{"messages": [{"content": "Find the value at position (5, 4) of the 7th power of the matrix:\n[[12, -2, -9, 4, 2, 6, -6, -6, 7, 7, -14, 5],\n [-15, 7, 13, -15, 4, 16, -5, 5, 8, 10, 11, -1],\n [-2, -14, -10, 4, -8, 1, -13, 8, -3, -8, 9, -15],\n [3, 11, -10, -9, -3, 0, -13, -15, -11, -13, 12, 1],\n [9, -7, -3, 14, -2, -9, -3, 6, 4, -1, 1, 7],\n [9, 8, 12, -2, -16, 8, -10, -8, 7, -16, -9, 7],\n [-6, 0, -9, 16, -12, 11, -10, -8, -9, -5, 16, 6],\n [7, 5, 10, -16, -3, -14, -16, -12, 9, -3, 10, -8],\n [-2, -2, 9, -4, 15, 15, -13, 13, 6, -2, 12, -4],\n [15, -10, 5, 11, -15, -11, 11, 11, 3, 13, -6, 11],\n [8, 16, -16, 10, -4, -14, -11, -9, 10, -8, 16, 7],\n [-2, 15, 15, 7, -5, -15, -14, 0, -15, -15, 11, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8914280903", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[15, 16, -16, 2, -15, 9, 15, -11, 15, -13, -6, 0],\n [7, -12, -11, 5, -6, -1, 16, -8, -11, -1, 12, -14],\n [3, 2, 9, -14, 2, 3, 15, -10, 16, 1, -16, -6],\n [11, 8, 6, 14, 13, -10, -1, 9, -15, -16, -5, -12],\n [15, -8, 2, -1, -14, 3, 7, 16, 7, -6, -9, 3],\n [8, 8, 12, 1, 1, -15, -1, 16, -13, 16, -3, 4],\n [3, -9, -10, -14, 0, 16, -5, 5, 5, 13, -9, 10],\n [10, 4, 13, 16, 11, 16, -12, 2, -13, 0, 11, 13],\n [12, -11, 7, 12, 14, 16, 4, 15, 6, 16, -14, 1],\n [8, 14, -14, 7, 15, 5, 6, -15, 10, -15, 9, 0],\n [16, -8, 12, 9, 8, 7, -4, -10, 3, -16, -9, -1],\n [-3, -5, 6, -2, 11, -15, 15, 6, 5, 8, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-318702129598292", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-11, 0, 12, -6, -3, -7, -14, 14, 10, 1, 5, 10],\n [0, 0, -7, 11, 1, -3, 11, 0, -2, -4, -7, 14],\n [12, -7, -1, -12, -4, 12, -10, -6, 12, 2, 2, 3],\n [-6, 11, -12, 13, 1, 5, 6, 9, 8, 0, 2, 7],\n [-3, 1, -4, 1, -7, 6, 6, -13, -3, -6, -3, 1],\n [-7, -3, 12, 5, 6, 3, 1, -9, 16, 6, 2, -11],\n [-14, 11, -10, 6, 6, 1, 14, -10, 0, 1, 6, -8],\n [14, 0, -6, 9, -13, -9, -10, 12, 2, 0, 0, -4],\n [10, -2, 12, 8, -3, 16, 0, 2, 6, 0, 6, -5],\n [1, -4, 2, 0, -6, 6, 1, 0, 0, -10, 4, -4],\n [5, -7, 2, 2, -3, 2, 6, 0, 6, 4, 14, -10],\n [10, 14, 3, 7, 1, -11, -8, -4, -5, -4, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169812760772", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 1) of the 7th power of the matrix:\n[[-15, -12, 12, 2, -9, -16, 5, 0, -10, 8, -13, -11],\n [14, 2, 10, -7, 9, 2, -14, -4, 11, 3, 11, -9],\n [-16, -14, -4, 11, 8, 16, -11, 15, 4, -1, 4, -6],\n [2, 3, 1, -3, -2, 14, -16, -14, -1, 6, -6, -5],\n [-7, 15, -1, -9, -5, 7, 11, -9, 11, 9, -9, 11],\n [11, 10, 0, -8, 16, 3, -4, 11, 12, -4, -11, 1],\n [-12, 8, -15, -7, 13, -12, 16, -16, 1, 15, -6, 4],\n [9, 8, 5, 10, -4, 16, -16, 4, -11, 11, 0, -12],\n [14, -12, -14, 6, -7, -7, 2, 0, 4, -3, -8, -16],\n [-4, -13, -16, 15, 11, 14, -9, 9, -14, -5, -16, -12],\n [13, 13, 0, 6, -2, 4, -3, -15, -6, 1, 13, -2],\n [10, 16, 7, -2, 13, 0, -12, 12, -13, -7, 0, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9834656281", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[0, 1, 6, -2, -7, -7, 2, 0, 10, -8, 8, 0],\n [1, -9, -12, -2, 8, -8, 1, -5, 8, 5, 5, -2],\n [6, -12, 1, 2, 8, 6, -9, -14, 1, -6, -4, -9],\n [-2, -2, 2, 9, 6, 12, -7, -1, -14, -9, 4, 0],\n [-7, 8, 8, 6, -3, 0, -7, -2, -9, 0, -8, -4],\n [-7, -8, 6, 12, 0, 0, 5, 11, 6, -6, -5, 3],\n [2, 1, -9, -7, -7, 5, -9, -2, 0, -1, -8, 0],\n [0, -5, -14, -1, -2, 11, -2, 13, 4, 8, -11, -11],\n [10, 8, 1, -14, -9, 6, 0, 4, -13, -8, 2, 6],\n [-8, 5, -6, -9, 0, -6, -1, 8, -8, 2, -4, 4],\n [8, 5, -4, 4, -8, -5, -8, -11, 2, -4, -7, -9],\n [0, -2, -9, 0, -4, 3, 0, -11, 6, 4, -9, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1546303416869", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (7, 6) of the matrix A^7 where A is:\n[[7, 13, 14, -12, -3, -6, -8, -5, -16, 5, 12, -9],\n [-6, -3, 13, 4, -12, 2, -3, 9, -13, 8, 8, 1],\n [-9, -3, 15, 16, 6, -2, 16, 8, 0, 16, -15, -3],\n [-11, -11, -14, -10, -9, -2, 12, 16, 13, 10, 12, 16],\n [10, 16, -13, 5, -15, -7, -12, -7, 16, -4, 14, 7],\n [-2, 12, -9, -12, 12, -13, -5, -15, 10, 14, 9, 10],\n [-12, 3, -6, -7, -11, -9, 6, 9, -5, 9, -4, 1],\n [8, 16, -5, -13, -12, -9, 11, 14, -8, 12, -3, 5],\n [-6, 6, -16, 4, 9, 6, -16, -2, 4, -8, -8, -7],\n [9, 8, 9, -6, -15, -10, 1, 10, 10, 0, 7, 8],\n [-10, -11, 7, 16, 12, 5, 9, 11, 4, -10, 0, 3],\n [3, 5, 11, -10, -16, 15, -4, 13, 6, 2, 15, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19188174720", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[12, 12, 13, -1, 2, 1, -16, -3, -15, 11, 13, -13],\n [-16, -9, 12, -14, 15, -7, -7, 2, 16, 6, 11, 15],\n [-10, 12, -9, -16, -14, 7, 6, -9, -14, 16, 11, -9],\n [15, 7, -3, 15, -1, -13, 4, -3, 14, 1, -10, -7],\n [-10, 16, 6, 4, 2, 2, 12, 1, -15, -16, -12, 3],\n [-6, -15, -14, 6, -5, 3, -12, 13, -8, 5, 7, 0],\n [-7, 13, 6, 15, 0, 0, -3, -8, -15, 8, -8, 5],\n [-13, 9, 12, 6, -6, -11, 1, 4, 0, 8, -5, 6],\n [5, 4, 10, 14, -11, 10, -5, -10, -7, 0, 9, 4],\n [11, -15, -16, 9, 12, 4, -6, -6, 7, 5, -12, 16],\n [3, 2, 0, -8, 9, -15, -8, -8, 0, -16, 8, 8],\n [-14, 13, -5, 2, 0, -7, -5, -1, 7, 2, -9, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1352435973718", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[4, 0, 6, -1, -11, -9, 8, 1, 8, -5, -2, 9],\n [9, 15, -7, -1, -10, 0, 6, 9, 4, 5, -10, -3],\n [-2, -10, -8, -9, 6, 12, 1, 14, 13, 1, 0, -3],\n [14, 7, -14, 9, 6, -2, -13, 12, 5, 8, -4, 1],\n [16, -1, -15, 13, -4, -4, 1, 15, 15, 12, 12, -1],\n [-7, 13, 8, 3, -12, -16, 13, -14, -3, 13, -13, 1],\n [8, -16, -2, -8, -2, 7, -13, -5, -11, 7, -6, -4],\n [8, -10, -13, -9, 3, 12, -7, 9, -14, -11, -12, -12],\n [6, -8, 3, 1, 0, 7, -14, 15, -4, 8, -8, -13],\n [-3, -6, -14, 11, 12, -8, -14, 8, -5, -8, -2, 8],\n [-12, -6, 7, -2, -9, -12, 9, 1, -11, -4, 11, -12],\n [-4, 0, 15, 12, -14, 10, -4, 16, -11, 7, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "859402621949", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[11, 15, 5, 6, 8, -6, -9, 9, 4, -10, 4, 7],\n [15, 1, -4, -8, 2, 14, 5, -8, 6, 4, 8, 7],\n [5, -4, -11, 2, 7, -8, -11, 9, 5, 2, -1, 14],\n [6, -8, 2, 15, -8, 8, -2, -8, 8, -7, 0, -11],\n [8, 2, 7, -8, 12, 2, -1, -4, 2, -2, 4, -2],\n [-6, 14, -8, 8, 2, 12, -4, -6, 2, -2, 3, 14],\n [-9, 5, -11, -2, -1, -4, -6, -2, -7, 4, 4, 2],\n [9, -8, 9, -8, -4, -6, -2, -16, 5, 10, 4, -6],\n [4, 6, 5, 8, 2, 2, -7, 5, -9, -2, 0, -2],\n [-10, 4, 2, -7, -2, -2, 4, 10, -2, -10, 2, 5],\n [4, 8, -1, 0, 4, 3, 4, 4, 0, 2, 1, 6],\n [7, 7, 14, -11, -2, 14, 2, -6, -2, 5, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8665538073868128", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[15, 7, -6, 0, 8, 4, 15, -10, 2, 6, -1, 2],\n [7, -4, 2, 10, -4, 12, 6, -7, 3, 2, -11, -6],\n [-6, 2, -11, -4, 5, 0, -1, -2, 0, 12, -4, -6],\n [0, 10, -4, -13, -2, 8, -2, -8, 0, -6, 2, -10],\n [8, -4, 5, -2, 2, -8, 12, 16, -7, -9, -4, -3],\n [4, 12, 0, 8, -8, 12, 0, 12, -10, -10, 4, 4],\n [15, 6, -1, -2, 12, 0, 7, 3, -8, -2, -14, 2],\n [-10, -7, -2, -8, 16, 12, 3, 13, 7, -2, 0, -2],\n [2, 3, 0, 0, -7, -10, -8, 7, 11, -11, 0, -16],\n [6, 2, 12, -6, -9, -10, -2, -2, -11, 12, -6, -8],\n [-1, -11, -4, 2, -4, 4, -14, 0, 0, -6, 11, -7],\n [2, -6, -6, -10, -3, 4, 2, -2, -16, -8, -7, 16]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606660518911644", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-3, -5, 3, 7, 8, 12, 14, 6, 3, 6, -1, -9],\n [4, -16, -9, 12, 15, -12, 5, -16, 9, -7, 13, 1],\n [0, 9, -9, -5, 10, -9, 8, -13, 16, -16, 2, 14],\n [-1, -3, -12, 9, 11, -15, -11, -8, 16, 8, -4, -8],\n [-4, 14, -6, -13, -13, 2, -11, 1, -4, 6, 2, -6],\n [-16, 7, -10, 8, 4, -2, -16, -5, -10, -2, 4, 2],\n [12, 8, 16, 15, 9, -6, -9, -3, -7, -15, -8, -14],\n [4, 9, -9, -15, -11, 11, 12, 9, 8, -5, -12, -2],\n [-2, 6, -11, 4, 6, -1, -2, 8, -6, -2, -13, 4],\n [-4, 5, 2, -3, -13, 10, 12, 11, -9, -1, 13, 1],\n [-15, -4, -13, 9, 8, 13, -6, -10, 14, -7, -4, 14],\n [-10, 3, -13, -10, -16, -4, 5, 4, 5, 11, -8, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "505354343427958", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-8, -2, -7, 7, -9, 7, -1, 9, 10, -13, 7, 2],\n [-7, 8, 1, 2, -7, 16, -12, 16, 4, 0, 5, -2],\n [11, -10, 15, -6, -7, -8, -3, -4, 8, -15, -10, 4],\n [1, -14, -6, 7, 2, -13, 9, 15, 16, -14, -8, -9],\n [16, -11, -13, -4, -15, -12, 10, 15, 4, -9, -9, -14],\n [-14, 5, -11, -15, 6, -15, 0, 6, 13, -9, 5, -12],\n [-4, 12, 14, -1, 13, -1, -5, 0, -1, -5, -9, 3],\n [-14, -1, 13, 6, 11, -12, 3, -16, 13, 4, 3, -11],\n [5, 1, -9, 15, 16, -1, -5, -3, 16, 6, -15, 4],\n [-15, 10, -8, -16, -6, -14, 6, 9, -13, 1, -11, 5],\n [-2, 5, -5, 1, 13, 7, 13, -3, -11, -14, -1, -10],\n [-3, -8, -2, 4, -15, 10, -15, 1, -3, 3, 1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1271344850927363", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[8, -15, 8, 16, 14, -3, -16, -1, -14, -11, 8, -4],\n [-9, 4, -13, 8, -2, -13, -5, 15, 15, 11, -4, 14],\n [-3, 3, 1, 12, -11, 15, 12, -15, 6, 2, 14, -12],\n [2, -7, 8, -15, -6, 14, -2, -8, 6, 2, -8, 4],\n [-8, 11, -10, -1, -1, 16, -13, -13, 0, 12, -10, 10],\n [11, 5, -3, -10, 5, -12, -15, 10, 4, -2, 4, -7],\n [6, -12, -16, -4, 4, 9, 4, 1, 15, 0, -6, 4],\n [9, -13, 1, 12, 12, 4, -4, 0, -8, -16, -15, 12],\n [16, -7, 4, 11, -6, -9, 5, -9, -2, 0, 6, 7],\n [2, -12, 15, -16, 6, -9, -4, -9, 6, -16, 7, 7],\n [0, -12, 3, 4, 14, -6, -2, 2, -10, 11, -12, -12],\n [13, 15, -9, -7, 15, 11, 0, 14, -9, 8, -8, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1175755398228", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-2, -14, -13, -3, 8, -7, 4, -5, 10, -15, -4, 15],\n [14, -1, 15, 15, -6, -7, -2, 0, 1, -8, 8, -3],\n [8, 5, 13, 3, 4, 15, 4, 15, 13, -5, 1, 4],\n [-4, 4, -9, -10, 6, 15, -6, 5, 5, 8, 5, 11],\n [12, -4, 1, -15, 12, 4, -2, 10, 14, -2, 6, 7],\n [-4, 5, 16, -14, 2, 6, 12, 13, 8, -9, -1, -9],\n [-16, -12, -14, -16, -13, 15, 8, -7, 4, 10, 10, -15],\n [-4, -8, 5, 9, -5, 0, -3, -3, 3, -6, -1, 14],\n [-11, 2, -13, -13, 3, -7, 7, 9, 4, 4, -7, -13],\n [3, 0, -10, -13, 12, -3, -14, 7, -1, -13, 7, 13],\n [1, 2, 14, 2, 2, 5, 7, -5, 13, 14, 2, 13],\n [16, 1, 11, -6, 16, 0, -11, -13, 3, 10, -2, -11]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33282623987875", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-3, -2, 0, 0, 0, -2, 0, -2, -6, 9, -12, 4],\n [-2, 9, -12, 12, 4, 1, -2, -4, -6, 4, -11, -2],\n [0, -12, 14, 0, -3, -1, 6, 6, 6, 8, 10, 8],\n [0, 12, 0, -7, 8, 2, 9, -2, -4, -6, -10, -3],\n [0, 4, -3, 8, 10, 0, -8, -6, 4, 10, 0, -2],\n [-2, 1, -1, 2, 0, -3, 10, -8, -10, -2, 7, 4],\n [0, -2, 6, 9, -8, 10, -13, -8, 10, 6, 1, 4],\n [-2, -4, 6, -2, -6, -8, -8, 4, -11, -2, -4, -6],\n [-6, -6, 6, -4, 4, -10, 10, -11, 4, 7, 2, -12],\n [9, 4, 8, -6, 10, -2, 6, -2, 7, 9, -10, 2],\n [-12, -11, 10, -10, 0, 7, 1, -4, 2, -10, -7, -12],\n [4, -2, 8, -3, -2, 4, 4, -6, -12, 2, -12, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1774741669356", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -14, -14, 10, 16, 11, -16, -9, 15, -13, 13, -11],\n [2, 15, -8, -5, -6, -1, -16, 4, 13, -4, -13, 11],\n [14, 10, -12, 8, -14, 16, -13, 8, 3, 9, -12, 11],\n [12, -8, -11, 2, -6, -15, -8, 4, 7, 5, -14, -5],\n [11, 13, 9, 4, 11, 9, 16, 4, 1, -6, 6, 5],\n [0, -12, -6, 13, -2, 10, 16, 3, -1, -15, 11, -11],\n [-8, 3, -16, -9, 6, -14, -13, 8, -2, 4, -3, -5],\n [0, -8, -4, -2, 1, 16, -11, 10, 6, 10, -3, -9],\n [2, 13, -3, 3, 8, 7, -3, 9, 6, 5, 2, -14],\n [2, -8, 11, 3, -10, -3, -8, 2, -3, 0, 13, -8],\n [16, 8, -3, -6, -3, 13, -13, -13, 11, -9, -15, 5],\n [-1, 12, 13, -5, -6, 4, 4, -12, 3, -14, 16, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1540871087266972", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-8, -13, 0, 7, 15, -16, -9, 6, -5, -5, -2, 2],\n [9, 12, 5, 4, 3, 12, -13, -10, 11, 11, -13, 5],\n [-5, -14, 5, -15, 7, 10, -16, -9, 6, -11, 5, 8],\n [1, 0, -5, -11, 9, 10, -9, 2, -16, 12, -3, 3],\n [-4, -9, 3, 16, 9, 4, -8, 7, 0, 7, 4, -4],\n [-6, 2, -6, -4, -16, 2, -5, -9, -9, -5, 16, 9],\n [11, -12, -9, 8, 10, 6, 13, 6, 3, 1, 1, -15],\n [-13, 13, 16, 1, 2, 11, 3, 16, -5, -2, -15, 12],\n [-7, -15, -6, -4, -7, -3, 1, -8, 11, -14, 3, -11],\n [10, -15, 12, -14, -1, 13, -15, 0, -5, -16, -2, 9],\n [4, 14, 8, 6, 7, 11, 4, 1, -8, 13, 15, -14],\n [-14, 11, -2, 6, -6, 15, 16, 7, 11, -10, -13, -16]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19193090642596", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 9) of the 8th power of the matrix:\n[[-16, -1, 6, 14, -10, -4, 6, 10, 0, 4, 0, -6],\n [-1, -16, 2, -4, -14, 12, 5, -8, -3, -4, 6, 0],\n [6, 2, -2, 0, 8, -12, -9, 6, -4, 12, -6, -6],\n [14, -4, 0, -12, 2, 2, -2, -10, 16, 4, 6, -7],\n [-10, -14, 8, 2, -4, -2, 0, 0, 10, -4, -4, -6],\n [-4, 12, -12, 2, -2, 10, -2, -4, -2, -6, 12, -14],\n [6, 5, -9, -2, 0, -2, 9, 12, -4, -1, 3, 6],\n [10, -8, 6, -10, 0, -4, 12, 1, -2, -7, -12, -8],\n [0, -3, -4, 16, 10, -2, -4, -2, -12, -4, -1, -2],\n [4, -4, 12, 4, -4, -6, -1, -7, -4, -15, 8, 0],\n [0, 6, -6, 6, -4, 12, 3, -12, -1, 8, -16, 6],\n [-6, 0, -6, -7, -6, -14, 6, -8, -2, 0, 6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-254485665084", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-6, -12, 0, -5, 1, 12, -2, 0, 0, -2, -4, -2],\n [-12, 9, -4, 2, -12, -4, -5, 2, 8, 6, -12, -6],\n [0, -4, 4, 2, 2, 12, 4, 12, -3, 8, 4, -2],\n [-5, 2, 2, 15, -4, 8, 0, 5, 2, 7, -4, 4],\n [1, -12, 2, -4, 14, -2, 6, 5, -9, -2, 15, -2],\n [12, -4, 12, 8, -2, 6, -3, 0, -2, -11, 9, 8],\n [-2, -5, 4, 0, 6, -3, 1, 3, 4, -1, -10, -4],\n [0, 2, 12, 5, 5, 0, 3, -7, -1, 2, 6, -6],\n [0, 8, -3, 2, -9, -2, 4, -1, 4, 0, -4, -2],\n [-2, 6, 8, 7, -2, -11, -1, 2, 0, 14, -12, -2],\n [-4, -12, 4, -4, 15, 9, -10, 6, -4, -12, 1, -4],\n [-2, -6, -2, 4, -2, 8, -4, -6, -2, -2, -4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60298678892", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -8, 6, -8, 3, -2, -6, 2, 10, 12, 8, 11],\n [-8, 3, 10, 8, 3, 8, 4, 4, 0, -11, -10, 0],\n [6, 10, 16, -2, 2, 0, 5, 6, 2, -4, 1, -3],\n [-8, 8, -2, 8, -11, 7, -10, -5, 0, 0, 12, 0],\n [3, 3, 2, -11, 9, -9, -14, 2, 8, 2, -1, 11],\n [-2, 8, 0, 7, -9, 9, 8, -9, -4, -6, -2, -2],\n [-6, 4, 5, -10, -14, 8, 14, 7, 2, -2, -10, 14],\n [2, 4, 6, -5, 2, -9, 7, 1, -2, 0, -6, 10],\n [10, 0, 2, 0, 8, -4, 2, -2, -6, -2, -5, 3],\n [12, -11, -4, 0, 2, -6, -2, 0, -2, 2, -2, -3],\n [8, -10, 1, 12, -1, -2, -10, -6, -5, -2, 13, 13],\n [11, 0, -3, 0, 11, -2, 14, 10, 3, -3, 13, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215031528984463", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[4, 7, -15, -9, 10, 5, 10, 12, -14, -4, -7, -8],\n [10, -16, 15, 8, 12, -10, -14, 3, 3, 13, 10, 9],\n [-3, 0, 1, 12, 3, 10, 1, -13, -16, -16, 9, 3],\n [6, -7, -6, -12, -16, 0, 5, 12, -13, -12, -6, 4],\n [-5, 9, 2, -10, -10, 9, -12, 4, -3, -13, 6, 3],\n [-2, 12, -9, 2, 11, 10, -13, -2, -16, -14, 7, 10],\n [12, 7, 7, -13, -14, 6, 6, -12, 14, -11, -7, -10],\n [4, 3, -14, 5, -13, 11, -5, -12, -4, 6, 13, 8],\n [10, -3, -1, 5, 4, 4, -9, -1, 14, -7, 15, -8],\n [0, -6, 15, -7, 5, 0, -13, 8, 4, -16, 8, 0],\n [7, -15, -2, 15, -11, -16, 6, 0, 12, -8, -4, -11],\n [-11, 3, -14, 0, -5, -16, 0, -14, 9, -2, 15, 15]], determine the value at position (6, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4668107226844", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-13, 2, 2, -1, 2, -4, -6, 4, 2, 4, -12, 14],\n [2, -16, 1, 4, 5, -4, -6, 6, 0, -8, -12, -4],\n [2, 1, -13, -2, -9, -2, -9, -4, 3, -12, 0, -6],\n [-1, 4, -2, 16, -8, -4, -2, 10, 2, -1, -1, 3],\n [2, 5, -9, -8, 16, 4, 8, -8, -2, 12, -2, 4],\n [-4, -4, -2, -4, 4, -3, 0, -4, 8, -2, 2, 4],\n [-6, -6, -9, -2, 8, 0, 0, -14, 0, -10, 4, -14],\n [4, 6, -4, 10, -8, -4, -14, -7, 6, 8, -5, 0],\n [2, 0, 3, 2, -2, 8, 0, 6, 2, 9, -6, 2],\n [4, -8, -12, -1, 12, -2, -10, 8, 9, -11, -5, 14],\n [-12, -12, 0, -1, -2, 2, 4, -5, -6, -5, 13, 12],\n [14, -4, -6, 3, 4, 4, -14, 0, 2, 14, 12, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3163017526517757", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[0, -2, 4, 2, 4, -2, 0, 1, 4, -4, 2, 12],\n [-2, 11, 0, -2, 6, 6, 2, 2, 0, -5, 4, -2],\n [4, 0, 13, -9, -2, -7, -8, -13, -4, -16, 10, -12],\n [2, -2, -9, 8, 4, 10, -12, 0, -5, -13, -4, 2],\n [4, 6, -2, 4, -13, 8, -12, 12, 0, 6, -2, -16],\n [-2, 6, -7, 10, 8, -12, -6, 8, 4, 2, -6, 8],\n [0, 2, -8, -12, -12, -6, 10, -1, 0, 4, 2, 2],\n [1, 2, -13, 0, 12, 8, -1, -11, 8, 2, 8, -8],\n [4, 0, -4, -5, 0, 4, 0, 8, 6, 4, 11, 9],\n [-4, -5, -16, -13, 6, 2, 4, 2, 4, 0, 3, -4],\n [2, 4, 10, -4, -2, -6, 2, 8, 11, 3, -8, 14],\n [12, -2, -12, 2, -16, 8, 2, -8, 9, -4, 14, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3411306783", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[9, -1, -10, 6, 0, -3, -12, 0, -11, -7, 3, -12],\n [-1, 12, 6, 0, 6, 0, 11, -2, -9, 12, 2, -8],\n [-10, 6, 12, 4, -6, -2, -5, -10, -4, -2, -6, -5],\n [6, 0, 4, -11, -2, 6, 11, -2, -8, 4, 6, -4],\n [0, 6, -6, -2, -14, -2, -12, -6, 12, 15, 8, 8],\n [-3, 0, -2, 6, -2, 8, 2, -4, 0, 6, -4, 14],\n [-12, 11, -5, 11, -12, 2, 0, -5, 0, 9, -4, 1],\n [0, -2, -10, -2, -6, -4, -5, -15, 11, 4, -1, -10],\n [-11, -9, -4, -8, 12, 0, 0, 11, 6, 6, 9, -12],\n [-7, 12, -2, 4, 15, 6, 9, 4, 6, -10, 0, 0],\n [3, 2, -6, 6, 8, -4, -4, -1, 9, 0, 16, 12],\n [-12, -8, -5, -4, 8, 14, 1, -10, -12, 0, 12, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6804969683124357", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (8, 2) of the result:\nA =\n[[-4, 1, -15, -9, -6, 16, 10, 3, -5, 14, 10, 15],\n [-7, -14, 10, 14, -2, -1, -4, -6, 4, -6, 13, 5],\n [14, -3, 7, 15, 15, -2, -14, -1, -12, 4, -7, 2],\n [8, -13, 12, 2, -15, -7, 8, 3, 2, 6, 7, -6],\n [11, -12, -12, 4, -5, -13, 3, 8, -3, -6, 15, -6],\n [1, 10, 1, 6, -6, 4, -12, 6, 8, -7, 5, 2],\n [-16, -10, -13, -16, -2, -5, 5, 5, 0, 12, -3, 3],\n [16, -2, -5, 3, 13, -14, 11, 9, 13, -4, -4, -15],\n [-15, 9, -6, -9, 5, 3, -9, 12, 9, 13, 0, 3],\n [-1, -10, -1, 10, 6, 7, -8, 3, 0, 14, -9, -2],\n [14, 13, 3, -5, 0, 13, 12, 2, -6, -10, 3, 7],\n [-7, 15, -2, 3, -14, -9, 6, -6, -9, 12, 13, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-499179096", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[11, -4, 15, 9, 5, -13, 14, 1, 7, 6, 5, -15],\n [14, -6, 11, 15, -12, -7, 7, 6, 0, -16, 14, 14],\n [-8, 5, -4, 8, 1, -5, 0, -2, -2, -2, -4, 0],\n [15, -8, 3, 9, 10, 4, 1, -4, -1, -8, -5, 2],\n [-10, 1, -1, -13, 8, 15, -4, 0, -11, 2, -4, 9],\n [-3, 14, -13, -9, 8, -4, 15, 11, 13, -14, 11, -14],\n [-1, 5, 15, -9, -9, -11, -3, 15, -7, -14, -5, 14],\n [12, -12, 8, 14, 4, 3, 5, -13, -4, 3, -4, 0],\n [16, -16, -2, -4, 0, 7, -9, 10, 6, -9, -9, 9],\n [-4, 11, 8, -1, -15, 1, 0, 13, -4, 15, 12, 13],\n [1, -4, 4, 13, 4, 0, 2, -2, -8, -7, 14, 6],\n [13, 16, -8, -16, -6, -1, -8, 15, -2, -5, 16, -3]], determine the value at position (3, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315760024", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-9, -9, 10, -5, -16, -6, 14, 0, 16, 15, 12, 4],\n [4, 6, -11, 5, -9, -6, 7, 4, -15, 2, 11, 0],\n [-11, 2, 11, -15, -13, 5, 9, -4, 15, 0, 2, 11],\n [-16, 1, 16, -5, -9, 7, -1, -13, 10, -8, -1, -5],\n [14, 7, -3, 8, -14, 7, -8, 9, 3, -7, 2, -14],\n [7, -12, -14, 10, -1, -2, -5, 9, 6, 14, 3, -5],\n [6, -13, 6, -16, 8, -15, 13, -14, 4, 8, 3, 5],\n [4, 16, -2, -2, 8, 4, 7, -12, -11, 6, -13, 10],\n [1, 4, 11, 5, 6, -14, -7, 8, -9, -6, -12, 12],\n [-12, -8, -15, -16, 13, -6, 11, -5, 9, -4, -9, 11],\n [13, -8, 14, 4, 14, 8, -5, -16, 5, -16, -16, 4],\n [-2, 0, 5, -1, -9, 0, 0, 9, -4, 0, 0, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66542211527939", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-11, 3, -10, -3, -2, 4, 2, 2, -4, -1, 2, 1],\n [3, -12, 4, -4, 2, -9, 8, -13, -3, 0, -5, -2],\n [-10, 4, 2, -2, -6, 2, 8, -3, -2, -11, -11, 8],\n [-3, -4, -2, -2, -11, -6, 4, 0, -14, 8, 2, 12],\n [-2, 2, -6, -11, 7, 5, 14, -3, -12, 2, -3, -1],\n [4, -9, 2, -6, 5, 6, -10, 0, -8, -2, 8, -2],\n [2, 8, 8, 4, 14, -10, -7, 9, -2, -2, 0, -2],\n [2, -13, -3, 0, -3, 0, 9, 5, -7, 6, -13, 0],\n [-4, -3, -2, -14, -12, -8, -2, -7, 16, -3, -4, -4],\n [-1, 0, -11, 8, 2, -2, -2, 6, -3, -3, -1, -4],\n [2, -5, -11, 2, -3, 8, 0, -13, -4, -1, -5, 5],\n [1, -2, 8, 12, -1, -2, -2, 0, -4, -4, 5, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-643415963553874", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[10, -2, -6, -6, -4, 4, 7, 4, 8, -12, -10, 2],\n [-2, 11, 7, -2, 8, 1, 7, -10, 4, -8, 14, -11],\n [-6, 7, -4, -4, 1, 2, -6, 1, -14, -14, 0, 5],\n [-6, -2, -4, 13, 8, 10, -6, 8, 8, 1, 0, -1],\n [-4, 8, 1, 8, -13, -4, -14, -5, -2, -10, 5, -10],\n [4, 1, 2, 10, -4, -13, -6, 2, 0, 2, 8, -2],\n [7, 7, -6, -6, -14, -6, 7, 4, 11, -8, 4, 14],\n [4, -10, 1, 8, -5, 2, 4, -5, 0, 6, 8, -2],\n [8, 4, -14, 8, -2, 0, 11, 0, 2, 6, 4, -10],\n [-12, -8, -14, 1, -10, 2, -8, 6, 6, 11, 8, 0],\n [-10, 14, 0, 0, 5, 8, 4, 8, 4, 8, 8, -4],\n [2, -11, 5, -1, -10, -2, 14, -2, -10, 0, -4, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3948227267193030", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-15, 6, 6, -9, 11, 0, -7, -2, -4, 9, 3, -12],\n [6, 1, 5, -7, 0, -4, -14, -6, 4, 2, 2, 3],\n [6, 5, 1, -10, 2, 4, 1, -14, -9, 3, -2, 2],\n [-9, -7, -10, -1, -1, 9, 2, -5, 9, -6, 7, -9],\n [11, 0, 2, -1, 16, 2, 8, -2, 2, -2, 6, -8],\n [0, -4, 4, 9, 2, 8, 4, 8, -12, -2, 2, 8],\n [-7, -14, 1, 2, 8, 4, 7, -2, 0, 9, 4, -1],\n [-2, -6, -14, -5, -2, 8, -2, -11, -4, 9, 13, -2],\n [-4, 4, -9, 9, 2, -12, 0, -4, 10, -4, -5, 0],\n [9, 2, 3, -6, -2, -2, 9, 9, -4, 11, -3, 5],\n [3, 2, -2, 7, 6, 2, 4, 13, -5, -3, -11, 5],\n [-12, 3, 2, -9, -8, 8, -1, -2, 0, 5, 5, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15815007767092", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 9) of the 9th power of the matrix:\n[[8, -13, -6, 15, -10, -6, 11, 6, 6, 11, 9, 8],\n [12, 2, 16, -3, -3, 13, 11, 0, -14, -1, 13, 12],\n [-2, 8, 6, 8, -10, 5, 0, 1, -7, -7, -10, 10],\n [16, -16, -13, 0, -13, 9, -13, -16, -10, 13, -8, -9],\n [7, 2, 10, 15, -3, 1, 11, 12, -1, 14, -13, 0],\n [9, -13, 13, 13, 5, -6, -15, -5, 13, 1, 9, -10],\n [-16, 9, 6, 9, -11, -11, -9, 7, 5, 2, 1, 14],\n [13, 16, -7, -5, 13, 10, -8, 4, -5, 12, 16, -2],\n [-15, 1, -14, -10, 1, 16, 14, -6, -13, 1, -13, 12],\n [7, 5, -15, -11, 8, 4, -1, 14, -3, 11, 15, 11],\n [-8, 5, 15, -12, 6, -12, 15, -7, -2, -10, 12, -14],\n [2, -7, 11, 12, -2, -11, -5, -4, 12, 2, -14, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25324278794410", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-9, 3, -13, 4, -14, -9, 6, -1, -4, -14, -8, -3],\n [-4, -10, -2, -10, 5, 7, -16, -7, -1, -9, 8, -5],\n [8, 0, 9, -3, 6, -11, -12, 8, 1, -4, -3, 11],\n [1, 11, 10, 15, -8, 15, 3, 11, 16, -13, -14, 9],\n [-9, -11, -1, 7, 13, -4, -12, 8, 3, 1, 1, -15],\n [-7, -5, -4, -6, 2, 9, -3, 7, -16, 5, 6, 2],\n [1, -5, 11, 11, 16, 2, 11, 9, -1, -4, 6, 5],\n [-1, 11, -9, 5, 4, 9, 4, 8, -16, -11, 6, 6],\n [6, 15, 13, -4, 1, 6, -2, 16, 4, 6, 10, 1],\n [7, -10, 3, 10, -11, 10, -8, 14, 4, 9, -4, 6],\n [3, 11, 0, 11, -15, 8, -11, -6, -11, -6, -3, -15],\n [-14, 16, 7, 2, 1, 7, -16, 8, 8, -1, 12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1969280075486336", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[6, 2, 8, -1, -8, -16, 2, 16, -1, 1, 8, -11],\n [4, -11, 15, 14, -7, 13, 1, 7, -8, 14, -2, -13],\n [-8, -8, 9, -13, 0, -1, -2, -12, -12, 3, -2, 1],\n [-15, 12, -4, -13, -7, 14, -9, -14, -8, 13, -6, -4],\n [-4, -5, -7, -8, -10, -15, 6, 4, 6, 12, -3, 9],\n [-12, 14, 8, 14, 3, 0, -15, 8, -4, 11, -11, -14],\n [1, -6, 3, -12, 2, 5, 2, -1, 7, -13, -2, 8],\n [-3, 2, -10, 13, 2, 8, -1, -9, 1, 11, -1, 2],\n [0, -4, -10, 10, -7, 8, -11, 7, 1, 6, -11, 12],\n [8, 0, 7, -6, 9, 11, -14, -6, -3, 9, 4, 13],\n [-9, 3, 15, 5, -10, -8, -16, 12, -9, -13, -14, -10],\n [10, -16, 10, -1, -10, 6, -6, 16, 0, -12, 15, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-616123959548", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-3, 6, 6, -2, 6, -1, -6, -1, -6, 2, -4, -2],\n [6, -9, 5, -3, 4, 6, 1, 6, 9, 3, -2, 0],\n [6, 5, 1, 2, 0, 10, 4, -2, -12, 0, -16, -8],\n [-2, -3, 2, 12, 2, 4, 8, -2, -6, -8, 0, -4],\n [6, 4, 0, 2, 8, 0, 2, 2, 6, 0, 0, -2],\n [-1, 6, 10, 4, 0, 16, 8, -2, -6, 3, -8, -2],\n [-6, 1, 4, 8, 2, 8, 11, 1, 4, 4, 4, -10],\n [-1, 6, -2, -2, 2, -2, 1, -13, -8, -2, -1, -13],\n [-6, 9, -12, -6, 6, -6, 4, -8, -8, 4, -2, 6],\n [2, 3, 0, -8, 0, 3, 4, -2, 4, 12, 6, -1],\n [-4, -2, -16, 0, 0, -8, 4, -1, -2, 6, -2, 2],\n [-2, 0, -8, -4, -2, -2, -10, -13, 6, -1, 2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12480960072126", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-1, 5, -16, 2, 6, 4, 3, -6, 2, -6, 6, 3],\n [5, -10, 2, 6, -3, -8, -4, 2, -13, 8, 1, 6],\n [-16, 2, 2, 8, -6, 0, 0, 6, 12, 2, -4, 4],\n [2, 6, 8, -2, -2, -8, -8, 10, 3, 0, 1, 3],\n [6, -3, -6, -2, 6, 14, 16, 8, -9, -7, 4, 12],\n [4, -8, 0, -8, 14, -11, -4, 3, -2, 7, 0, 0],\n [3, -4, 0, -8, 16, -4, 10, 2, 0, -6, -6, 6],\n [-6, 2, 6, 10, 8, 3, 2, -7, 4, 4, 13, -7],\n [2, -13, 12, 3, -9, -2, 0, 4, 13, -3, 1, -6],\n [-6, 8, 2, 0, -7, 7, -6, 4, -3, -8, 4, 14],\n [6, 1, -4, 1, 4, 0, -6, 13, 1, 4, 2, 6],\n [3, 6, 4, 3, 12, 0, 6, -7, -6, 14, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5009920803824", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[16, -5, -14, 9, -9, -10, -1, 7, -16, 8, -7, -1],\n [-1, -9, 12, 11, -11, -1, 3, -1, -10, -3, 9, 9],\n [-3, -10, 16, 9, 3, -14, -13, 9, -6, -15, -3, 13],\n [-5, 9, 16, -4, -3, 7, 9, 4, 11, -15, -8, 6],\n [-2, -4, 6, 0, -15, 3, 3, -14, -5, -15, -3, -1],\n [2, -11, -4, 5, 1, -5, 13, -10, 15, 2, -11, 3],\n [10, -10, -12, -6, -2, -14, -12, 6, -8, -2, -14, 12],\n [-11, 0, 9, 4, -9, 4, -6, -9, 7, -3, -3, -7],\n [-5, -7, 0, 0, -14, 14, -16, -5, -13, -4, 4, 5],\n [-13, 1, -12, 2, -15, -5, 0, -7, -11, -9, -6, -5],\n [-8, -15, -9, -6, -7, 4, 3, -9, 12, -5, -3, 4],\n [5, 4, 13, 3, 7, 6, -10, -8, -16, 9, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4026532210627938", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-11, 8, -2, 0, -2, 8, -10, -1, 0, 15, -1, 2],\n [8, -5, 13, -6, 7, -2, 8, -6, 8, 7, 3, 4],\n [-2, 13, 4, -15, -8, 12, 6, -2, 6, -7, 0, -10],\n [0, -6, -15, 9, 6, -4, 8, -8, 7, 5, 14, 8],\n [-2, 7, -8, 6, 7, -12, -2, -11, 6, 14, -7, 2],\n [8, -2, 12, -4, -12, -6, 5, 6, 3, 8, -7, -8],\n [-10, 8, 6, 8, -2, 5, 6, 4, 6, -5, -6, -2],\n [-1, -6, -2, -8, -11, 6, 4, -2, 5, -8, -9, -4],\n [0, 8, 6, 7, 6, 3, 6, 5, -1, 0, -8, -3],\n [15, 7, -7, 5, 14, 8, -5, -8, 0, 11, -12, -9],\n [-1, 3, 0, 14, -7, -7, -6, -9, -8, -12, 12, -3],\n [2, 4, -10, 8, 2, -8, -2, -4, -3, -9, -3, 1]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89896984777", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 7) of the 8th power of the matrix:\n[[-3, -13, 12, -2, 11, -1, -5, -12, -16, 15, 9, 0],\n [10, 7, 9, 6, 5, -13, -8, -13, -10, 6, -15, 7],\n [14, 14, 7, 9, -1, -4, -2, 10, -13, -1, 13, 13],\n [-14, 5, 5, -5, 4, -13, 14, 14, 6, 3, -2, 6],\n [11, -1, 4, -2, 0, -4, 2, 13, 1, -3, 3, 2],\n [-10, -13, -15, -12, -7, 15, -4, -12, -7, -7, 10, 4],\n [-9, -16, 11, -3, 4, 13, 4, -8, 0, -12, 14, 2],\n [16, -4, -3, 16, 12, -7, 14, -11, -16, -10, 10, 4],\n [11, -1, 6, 3, 8, 11, -12, 4, 1, -11, 12, 2],\n [16, -16, -14, 4, -14, 8, 3, 4, 6, -11, -4, 6],\n [-8, 0, -15, 2, 2, -10, 3, -8, 0, 10, -15, 2],\n [0, -12, 1, -10, 0, -13, 8, -12, 13, -5, -13, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-364192225888", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[12, -8, -13, 7, -3, -12, 1, 2, -5, 1, 0, 13],\n [7, -6, 6, 0, -16, -2, 15, -8, -2, 11, 7, 5],\n [10, 2, -5, 3, -16, 4, -16, -7, 15, 5, 1, 15],\n [10, 11, 1, 12, 1, -9, 14, -10, 1, -8, -8, -9],\n [1, -12, -3, 11, 13, -13, 3, 8, 11, -5, -15, -3],\n [5, 14, 6, 3, -13, -2, 7, 8, -16, -10, 14, -5],\n [-12, -5, 1, -15, -7, -2, 13, 0, -13, -10, 14, -11],\n [-2, -3, -11, 15, -14, -14, 5, 5, -7, -14, -5, 12],\n [0, -10, -4, -15, -13, -7, 7, 0, -11, 2, -12, 15],\n [-7, -8, 10, -4, 2, 4, 7, -13, 7, -14, -13, 14],\n [8, -4, -13, -3, -4, 10, -11, 0, 0, -15, -4, -15],\n [11, 9, 5, -14, -5, 7, -12, 3, -4, -5, -4, -7]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "441018063982865", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 2) of the 8th power of the matrix:\n[[16, -6, -4, -12, 11, -9, 1, -12, -14, 0, 0, -2],\n [-6, -15, 0, 8, 0, 2, 1, 4, 2, -4, 2, -10],\n [-4, 0, -11, -1, 2, 7, 12, 4, 2, -10, 12, 10],\n [-12, 8, -1, 14, -10, -2, -2, -5, 6, -2, 10, -2],\n [11, 0, 2, -10, 11, 9, 8, 9, 8, 4, 2, -9],\n [-9, 2, 7, -2, 9, 9, 15, 2, -10, -2, -11, -8],\n [1, 1, 12, -2, 8, 15, 4, 0, -14, 4, -8, 7],\n [-12, 4, 4, -5, 9, 2, 0, -15, -3, -10, 2, 0],\n [-14, 2, 2, 6, 8, -10, -14, -3, -12, 12, -3, 1],\n [0, -4, -10, -2, 4, -2, 4, -10, 12, -4, 2, 8],\n [0, 2, 12, 10, 2, -11, -8, 2, -3, 2, -9, 2],\n [-2, -10, 10, -2, -9, -8, 7, 0, 1, 8, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-177458346578", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -10, 6, 12, -1, 11, 14, -3, 16, -8, 10, 7],\n [-4, 9, 12, 11, 11, -9, 6, 12, -12, -10, 10, -15],\n [8, -8, 10, -16, 6, -7, 8, -14, -11, -11, -15, 1],\n [6, -15, -5, 5, 3, 7, 3, -16, -16, 0, -16, 13],\n [-14, -6, 7, 5, 9, -4, -16, 7, -7, 7, 11, -1],\n [-1, 0, -2, -1, -2, -6, -16, -2, 9, -13, -12, -4],\n [-7, -6, 1, 6, -10, -14, -5, -10, 9, 16, -2, -15],\n [-10, 15, -13, 3, 15, 11, -4, -16, 13, 8, -1, 2],\n [-16, -12, 5, 7, -13, 1, -1, 1, 5, -15, 4, 12],\n [9, 4, 0, -1, 14, -8, 14, -3, -15, -3, 16, 3],\n [-15, 2, 1, -1, -13, -5, 12, -10, -3, -5, -12, 0],\n [15, -7, 0, -12, -8, 16, 1, -8, 12, -3, 8, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2143220461500", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-11, 12, -2, 12, -13, 1, -1, -6, -3, -14, 1, 3],\n [8, -4, -13, -3, 16, 11, -9, -12, -12, 14, -8, 15],\n [16, -14, 13, -5, 12, -14, 9, 13, -8, 9, -15, -14],\n [-13, 8, -4, 6, -8, -15, 14, -15, 15, 