 22, -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, -24, -5, -30, -7],\n [26, -64, 22, 14, -22],\n [-1, 48, -16, 12, 11],\n [-53, -2, 4, 22, -1],\n [8, 18, -13, 27, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Compute the rank of the given 5x5 matrix:\n[[-8, -4, 32, 12, 16],\n [-50, -25, 0, -45, 10],\n [10, 5, -40, -15, -20],\n [42, 21, -8, 33, -12],\n [-30, -15, 0, -27, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}