1, -4, -12],\n [-7, 8, 13, -10, -11, -14, -4, -14, 9, 7, -11, -5],\n [-15, -6, 9, 1, 4, 5, 13, 13, -9, -8, 3, 8],\n [2, -12, -6, -2, -9, 2, 6, 10, 15, 9, 10, 2],\n [12, 16, 2, 2, 16, -1, 6, -10, 9, 15, -5, -9],\n [-12, 11, -12, 9, -12, 5, -2, -4, 11, 16, 6, 16],\n [1, 13, 9, -1, -4, 16, 9, -16, -15, -11, 7, 1],\n [10, -9, 11, -7, 0, 12, -11, -3, 5, -11, 9, -5],\n [-3, 5, 6, -10, 8, -4, 4, -7, -8, -2, -15, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17312983064004", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (1, 4) of the result:\nA =\n[[-4, -14, -11, 2, -14, 1, -8, -5, -12, -14, -6, 13],\n [-13, -12, -16, 10, 11, 12, 1, -5, -4, -15, -1, 7],\n [5, -6, 12, -2, 14, -1, -7, 15, -15, 7, 6, -15],\n [14, 9, 12, -14, -3, 8, -16, -14, 9, 1, -8, 6],\n [4, -16, 4, 10, -11, 11, 0, -14, -5, -5, -15, 5],\n [6, 13, -12, -8, 4, -6, -12, 10, -15, 7, 14, 16],\n [13, 11, 14, -6, 6, -15, 10, -15, 4, -12, 4, 12],\n [3, 3, 8, -15, 15, 9, -11, -14, 16, -16, -12, -4],\n [2, -5, 8, -5, 13, -12, 5, -4, -14, 3, 14, -12],\n [7, 16, -9, 7, 3, -1, -5, -4, 8, 15, 7, -8],\n [6, -4, 15, -2, -12, 5, -1, -7, 7, 1, 1, -10],\n [-13, 9, -12, -1, 9, 1, 12, 6, -3, -2, 16, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271821291801", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[4, 0, 6, 0, -3, 12, 3, 13, 2, -4, 1, 6],\n [16, 1, -8, 16, 15, 0, 2, 10, -11, 3, 8, -13],\n [-7, -7, 7, 4, -6, 10, -1, 9, 13, -1, -10, -1],\n [-1, -5, 4, 0, 15, -11, 7, 10, 3, 8, -15, -8],\n [11, -14, 3, -11, 16, -16, -11, -2, 9, -3, -10, 14],\n [7, 14, 12, 15, 0, -3, 7, 10, 8, 15, 1, 1],\n [9, -8, -9, 3, 5, 2, 13, 11, -6, 14, 13, 6],\n [2, -5, -2, 14, -2, 12, 9, -15, 3, -2, -13, 5],\n [6, 9, -6, 11, -15, -9, 12, -6, 1, -3, -7, -8],\n [-6, -5, -14, -3, 11, -6, 8, 4, -7, -2, 2, 5],\n [4, 15, 6, -4, -12, -13, 11, -3, -9, -8, 4, 1],\n [16, -9, 0, 14, -11, 5, -3, -14, -5, -5, -15, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-510941524679", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-2, -2, 6, 0, 2, -4, 5, 14, 5, 12, 4, 16],\n [-2, 7, -8, 10, 6, 4, 8, -4, -10, -6, -4, -8],\n [6, -8, 11, -2, 8, -1, -2, 4, 2, 14, 4, 4],\n [0, 10, -2, -9, -6, -14, 4, 0, 0, 14, -2, 0],\n [2, 6, 8, -6, -13, 4, 4, -2, 12, -12, -10, 15],\n [-4, 4, -1, -14, 4, -10, 8, -12, 9, -4, -4, 10],\n [5, 8, -2, 4, 4, 8, -7, -6, -2, 1, -2, -4],\n [14, -4, 4, 0, -2, -12, -6, -6, -12, -6, 0, 8],\n [5, -10, 2, 0, 12, 9, -2, -12, 16, -2, 6, 10],\n [12, -6, 14, 14, -12, -4, 1, -6, -2, -10, 6, -4],\n [4, -4, 4, -2, -10, -4, -2, 0, 6, 6, -2, -4],\n [16, -8, 4, 0, 15, 10, -4, 8, 10, -4, -4, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6249633148254132", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 8) of the 9th power of the matrix:\n[[-4, -16, 3, -9, -7, -8, -14, -6, -5, -7, 8, 8],\n [-6, 9, -3, -16, -13, 13, -5, -4, 14, 6, -13, -1],\n [-10, 5, 12, -6, 16, 12, -5, -10, 9, -8, -4, 8],\n [7, 0, -15, -4, 14, 12, 11, 10, -2, 14, -2, 16],\n [3, -5, -8, 6, -9, 15, -3, 10, 8, -4, 4, 14],\n [-12, -4, 11, 8, -10, 15, -14, 5, -9, 0, 10, 16],\n [0, -5, 10, -9, 6, 12, 3, -1, 0, -1, 2, -9],\n [12, 9, 14, -5, 0, -2, -8, -5, 15, 8, 1, -2],\n [15, -11, -12, 1, -1, -9, 8, 15, 9, 5, 14, -7],\n [-5, 11, -11, 3, -12, 6, -8, 12, -1, 5, -9, 3],\n [-3, -6, 16, 14, -10, 6, -10, 8, -14, 3, 13, 0],\n [-7, 3, 1, 10, 6, 15, -7, -6, -11, 0, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4146051490366", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[2, -5, -4, -2, -6, 4, -8, 2, 2, -5, -4, -4],\n [-5, 7, 2, 2, -2, 1, 10, -13, 0, -5, 12, -5],\n [-4, 2, -13, 12, -2, 4, 9, -4, 2, 10, -10, 0],\n [-2, 2, 12, -4, 9, -13, -9, -2, -12, -4, 5, -9],\n [-6, -2, -2, 9, 2, 1, -10, -4, -14, -4, 6, -2],\n [4, 1, 4, -13, 1, -15, 2, 0, -11, 7, 3, -12],\n [-8, 10, 9, -9, -10, 2, -7, 10, -1, 14, -8, 4],\n [2, -13, -4, -2, -4, 0, 10, 0, 4, 10, 2, 1],\n [2, 0, 2, -12, -14, -11, -1, 4, 8, 0, 6, 6],\n [-5, -5, 10, -4, -4, 7, 14, 10, 0, 7, -9, 10],\n [-4, 12, -10, 5, 6, 3, -8, 2, 6, -9, 16, 0],\n [-4, -5, 0, -9, -2, -12, 4, 1, 6, 10, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14911714428667", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[4, 6, 3, -6, -7, -7, -11, 7, -5, 6, 10, -11],\n [-16, -11, 5, 7, 8, -2, 9, -9, 7, -11, -16, -5],\n [-6, -5, -10, -6, 14, 16, -4, 1, 7, -8, 14, -7],\n [-15, -2, -14, 14, -11, -14, -6, -2, 11, -7, -10, -2],\n [1, 1, 7, -15, 3, 9, -10, 13, -12, -6, -16, -16],\n [2, -15, 4, 3, 6, 4, 7, -13, -5, 5, 3, 1],\n [-16, 13, 16, 7, -3, -12, -6, 7, 14, -4, -1, 7],\n [-4, 7, 9, -15, -1, -16, -6, 12, 0, 11, 12, -14],\n [-7, -3, -5, 13, 15, 15, 15, 9, -16, -15, 0, 13],\n [-10, 10, -8, 5, -16, -8, 3, 2, -13, -8, 5, 1],\n [-5, -8, -11, 2, -10, -1, -12, -1, -16, 2, 0, 9],\n [5, -9, 16, -15, 13, 3, 1, -7, 7, -13, -13, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1593475143665643", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[8, -6, -5, 1, -11, 15, -4, -12, 0, -7, -1, 8],\n [-6, -2, 1, 2, 6, -2, 5, -2, -2, -12, -10, 12],\n [-5, 1, 12, 4, 7, -4, 2, 6, 12, -6, -6, 0],\n [1, 2, 4, 1, -7, -2, -14, -5, -16, -4, -8, -4],\n [-11, 6, 7, -7, 3, -10, -8, -12, 2, 1, -8, 10],\n [15, -2, -4, -2, -10, -6, 12, 10, 6, 2, 0, -1],\n [-4, 5, 2, -14, -8, 12, 14, 3, -6, 4, -4, -4],\n [-12, -2, 6, -5, -12, 10, 3, -5, -12, -3, 8, 4],\n [0, -2, 12, -16, 2, 6, -6, -12, -9, -6, -6, 2],\n [-7, -12, -6, -4, 1, 2, 4, -3, -6, 9, 12, 0],\n [-1, -10, -6, -8, -8, 0, -4, 8, -6, 12, -6, 2],\n [8, 12, 0, -4, 10, -1, -4, 4, 2, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175557151532619", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[8, -15, -15, -1, -8, 11, -4, -4, 14, 4, 15, -9],\n [-15, 15, 11, -16, -7, -13, -7, -6, -3, -5, 0, -1],\n [-15, -6, -14, 12, 1, 3, -3, 14, 1, 13, 8, 2],\n [-9, 11, -9, 14, -14, -14, 5, 0, 0, -3, -8, 13],\n [4, -5, 15, -6, 3, -6, -9, -13, 10, 13, 10, 4],\n [3, -13, -6, -4, -8, -13, -5, -8, -4, 9, -4, 11],\n [2, 7, 2, -4, -4, 11, -15, -7, 5, -4, -8, 16],\n [-3, 3, -2, 15, 16, 0, 7, 13, -4, -1, -15, 0],\n [15, -9, -14, -5, 3, -1, -3, -1, 16, 13, -5, -2],\n [1, 11, 6, -3, 13, 16, -2, -10, -2, -6, 12, 14],\n [8, 7, 2, -15, 5, 3, 16, -9, 8, -8, 6, -12],\n [8, -9, -1, -2, -16, 5, -14, -3, 1, 1, -14, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5532685566796", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-16, 10, 10, -6, -12, -10, 2, 12, -2, -5, 13, 3],\n [-14, -8, 9, -15, 6, 6, 4, -1, -8, -4, 11, 10],\n [0, -16, 1, -8, -4, -2, -13, 16, 7, -7, 3, -6],\n [-5, 1, 13, 3, 8, -5, 4, 8, -6, -8, 8, 15],\n [-3, -16, 0, 8, -9, -12, -12, 2, 6, -8, 13, -1],\n [16, -15, -3, -16, 9, 8, -1, -2, 9, -1, -3, 12],\n [7, -2, 2, -9, -15, 10, -7, 6, -9, 11, 6, -13],\n [-3, 12, -16, -13, 15, 16, 9, 0, 6, 15, -2, -4],\n [-15, 2, 7, 7, -6, 5, -2, -7, 10, -8, 11, -16],\n [0, 14, -7, 12, 1, -11, -5, -3, -7, 3, -2, 14],\n [-10, -7, -7, 11, 13, -14, -2, 4, -5, -13, -8, 11],\n [6, 5, 7, 9, 13, 16, -1, 5, 1, -10, 9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22033435916", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-11, 8, 10, 4, 6, -11, 6, 2, -7, -6, -4, 4],\n [8, 14, 10, 6, 12, -13, -2, 12, 12, -3, 13, 6],\n [10, 10, -2, -7, 6, 3, -4, -1, 4, 12, 7, 10],\n [4, 6, -7, -3, 6, -2, 2, -8, 6, 8, 10, 3],\n [6, 12, 6, 6, 12, 4, -10, 11, -3, -10, 3, 5],\n [-11, -13, 3, -2, 4, -9, 4, 1, 6, -10, -2, -10],\n [6, -2, -4, 2, -10, 4, 2, 0, -10, 11, -13, -2],\n [2, 12, -1, -8, 11, 1, 0, 0, -12, 4, -8, -5],\n [-7, 12, 4, 6, -3, 6, -10, -12, 1, -8, 14, 0],\n [-6, -3, 12, 8, -10, -10, 11, 4, -8, 7, -10, -13],\n [-4, 13, 7, 10, 3, -2, -13, -8, 14, -10, 5, -8],\n [4, 6, 10, 3, 5, -10, -2, -5, 0, -13, -8, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13319300432549", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[5, 5, 0, -2, -4, -2, 15, -8, -1, -4, 7, 0],\n [5, -16, -14, 4, 6, 10, 0, 12, 14, 4, -2, -2],\n [0, -14, 7, -6, 8, -9, 0, -6, 0, -7, -6, 6],\n [-2, 4, -6, 0, -3, 8, -8, -2, -8, 2, 5, 0],\n [-4, 6, 8, -3, 13, -3, -2, -3, -4, -4, 4, 0],\n [-2, 10, -9, 8, -3, 5, -10, 6, 7, 4, 15, 12],\n [15, 0, 0, -8, -2, -10, 10, 4, 3, -5, 0, -6],\n [-8, 12, -6, -2, -3, 6, 4, 4, 2, 2, 0, 0],\n [-1, 14, 0, -8, -4, 7, 3, 2, -6, -6, -4, -8],\n [-4, 4, -7, 2, -4, 4, -5, 2, -6, -8, 9, 10],\n [7, -2, -6, 5, 4, 15, 0, 0, -4, 9, -10, 4],\n [0, -2, 6, 0, 0, 12, -6, 0, -8, 10, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14997838085612", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-12, -14, 6, 4, 12, -7, 2, 0, 10, -7, 9, 4],\n [-14, 15, -3, -8, -4, 2, 14, -8, -6, -6, -10, -8],\n [6, -3, -16, 6, -4, -9, -9, 9, 14, 8, 0, 4],\n [4, -8, 6, 10, 12, 0, -10, 11, -4, 11, -10, -6],\n [12, -4, -4, 12, -6, 14, -4, -14, 6, 10, -8, -6],\n [-7, 2, -9, 0, 14, 16, 2, -13, -10, 2, 4, 9],\n [2, 14, -9, -10, -4, 2, 14, -7, -8, 7, -3, 4],\n [0, -8, 9, 11, -14, -13, -7, 7, -4, 2, 6, 4],\n [10, -6, 14, -4, 6, -10, -8, -4, -12, 10, -2, 7],\n [-7, -6, 8, 11, 10, 2, 7, 2, 10, 9, 2, -2],\n [9, -10, 0, -10, -8, 4, -3, 6, -2, 2, -14, 16],\n [4, -8, 4, -6, -6, 9, 4, 4, 7, -2, 16, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1423252871616634", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[4, 3, -9, -8, 8, 8, 16, -15, 2, 3, 12, -11],\n [0, 8, -13, 13, 3, -14, 6, 1, 9, -9, 0, 14],\n [16, 10, -13, 5, 9, 15, 7, 15, -10, 16, 14, -5],\n [-6, 7, -9, 15, 5, 2, 3, -3, 16, -7, -1, -13],\n [10, 11, -1, 16, 2, 4, 5, -8, -8, -8, 10, 0],\n [-9, -1, 1, 16, -16, -5, -11, -12, -1, 1, 1, -16],\n [2, -9, -14, 8, -12, 2, 1, 14, 16, 1, -1, -1],\n [-10, -3, 8, 15, 5, -1, 12, -1, -5, 0, 10, 8],\n [-4, -9, -12, -5, -14, 16, 5, -8, 1, 12, 10, 0],\n [-14, -12, -3, -14, 6, 13, 6, 10, -7, 8, -4, -1],\n [5, 0, 6, -8, -15, 15, 5, -4, -9, -16, 0, -5],\n [-13, -4, 14, -10, 6, 7, -12, -12, 0, 13, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201351616176", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[8, 2, -6, 3, -2, -5, 2, -8, 5, -2, 10, -10],\n [2, 9, -4, 0, 11, 2, 0, -2, 0, -2, -1, -12],\n [-6, -4, -14, 5, 5, 8, -10, -1, -2, -3, 8, 11],\n [3, 0, 5, 16, -2, 2, 5, -4, 2, 8, -14, -6],\n [-2, 11, 5, -2, 2, -2, 6, 3, 0, 6, 2, 1],\n [-5, 2, 8, 2, -2, -11, 0, -3, -10, -4, -14, 8],\n [2, 0, -10, 5, 6, 0, 5, -6, -6, -6, -8, 7],\n [-8, -2, -1, -4, 3, -3, -6, 11, -8, -6, 4, 2],\n [5, 0, -2, 2, 0, -10, -6, -8, 11, 8, -2, 6],\n [-2, -2, -3, 8, 6, -4, -6, -6, 8, 15, 0, -10],\n [10, -1, 8, -14, 2, -14, -8, 4, -2, 0, -7, -6],\n [-10, -12, 11, -6, 1, 8, 7, 2, 6, -10, -6, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105157555449503", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-13, -10, 12, 13, -6, 0, 2, 6, 2, 2, -8, 1],\n [-10, -12, 0, 7, 6, 14, 6, 4, 2, -8, 15, 3],\n [12, 0, 16, 14, -4, -4, -2, 6, -10, -8, 1, -2],\n [13, 7, 14, -13, -2, -6, -4, 0, 4, -10, -6, 6],\n [-6, 6, -4, -2, -10, -8, -4, -2, 2, 14, 0, -4],\n [0, 14, -4, -6, -8, -8, 0, 1, -6, -11, -7, -10],\n [2, 6, -2, -4, -4, 0, -6, 0, 4, 10, -2, 13],\n [6, 4, 6, 0, -2, 1, 0, -5, 2, 6, 13, -4],\n [2, 2, -10, 4, 2, -6, 4, 2, 11, 2, 5, -8],\n [2, -8, -8, -10, 14, -11, 10, 6, 2, 12, 10, -6],\n [-8, 15, 1, -6, 0, -7, -2, 13, 5, 10, -3, -2],\n [1, 3, -2, 6, -4, -10, 13, -4, -8, -6, -2, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-147709169319", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-7, 0, 13, -7, 2, 12, -15, 2, -10, 9, -2, -14],\n [-1, -15, 14, 11, -10, 13, -10, 12, 7, -13, 12, -12],\n [12, 13, 12, 9, 2, 9, 10, 13, 13, -14, -10, -8],\n [-4, -2, -12, 12, 10, 10, -9, 15, 3, -7, -4, 12],\n [-9, 12, 14, 13, 5, 4, -5, -6, -15, -15, -14, -1],\n [-13, 6, 3, 8, 13, 1, -6, 12, 0, 9, 6, 3],\n [-15, 7, 14, 10, -15, -3, -13, -4, -9, -15, -11, 14],\n [-7, 4, -7, 6, -14, 15, 3, -7, 12, 3, -9, -10],\n [-11, -6, 1, 12, 8, 4, -14, 1, 7, -7, 10, -5],\n [-10, 0, -16, 9, -2, 16, 14, -16, -9, -5, 2, 8],\n [15, -5, -4, 11, -16, -11, -9, -13, -12, 8, 5, 11],\n [6, -13, -13, 4, -15, -10, -1, 0, 3, 6, -6, 16]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "186967438742921", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[9, -8, 8, -4, -8, 3, 2, 0, 8, 6, -4, -4],\n [-8, 16, 4, 0, -8, 4, -2, 2, -2, -4, 2, -8],\n [8, 4, 7, 1, -6, -8, -12, 6, 2, -4, 8, -8],\n [-4, 0, 1, -7, -8, 2, -2, 4, 1, 10, -8, 6],\n [-8, -8, -6, -8, 8, -7, 0, 9, -8, -12, 10, 8],\n [3, 4, -8, 2, -7, -12, -12, 2, -14, -6, 4, -2],\n [2, -2, -12, -2, 0, -12, -12, 1, 0, -10, 11, 0],\n [0, 2, 6, 4, 9, 2, 1, 14, 9, 13, -8, -10],\n [8, -2, 2, 1, -8, -14, 0, 9, 4, -2, 1, 2],\n [6, -4, -4, 10, -12, -6, -10, 13, -2, 0, 8, 0],\n [-4, 2, 8, -8, 10, 4, 11, -8, 1, 8, -11, 8],\n [-4, -8, -8, 6, 8, -2, 0, -10, 2, 0, 8, 12]], determine the value at position (12, 9).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-253194292248", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-5, 0, 3, 9, 2, -5, 4, -10, -2, -16, 9, 8],\n [-2, 5, -11, -2, 7, 4, -10, 12, 15, 15, -12, -13],\n [5, 1, 0, 7, -15, -4, -2, -12, -14, -14, 6, 11],\n [13, 1, 16, 9, 0, -10, -9, 14, -5, 14, 2, -7],\n [-5, 3, -10, -3, -6, -10, 12, -7, 12, -8, -7, 2],\n [14, 0, -8, 16, 7, -8, -10, -1, 2, -11, -6, -5],\n [-4, -5, 4, -7, 3, 11, 7, -12, -5, -15, -8, 5],\n [-12, -5, -16, 5, 2, -1, 14, -14, 6, 1, 9, -4],\n [1, -14, 6, -14, 8, 10, 10, 8, 7, -9, -8, 13],\n [2, -1, 7, 4, -11, -12, -3, -13, -9, 7, -6, 0],\n [4, 9, 10, -1, 9, 16, 14, -11, -9, -10, -3, -1],\n [-8, -7, 0, -5, -11, 2, 12, -11, 8, 7, 8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1445790718359", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (9, 1) of the matrix A^9 where A is:\n[[-1, -11, 4, -13, 11, 11, 0, -3, -10, 5, -16, 12],\n [14, 13, -2, 1, 13, -6, 10, 7, -9, 1, -4, 7],\n [6, -5, 13, 14, 11, 5, 11, -4, 8, -10, -11, 7],\n [2, 2, -8, 12, 7, -12, 9, -3, 12, -11, -10, 1],\n [6, -16, -13, 6, 10, 9, -9, -1, -14, 15, -12, 3],\n [-3, 15, 9, -11, -12, -4, 15, -1, -16, -4, -6, -9],\n [8, 15, 7, 11, -3, -14, 10, 3, -2, 10, 11, 8],\n [16, -3, -9, -3, -16, -1, 1, -10, -2, 7, -4, -8],\n [-2, 7, 16, -1, -9, 12, 6, 14, -3, 13, 10, -1],\n [-11, 16, 1, -1, -5, 3, 12, 13, 9, 5, 16, 12],\n [5, -4, -8, 7, -2, -4, 10, -10, -9, -3, -5, 0],\n [12, 10, -16, -13, 7, 4, 16, -10, -16, -14, -2, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28217855620672", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 9) of the 7th power of the matrix:\n[[-1, -7, 12, -11, 12, 0, 5, 7, 0, 4, -6, -10],\n [-12, 4, 1, 3, -2, -12, -4, -5, 4, -11, -10, 9],\n [-9, -8, 10, -13, 4, 14, 4, 8, -2, 11, -3, -13],\n [3, -5, 16, 7, 3, -12, 13, 7, -10, -1, -2, 6],\n [-5, 12, -2, 12, 4, -2, -3, -1, -2, -13, 10, 6],\n [12, -8, -10, -13, -12, -12, -6, 11, -1, 13, -13, -15],\n [-14, 4, -11, 1, -12, -8, 3, 11, 9, 1, 2, -14],\n [-8, 14, 0, 6, -12, -2, -14, 2, 11, -14, -13, 7],\n [14, -6, -16, -8, 0, -16, -14, 9, 14, 9, 6, 13],\n [-7, -9, 8, 5, -2, -7, 3, 6, -16, -15, 2, -3],\n [-9, -5, 9, 10, 12, -2, -16, 11, -14, 1, 15, 12],\n [8, 9, -9, 2, 5, 12, 16, -14, 2, -7, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8694027547", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-6, 9, 7, -4, 15, -13, -4, -8, -10, -16, -5, 4],\n [-6, -3, 8, -13, 9, -1, -7, -15, 2, -11, 2, -9],\n [-3, -7, -14, 12, -2, 6, 6, 1, 2, 11, 9, -7],\n [-13, -15, -14, -10, -1, 14, -7, 2, 11, 0, 11, 2],\n [6, 3, -4, -4, -6, -2, 0, 11, 2, -13, 5, 5],\n [16, 16, -5, -15, 11, -7, 5, 0, 9, -14, -10, -9],\n [3, -5, 0, 11, -7, 5, 16, 5, -4, 10, -2, 5],\n [13, 2, -9, 16, 11, 8, 0, 7, 4, -15, 14, 16],\n [13, -5, -5, 7, 7, -6, -4, 10, -9, -7, -9, 3],\n [-9, -8, -10, -3, 11, -15, -9, -4, 4, 11, 6, -2],\n [-15, -5, -14, -12, -14, 2, -15, 0, -3, 11, 10, -7],\n [-14, 8, 5, 13, 4, 13, 11, 14, 9, 5, 4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1959277496448", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-4, 4, -8, 0, 4, 14, 5, -5, -11, -1, 9, -12],\n [-8, -3, 13, 9, 12, 2, -9, 6, 14, 15, -12, -1],\n [0, 15, 15, 3, -15, 3, 1, -16, 12, 12, 2, -11],\n [-9, 7, 3, -3, -12, -1, -10, -1, -10, 10, -3, -3],\n [16, 16, 3, -10, 15, -14, 12, 7, 5, -11, 7, 6],\n [-7, -1, -6, 15, -11, 7, 16, -5, 10, 1, -4, 13],\n [-4, 13, 8, -15, 1, -12, 2, 1, 15, 4, -7, 5],\n [-4, 0, -8, 7, -3, -9, 2, 11, 13, -10, 9, -6],\n [-3, 4, -9, -14, 11, 12, 6, 1, -4, -5, -12, -6],\n [-6, 14, 14, -4, -3, 8, 16, 16, -2, -1, -11, 8],\n [-2, -13, -13, 13, 10, 14, 15, -8, -9, -3, 16, 6],\n [4, -5, -15, -4, -13, 3, -3, 13, 12, -9, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333503589873650", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (4, 10) of the result:\nA =\n[[-15, 2, 2, 13, 4, 12, 5, 0, 1, 8, -1, -1],\n [2, -1, 2, 2, -4, 6, 10, -2, 6, -2, 0, 3],\n [2, 2, 5, 6, -2, -8, 6, -4, 4, -2, 12, 6],\n [13, 2, 6, -10, -4, -2, 2, 10, -1, 8, -3, 0],\n [4, -4, -2, -4, 6, -11, 6, -2, -7, 12, 2, 4],\n [12, 6, -8, -2, -11, 11, -12, 2, 8, 0, -2, 10],\n [5, 10, 6, 2, 6, -12, 12, -8, -5, -1, -1, -2],\n [0, -2, -4, 10, -2, 2, -8, -11, -2, 3, -4, -14],\n [1, 6, 4, -1, -7, 8, -5, -2, 10, -4, -3, 4],\n [8, -2, -2, 8, 12, 0, -1, 3, -4, 10, -8, -12],\n [-1, 0, 12, -3, 2, -2, -1, -4, -3, -8, -5, 1],\n [-1, 3, 6, 0, 4, 10, -2, -14, 4, -12, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11829046642", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 10) of the matrix A^8 where A is:\n[[13, 11, 9, -9, -7, -3, -2, 0, 1, 15, 6, 6],\n [-2, 7, 11, -1, -1, -11, -15, -4, -8, 0, 10, 12],\n [5, 7, -10, -5, 6, -2, 16, -4, 6, 15, -16, -12],\n [-4, -12, 15, 4, 7, 1, 4, -7, 7, 4, 8, 6],\n [5, -13, -11, 11, 14, 6, -11, -1, -15, 7, 0, -16],\n [-11, -12, 12, -5, -14, -16, 10, 7, 2, -9, -15, 13],\n [13, 15, -16, -4, -6, -7, 9, 3, 0, 0, -13, -12],\n [6, -7, 11, 16, 9, 12, 10, 1, -7, -12, -7, 4],\n [7, -14, 14, -15, -15, 3, 16, -13, -6, -12, 8, -8],\n [-11, 1, -3, 2, -3, 0, 12, 0, -9, -16, -10, -12],\n [7, 11, 0, 3, -14, 9, -2, -9, -4, -14, -16, -8],\n [14, 9, 0, -8, -4, -12, -4, -16, 8, -13, -7, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636688038022", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 6) of the 7th power of the matrix:\n[[-11, -2, -8, -14, 6, 4, 4, -6, -7, 6, -8, -8],\n [-2, 5, -6, -1, -4, 2, 7, -2, 8, -1, 11, -6],\n [-8, -6, 16, 4, 4, 4, -4, -7, 6, 10, 1, -13],\n [-14, -1, 4, 6, -2, 8, -6, -5, -1, 12, -3, 2],\n [6, -4, 4, -2, 4, 2, 8, 2, -2, 0, 9, -4],\n [4, 2, 4, 8, 2, 2, 2, -2, 2, 14, 2, -2],\n [4, 7, -4, -6, 8, 2, -12, -6, -8, 9, -4, -6],\n [-6, -2, -7, -5, 2, -2, -6, 12, -9, -2, -6, -7],\n [-7, 8, 6, -1, -2, 2, -8, -9, -14, -5, 13, 2],\n [6, -1, 10, 12, 0, 14, 9, -2, -5, 5, 0, -10],\n [-8, 11, 1, -3, 9, 2, -4, -6, 13, 0, 10, 1],\n [-8, -6, -13, 2, -4, -2, -6, -7, 2, -10, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15831556204", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[16, 1, 2, 2, 2, 14, 0, -2, -8, -5, 6, -4],\n [1, -14, 7, 12, 0, -5, 0, 3, 11, -14, 10, -1],\n [2, 7, -9, 10, -4, 9, 9, 2, 8, 0, -11, -8],\n [2, 12, 10, -4, 2, -2, -4, -2, 0, 8, 4, 10],\n [2, 0, -4, 2, -10, 0, -2, -8, -5, -2, 2, -4],\n [14, -5, 9, -2, 0, -13, 10, 2, 6, -9, 7, -11],\n [0, 0, 9, -4, -2, 10, 4, 10, -1, 12, 6, 2],\n [-2, 3, 2, -2, -8, 2, 10, -11, -11, -2, -5, 1],\n [-8, 11, 8, 0, -5, 6, -1, -11, 1, -4, 8, -4],\n [-5, -14, 0, 8, -2, -9, 12, -2, -4, -9, 10, 6],\n [6, 10, -11, 4, 2, 7, 6, -5, 8, 10, 9, 2],\n [-4, -1, -8, 10, -4, -11, 2, 1, -4, 6, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8869386912287", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-9, 4, -6, -8, 5, -9, -10, 2, 8, -6, 8, 2],\n [4, -8, -10, 4, -2, -12, 0, -4, 8, -6, -12, 4],\n [-6, -10, 4, 0, -5, 6, -9, -3, 3, -2, -4, 4],\n [-8, 4, 0, 0, 2, 2, -10, 5, -8, -6, 8, 0],\n [5, -2, -5, 2, -15, 10, 11, -2, 7, -1, -8, -8],\n [-9, -12, 6, 2, 10, -10, 6, -4, -14, 2, -5, 8],\n [-10, 0, -9, -10, 11, 6, 13, 0, -9, 0, 2, -4],\n [2, -4, -3, 5, -2, -4, 0, -5, -6, 0, 6, 4],\n [8, 8, 3, -8, 7, -14, -9, -6, -16, 9, 0, -4],\n [-6, -6, -2, -6, -1, 2, 0, 0, 9, -4, 4, -1],\n [8, -12, -4, 8, -8, -5, 2, 6, 0, 4, 13, 6],\n [2, 4, 4, 0, -8, 8, -4, 4, -4, -1, 6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3523912244138", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the 9th power of the matrix:\n[[10, -6, -7, 10, -4, 8, 2, 2, -5, 5, -2, -4],\n [-6, 0, -8, -4, -13, 0, -6, -2, 8, -7, -8, -13],\n [-7, -8, 2, 10, 6, 1, 4, 0, -4, -2, -2, -4],\n [10, -4, 10, 6, 4, -10, 0, -5, -8, 4, 1, -6],\n [-4, -13, 6, 4, -7, -6, 2, -4, -10, 8, 2, 3],\n [8, 0, 1, -10, -6, -4, 4, -6, 10, -12, 2, 4],\n [2, -6, 4, 0, 2, 4, -13, 3, -4, -2, -13, 8],\n [2, -2, 0, -5, -4, -6, 3, 7, -4, -9, 2, -6],\n [-5, 8, -4, -8, -10, 10, -4, -4, 10, -7, 7, -8],\n [5, -7, -2, 4, 8, -12, -2, -9, -7, 4, -10, 0],\n [-2, -8, -2, 1, 2, 2, -13, 2, 7, -10, -1, -9],\n [-4, -13, -4, -6, 3, 4, 8, -6, -8, 0, -9, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99498984808762", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[14, 5, -4, -6, -10, -12, 5, -10, -14, -2, -12, 0],\n [5, -7, -12, 2, 7, -6, 1, -2, 0, -6, 0, -10],\n [-4, -12, 15, 0, -2, 0, 4, -6, 5, -4, -7, -2],\n [-6, 2, 0, 3, 12, -11, 2, -7, -8, -2, 6, 10],\n [-10, 7, -2, 12, 3, -4, -8, -2, -2, 0, 5, 8],\n [-12, -6, 0, -11, -4, -7, -1, -2, -4, -4, -4, 1],\n [5, 1, 4, 2, -8, -1, -14, 4, 1, -6, 6, 3],\n [-10, -2, -6, -7, -2, -2, 4, -16, -8, -2, 4, 0],\n [-14, 0, 5, -8, -2, -4, 1, -8, -2, 0, -2, 4],\n [-2, -6, -4, -2, 0, -4, -6, -2, 0, -3, -7, -12],\n [-12, 0, -7, 6, 5, -4, 6, 4, -2, -7, 2, 14],\n [0, -10, -2, 10, 8, 1, 3, 0, 4, -12, 14, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1922482364752", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[5, -12, -1, -4, 9, 14, 6, -5, -3, 1, 10, 11],\n [1, -1, -1, -4, 12, -8, 9, 11, -4, -8, -3, -5],\n [15, -14, -1, 3, 15, 6, 0, -1, -9, 2, 13, -3],\n [5, 0, -2, 15, -4, 4, 16, 10, -1, 11, -16, 14],\n [16, 16, 1, 6, 6, -2, 9, 13, 8, -1, -3, 0],\n [-5, 12, 15, 7, -4, 3, -2, -13, 11, -15, 13, 9],\n [9, 3, 11, 3, -6, -7, 6, 2, 1, 10, -11, -7],\n [-15, 7, 11, 11, -15, -12, -6, -7, -15, -2, -10, 3],\n [5, 14, 6, 2, -13, 7, 3, 11, 0, 2, 15, 13],\n [0, 12, -11, 0, 0, -3, 7, 15, -3, 10, 2, 14],\n [-8, 0, 2, -13, -6, 5, -13, 0, -9, -6, 14, -6],\n [4, 13, -7, 9, 10, -9, -9, -9, -1, -4, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108757069574832", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (5, 10) of the result:\nA =\n[[10, 9, 6, 4, -5, 6, 12, -2, 3, -6, 6, -3],\n [9, -9, 2, -10, -2, 3, 4, 4, 1, -1, 0, 5],\n [6, 2, -12, 1, -2, -4, 0, -6, 9, 7, -3, 7],\n [4, -10, 1, 5, -6, -4, 2, -6, -6, -2, -3, -7],\n [-5, -2, -2, -6, 16, -8, 0, 10, 7, 5, 6, 6],\n [6, 3, -4, -4, -8, 1, 4, 3, -1, 14, 1, 5],\n [12, 4, 0, 2, 0, 4, -9, -3, 6, 5, 6, -1],\n [-2, 4, -6, -6, 10, 3, -3, -3, -10, -4, -12, 14],\n [3, 1, 9, -6, 7, -1, 6, -10, -15, 3, 8, -4],\n [-6, -1, 7, -2, 5, 14, 5, -4, 3, -4, -4, -8],\n [6, 0, -3, -3, 6, 1, 6, -12, 8, -4, -2, 4],\n [-3, 5, 7, -7, 6, 5, -1, 14, -4, -8, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1931595387493", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-2, -9, -7, -5, 10, 6, -6, 0, -7, 4, 2, 4],\n [-9, -2, -3, 0, -2, -8, -6, -9, -12, 12, 8, -4],\n [-7, -3, -16, -2, 1, 7, 9, -6, 4, -1, -9, -6],\n [-5, 0, -2, 6, -2, -10, 0, 13, 2, 5, 0, -6],\n [10, -2, 1, -2, -14, 7, -8, 5, 4, -16, -14, 2],\n [6, -8, 7, -10, 7, 1, -6, 1, 12, 0, 9, 12],\n [-6, -6, 9, 0, -8, -6, -7, 5, 4, -8, 8, 14],\n [0, -9, -6, 13, 5, 1, 5, -4, 0, 0, 6, -6],\n [-7, -12, 4, 2, 4, 12, 4, 0, 2, -2, -3, 0],\n [4, 12, -1, 5, -16, 0, -8, 0, -2, 3, 1, -3],\n [2, 8, -9, 0, -14, 9, 8, 6, -3, 1, 14, 2],\n [4, -4, -6, -6, 2, 12, 14, -6, 0, -3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18145907332636", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[7, -11, -2, -7, -3, -8, -1, 12, -8, 5, 0, -1],\n [-11, 4, 11, -10, 4, 8, -2, -4, -6, 2, 4, 2],\n [-2, 11, -2, 0, -1, 0, 0, -4, 7, -5, 6, 10],\n [-7, -10, 0, 3, 10, 2, 12, 6, 8, 0, -2, 1],\n [-3, 4, -1, 10, -15, 0, 0, -2, -6, 6, 0, -8],\n [-8, 8, 0, 2, 0, 13, -4, 10, 4, -4, 3, 9],\n [-1, -2, 0, 12, 0, -4, -2, -5, 2, -16, 12, -2],\n [12, -4, -4, 6, -2, 10, -5, -2, 6, -4, -4, 7],\n [-8, -6, 7, 8, -6, 4, 2, 6, 15, 12, -9, 14],\n [5, 2, -5, 0, 6, -4, -16, -4, 12, -15, -1, -1],\n [0, 4, 6, -2, 0, 3, 12, -4, -9, -1, -1, 0],\n [-1, 2, 10, 1, -8, 9, -2, 7, 14, -1, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "821011832242", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 12) of the matrix A^8 where A is:\n[[10, 2, 0, 10, -2, 3, -4, 1, 0, 10, -4, -8],\n [2, -7, -1, 0, -2, 6, -4, 2, -8, -6, 12, 0],\n [0, -1, -3, 8, 8, -8, 8, 3, 6, 8, 6, -5],\n [10, 0, 8, -9, -9, -8, 11, 0, 2, 6, -12, 5],\n [-2, -2, 8, -9, 6, -8, 4, 2, 2, 6, 6, 2],\n [3, 6, -8, -8, -8, -11, -2, 2, 10, -5, 0, 0],\n [-4, -4, 8, 11, 4, -2, -5, 2, 12, -2, -4, -8],\n [1, 2, 3, 0, 2, 2, 2, 3, -6, -9, -6, -2],\n [0, -8, 6, 2, 2, 10, 12, -6, 10, 6, 12, 2],\n [10, -6, 8, 6, 6, -5, -2, -9, 6, 5, 8, 6],\n [-4, 12, 6, -12, 6, 0, -4, -6, 12, 8, -10, -2],\n [-8, 0, -5, 5, 2, 0, -8, -2, 2, 6, -2, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-115648453813", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[13, -15, -9, -8, -16, -4, -2, 15, 14, -3, -3, 12],\n [2, 10, -8, 11, 7, 11, 1, 8, -13, -3, 9, -9],\n [7, -1, 3, -2, -10, 0, 5, 5, -5, 1, -2, -1],\n [-12, -15, 11, 10, 14, -16, 12, -16, -9, -1, 11, 5],\n [1, 5, -5, 2, 8, -12, -7, -10, -2, 7, 9, 9],\n [9, -7, 0, -3, -15, -4, 10, -8, -10, -7, -8, 5],\n [6, -10, -8, 10, 7, 12, 0, 3, -10, -10, 11, 2],\n [3, -10, -11, 8, -4, 5, 0, 5, -9, 1, 7, -15],\n [-15, 10, -3, -5, 15, 11, 11, 8, -13, 9, -14, -16],\n [0, -10, -12, 2, -1, 10, 8, 9, -3, -3, -3, 8],\n [-13, -2, 15, 1, -3, -16, 3, -7, -7, 7, 11, 10],\n [-16, 16, -13, -10, -8, -1, -12, 6, 8, -4, 7, -6]], determine the value at position (5, 9).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1650880393561", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[0, -6, 6, -4, 12, 0, -12, 6, -6, -12, -1, 2],\n [-6, -7, 1, -2, -6, -6, 0, -2, 0, 8, -6, -2],\n [6, 1, 0, -9, -10, 7, -10, 9, -8, 10, 4, 12],\n [-4, -2, -9, -1, 3, 2, 11, 2, -11, -2, -6, -2],\n [12, -6, -10, 3, 4, -9, 5, 6, -9, -6, -9, -8],\n [0, -6, 7, 2, -9, 15, 0, 1, 6, -8, 7, 0],\n [-12, 0, -10, 11, 5, 0, -6, 12, 2, -10, 0, -8],\n [6, -2, 9, 2, 6, 1, 12, -13, 3, -9, 3, -2],\n [-6, 0, -8, -11, -9, 6, 2, 3, -2, -6, -6, 8],\n [-12, 8, 10, -2, -6, -8, -10, -9, -6, 14, -2, -6],\n [-1, -6, 4, -6, -9, 7, 0, 3, -6, -2, -5, 4],\n [2, -2, 12, -2, -8, 0, -8, -2, 8, -6, 4, -10]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29093818815", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-5, -2, -6, -1, -14, 8, -13, 2, -14, 4, 11, -2],\n [-2, 7, 2, -8, 14, -2, -9, 4, 4, 11, 12, -2],\n [-6, 2, -10, 0, 10, -6, 0, -6, 0, 0, -3, -8],\n [-1, -8, 0, -9, 4, -7, 0, 2, 2, -3, -6, 0],\n [-14, 14, 10, 4, 14, 0, -2, -5, 16, -4, -13, 1],\n [8, -2, -6, -7, 0, -11, 12, 2, 2, -7, 8, -3],\n [-13, -9, 0, 0, -2, 12, 11, 2, 4, 6, -3, 6],\n [2, 4, -6, 2, -5, 2, 2, -15, 3, -4, -10, 8],\n [-14, 4, 0, 2, 16, 2, 4, 3, 0, 9, 0, -3],\n [4, 11, 0, -3, -4, -7, 6, -4, 9, 14, -12, 6],\n [11, 12, -3, -6, -13, 8, -3, -10, 0, -12, 15, -8],\n [-2, -2, -8, 0, 1, -3, 6, 8, -3, 6, -8, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "529240869559", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-14, -14, 1, 8, 3, 12, 5, -2, -7, 4, 12, 15],\n [-7, -4, 6, 6, 14, -13, -14, 4, -15, -13, -16, -2],\n [16, -11, -10, 2, -16, 2, 9, -5, 5, -4, 11, -3],\n [5, 13, 3, 10, -16, -2, 15, -9, 16, 1, 12, 15],\n [16, -12, 1, -7, 16, 6, -12, 7, 0, 14, -10, 0],\n [11, 5, -2, -2, 8, 4, -15, 10, 15, 4, -13, 2],\n [-15, 9, -3, -2, 3, 2, -8, -10, 13, -4, 10, -4],\n [-2, -8, 6, -14, 2, 11, 6, -10, -5, -3, -2, -14],\n [-2, 7, -9, -12, -13, -3, -1, 3, 7, -11, 14, -11],\n [-2, 12, -14, -6, -14, 11, -7, 16, -1, -7, 16, -14],\n [-12, -5, -4, 7, 15, -1, 15, 4, -5, 4, 4, -11],\n [-8, -16, -5, -3, -11, -16, 5, -6, -14, -11, -11, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1142060121532208", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (7, 9) of the result:\nA =\n[[4, -9, 2, 9, 6, 3, 3, 0, -11, -4, 10, 14],\n [-9, 15, 2, 6, 2, -6, -8, 3, 6, 14, -3, -10],\n [2, 2, 12, -8, -1, 4, -4, 8, -8, 0, 0, -6],\n [9, 6, -8, -16, 8, -8, -3, 10, -8, 2, 1, 5],\n [6, 2, -1, 8, -9, 0, -10, 6, 8, 3, -10, -11],\n [3, -6, 4, -8, 0, -12, 10, 0, 8, 0, -5, -5],\n [3, -8, -4, -3, -10, 10, -11, 7, 7, -1, 6, 6],\n [0, 3, 8, 10, 6, 0, 7, 14, 0, -6, 0, 2],\n [-11, 6, -8, -8, 8, 8, 7, 0, -7, 1, -2, 11],\n [-4, 14, 0, 2, 3, 0, -1, -6, 1, 11, 3, 4],\n [10, -3, 0, 1, -10, -5, 6, 0, -2, 3, -16, 2],\n [14, -10, -6, 5, -11, -5, 6, 2, 11, 4, 2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19642491384797", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (3, 9) of the result:\nA =\n[[-4, -1, -10, 10, -2, 11, -10, 3, 15, 15, 9, 3],\n [1, -2, 5, 5, 4, -15, 1, 6, -4, -8, -10, -16],\n [-15, -13, -3, 15, -15, -3, 3, 8, -9, 11, 4, 6],\n [15, -9, 14, -1, 10, 1, -2, 10, 0, -15, 14, -14],\n [0, -3, -3, -16, 12, -13, 16, 0, 11, 9, -9, 1],\n [14, 10, -1, -7, -5, 5, -1, -5, -6, 3, -16, 10],\n [-14, -5, 13, -8, -16, -13, -2, 10, -9, 6, -2, 10],\n [14, -9, 13, 1, -13, 5, -14, -2, 16, -3, -16, 9],\n [-9, -1, -7, 9, 11, -5, 3, -3, 12, -5, 1, -15],\n [-15, 0, -7, 1, 5, 2, -16, 7, 8, 14, 14, -15],\n [2, -5, -7, 14, 5, 6, 6, -2, 9, -14, 6, 3],\n [-9, 1, -11, 10, -2, -12, -8, -10, 3, -7, 9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5104746999", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 7) of the 9th power of the matrix:\n[[7, 0, -8, -7, -3, 12, -5, -8, -4, -5, -12, -9],\n [0, -7, 12, -10, -6, 6, 3, 0, -4, 1, -3, 7],\n [-8, 12, -16, 3, 7, 8, 8, -4, -5, 6, 11, 3],\n [-7, -10, 3, -14, -2, 4, 4, 2, 0, 6, -10, -8],\n [-3, -6, 7, -2, -4, 4, 8, 12, 3, 7, -2, 6],\n [12, 6, 8, 4, 4, -1, -6, 0, -4, 12, 2, -8],\n [-5, 3, 8, 4, 8, -6, 11, 1, 4, -1, -3, 0],\n [-8, 0, -4, 2, 12, 0, 1, -7, 6, 7, 12, 5],\n [-4, -4, -5, 0, 3, -4, 4, 6, 6, -8, -4, 2],\n [-5, 1, 6, 6, 7, 12, -1, 7, -8, 0, -8, 0],\n [-12, -3, 11, -10, -2, 2, -3, 12, -4, -8, -7, -6],\n [-9, 7, 3, -8, 6, -8, 0, 5, 2, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11805277332809", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -9, 15, 4, 2, 12, 14, -11, -13, 12, -14, -16],\n [-2, 4, 14, -10, 0, 2, -14, 13, 12, -3, 11, 13],\n [9, -10, 14, -12, -3, 10, 7, 12, 5, -9, -2, -12],\n [-13, -6, 1, 13, -2, -11, -1, -8, 10, -4, 10, -8],\n [-12, 5, 14, -14, 13, 4, -11, 11, 15, 8, 15, 5],\n [7, 13, 15, 14, 6, 16, 8, 7, 14, -4, -7, 6],\n [1, 15, 16, 11, -1, -1, 1, -9, -1, -6, -11, -16],\n [-5, 11, 0, -16, 15, -9, 7, -7, -7, 8, -7, 2],\n [-2, -1, -15, 12, -13, 12, 14, 0, -7, 10, -2, 14],\n [4, 9, 0, -14, -3, -4, 10, -16, 0, -3, 0, -14],\n [8, -15, 9, 14, -8, 13, 3, 4, 12, 8, 8, -8],\n [9, -1, -5, 7, 9, 3, -8, 6, 12, 14, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86428447424252", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (4, 11) of the result:\nA =\n[[6, 6, 4, -1, -7, 10, -10, 2, 2, 4, 4, -4],\n [6, 6, 12, 2, 10, -8, 0, -1, 16, -15, 7, -4],\n [4, 12, 11, -5, 2, -12, -4, 0, 8, 10, -3, -8],\n [-1, 2, -5, 4, -8, 10, 5, -10, 4, -6, 12, 8],\n [-7, 10, 2, -8, 2, -13, 0, -4, -2, -1, 2, -12],\n [10, -8, -12, 10, -13, -8, -8, 4, 0, -6, -4, -2],\n [-10, 0, -4, 5, 0, -8, 1, 8, -2, 6, -10, 2],\n [2, -1, 0, -10, -4, 4, 8, 6, -1, 2, -6, 12],\n [2, 16, 8, 4, -2, 0, -2, -1, -10, -4, 6, 8],\n [4, -15, 10, -6, -1, -6, 6, 2, -4, 7, 8, -6],\n [4, 7, -3, 12, 2, -4, -10, -6, 6, 8, 14, 2],\n [-4, -4, -8, 8, -12, -2, 2, 12, 8, -6, 2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16356272063", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[9, -6, -2, 2, -15, -4, -6, 0, 0, -3, 12, 0],\n [-6, -2, 0, 2, -2, 10, -4, 5, 5, 3, 3, -9],\n [-2, 0, 11, 2, -2, 12, -6, 5, -4, 8, -4, 2],\n [2, 2, 2, -13, -4, 11, 4, 3, 10, 12, 9, -6],\n [-15, -2, -2, -4, 16, 0, -7, -2, -2, 2, -2, -8],\n [-4, 10, 12, 11, 0, -13, -14, 8, -4, -2, 7, 10],\n [-6, -4, -6, 4, -7, -14, -13, 12, 2, 2, -2, 11],\n [0, 5, 5, 3, -2, 8, 12, -5, 12, 7, -5, 8],\n [0, 5, -4, 10, -2, -4, 2, 12, -4, -8, -6, -4],\n [-3, 3, 8, 12, 2, -2, 2, 7, -8, 9, 10, -6],\n [12, 3, -4, 9, -2, 7, -2, -5, -6, 10, 1, 11],\n [0, -9, 2, -6, -8, 10, 11, 8, -4, -6, 11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6715088678861293", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[10, 6, 16, -13, 4, 7, 14, 7, -7, -15, 14, 8],\n [-13, -6, 0, -15, -11, -8, -12, 3, 12, 4, -8, 11],\n [-9, 14, 3, 10, -9, 4, 11, 6, -11, -14, -12, -8],\n [-10, -13, -12, -6, -2, -4, -10, -11, 13, 5, 8, 11],\n [3, -14, -12, -16, -2, 9, -14, -12, 14, -4, -16, 5],\n [-2, 9, 1, -8, -16, -8, 6, -15, -3, 1, -1, 12],\n [-6, -11, -14, -3, -15, 15, 14, -6, 5, -14, 14, 16],\n [7, -16, -2, 10, 10, -5, -14, 13, 15, 6, -15, -10],\n [15, 15, -3, -14, 15, 0, -14, -7, 1, -14, -7, -8],\n [-6, 16, 9, 10, 5, 9, 5, -12, -15, -8, 1, -5],\n [-14, 1, -10, 16, -11, 1, 5, -8, 6, -5, 7, -8],\n [-4, 0, -10, 0, 7, -15, 11, 2, 16, 4, -7, -8]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43774686936", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 7) of the 7th power of the matrix:\n[[-11, 1, 2, -12, 8, -6, -7, 0, 9, 14, 15, 4],\n [1, 1, -16, -3, -9, -15, -2, -16, 4, -16, 15, 3],\n [13, -10, 5, -7, -9, 10, -7, -3, -6, -11, 4, 16],\n [2, 7, 1, 2, 7, 5, -13, -7, -15, -9, 16, 11],\n [-7, -16, -14, -8, -12, -7, -5, 1, 4, 4, -16, -14],\n [-12, 8, -9, 0, -8, 15, -11, 4, -10, -10, 10, -9],\n [-8, 11, -2, -15, -10, 1, 5, -7, 16, -10, -14, -3],\n [-4, -1, -1, -12, 8, 9, -4, 9, -16, -9, -13, 4],\n [5, -14, 2, -16, 12, 6, 16, 6, -12, -10, -11, 5],\n [-4, -5, -13, -9, 14, 9, -9, 16, 12, -12, 11, 0],\n [6, -8, -15, 15, 14, -10, 13, -14, -8, -7, 9, -16],\n [13, -2, 8, -11, 1, -16, -14, 0, -9, 0, 8, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33319898205", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (2, 7) of the result:\nA =\n[[12, 4, 6, 2, 2, -14, -2, 2, -14, -2, 4, -4],\n [4, -3, 6, 10, -10, 5, 0, 0, -5, -12, -8, -16],\n [6, 6, 15, 6, 4, 12, -6, -4, 0, 0, 8, 7],\n [2, 10, 6, -16, -1, -10, 2, -14, -10, 10, -2, 12],\n [2, -10, 4, -1, -11, -5, 6, -10, 6, -8, 2, 10],\n [-14, 5, 12, -10, -5, -11, 10, -1, 6, -14, -4, 4],\n [-2, 0, -6, 2, 6, 10, -12, -2, 6, 13, 0, 2],\n [2, 0, -4, -14, -10, -1, -2, 5, 10, 0, 6, -10],\n [-14, -5, 0, -10, 6, 6, 6, 10, -9, 10, 0, -10],\n [-2, -12, 0, 10, -8, -14, 13, 0, 10, 1, 10, 11],\n [4, -8, 8, -2, 2, -4, 0, 6, 0, 10, -12, 4],\n [-4, -16, 7, 12, 10, 4, 2, -10, -10, 11, 4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6674743014", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[14, -12, -4, 9, -4, 4, 8, 10, 0, -4, 2, -2],\n [-12, -2, 12, 4, -3, 2, -2, 0, 1, 4, 8, 4],\n [-4, 12, 4, -8, -2, 0, -12, 4, 7, -16, -14, -2],\n [9, 4, -8, 9, 5, -10, 0, 2, 6, 1, -14, 5],\n [-4, -3, -2, 5, -12, 5, -4, -3, 0, -8, -4, -7],\n [4, 2, 0, -10, 5, 7, 2, 12, -10, 6, -2, 2],\n [8, -2, -12, 0, -4, 2, 8, 4, 0, -6, -4, -12],\n [10, 0, 4, 2, -3, 12, 4, -16, 2, 4, -8, -8],\n [0, 1, 7, 6, 0, -10, 0, 2, -12, 11, 5, -4],\n [-4, 4, -16, 1, -8, 6, -6, 4, 11, 13, 6, 8],\n [2, 8, -14, -14, -4, -2, -4, -8, 5, 6, -1, -4],\n [-2, 4, -2, 5, -7, 2, -12, -8, -4, 8, -4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-155324187974", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[8, -2, 4, -12, -6, 2, 2, 11, 11, 5, 4, -1],\n [-2, 4, -13, 16, -6, -7, -5, 0, 1, 8, -2, 3],\n [4, -13, -12, -9, 1, -8, 14, 6, 2, -2, 4, -3],\n [-12, 16, -9, 13, 6, -9, 13, -12, -1, 0, 7, 14],\n [-6, -6, 1, 6, 3, 4, 10, -8, -4, 10, 2, -1],\n [2, -7, -8, -9, 4, -3, 4, -8, 7, -8, 3, -3],\n [2, -5, 14, 13, 10, 4, -4, -2, -6, 8, -8, 12],\n [11, 0, 6, -12, -8, -8, -2, 7, -8, 12, -3, 4],\n [11, 1, 2, -1, -4, 7, -6, -8, -13, -8, -4, 7],\n [5, 8, -2, 0, 10, -8, 8, 12, -8, 5, 6, 0],\n [4, -2, 4, 7, 2, 3, -8, -3, -4, 6, -16, 0],\n [-1, 3, -3, 14, -1, -3, 12, 4, 7, 0, 0, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20549628013809", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[4, -8, -15, -13, -9, 15, -3, -4, 4, 7, 1, 9],\n [15, 16, 14, 1, -5, 8, 14, -7, -14, -9, 15, 12],\n [5, 3, -11, 12, 0, 14, -13, -15, -5, -11, -9, 4],\n [-2, -10, -2, -11, 0, -13, 5, 15, 5, 10, -2, 5],\n [11, -8, -8, -2, 3, -9, 11, 2, -1, -6, -9, 16],\n [-7, 1, -14, 10, 11, -11, -3, -10, -7, -2, 14, 12],\n [0, 12, -2, 9, -5, 8, -12, -13, 14, -14, -14, 9],\n [0, -7, -15, 7, -6, 7, 6, 15, 6, 2, -15, -15],\n [-2, 4, -12, 10, 7, -10, -11, 16, 0, 13, -9, -10],\n [-11, -13, -16, -2, 14, 8, 16, -12, -12, 0, -3, 12],\n [-9, -16, 12, 12, -12, 15, 7, 2, -5, -16, -10, 0],\n [-10, 0, -14, 12, 5, 12, -12, 13, 6, 4, 9, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-197390966671461", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[3, -3, -8, -2, -5, -12, 6, 2, 6, -3, 0, -12],\n [-3, -10, 11, 6, -2, -10, 4, 1, -15, -4, 0, 4],\n [-8, 11, 7, 9, -2, -2, 2, 2, -6, -6, -8, -1],\n [-2, 6, 9, 0, 0, 6, 9, -12, -9, 0, 0, 2],\n [-5, -2, -2, 0, 1, 6, 2, 6, 1, -8, -10, 2],\n [-12, -10, -2, 6, 6, -5, 6, 13, -6, 12, -5, -2],\n [6, 4, 2, 9, 2, 6, 1, 8, 4, -2, 2, -7],\n [2, 1, 2, -12, 6, 13, 8, -8, 2, 12, 8, 2],\n [6, -15, -6, -9, 1, -6, 4, 2, -9, 5, -2, 2],\n [-3, -4, -6, 0, -8, 12, -2, 12, 5, 0, -4, 2],\n [0, 0, -8, 0, -10, -5, 2, 8, -2, -4, -7, -8],\n [-12, 4, -1, 2, 2, -2, -7, 2, 2, 2, -8, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10475660005314", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (7, 11) of the matrix A^9 where A is:\n[[10, 8, -2, -2, 5, 7, 2, 1, -6, 6, -2, 6],\n [8, 10, 8, -1, 2, 8, -2, -2, 4, -14, -8, 10],\n [-2, 8, -2, -2, 1, 1, -4, 4, 4, -8, 11, 0],\n [-2, -1, -2, 15, 2, 6, -4, 7, 8, -15, -12, 4],\n [5, 2, 1, 2, 15, -6, -14, -2, 0, -11, 0, 12],\n [7, 8, 1, 6, -6, 6, -10, -5, -7, 6, 2, -4],\n [2, -2, -4, -4, -14, -10, 15, -5, 0, -12, -6, 0],\n [1, -2, 4, 7, -2, -5, -5, 15, -6, -6, 6, 2],\n [-6, 4, 4, 8, 0, -7, 0, -6, 1, -2, 6, 2],\n [6, -14, -8, -15, -11, 6, -12, -6, -2, 16, -6, 4],\n [-2, -8, 11, -12, 0, 2, -6, 6, 6, -6, 9, -8],\n [6, 10, 0, 4, 12, -4, 0, 2, 2, 4, -8, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-241105821879", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-11, 14, 11, -9, 12, 4, 0, 7, 14, -15, -14, 13],\n [-9, -10, -5, 2, 9, 11, -2, -3, -3, -14, 12, -11],\n [6, 11, -3, -3, 3, -4, 10, -15, 7, 12, -14, -13],\n [-15, 3, -2, 15, -16, -10, -4, -16, -3, 12, -14, 7],\n [-16, -7, -4, -8, -3, -7, 6, -10, -15, -2, -8, 0],\n [1, -2, 1, 7, 6, -5, 6, 4, 9, -9, 13, -15],\n [-12, 14, 16, -13, -11, 6, 2, -9, -4, -16, -11, -10],\n [10, -2, 6, 7, -2, -13, 0, 14, -7, 10, -11, -11],\n [-2, -13, -10, 9, 14, -15, 11, -4, 1, 13, -6, -4],\n [7, 12, -12, 2, -4, -12, -3, 5, -8, 9, -12, 12],\n [5, -14, 11, -3, -3, -6, -8, -11, -16, 8, -1, -2],\n [0, -14, -14, 0, -16, -10, 9, 2, 13, -3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1299263434730", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[9, 4, -2, -4, -8, -2, -2, 6, -12, -15, 3, 6],\n [4, 11, -5, 2, -8, -8, 4, -2, 10, 10, 6, 2],\n [-2, -5, -5, -2, -2, -5, -10, -14, 5, -2, -2, -2],\n [-4, 2, -2, 14, -1, 8, 4, -6, -10, 2, 2, 2],\n [-8, -8, -2, -1, 15, -6, 2, -2, 5, 9, -8, -8],\n [-2, -8, -5, 8, -6, 2, -1, -5, 0, 0, 6, -4],\n [-2, 4, -10, 4, 2, -1, 6, -8, -7, -10, 1, -6],\n [6, -2, -14, -6, -2, -5, -8, -4, 8, 4, -7, -4],\n [-12, 10, 5, -10, 5, 0, -7, 8, 5, -14, -6, 4],\n [-15, 10, -2, 2, 9, 0, -10, 4, -14, -8, -8, -2],\n [3, 6, -2, 2, -8, 6, 1, -7, -6, -8, 12, 6],\n [6, 2, -2, 2, -8, -4, -6, -4, 4, -2, 6, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-97287678534", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[1, -1, -1, -8, -6, 7, -8, 5, 4, 0, -2, -8],\n [-1, -6, 8, 3, 4, 10, -14, -3, -12, -3, 4, 10],\n [-1, 8, -9, 4, -4, -3, -2, -4, 14, 6, 1, -12],\n [-8, 3, 4, -15, 4, 11, -8, 10, -7, -8, -2, 0],\n [-6, 4, -4, 4, -2, -1, -3, 8, -4, -11, 0, 14],\n [7, 10, -3, 11, -1, -11, -15, 2, 5, 6, -9, -6],\n [-8, -14, -2, -8, -3, -15, 9, 4, -5, 4, 8, -6],\n [5, -3, -4, 10, 8, 2, 4, 5, 6, 4, 6, -14],\n [4, -12, 14, -7, -4, 5, -5, 6, 9, 3, 2, 0],\n [0, -3, 6, -8, -11, 6, 4, 4, 3, -12, -4, -2],\n [-2, 4, 1, -2, 0, -9, 8, 6, 2, -4, 14, 11],\n [-8, 10, -12, 0, 14, -6, -6, -14, 0, -2, 11, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8415081445348585", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (4, 5) of the result:\nA =\n[[-11, -3, -14, -16, 13, 2, 2, -8, -10, -10, -8, -13],\n [8, -5, -11, 1, 4, -2, -14, -15, -13, 15, -15, 12],\n [-15, 10, 1, 2, 10, 3, 4, 6, 13, 8, 14, 10],\n [-9, 2, 9, 11, -13, 14, -1, -7, -7, -8, 2, 2],\n [-5, -4, 8, 8, 11, 13, -12, 0, 1, 4, 5, -11],\n [-1, -15, -16, 13, 6, -16, 2, -14, -15, 0, 11, 1],\n [16, -2, 5, 10, 15, 2, 11, 11, -7, 3, 8, 4],\n [-3, 5, 9, -6, -10, 0, 1, -10, 3, -6, -1, 10],\n [-6, -1, 6, -5, -14, -15, 7, 12, 3, 1, -3, 1],\n [-15, -16, 3, -6, 10, 6, -14, -5, 13, 14, 6, -16],\n [3, -11, -6, -13, 12, -7, 12, -16, -9, 0, 2, 16],\n [-2, 14, 4, -14, -15, -1, 4, -5, 11, -5, 16, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27013310823", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 11) of the 7th power of the matrix:\n[[4, -4, 10, -8, 0, 0, 8, 10, 6, 5, 2, 2],\n [-4, 4, 6, 0, -4, 7, 3, -4, 0, 8, -2, 4],\n [10, 6, -11, 2, -2, -9, 6, 0, 5, 11, -2, 8],\n [-8, 0, 2, 12, 2, -1, 0, 1, -6, 0, 2, -12],\n [0, -4, -2, 2, -3, 0, 0, 2, 0, -2, 7, 10],\n [0, 7, -9, -1, 0, -15, -4, 8, -3, -1, -4, -14],\n [8, 3, 6, 0, 0, -4, -16, 2, -10, 10, 2, -6],\n [10, -4, 0, 1, 2, 8, 2, -11, -2, -4, -6, 2],\n [6, 0, 5, -6, 0, -3, -10, -2, 1, 5, 8, 16],\n [5, 8, 11, 0, -2, -1, 10, -4, 5, -13, -8, 2],\n [2, -2, -2, 2, 7, -4, 2, -6, 8, -8, -4, 4],\n [2, 4, 8, -12, 10, -14, -6, 2, 16, 2, 4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15772564404", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[-11, 12, -1, -1, -5, -3, -1, -8, -12, -15, -4, -8],\n [12, -4, -8, 0, 14, 7, 8, 6, 6, 5, 2, 10],\n [-1, -8, 4, -4, 6, 6, 2, -12, -4, 8, 2, -8],\n [-1, 0, -4, -5, 3, 0, 2, 9, -6, -12, -2, 3],\n [-5, 14, 6, 3, 11, -1, -10, -2, 14, 12, 1, 12],\n [-3, 7, 6, 0, -1, 14, 6, 0, -6, -1, 7, 11],\n [-1, 8, 2, 2, -10, 6, -2, 2, 5, -10, 0, 0],\n [-8, 6, -12, 9, -2, 0, 2, 16, 0, 2, 4, -6],\n [-12, 6, -4, -6, 14, -6, 5, 0, 5, -1, 6, -16],\n [-15, 5, 8, -12, 12, -1, -10, 2, -1, -8, -10, 6],\n [-4, 2, 2, -2, 1, 7, 0, 4, 6, -10, 6, -2],\n [-8, 10, -8, 3, 12, 11, 0, -6, -16, 6, -2, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56862190250313", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[2, 0, 6, -11, -4, -6, 4, 2, -4, 4, 2, 4],\n [0, 14, 4, 2, -2, -2, 11, 0, 8, -10, 8, -8],\n [6, 4, 10, -8, -5, -8, 5, -11, 4, -4, 4, 2],\n [-11, 2, -8, -1, 4, 10, 15, 2, -8, 8, -5, 3],\n [-4, -2, -5, 4, 16, -4, 0, 3, -7, 10, 2, -12],\n [-6, -2, -8, 10, -4, -12, 4, -2, 0, -14, 2, 0],\n [4, 11, 5, 15, 0, 4, 4, -6, 0, 3, 8, -2],\n [2, 0, -11, 2, 3, -2, -6, -14, 10, 2, -2, 2],\n [-4, 8, 4, -8, -7, 0, 0, 10, 6, 6, 2, 7],\n [4, -10, -4, 8, 10, -14, 3, 2, 6, -6, 2, 13],\n [2, 8, 4, -5, 2, 2, 8, -2, 2, 2, -14, 10],\n [4, -8, 2, 3, -12, 0, -2, 2, 7, 13, 10, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34743573169101", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-14, 1, -4, 2, 0, -7, 14, 12, -10, 7, -12, -4],\n [1, 8, 4, 2, -2, -8, 6, 1, -4, 12, -11, -7],\n [-4, 4, 0, 0, 0, -6, 4, 2, 13, -11, 0, 1],\n [2, 2, 0, 12, -6, -13, 0, 7, -4, 5, 4, 7],\n [0, -2, 0, -6, -16, -10, 8, -14, -2, -1, -8, -10],\n [-7, -8, -6, -13, -10, 6, -5, -4, 3, 0, 0, 6],\n [14, 6, 4, 0, 8, -5, -7, -3, -8, 12, 9, 2],\n [12, 1, 2, 7, -14, -4, -3, 5, 4, 6, -2, 0],\n [-10, -4, 13, -4, -2, 3, -8, 4, -11, -6, 1, -8],\n [7, 12, -11, 5, -1, 0, 12, 6, -6, 7, -4, 7],\n [-12, -11, 0, 4, -8, 0, 9, -2, 1, -4, -15, -2],\n [-4, -7, 1, 7, -10, 6, 2, 0, -8, 7, -2, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7709541281198519", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-13, 5, -10, 8, -12, 8, 4, 16, 8, 5, -6, 14],\n [5, 16, 2, -8, 6, 4, -8, 1, 6, 4, -1, -8],\n [-10, 2, 1, 8, -2, -1, 6, 2, 8, -10, 6, 5],\n [8, -8, 8, 10, -4, 4, 3, -14, -12, -1, 4, -5],\n [-12, 6, -2, -4, -8, -7, -5, -14, -4, 0, -2, -6],\n [8, 4, -1, 4, -7, -11, 4, -4, 12, -10, 0, 0],\n [4, -8, 6, 3, -5, 4, 9, 6, -6, -7, -4, -1],\n [16, 1, 2, -14, -14, -4, 6, -2, -8, -6, -4, 1],\n [8, 6, 8, -12, -4, 12, -6, -8, -12, 1, 10, 4],\n [5, 4, -10, -1, 0, -10, -7, -6, 1, 14, -6, -12],\n [-6, -1, 6, 4, -2, 0, -4, -4, 10, -6, 7, -3],\n [14, -8, 5, -5, -6, 0, -1, 1, 4, -12, -3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10683267526293648", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (7, 11) of the 8th power of the matrix:\n[[-11, -3, 16, -9, 9, -2, -3, 3, 2, 16, 7, -7],\n [-1, -2, 1, -10, 5, 15, 2, -16, -12, -5, -5, 4],\n [2, -8, 15, 14, 15, 15, 13, 15, -15, -6, 3, -8],\n [2, -10, -12, 7, -10, -6, -8, 13, -14, 5, 3, 15],\n [-10, -10, 3, 8, 7, -4, -13, -5, 0, -16, 0, -15],\n [-11, -6, 1, 8, 11, -1, -5, 12, 6, 4, -1, 9],\n [5, -7, -10, -8, 8, -2, -4, 9, 4, 6, 11, -5],\n [7, -4, -15, -5, -3, 13, 2, 14, 8, -13, -4, -14],\n [-1, 9, 2, -2, 15, 4, -16, -11, 10, 6, 14, -5],\n [4, -15, -12, -8, 3, 1, 5, -9, -8, -10, 13, 1],\n [10, -1, 4, -12, 12, 5, -3, 2, 7, -11, -14, -15],\n [-2, -2, 15, 4, 0, 15, 6, 16, 8, 4, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "131011889225", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 5) of the matrix A^8 where A is:\n[[-8, -14, -9, 2, 2, 4, 10, 6, -6, -2, -2, 5],\n [-14, -14, 0, -3, -6, -15, -3, 0, -8, 0, 7, -8],\n [-9, 0, -13, 4, 0, -10, 0, -4, 4, -2, -3, 2],\n [2, -3, 4, 11, -7, 4, 8, -2, -5, 2, 6, 14],\n [2, -6, 0, -7, -4, -2, -4, 6, 2, 2, -2, 2],\n [4, -15, -10, 4, -2, -8, -5, 4, -5, -5, -11, 10],\n [10, -3, 0, 8, -4, -5, -10, 2, 0, -2, 6, -8],\n [6, 0, -4, -2, 6, 4, 2, 10, -5, 4, -7, 0],\n [-6, -8, 4, -5, 2, -5, 0, -5, -13, 4, -6, -2],\n [-2, 0, -2, 2, 2, -5, -2, 4, 4, 16, -1, 8],\n [-2, 7, -3, 6, -2, -11, 6, -7, -6, -1, 10, -7],\n [5, -8, 2, 14, 2, 10, -8, 0, -2, 8, -7, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316357707566", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 11) of the matrix A^8 where A is:\n[[11, -2, 6, 7, -4, 4, -5, -4, 6, 11, -3, 0],\n [7, 5, -7, -9, 4, -10, 9, -4, -1, 13, 14, -12],\n [15, -1, -8, 5, -3, -1, 3, -2, 9, -8, -16, 3],\n [-11, -7, 16, -1, -11, 2, 14, -15, 1, 11, -13, -16],\n [-1, -15, -16, 6, 9, -6, -16, -6, 7, -7, -3, -3],\n [-10, 6, 5, 10, -15, 2, -10, -5, -14, -12, -9, -3],\n [-10, -10, 15, -9, -5, -7, -3, -8, 13, -12, -16, -16],\n [3, -6, 9, -14, -11, -6, -9, 12, -7, 7, 0, 15],\n [-6, 7, -12, 12, -1, 8, -9, 12, 8, 6, -14, 13],\n [15, 12, -8, -15, -10, -12, -9, 15, 1, 1, -1, 4],\n [-7, -13, -9, 2, -8, 13, 0, -2, -13, -11, -1, 9],\n [6, -4, 0, 10, 5, 2, -4, -3, 14, -15, -3, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-109905456494", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-7, -2, 8, -4, 4, -6, 6, -14, -6, 8, -11, 6],\n [-2, -9, -1, 14, -6, 7, -5, -2, 0, -5, -5, 6],\n [8, -1, -13, 2, -3, 0, 6, -2, 2, 13, -2, 2],\n [-4, 14, 2, 7, 1, 10, -10, -2, 2, 4, -2, 4],\n [4, -6, -3, 1, -4, 2, -8, 0, 0, 7, 2, 6],\n [-6, 7, 0, 10, 2, -12, -7, -8, -4, -6, 7, 6],\n [6, -5, 6, -10, -8, -7, -2, -2, -2, -8, 3, -3],\n [-14, -2, -2, -2, 0, -8, -2, 11, 2, 8, 10, 2],\n [-6, 0, 2, 2, 0, -4, -2, 2, 0, 6, 2, -2],\n [8, -5, 13, 4, 7, -6, -8, 8, 6, 8, 1, -6],\n [-11, -5, -2, -2, 2, 7, 3, 10, 2, 1, -8, -4],\n [6, 6, 2, 4, 6, 6, -3, 2, -2, -6, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13240897890181", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[7, -8, 9, 6, -14, 11, -1, 2, -5, -2, -3, -10],\n [-8, 12, 2, 0, -2, 10, -6, 6, 6, 9, -2, -6],\n [9, 2, -13, 0, -12, 4, 0, 12, -3, 5, 1, 14],\n [6, 0, 0, -15, -2, -12, 1, 5, -2, -7, 7, 9],\n [-14, -2, -12, -2, 3, 12, 3, -8, 2, 3, 0, -2],\n [11, 10, 4, -12, 12, 14, -6, -4, -4, -6, 4, -2],\n [-1, -6, 0, 1, 3, -6, 16, 6, 5, -10, 1, 9],\n [2, 6, 12, 5, -8, -4, 6, 6, -2, -2, 9, 5],\n [-5, 6, -3, -2, 2, -4, 5, -2, -9, 12, -4, -2],\n [-2, 9, 5, -7, 3, -6, -10, -2, 12, 11, -4, 6],\n [-3, -2, 1, 7, 0, 4, 1, 9, -4, -4, 16, -7],\n [-10, -6, 14, 9, -2, -2, 9, 5, -2, 6, -7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57453997171933", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (11, 10) of the matrix A^9 where A is:\n[[1, -12, -6, 2, 2, 6, -9, -8, -12, -10, -8, 4],\n [-12, -7, 12, -12, 0, 12, -6, -14, 2, -4, -8, 6],\n [-6, 12, -15, -16, -9, 2, -5, -3, -2, -4, -5, -2],\n [2, -12, -16, -16, 3, 3, -6, 4, 0, -2, -2, 3],\n [2, 0, -9, 3, 16, -1, -4, 10, 0, 4, -2, -4],\n [6, 12, 2, 3, -1, -9, -2, 0, 6, -2, 2, -12],\n [-9, -6, -5, -6, -4, -2, 9, 6, -4, -8, 12, 5],\n [-8, -14, -3, 4, 10, 0, 6, 6, 0, 12, -10, 6],\n [-12, 2, -2, 0, 0, 6, -4, 0, 12, 14, -8, 1],\n [-10, -4, -4, -2, 4, -2, -8, 12, 14, -9, 4, 15],\n [-8, -8, -5, -2, -2, 2, 12, -10, -8, 4, -15, -6],\n [4, 6, -2, 3, -4, -12, 5, 6, 1, 15, -6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4464603974863", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 7th power of the matrix:\n[[9, -5, -3, -16, 0, 16, 12, 14, -9, 13, -4, -1],\n [-15, 1, 2, -4, -13, 2, 8, 14, -13, -10, -1, -12],\n [6, 15, 7, 8, 11, 2, -10, 0, -15, -1, 1, -16],\n [-14, 4, 13, -6, 5, 8, -14, 13, 7, 6, -9, -13],\n [14, 12, -4, -8, 4, -14, 8, 8, -5, 12, -6, -6],\n [9, -3, -1, -7, 14, 14, -7, 9, 3, -8, -2, -8],\n [-10, 9, 7, -5, 3, -3, 5, -1, 12, 15, 2, 15],\n [3, 3, -9, -4, -11, -1, -12, -11, 16, -2, -2, -3],\n [-12, 9, 0, -1, 6, -4, 16, 12, 10, -2, -8, 9],\n [-14, -12, 3, 3, -12, -7, -1, 8, 8, 13, -3, 5],\n [11, 13, 2, 3, 5, -2, -6, 7, -11, 0, 11, 14],\n [-8, -7, 4, 14, 12, -6, 16, -16, 4, 6, -8, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13491351782", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[4, 5, -13, -16, -7, -2, 12, -12, 12, 10, 8, -1],\n [-1, 8, -16, -12, 3, -12, 12, 1, -15, -1, 12, 16],\n [-1, 0, -13, -13, 8, 16, -3, 7, -6, 8, 11, -10],\n [-7, 14, 2, 1, -11, 11, -10, -5, 8, 0, 16, 6],\n [-8, -11, -15, -8, -14, -1, 8, 7, 12, 9, 6, -13],\n [-3, -10, -9, 2, -15, -16, -4, 7, 15, 13, -11, 16],\n [6, -7, -2, 6, -16, -9, -14, -3, 0, -11, -12, 12],\n [1, 13, -2, -2, -1, 16, -7, 2, -14, -13, -6, 16],\n [11, 15, -1, -8, -6, -11, 10, -5, 5, 4, 16, 0],\n [12, -7, 1, -4, 10, -7, 15, -14, 5, 10, -14, 16],\n [-15, -6, -7, 16, -10, -2, 9, -6, 10, -10, -16, -7],\n [4, -2, 13, 13, -9, 7, 2, -14, -2, -11, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-396308406800", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[13, 0, -1, 4, 3, -11, -8, -4, -2, -2, -10, -4],\n [0, -9, -8, -7, -4, -2, 6, -4, 0, 0, -8, -10],\n [-1, -8, 10, 9, 4, -4, 4, -8, 2, -2, -10, 10],\n [4, -7, 9, 11, -12, 1, 4, 5, 7, 4, -10, -5],\n [3, -4, 4, -12, -11, 2, 6, -6, -8, -6, 4, -6],\n [-11, -2, -4, 1, 2, 14, 2, -8, 2, 12, 1, -5],\n [-8, 6, 4, 4, 6, 2, 6, 1, -8, 6, 3, -2],\n [-4, -4, -8, 5, -6, -8, 1, -8, -3, -15, 8, -5],\n [-2, 0, 2, 7, -8, 2, -8, -3, -6, -2, -1, 0],\n [-2, 0, -2, 4, -6, 12, 6, -15, -2, -8, -12, -1],\n [-10, -8, -10, -10, 4, 1, 3, 8, -1, -12, -5, 0],\n [-4, -10, 10, -5, -6, -5, -2, -5, 0, -1, 0, -14]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-823143196504972", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[8, 4, 7, 4, 2, 4, -6, -6, 5, -4, -8, -4],\n [4, -8, 6, -9, 6, 6, -2, 2, 11, -5, 10, 13],\n [7, 6, -7, 10, -2, -8, -7, -6, 6, 0, -10, -6],\n [4, -9, 10, -7, -5, 0, -8, 2, 6, 8, -5, 14],\n [2, 6, -2, -5, -10, -5, -2, -2, -11, -6, -2, -2],\n [4, 6, -8, 0, -5, 14, 3, 8, -8, 0, -2, -14],\n [-6, -2, -7, -8, -2, 3, 8, -16, -10, -4, -7, 4],\n [-6, 2, -6, 2, -2, 8, -16, -14, -2, -5, 4, -4],\n [5, 11, 6, 6, -11, -8, -10, -2, -8, 1, -10, -10],\n [-4, -5, 0, 8, -6, 0, -4, -5, 1, 14, -6, -4],\n [-8, 10, -10, -5, -2, -2, -7, 4, -10, -6, 10, 6],\n [-4, 13, -6, 14, -2, -14, 4, -4, -10, -4, 6, -9]], determine the value at position (4, 12).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348097592937795", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-12, 2, -2, 12, -14, 0, -12, 6, -6, -3, -1, -9],\n [2, 13, 3, 0, 6, -2, -12, 0, -8, -2, -4, -2],\n [-2, 3, 5, 9, -10, 1, 1, -8, -1, 3, 6, 4],\n [12, 0, 9, -8, 1, -7, 2, -1, 4, -2, -2, -7],\n [-14, 6, -10, 1, 0, 5, 6, 6, 4, 0, -4, 0],\n [0, -2, 1, -7, 5, -2, 4, 8, 12, 7, 2, -11],\n [-12, -12, 1, 2, 6, 4, -7, -2, 4, 2, 3, 14],\n [6, 0, -8, -1, 6, 8, -2, -9, -11, 8, 11, 11],\n [-6, -8, -1, 4, 4, 12, 4, -11, 5, -6, 10, -2],\n [-3, -2, 3, -2, 0, 7, 2, 8, -6, -13, -8, 11],\n [-1, -4, 6, -2, -4, 2, 3, 11, 10, -8, 7, -8],\n [-9, -2, 4, -7, 0, -11, 14, 11, -2, 11, -8, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3211524059521", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[3, -4, 7, -14, -7, -16, -4, -3, 16, -15, -15, 14],\n [-13, 2, -8, 7, -4, 13, 2, -7, -3, 3, -13, -12],\n [15, -11, -3, -11, -3, -5, 10, 9, -5, -9, -7, -1],\n [9, -9, 12, 3, 0, 2, 0, -16, 12, -3, 0, -4],\n [12, 10, 16, 12, 2, 7, -3, -12, 7, 14, 13, -8],\n [10, 11, 9, 1, -9, 1, 3, 15, 12, 1, -10, -16],\n [11, 16, -13, 3, 14, 11, -14, -11, 6, -10, -16, -11],\n [7, 7, 12, 15, 8, -7, 8, 10, 15, -5, -13, 9],\n [-14, 0, -8, 12, -16, 1, 3, 11, -1, 4, -4, 15],\n [-11, -4, -4, -5, 16, 11, -14, 1, 9, -15, -13, 11],\n [11, 8, 9, -15, 13, 4, 6, 16, -15, 10, 5, -1],\n [3, 9, -1, -11, 6, -9, -11, 5, -11, 15, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1096811069197", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 1) of the 9th power of the matrix:\n[[6, -4, 15, 5, -10, 5, 4, -11, -3, -1, -14, -8],\n [4, 13, 13, 15, 6, -14, -16, -14, -10, -14, -14, -13],\n [14, -15, -3, 14, -15, 14, 5, -7, 13, 16, 2, 8],\n [-16, 15, 8, 0, -3, -4, -15, 15, 15, -11, 8, -14],\n [1, -14, -12, 7, 7, 11, -1, -10, 1, -11, 11, 12],\n [-13, -3, -12, 8, -9, -2, 2, -6, 3, 1, -3, 8],\n [-1, 1, -16, -16, -16, 4, 8, 10, -7, -5, 11, 15],\n [16, -9, 9, -15, -11, 14, 6, -5, 11, -2, 2, -5],\n [-15, -6, 8, 4, -8, -5, -7, -12, 16, -12, -1, 12],\n [1, 12, -11, 1, 15, 14, -6, 9, 11, 10, 2, 10],\n [3, -14, -1, 12, -2, 13, -16, 12, 13, 15, -7, 10],\n [-9, 8, 3, 0, 6, 8, 14, -11, -13, 3, -16, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11004582873465", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-7, 6, 7, -4, 12, 10, 14, -7, 14, -7, 7, 16],\n [-3, 0, 4, 15, -14, -2, -9, 15, 9, 13, -8, 15],\n [-6, 5, 1, 2, 1, 1, -5, -13, 10, -12, -11, -4],\n [6, 8, -13, 15, -2, 9, -6, -8, -6, -15, 10, 9],\n [-9, 4, 4, -9, -16, -4, -8, 11, -11, 6, 0, -8],\n [-5, 5, -5, -11, -8, -14, -9, -7, -8, -3, 10, 15],\n [-13, -15, 16, 4, -16, -6, -16, -6, -10, -15, -2, -9],\n [9, 4, -9, 15, -9, -7, 6, -13, 13, 6, -12, 4],\n [-11, 0, 8, 7, 5, -4, 0, -3, 9, 2, 9, -14],\n [-15, 11, -15, 5, -10, -13, 3, -11, -8, 14, 9, 9],\n [11, -12, -7, 1, -2, 16, -12, 5, 5, 5, -2, 0],\n [11, 5, 4, 0, -12, 1, 0, -13, -10, 8, -8, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1700042880918", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-8, 1, 4, 10, 15, -8, 3, 13, 4, -12, 1, 10],\n [1, -15, -10, 0, -10, -2, -2, 13, 10, -14, -12, -1],\n [4, -10, -11, 10, -6, 10, -5, -5, 10, -6, 3, 4],\n [10, 0, 10, 6, 1, -6, 3, -3, 5, 2, 10, 6],\n [15, -10, -6, 1, -15, -2, -5, -10, -2, 7, -10, 7],\n [-8, -2, 10, -6, -2, -1, -8, 9, -4, 3, 2, -10],\n [3, -2, -5, 3, -5, -8, 5, 5, 14, -2, 4, 10],\n [13, 13, -5, -3, -10, 9, 5, 14, 5, -14, 10, -5],\n [4, 10, 10, 5, -2, -4, 14, 5, 13, 0, 2, -2],\n [-12, -14, -6, 2, 7, 3, -2, -14, 0, -13, 6, 0],\n [1, -12, 3, 10, -10, 2, 4, 10, 2, 6, 12, 2],\n [10, -1, 4, 6, 7, -10, 10, -5, -2, 0, 2, 8]], determine the value at position (12, 9).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1468031269683", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (8, 8) of the matrix A^7 where A is:\n[[15, -6, -3, 8, -9, -5, 2, -10, 0, 0, 1, 2],\n [-6, 8, -4, 8, 6, -8, -14, 11, 4, -8, -10, -6],\n [-3, -4, 11, -4, 0, -8, -4, 4, 1, 4, -8, 6],\n [8, 8, -4, -2, -6, -5, -4, 3, -2, 8, -10, -2],\n [-9, 6, 0, -6, 7, -4, 11, -11, 0, 1, 4, 1],\n [-5, -8, -8, -5, -4, 2, 2, -2, -8, 6, 0, 10],\n [2, -14, -4, -4, 11, 2, 12, 8, -2, -1, 0, 0],\n [-10, 11, 4, 3, -11, -2, 8, 8, -6, 2, -8, 10],\n [0, 4, 1, -2, 0, -8, -2, -6, 3, 10, 8, 1],\n [0, -8, 4, 8, 1, 6, -1, 2, 10, -16, -6, 6],\n [1, -10, -8, -10, 4, 0, 0, -8, 8, -6, 0, 0],\n [2, -6, 6, -2, 1, 10, 0, 10, 1, 6, 0, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20060207513", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[10, -10, -12, -2, -9, -8, -6, 5, -4, -6, 15, -2],\n [-16, 7, 5, -14, -3, -15, 15, 16, -11, 8, -6, -10],\n [5, -7, 4, -11, -16, -3, 10, -8, -11, 14, 0, 4],\n [10, 11, -1, 2, 4, 16, 6, -11, 15, 5, -14, -1],\n [8, 0, -4, 11, -6, -7, 7, 7, 16, 0, -11, -1],\n [11, 15, 9, -6, 8, 14, 4, -14, -5, 8, 0, 2],\n [-15, 0, 13, -7, 16, -16, 1, -13, 10, 8, 11, 5],\n [8, 0, -5, -1, -1, 0, 14, -2, -4, 10, 4, -15],\n [-9, -10, -7, -13, -14, 1, 7, 15, -15, -15, -7, 6],\n [-2, -5, 0, 1, -3, 0, -2, -5, -1, 15, 6, -1],\n [-10, 16, -13, -10, 1, -13, -6, 3, -6, -2, 0, -5],\n [11, -9, 10, 5, 7, -15, 14, 5, -16, -3, 8, -14]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340638067612159", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-12, -16, 2, 16, 13, -5, -7, -1, 12, -2, -6, 13],\n [-8, 1, 2, -13, -11, 16, 15, -1, -6, 5, 6, 9],\n [14, 12, -12, 8, -5, 5, -8, 3, 12, 12, 10, 0],\n [-12, -4, -2, -2, 1, -15, 6, -4, -13, 8, -6, -5],\n [-4, -8, -11, -7, 6, -2, 6, -1, 15, -12, 0, 5],\n [1, 11, -4, -16, 2, -13, -14, -7, 11, 2, -14, 6],\n [0, -10, 9, 1, -11, 14, 12, -8, 0, -5, 7, -7],\n [13, 12, -7, 11, 1, 0, -6, -16, 0, -8, 11, 16],\n [-14, -9, -11, -11, 12, -5, -8, 2, 0, 15, -3, -1],\n [4, -5, 7, -9, 4, -9, 11, -1, -7, -2, -13, 9],\n [-2, 15, -13, -8, 11, -8, -15, -14, -12, -7, 11, -2],\n [-3, 6, -4, -1, 13, -9, 0, 13, 0, -16, 7, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22839778971053", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-15, 9, -4, 6, -4, 14, -7, -2, 3, 13, -6, 0],\n [9, 10, 4, 8, 0, 6, -7, -2, 13, -8, -6, 10],\n [-4, 4, 12, 0, -6, 0, -2, -3, 3, -6, 4, -6],\n [6, 8, 0, 5, 4, 6, 6, -2, 5, 2, -10, 6],\n [-4, 0, -6, 4, 5, 3, -5, 0, -8, -4, 11, 4],\n [14, 6, 0, 6, 3, 1, -2, -6, -1, 0, 8, 6],\n [-7, -7, -2, 6, -5, -2, -14, -5, -2, 2, -2, 8],\n [-2, -2, -3, -2, 0, -6, -5, -13, -2, 6, 2, -4],\n [3, 13, 3, 5, -8, -1, -2, -2, -2, 8, -3, -11],\n [13, -8, -6, 2, -4, 0, 2, 6, 8, 14, -2, -3],\n [-6, -6, 4, -10, 11, 8, -2, 2, -3, -2, -3, 8],\n [0, 10, -6, 6, 4, 6, 8, -4, -11, -3, 8, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "805428270061", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[11, 4, 2, 3, -2, 3, -8, 14, -6, 8, -12, -2],\n [4, -3, -4, 12, -2, 2, -10, -8, 6, -3, -3, 8],\n [2, -4, 0, 13, -12, 6, -7, 0, 0, -3, -10, 0],\n [3, 12, 13, -4, 10, 4, 11, -6, -13, -7, 3, -1],\n [-2, -2, -12, 10, 2, 4, -6, -12, 8, 8, 2, 2],\n [3, 2, 6, 4, 4, 14, -11, 5, 8, -4, 10, 14],\n [-8, -10, -7, 11, -6, -11, -1, 12, 2, 3, -2, 1],\n [14, -8, 0, -6, -12, 5, 12, 2, 6, 5, -6, 8],\n [-6, 6, 0, -13, 8, 8, 2, 6, 3, 6, 2, 4],\n [8, -3, -3, -7, 8, -4, 3, 5, 6, -14, 12, 0],\n [-12, -3, -10, 3, 2, 10, -2, -6, 2, 12, 13, 1],\n [-2, 8, 0, -1, 2, 14, 1, 8, 4, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86465947256043", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[13, 5, 2, 14, 3, 2, -15, 10, -9, 10, -2, -5],\n [-3, -10, 0, 9, 3, -7, 2, 1, 13, 13, 8, 7],\n [-7, -15, 15, -10, -10, 10, -7, 16, -10, -11, -11, -4],\n [-4, -15, 2, 2, -15, 9, -11, 3, 6, -2, -11, 11],\n [-6, -9, 7, 4, -10, -12, 12, -1, -11, -3, -15, 8],\n [14, -4, 1, 0, 11, -5, 5, -16, 4, -16, -13, 15],\n [-16, -4, 0, -5, -10, -14, 9, 14, 9, -14, 11, 0],\n [13, -15, -9, -3, -6, -2, -15, 15, -4, 0, -2, 16],\n [-1, -4, 5, 6, -7, 0, 13, -4, 13, 13, -10, -7],\n [-15, 13, 2, -14, 8, 5, -3, -15, 15, -14, -9, 9],\n [15, -6, -16, -2, -13, -13, 11, -7, -6, 6, -14, 0],\n [5, 10, -1, -1, -14, 16, -15, 10, -2, -10, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2321046344915", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-5, 13, 3, 3, 10, 3, -10, 13, -9, -15, -3, -7],\n [1, 1, -1, -12, 14, 3, 6, 15, 0, -4, -4, 0],\n [-2, 9, 11, 13, 5, -7, -6, 16, -11, -10, -5, -10],\n [-15, -16, 6, 8, 1, -10, -14, 12, -7, -12, -9, -3],\n [-11, -16, 16, -6, 7, -7, 6, -1, -1, 14, -11, 13],\n [-16, 8, 4, -12, -5, -12, -8, -8, -16, -7, 0, -4],\n [-11, 15, -6, 0, -12, -11, -7, 16, 13, 4, 0, 10],\n [-14, 12, -15, 12, -16, 9, -16, -13, -3, 1, -16, 5],\n [-1, 5, -1, 11, 11, 5, -11, 8, -15, -10, 0, 3],\n [-15, -10, 15, 2, -5, -8, 10, -3, -15, 4, -13, 4],\n [5, -15, 0, 2, 7, 3, -5, 8, 6, 15, 7, 8],\n [-14, 8, 11, -5, 9, -9, -12, -6, 10, 2, 15, 11]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "681381479325", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[1, -8, 11, 4, -1, 1, 1, 6, -8, -4, -4, -1],\n [-8, 0, 8, 6, 7, -6, -13, -4, 11, 2, 12, 6],\n [11, 8, 0, 8, -8, -4, -6, 2, 6, -2, 6, 8],\n [4, 6, 8, 14, -8, -5, -8, -5, 4, 4, -4, -10],\n [-1, 7, -8, -8, 4, 7, 7, 1, -10, -2, 5, 4],\n [1, -6, -4, -5, 7, -14, -12, -1, -4, 2, 9, 1],\n [1, -13, -6, -8, 7, -12, 1, 7, 2, 0, -8, -7],\n [6, -4, 2, -5, 1, -1, 7, -10, -8, 4, -8, -10],\n [-8, 11, 6, 4, -10, -4, 2, -8, -4, 6, -2, 5],\n [-4, 2, -2, 4, -2, 2, 0, 4, 6, 14, 1, 7],\n [-4, 12, 6, -4, 5, 9, -8, -8, -2, 1, 5, 2],\n [-1, 6, 8, -10, 4, 1, -7, -10, 5, 7, 2, -15]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3643335632365234", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-4, -6, 9, 4, -15, 3, 0, -1, -12, -3, 7, -13],\n [7, -8, -14, -8, 1, 2, 7, -13, -8, 16, -16, -7],\n [-5, 1, -3, -7, -7, 1, 7, -16, 13, -2, -9, 1],\n [-1, 4, -2, -12, -10, -10, 10, 8, 5, -4, 0, -4],\n [9, -8, -12, 16, -13, 11, 9, -13, -1, 5, 8, -9],\n [0, 1, -5, 16, 6, -5, -6, -4, 10, 8, -14, 8],\n [-7, 0, -14, 5, -3, 10, 3, 1, -4, -11, -7, 12],\n [-11, -6, 8, 13, 3, -1, 14, 12, -11, 12, 15, -8],\n [6, -1, 1, 2, -15, -7, -5, 1, 2, 10, -3, -15],\n [16, 2, 10, 13, -10, 10, 4, -10, 8, 1, 16, 16],\n [15, 8, -3, -13, 1, -7, 6, 8, -16, 1, -2, 8],\n [15, 3, 0, -6, -4, 8, 3, 8, 14, -16, -1, 11]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357091621603", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[4, 13, -14, -11, 12, -14, 16, -6, -12, 15, 1, 3],\n [11, -4, 9, -1, 8, -7, 12, 3, 9, 15, 7, 14],\n [-5, -7, -11, -10, 14, 10, -9, -14, 4, -16, -2, -10],\n [-2, 8, -14, 13, -3, -13, -14, -12, 8, 14, -6, -9],\n [9, -15, 11, -7, 4, 11, 16, -6, -16, 16, -14, 9],\n [-2, -3, 6, -9, 3, -11, 16, 11, 13, 0, -8, 11],\n [-10, 11, 0, -12, -12, -3, -11, -10, 0, -8, 14, 5],\n [-8, -1, -4, 2, -5, -7, -1, 11, 2, -11, -13, 13],\n [14, 10, 4, -8, 4, 0, 7, 14, -11, -4, 8, 15],\n [-16, 2, -5, 3, 16, 12, -1, -3, -10, -11, 4, 5],\n [2, 8, -14, -6, 10, -15, -11, -15, 0, -3, -7, 16],\n [-5, 15, 7, -3, -12, -12, 15, 16, -13, 13, 0, -14]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3470072687567521", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-4, 1, 6, 16, 0, -5, -12, 10, -4, 9, -3, 15],\n [-6, -1, 5, -1, -4, -5, 1, 12, 1, -15, -15, -14],\n [12, -9, -6, -5, 15, -13, -8, 7, -1, 0, 5, -10],\n [-7, 12, 7, -3, -3, 8, 5, 6, 15, 9, 10, -5],\n [2, 2, 15, 12, 4, -12, -5, -10, -15, 8, -7, -11],\n [10, -7, -8, 3, -9, 14, -1, 11, -11, 15, 11, -6],\n [6, 13, -8, 11, 7, 11, 7, -2, 16, 5, 12, -7],\n [13, -6, 4, -4, 8, 4, -16, -12, 5, -10, -4, 6],\n [4, -11, 3, -5, -8, 11, -6, 15, -6, 7, -2, 0],\n [8, 2, 14, 0, 6, -16, -7, -9, 9, 2, -3, -9],\n [-16, 8, 7, 3, 13, -12, -14, 15, 0, -12, -6, -13],\n [2, 6, 0, -4, 10, -16, -15, 1, 16, -15, -13, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24062561322112", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 9) of the 9th power of the matrix:\n[[-13, 0, -2, -3, 0, -4, 8, -3, -6, 2, -8, -2],\n [0, 9, 14, 14, 0, -6, 6, 0, 2, -9, 1, 10],\n [-2, 14, 7, 4, 7, -6, 10, 10, 6, -2, 0, -10],\n [-3, 14, 4, -1, -1, 3, -6, -12, 5, 2, 4, -9],\n [0, 0, 7, -1, 12, 10, 9, 2, -6, -4, -8, 6],\n [-4, -6, -6, 3, 10, -10, 6, 5, 4, 4, 4, -10],\n [8, 6, 10, -6, 9, 6, 4, -4, 6, -7, -10, 0],\n [-3, 0, 10, -12, 2, 5, -4, 7, 0, 0, 9, -7],\n [-6, 2, 6, 5, -6, 4, 6, 0, 12, 0, -2, -2],\n [2, -9, -2, 2, -4, 4, -7, 0, 0, -16, -3, 0],\n [-8, 1, 0, 4, -8, 4, -10, 9, -2, -3, 0, 0],\n [-2, 10, -10, -9, 6, -10, 0, -7, -2, 0, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6128154515887", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-8, 11, 6, 3, 12, 6, 8, -1, 1, 4, -1, 6],\n [11, 9, 6, -7, 4, -8, 6, 0, 2, 0, 2, 12],\n [6, 6, 6, 5, 5, -3, -7, -8, 10, 0, -4, 10],\n [3, -7, 5, -9, -8, 11, -14, -6, 2, 0, 0, 2],\n [12, 4, 5, -8, -15, -1, 2, 4, 0, 0, 0, 8],\n [6, -8, -3, 11, -1, 5, -4, 6, 0, -2, 2, -4],\n [8, 6, -7, -14, 2, -4, 5, -4, 0, -3, 10, 8],\n [-1, 0, -8, -6, 4, 6, -4, -16, 4, -10, 1, -1],\n [1, 2, 10, 2, 0, 0, 0, 4, 2, 6, -2, -14],\n [4, 0, 0, 0, 0, -2, -3, -10, 6, 13, 0, 6],\n [-1, 2, -4, 0, 0, 2, 10, 1, -2, 0, -4, 0],\n [6, 12, 10, 2, 8, -4, 8, -1, -14, 6, 0, -16]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1813486323291", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-5, -4, 14, -7, 3, -2, -1, -5, 14, -12, 8, -6],\n [-4, 13, -8, 13, -6, -6, 0, -14, 9, -5, 10, -10],\n [14, -8, -12, 0, -8, 6, 13, -2, 8, 13, 10, 1],\n [-7, 13, 0, 3, -8, -14, -4, -1, -6, -2, -6, 0],\n [3, -6, -8, -8, 3, -6, -9, -10, 2, -4, 2, -5],\n [-2, -6, 6, -14, -6, 7, 14, 2, 2, -6, 0, 2],\n [-1, 0, 13, -4, -9, 14, 8, -2, -2, 4, -2, -8],\n [-5, -14, -2, -1, -10, 2, -2, 16, 2, -2, -8, 2],\n [14, 9, 8, -6, 2, 2, -2, 2, 0, 10, 6, 1],\n [-12, -5, 13, -2, -4, -6, 4, -2, 10, -3, -3, 10],\n [8, 10, 10, -6, 2, 0, -2, -8, 6, -3, -4, -4],\n [-6, -10, 1, 0, -5, 2, -8, 2, 1, 10, -4, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2873066247218", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[7, 0, 10, -2, -8, 1, -6, -12, 0, -14, -2, 3],\n [0, 1, -15, 7, 13, -4, 4, 6, 2, -13, 6, -12],\n [10, -15, 14, 4, 4, 6, 6, -3, 4, -3, -6, -9],\n [-2, 7, 4, -13, 5, 0, -6, 9, 0, -9, 4, 13],\n [-8, 13, 4, 5, 14, 7, 12, -1, 8, 13, 0, -8],\n [1, -4, 6, 0, 7, -16, -2, -1, -8, 0, 8, 6],\n [-6, 4, 6, -6, 12, -2, -11, -1, -10, 1, 0, 12],\n [-12, 6, -3, 9, -1, -1, -1, 3, 6, 6, 3, -4],\n [0, 2, 4, 0, 8, -8, -10, 6, -6, -1, -4, -8],\n [-14, -13, -3, -9, 13, 0, 1, 6, -1, -10, 0, 12],\n [-2, 6, -6, 4, 0, 8, 0, 3, -4, 0, -13, -4],\n [3, -12, -9, 13, -8, 6, 12, -4, -8, 12, -4, -8]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-165584050614000", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (1, 7) of the result:\nA =\n[[0, 3, -3, 12, -4, 0, -13, 3, -6, 5, -9, 11],\n [13, 16, 16, 10, 3, 16, 8, 2, 4, 16, -14, -3],\n [-2, 16, 5, -16, 14, 3, 15, -5, -1, -9, -3, 1],\n [13, 16, -10, -11, -11, 5, -9, -2, 9, -14, -7, -14],\n [13, 5, -14, -16, 16, 2, 14, 7, -5, -4, -1, -1],\n [3, 10, -4, -13, 15, 0, 7, 12, 11, 5, 11, 8],\n [-14, -4, 14, -4, 1, 0, 4, 2, -5, 11, -6, 11],\n [-2, -1, -10, -14, 14, -5, -9, 8, -5, 4, 9, -15],\n [-3, -13, 0, -12, 7, -10, 6, 0, -5, -6, -6, 12],\n [10, 5, -15, 13, -10, -5, -14, 0, 15, -9, 6, 13],\n [-2, -7, -2, 13, 9, -3, -14, 9, -3, 14, -3, -7],\n [-8, 1, -5, -14, 1, -10, 14, -16, 14, -4, 12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27305610065853", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[12, -2, 4, 2, 11, -13, -4, -2, 15, -14, 13, 3],\n [-15, 8, -6, -16, -7, 0, 13, 2, 15, -5, 0, -11],\n [-4, 5, -6, -10, 4, -16, 13, 2, 12, 3, -16, 6],\n [14, 5, -10, 16, -10, 10, -15, 0, -16, 13, 5, 11],\n [16, 9, -6, -10, 11, 8, 14, -14, 16, 4, 2, 4],\n [-3, -7, -10, 12, -9, -4, 2, -6, -15, -11, 12, -12],\n [13, 10, 1, -1, -12, -8, 14, 3, 0, 3, 11, 4],\n [2, -14, 13, -12, -11, -14, 7, -16, -2, 1, 6, 12],\n [5, 7, -4, 16, 5, 0, 5, -12, 8, -11, 0, 14],\n [0, 16, -13, -3, -4, 10, 7, 10, -9, 4, -6, 14],\n [10, 10, -9, 16, -5, -1, -15, -5, 10, 0, 3, 4],\n [13, 3, -9, 1, 1, 1, -15, -5, 15, -9, -7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3196878466423702", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-3, 0, 12, -14, 3, 11, -4, -12, -8, -4, 6, -11],\n [0, -13, 1, -2, -2, 2, 1, -5, -12, 2, -2, -2],\n [12, 1, -8, -9, 6, 6, -6, -4, 4, 3, -2, -8],\n [-14, -2, -9, -7, 0, -2, 4, -2, 12, -8, -4, -2],\n [3, -2, 6, 0, 14, -10, 12, -8, 14, 2, -12, -7],\n [11, 2, 6, -2, -10, 3, -8, 11, -4, 0, 0, 0],\n [-4, 1, -6, 4, 12, -8, -4, -6, 0, 5, -3, 0],\n [-12, -5, -4, -2, -8, 11, -6, -12, 3, 8, 4, 8],\n [-8, -12, 4, 12, 14, -4, 0, 3, -2, -10, -3, 10],\n [-4, 2, 3, -8, 2, 0, 5, 8, -10, -10, 2, 8],\n [6, -2, -2, -4, -12, 0, -3, 4, -3, 2, -1, 7],\n [-11, -2, -8, -2, -7, 0, 0, 8, 10, 8, 7, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66356084018", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-15, 0, 2, -8, 5, 2, 6, 2, -4, 8, -1, -8],\n [0, 9, -10, -4, -2, -10, -4, -6, -4, -8, -4, 2],\n [2, -10, 6, -4, 2, 7, 16, 10, -2, -4, 5, 3],\n [-8, -4, -4, -13, 2, -4, -6, 6, 2, 0, -2, 2],\n [5, -2, 2, 2, -15, 0, 3, 10, -4, 0, 0, 8],\n [2, -10, 7, -4, 0, -15, -3, -6, 12, 10, 5, 4],\n [6, -4, 16, -6, 3, -3, 3, 10, -4, 3, -2, 2],\n [2, -6, 10, 6, 10, -6, 10, 12, -5, -3, 7, -2],\n [-4, -4, -2, 2, -4, 12, -4, -5, 12, 1, -8, -4],\n [8, -8, -4, 0, 0, 10, 3, -3, 1, 11, -10, 0],\n [-1, -4, 5, -2, 0, 5, -2, 7, -8, -10, -10, -10],\n [-8, 2, 3, 2, 8, 4, 2, -2, -4, 0, -10, 11]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16085924781830", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-16, -2, -14, -2, 4, 5, -6, -8, 0, 2, -4, 0],\n [-2, -5, 4, -8, 2, -3, -9, 4, -1, -6, 6, 11],\n [-14, 4, 9, 4, 10, 7, 0, 6, 6, 7, 2, -12],\n [-2, -8, 4, -3, 0, -10, -1, 2, -8, -1, 5, 11],\n [4, 2, 10, 0, 11, 1, 8, -6, -2, 6, 12, -4],\n [5, -3, 7, -10, 1, 14, 4, 2, -9, -6, 2, -8],\n [-6, -9, 0, -1, 8, 4, -7, 1, -2, -9, 7, 4],\n [-8, 4, 6, 2, -6, 2, 1, 3, -4, -3, 10, 6],\n [0, -1, 6, -8, -2, -9, -2, -4, -3, 2, 12, -8],\n [2, -6, 7, -1, 6, -6, -9, -3, 2, 13, -1, -5],\n [-4, 6, 2, 5, 12, 2, 7, 10, 12, -1, -1, 8],\n [0, 11, -12, 11, -4, -8, 4, 6, -8, -5, 8, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29684781740626", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-5, 14, -2, -12, 0, -3, 0, -2, -6, 0, 0, -3],\n [14, -3, -5, 2, 13, 9, 6, -2, -2, 2, -2, 0],\n [-2, -5, -4, 4, 5, 2, -8, 12, 2, 10, 6, 16],\n [-12, 2, 4, 0, -1, -6, -12, 10, -2, -4, -2, -6],\n [0, 13, 5, -1, 10, -6, 16, 0, 8, -1, 10, 5],\n [-3, 9, 2, -6, -6, 10, -10, 8, 0, -8, -8, -7],\n [0, 6, -8, -12, 16, -10, -10, -11, -3, 2, -3, 5],\n [-2, -2, 12, 10, 0, 8, -11, 11, 14, -4, -12, 2],\n [-6, -2, 2, -2, 8, 0, -3, 14, -8, -2, 5, -2],\n [0, 2, 10, -4, -1, -8, 2, -4, -2, 0, 0, 2],\n [0, -2, 6, -2, 10, -8, -3, -12, 5, 0, -4, -4],\n [-3, 0, 16, -6, 5, -7, 5, 2, -2, 2, -4, -13]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12913341968136", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 6) of the 9th power of the matrix:\n[[-15, 10, 16, 15, 10, 11, -14, -9, 5, -3, -2, -13],\n [1, -16, -5, 0, 2, -10, -8, -9, 8, -10, -9, 7],\n [0, -5, 14, -5, -15, -5, 10, -10, -4, -16, 13, 14],\n [0, -9, -14, -7, 5, -13, 15, 12, -6, -4, -13, -15],\n [5, -12, -8, 3, 4, 0, -5, 11, 1, -14, -12, -3],\n [9, 2, 0, -13, 7, -4, 16, -2, -2, 14, 11, -7],\n [-10, 16, -10, -12, 9, -1, -9, 5, 11, -10, 11, -15],\n [-8, -11, -16, -14, -7, 6, 16, -8, -4, 11, -10, 9],\n [-1, 9, 15, -16, 4, -4, 9, -8, 6, -16, -15, 11],\n [14, -12, 8, -9, 15, -6, 8, -14, 15, 15, -12, 11],\n [11, -9, 10, -1, 1, 8, -16, -9, 4, 7, 9, -3],\n [12, 13, -14, -10, -6, 15, -5, -2, 7, -16, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35870275141497", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-15, 14, 16, 13, 14, -10, 8, -1, 5, 10, 0, -13],\n [5, -2, 4, -4, -6, 10, 14, 15, 13, 1, -1, -8],\n [-7, -5, -9, -14, 2, -6, -9, 9, 6, -7, 1, -5],\n [9, -6, -7, -14, -10, -13, -9, -4, -5, -15, -2, 9],\n [-12, 8, -13, 10, 12, -12, 1, -13, -16, 3, -11, 3],\n [3, 10, 9, 15, -7, 1, -5, -7, 7, 7, 8, -9],\n [-3, 14, 7, -1, 3, -2, -3, -5, -9, 2, -12, 10],\n [-4, 15, 14, -15, -10, -6, -6, 6, 14, -9, 15, 4],\n [14, -16, -4, -6, 12, -13, -2, -14, 12, 4, -15, -11],\n [14, 7, 0, -12, -15, -5, -12, 3, -9, -16, -11, -6],\n [-14, 14, 11, -12, 9, -1, 14, 11, -10, -8, 10, -5],\n [8, 12, 14, 16, 10, -15, -3, -4, 7, -12, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "269642147470032", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[13, -1, -6, -3, -2, -10, 12, 5, 6, 7, -7, -9],\n [-5, 12, 12, 6, 9, 15, -11, -9, 0, -5, 5, -3],\n [2, -11, 1, -2, -8, -11, -15, -1, -16, 13, 16, -16],\n [-1, 0, 1, 5, 5, 14, 10, -13, -12, 8, 14, -3],\n [13, -5, 10, 7, 13, 1, -3, 2, 5, 9, -10, 11],\n [-12, 1, -3, 6, -3, 15, -12, 5, 11, -5, 1, 14],\n [-4, 3, -10, 6, 15, 4, -11, -1, 3, -6, 15, -3],\n [7, 14, 0, 8, -8, 5, 0, 11, -16, -8, -4, 15],\n [11, 14, -9, -9, 6, -7, 8, 16, -13, -10, 16, -15],\n [15, -12, 0, -5, -5, 4, 4, -15, 4, -2, -6, -7],\n [1, 6, 14, 9, -15, -10, 7, 15, 9, 6, -3, 12],\n [8, 14, -15, -15, 6, -6, 12, -8, 15, 13, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-156735966702", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 5, 13, 0, -1, -9, 14, -5, 16, -5, 8, 1],\n [2, -14, -12, 10, 4, -1, 11, 8, 16, 0, 13, -13],\n [-15, -8, 14, 8, -12, 7, 7, 12, 14, 2, 6, -11],\n [-11, 13, -16, -9, 11, 8, 16, -3, -6, -15, 13, 13],\n [-13, -4, -10, -14, -8, -3, -6, -3, 2, -9, -10, -10],\n [-14, -14, 1, 16, 11, -1, -2, 12, 1, 2, 12, -11],\n [10, -10, 10, 2, 0, -6, -12, -15, -5, -6, -7, 11],\n [-10, -3, -4, -12, -9, -16, -12, -6, -7, -2, 12, 8],\n [-11, -6, 0, -2, -1, -15, 2, 4, -6, -14, 1, -2],\n [8, -2, 13, 0, 1, 14, 1, -4, -3, 1, -12, -3],\n [8, -5, 11, -16, -14, -10, -8, 6, 7, -7, -5, 2],\n [15, 7, 5, -14, 10, 2, -8, -4, -15, 12, -6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "729382112107", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 6) of the 8th power of the matrix:\n[[-13, -16, 8, 9, -6, 6, -15, 2, 12, -13, -1, 10],\n [-12, -2, 6, -14, 1, 9, -11, 0, 10, 3, -11, -5],\n [-14, -13, -13, -13, 4, -15, -1, -10, 2, 16, -8, 0],\n [10, 16, -5, -6, -4, 14, -4, 9, 14, 5, -11, 3],\n [4, -7, 2, 9, -10, -9, -12, 11, -14, -9, -2, 10],\n [-1, 9, -13, -5, 0, 9, 14, -2, 12, -8, -3, -13],\n [7, 0, -4, 3, 0, 10, 16, 4, 0, 5, 8, -14],\n [10, 10, -5, -2, 3, 5, -15, -13, -4, 15, 5, 8],\n [10, 0, -11, -1, -9, 16, -7, 2, -3, -14, 6, -6],\n [-11, -16, 8, 12, 6, 1, -3, 0, -15, 14, 2, 15],\n [11, -9, 5, 7, -15, 2, -15, 11, 15, 2, -1, 13],\n [5, -3, -16, -15, 5, 16, -2, 5, -6, -13, -10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-343653798819", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-10, -13, -5, 10, 0, 3, 14, 9, 14, -8, -12, -9],\n [4, -1, -1, 1, 11, 1, -3, -1, 4, -16, -6, -6],\n [-15, 15, 2, -12, -14, 11, 9, 6, 13, -9, 12, -4],\n [8, 5, 16, -10, 6, -11, -2, -2, -3, 12, -1, 12],\n [6, -7, -13, -5, -13, 3, 11, 11, -11, -3, -16, 2],\n [-16, -4, -9, 1, 6, 9, 3, -15, 9, 8, 13, 1],\n [-10, 10, -6, -9, -6, 7, 13, 13, -2, 7, -9, 3],\n [9, 7, 5, -12, -2, 12, -2, 10, -9, 12, 2, 14],\n [-8, -7, -7, 16, 8, -13, -12, 6, -12, -9, 0, -16],\n [-5, -3, 1, -7, -2, 16, 2, 8, -1, -9, 4, 2],\n [-6, -6, -6, 5, 4, 10, 1, 13, 16, 4, -15, -4],\n [-15, 14, -7, 6, 5, 12, 16, 14, -3, -7, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431331061916", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-14, -15, -9, 14, -9, -15, 5, -12, -10, 3, 11, -4],\n [-15, 15, 9, -14, -4, 4, 6, -10, 0, 11, 13, -12],\n [7, -10, 16, 10, -3, 2, -5, -14, -10, 8, -2, 2],\n [2, 6, -6, 4, -10, 10, 6, 3, 10, -9, -14, -15],\n [5, -11, 7, -5, 0, 5, 2, -8, -5, 15, 14, 0],\n [6, -7, 13, 2, 9, 9, -6, 3, -13, -5, 8, -7],\n [5, -10, 7, -15, 15, 4, -10, -9, 4, -9, 8, 11],\n [11, 14, 8, -5, 14, 1, 9, -11, -8, -6, 14, -15],\n [12, -12, 6, -10, -4, -7, -1, -2, 2, 4, -2, -3],\n [12, -12, 1, -16, 10, 10, 8, 4, -3, 3, 11, 4],\n [6, -6, -15, 3, 7, 8, 5, 7, -2, -5, 14, 14],\n [13, 3, -9, 13, 4, 11, 0, -5, 1, 11, -14, -2]], determine the value at position (11, 7).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41477427411", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 11) of the 7th power of the matrix:\n[[-1, 5, 14, 14, -16, -6, -11, 6, -8, -1, 2, -4],\n [15, -8, 14, 14, 2, -15, 15, -16, 4, -14, 10, -10],\n [16, -8, 13, 1, 9, 3, 14, -9, 6, 8, -16, 1],\n [2, -11, 0, -9, -8, 10, -11, -11, -13, 5, 10, -15],\n [-8, -6, 3, -3, 9, 13, -11, -14, -16, 1, 6, 15],\n [12, 6, -11, 0, 1, 14, -11, 10, 8, -7, -5, -6],\n [-14, 5, -13, -9, -3, 3, 7, -3, 11, -1, 15, -5],\n [-1, 2, -12, -5, 12, -12, 0, -9, 13, -7, 3, -1],\n [-1, -14, 6, 5, 11, -13, 7, 2, -6, 1, -5, -3],\n [1, -5, 10, -11, 7, 16, -1, -5, 14, -4, -9, -14],\n [3, -13, -15, 6, 2, -9, -1, 1, 7, -16, -16, -6],\n [1, -1, 0, 7, -13, -2, -15, 14, -8, -7, 8, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46476304", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, -15, 1, 12, 3, -9, 9, -13, 16, 5, -11, 16],\n [11, 7, -13, -15, -4, -6, -7, -7, -9, -12, 6, 15],\n [-1, -13, 11, -3, -5, 4, -1, -15, 6, 12, -8, -10],\n [12, 0, -8, -11, 3, -7, -8, -5, 16, 15, 2, 16],\n [-1, 6, 9, -8, 13, -4, -1, -15, 14, 2, -6, -3],\n [8, -10, -2, 13, 14, 7, 8, -9, 13, -3, 12, 10],\n [4, -6, 16, -2, -5, 7, -6, 2, -16, 0, -1, 9],\n [-2, -9, 13, -3, 16, -10, 1, -5, -15, 12, 4, -10],\n [10, -5, 3, -3, -7, 6, 13, 14, -7, 2, 2, 6],\n [15, 3, -13, 16, -16, -4, -14, -5, 12, 14, -15, 5],\n [5, 14, -3, 12, -8, 15, 10, -7, 8, 16, -6, -8],\n [-10, -10, 2, 3, 8, -12, 12, 10, 8, -2, -13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1224958140558597", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (7, 11) of the matrix A^8 where A is:\n[[0, 4, -1, 9, -8, -15, -2, 7, -3, -11, 1, 5],\n [1, -15, 15, 0, -16, -8, -4, 13, 14, 6, 11, -7],\n [8, 9, 9, -4, 0, -13, 6, -6, -5, -8, -2, -12],\n [2, -6, -8, 10, -4, -5, -8, 11, -4, 3, -4, 10],\n [9, 12, 12, 5, -8, 7, 2, 14, -2, 15, 12, -8],\n [-11, -3, -8, 2, 6, 11, -1, 9, 8, -12, -10, 6],\n [8, -16, 5, -13, 11, -3, 16, -13, -6, 15, -13, -16],\n [9, 16, 0, 10, -12, -10, 8, -9, -13, -5, 14, -6],\n [5, -16, -13, -9, 8, 11, -13, -4, 8, -14, 15, -16],\n [-6, -15, -12, 5, -4, 6, 14, -4, -10, -12, 12, -9],\n [-9, -10, 2, 6, 15, -13, 13, -12, -14, 5, 11, 5],\n [5, 12, -4, -10, -7, 11, -13, 15, 5, 3, 3, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26777931056", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-8, 11, -4, 14, -3, 5, 7, -9, -2, -11, 6, 8],\n [14, 12, 6, -7, -8, -4, 15, -16, -16, 1, 14, -16],\n [-8, 5, 11, 9, -7, -14, -15, 14, 16, 15, -5, -14],\n [9, -3, -5, 9, -1, -9, 11, -10, -2, -9, -7, -2],\n [1, -15, 5, -2, -12, -2, 10, -1, 1, 8, 5, 14],\n [6, -1, -11, -2, 1, -4, 7, -4, -16, 1, 16, -11],\n [0, -13, -3, 13, 3, -9, -15, -13, -7, 3, -7, 11],\n [-2, -16, 5, 10, 12, -2, -7, 3, 5, -8, 15, 0],\n [2, 10, -7, 13, 4, 4, -8, -5, 4, 3, -11, -5],\n [14, -15, -1, -16, -13, -16, -4, 14, 3, -10, 16, 11],\n [3, 15, -8, -3, -13, 12, -2, 0, 2, -8, 10, -2],\n [11, -13, 4, 2, -13, 15, -5, -1, -3, -16, 15, 4]], determine the value at position (6, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2833054423489", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-13, 1, -4, -1, 10, 0, 12, -13, 6, -5, -6, -1],\n [1, -1, 0, 15, -2, 2, -3, -3, 10, 6, -10, 0],\n [-4, 0, 2, 1, -2, 10, -12, 2, -9, -2, -2, -2],\n [-1, 15, 1, -13, -12, -6, -13, 3, -7, 15, 8, 4],\n [10, -2, -2, -12, 8, 0, -8, -6, 8, -7, 6, 0],\n [0, 2, 10, -6, 0, 13, 2, 0, -12, -10, 8, 13],\n [12, -3, -12, -13, -8, 2, 5, -2, 8, 8, -3, 2],\n [-13, -3, 2, 3, -6, 0, -2, -8, -8, 4, -6, 8],\n [6, 10, -9, -7, 8, -12, 8, -8, -3, 4, 6, 0],\n [-5, 6, -2, 15, -7, -10, 8, 4, 4, 7, -6, 0],\n [-6, -10, -2, 8, 6, 8, -3, -6, 6, -6, -11, -6],\n [-1, 0, -2, 4, 0, 13, 2, 8, 0, 0, -6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4217466196454", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[4, -11, -4, -11, -6, 9, -12, 2, -4, -2, 7, 0],\n [-11, -6, -3, 3, 0, 2, -5, 10, 4, -2, 4, -6],\n [-4, -3, 6, 4, 2, -10, 6, 3, -1, -1, 4, 8],\n [-11, 3, 4, -1, -2, 8, -6, -11, 1, -3, -1, -8],\n [-6, 0, 2, -2, -6, 11, 1, 2, -7, -2, -5, -2],\n [9, 2, -10, 8, 11, -14, -2, -2, -7, -5, 9, 4],\n [-12, -5, 6, -6, 1, -2, -12, 8, 7, -2, 4, -5],\n [2, 10, 3, -11, 2, -2, 8, 5, -4, 4, 4, -3],\n [-4, 4, -1, 1, -7, -7, 7, -4, -12, -11, -13, -8],\n [-2, -2, -1, -3, -2, -5, -2, 4, -11, 1, -6, -4],\n [7, 4, 4, -1, -5, 9, 4, 4, -13, -6, 3, -6],\n [0, -6, 8, -8, -2, 4, -5, -3, -8, -4, -6, -8]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-650567500286816", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-15, -15, 1, 0, -9, -12, 12, 11, -1, -3, -15, -13],\n [14, 9, 10, 14, -6, -9, -5, -4, 10, -9, 4, -6],\n [5, 4, 11, -14, -10, -3, -2, -8, -10, -5, 2, 10],\n [1, -4, -16, 4, -4, 6, -16, 6, 11, 15, -9, 9],\n [-3, 7, 12, -13, 1, -3, 10, -14, 13, 6, 1, -7],\n [-5, -9, 15, 0, -3, -8, 9, 7, 6, 14, -15, 1],\n [-1, 12, -6, -15, -3, -13, -8, -10, 0, 6, -6, 5],\n [1, 11, -1, -13, 5, -6, 4, -1, -8, -8, -4, -11],\n [-13, 11, -6, -12, -6, -5, 2, -4, -13, -3, -15, -9],\n [5, -4, 4, 4, 11, 16, 12, 5, 9, -6, -6, 2],\n [-3, 12, 2, 4, 7, 9, -5, 2, 13, -2, -14, -4],\n [-8, -4, -1, -3, -9, 2, 15, 6, 4, 1, -3, -1]], determine the value at position (11, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3544898164183", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 5) of the matrix A^8 where A is:\n[[7, 0, 0, 3, -8, -2, -13, 10, -8, 9, 2, -4],\n [0, -7, 4, -10, 4, 0, 8, -14, -6, 4, -2, 13],\n [0, 4, 14, 16, 0, 2, 0, 2, -10, 6, 8, 0],\n [3, -10, 16, 14, -4, 0, -6, 4, -8, 8, 15, 4],\n [-8, 4, 0, -4, -7, -3, 0, 9, 14, -2, 9, 0],\n [-2, 0, 2, 0, -3, 3, 2, -6, 4, 9, -4, 4],\n [-13, 8, 0, -6, 0, 2, 16, -5, -2, 5, -12, 6],\n [10, -14, 2, 4, 9, -6, -5, 5, 8, 0, 6, -6],\n [-8, -6, -10, -8, 14, 4, -2, 8, 12, -12, -9, 14],\n [9, 4, 6, 8, -2, 9, 5, 0, -12, -11, -5, -8],\n [2, -2, 8, 15, 9, -4, -12, 6, -9, -5, -4, 7],\n [-4, 13, 0, 4, 0, 4, 6, -6, 14, -8, 7, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1624688301965", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-12, 13, -16, -12, -3, -6, 12, 1, -2, 8, 13, -15],\n [10, -2, 15, 3, -3, 10, -14, -14, -4, 8, 1, -16],\n [-12, -15, 13, 0, 12, -13, -8, 4, -5, -5, -13, 11],\n [-8, 15, -4, 2, -3, -12, 10, 11, 9, -7, 7, 0],\n [-1, 0, -16, 4, 5, -12, 4, -8, 10, -5, 1, -2],\n [13, 16, 13, 9, 4, 14, 0, 0, 7, 16, -13, -8],\n [-15, -2, -14, 14, 6, -5, -9, 4, 4, 15, 0, 7],\n [-9, 1, -6, -7, 9, -11, 0, 6, 11, -1, -5, 4],\n [7, 11, 4, 16, -15, 2, 11, -2, -16, 11, 15, 11],\n [-8, 7, -13, -14, 5, 8, 5, 3, 10, 15, 12, 15],\n [7, -14, 10, -8, 6, -10, 0, -10, 13, -4, 1, 14],\n [5, -3, 1, 0, 2, 14, -2, 12, -1, 16, 8, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931236074961", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[13, -15, 1, -12, -11, -5, -5, -5, -8, 5, -1, -13],\n [-14, -1, -3, -13, -15, -7, -6, 9, 9, -13, 9, 11],\n [-15, -15, -1, 6, 6, -4, 4, 8, -4, -2, 11, -14],\n [6, -13, -14, -9, 8, -5, -12, 16, 8, 8, -2, 9],\n [-7, 7, 12, -12, 7, 2, -8, 9, 8, -3, -11, 15],\n [9, -2, 14, 2, -3, -6, 10, -15, 5, -15, 3, 0],\n [-13, -3, -10, -2, 13, -1, -15, 2, -16, 14, -13, 10],\n [8, 5, -7, 16, 13, 13, -1, -8, 0, -2, 11, 3],\n [16, 16, -4, -13, 6, -9, -4, 7, 13, 13, 8, 16],\n [-8, 9, 7, 16, 8, -2, -11, 3, -1, 4, -2, -13],\n [7, -14, -16, 13, -4, 1, -6, 12, -13, 8, 11, -9],\n [4, 1, 8, -12, -9, 6, -14, 14, 12, 3, -14, 6]], determine the value at position (10, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-262094189984", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[4, -8, -6, -12, 4, -14, 0, -13, 8, 0, -2, -2],\n [-8, 16, 5, -4, -11, -8, -13, 7, 10, -7, -2, 2],\n [-6, 5, -2, -5, -13, -1, -10, 1, -2, -2, 2, 2],\n [-12, -4, -5, -16, 2, 2, 3, -14, -8, -6, 10, -8],\n [4, -11, -13, 2, -16, 0, 8, -6, 8, 1, 4, -6],\n [-14, -8, -1, 2, 0, -4, -8, 10, -4, 4, 2, 5],\n [0, -13, -10, 3, 8, -8, 13, -4, 8, 0, 15, -7],\n [-13, 7, 1, -14, -6, 10, -4, -15, -2, 2, 8, 0],\n [8, 10, -2, -8, 8, -4, 8, -2, 0, -10, 3, 7],\n [0, -7, -2, -6, 1, 4, 0, 2, -10, 8, 2, 12],\n [-2, -2, 2, 10, 4, 2, 15, 8, 3, 2, -14, -4],\n [-2, 2, 2, -8, -6, 5, -7, 0, 7, 12, -4, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5696547120668", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[14, -5, 13, -13, 13, -12, -1, 10, -13, -9, -9, 0],\n [-14, 10, 4, 7, 12, -11, -3, -3, 7, -4, -16, -5],\n [7, 3, -11, -5, 4, -14, 10, 0, -2, -13, 0, -6],\n [-5, 15, 10, 10, 12, -8, -14, 12, 4, -7, 6, 8],\n [7, 3, -2, 4, -5, 1, 6, 12, -12, 9, -6, -6],\n [1, -5, -1, 10, 0, 4, 14, 10, 6, 15, 0, -6],\n [-16, 11, 1, 3, -10, -1, 6, 15, 0, 2, -3, -14],\n [8, -6, -2, 2, -2, -2, -2, -8, -12, 2, 7, 12],\n [-12, 5, -4, 12, -1, 0, 3, -3, -11, 5, -8, 15],\n [7, 16, -4, -11, 13, -1, -16, 1, 5, 9, -3, -3],\n [9, 6, -15, -10, 5, 11, 3, 1, 7, 16, 9, 2],\n [-4, -7, -3, -8, -6, -14, -5, 15, -3, -16, 10, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2316224890854", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[12, 2, 2, 0, 14, 4, 6, -4, 10, 1, 10, 10],\n [2, 2, 14, 6, -5, 6, -2, -6, 10, 4, 4, -7],\n [2, 14, 8, 10, -8, -2, -4, 4, 12, -10, 5, -12],\n [0, 6, 10, 15, 2, -2, 7, -3, -8, -4, -15, 2],\n [14, -5, -8, 2, 7, -6, -2, -10, 4, -7, 10, -5],\n [4, 6, -2, -2, -6, 3, 0, 1, -14, -8, 0, -8],\n [6, -2, -4, 7, -2, 0, 6, -3, 8, -2, 5, 2],\n [-4, -6, 4, -3, -10, 1, -3, -3, 7, -10, -6, -6],\n [10, 10, 12, -8, 4, -14, 8, 7, 4, 1, -2, -8],\n [1, 4, -10, -4, -7, -8, -2, -10, 1, 5, 10, -8],\n [10, 4, 5, -15, 10, 0, 5, -6, -2, 10, -1, 2],\n [10, -7, -12, 2, -5, -8, 2, -6, -8, -8, 2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81690830663992", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-3, 10, -8, 12, 3, -2, -14, 6, -8, 13, 2, -14],\n [-14, -15, 10, 6, 15, 1, 10, -6, 2, 8, -10, 14],\n [-15, -12, -3, 1, -13, 7, -4, 4, 16, 3, -12, 7],\n [13, 11, -10, 13, -8, -5, 12, -7, 10, 2, -4, 15],\n [-2, 4, -14, -9, -11, 12, 2, 0, -7, 16, -4, 10],\n [-5, -15, -7, 4, 6, -16, 16, 9, -2, 5, 8, -16],\n [9, 4, 7, -1, 15, -1, -4, 15, 7, -4, -6, -2],\n [-7, -14, -1, 0, 8, 13, -4, 7, 9, -8, 2, 11],\n [-10, 5, 13, -1, -12, 12, 6, -11, 16, -1, 9, -4],\n [0, 15, 15, 11, 12, 8, 5, 10, 3, 7, -9, -3],\n [-3, -12, 4, -2, 16, 0, 3, -16, -1, 1, -7, 6],\n [1, -8, 13, -4, 14, -4, 15, 0, -14, -16, -12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86945422467591", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[8, -12, 6, -5, 6, -1, -12, 11, -11, -4, 13, 9],\n [0, -8, -1, 1, -4, 12, 7, -4, 8, -16, -8, -13],\n [11, -5, 7, -8, 16, 3, -15, 9, -4, 13, 15, 2],\n [5, -16, -6, 9, 2, 2, -5, -14, 1, -12, 7, -3],\n [-14, -11, -5, -6, 9, -16, -1, -8, -12, -9, 4, 16],\n [3, 5, -4, -6, 1, 13, 16, -14, -16, -11, 12, -6],\n [-4, -6, 8, -2, -4, 16, -4, 7, 3, 0, 7, 9],\n [15, 12, -3, 5, 10, 11, 5, -14, 5, 4, -1, -8],\n [-4, -7, 4, -10, 5, 1, 4, -3, -7, 16, -8, 1],\n [-4, 0, 6, 8, -1, 7, 14, -6, 6, 5, 16, 1],\n [-3, 11, -6, 7, 2, -4, 16, 2, 15, -2, -6, 6],\n [-12, 5, 1, -10, 16, -14, 11, -16, 5, 2, -3, -14]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "272020298643348", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[2, 16, 4, -16, 9, -7, -4, -11, -11, -1, -9, -14],\n [-12, 4, 14, -3, 2, 3, -15, -10, 16, -11, -10, 1],\n [12, 2, 8, -13, -4, 15, 10, 11, -8, -9, 4, 13],\n [12, -8, -4, 1, 5, 14, -7, -8, 14, 7, -9, 3],\n [0, 11, -11, 16, 11, -16, 7, -11, -10, -8, -1, 3],\n [6, 6, -13, -7, -6, -8, -5, 0, 15, 6, -2, 11],\n [-12, 1, 4, -2, -14, 9, -2, 3, 4, 9, 6, 8],\n [-13, -7, 5, -14, 2, 14, -8, 12, -10, 7, -9, 9],\n [11, 11, -10, -14, 5, 1, -5, 14, -12, 12, -3, 1],\n [-10, 6, 16, -1, 8, -8, 11, -8, -5, 1, 10, 9],\n [9, -7, 0, 15, 7, -9, 13, 9, 7, 10, -2, 11],\n [-6, -15, -8, 6, 16, 2, -4, -3, 15, 5, 3, 16]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2001553492755342", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-12, -5, -6, 10, 4, 6, 0, -2, -2, -4, 10, 0],\n [-5, -14, 10, -6, -10, 6, 5, 2, 4, 12, -1, 2],\n [-6, 10, 9, -6, -14, -14, 2, -4, 4, 4, -4, 4],\n [10, -6, -6, -4, -4, 7, -1, 8, 15, -14, 9, -14],\n [4, -10, -14, -4, 3, 13, 2, -10, 5, 2, -2, 1],\n [6, 6, -14, 7, 13, 1, -3, 7, -8, 2, -10, 16],\n [0, 5, 2, -1, 2, -3, 7, 8, -10, 5, 12, -8],\n [-2, 2, -4, 8, -10, 7, 8, -11, -5, 10, 2, -12],\n [-2, 4, 4, 15, 5, -8, -10, -5, 6, 10, 0, -10],\n [-4, 12, 4, -14, 2, 2, 5, 10, 10, -12, 8, 12],\n [10, -1, -4, 9, -2, -10, 12, 2, 0, 8, -15, 0],\n [0, 2, 4, -14, 1, 16, -8, -12, -10, 12, 0, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-270054650252", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 5) of the matrix A^8 where A is:\n[[0, 2, 2, -12, -12, -3, 10, 4, -12, 7, 7, -4],\n [-16, -7, -15, -1, -1, 6, 9, -1, 10, 13, 16, 15],\n [-8, -6, -11, 13, -2, 13, 1, -5, -13, -1, 6, -6],\n [7, 5, -2, -2, -7, 11, 0, 5, 6, 12, 5, -6],\n [12, 15, -3, 1, 6, 15, -14, 5, 6, -13, -4, 15],\n [12, -7, -4, 0, -15, 0, 9, -12, 8, -8, 11, 5],\n [12, 3, -12, 15, -7, 0, -2, -8, 15, 6, -6, -4],\n [1, -8, -12, 5, 15, -15, 4, 11, 7, 7, -3, 10],\n [7, -11, 9, -2, 12, -7, 11, -8, 4, -7, -13, -13],\n [-11, 9, -1, -9, 11, -1, -16, 2, 0, 11, -5, -11],\n [-10, -9, -14, 4, -9, 11, 13, 15, -6, 3, -1, 8],\n [-8, -14, -1, -5, -2, -13, 6, 10, -4, 4, 12, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54928875084", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 7) of the matrix A^9 where A is:\n[[-6, 10, -7, -6, -2, 6, 0, 6, -2, 10, -6, 8],\n [10, -13, -8, -7, -4, -5, -4, 3, 4, 8, -2, -3],\n [-7, -8, -1, -8, -4, 5, 6, 6, -5, -5, 4, 4],\n [-6, -7, -8, 2, -8, -2, 0, 4, 0, 1, -8, -10],\n [-2, -4, -4, -8, -5, -2, 9, 4, 10, 5, 6, 6],\n [6, -5, 5, -2, -2, -1, -4, -7, -5, -5, 6, -10],\n [0, -4, 6, 0, 9, -4, -9, 0, -10, 0, -12, 2],\n [6, 3, 6, 4, 4, -7, 0, 16, 8, -1, 13, 0],\n [-2, 4, -5, 0, 10, -5, -10, 8, 11, -9, -6, 0],\n [10, 8, -5, 1, 5, -5, 0, -1, -9, -2, 8, -8],\n [-6, -2, 4, -8, 6, 6, -12, 13, -6, 8, 3, -8],\n [8, -3, 4, -10, 6, -10, 2, 0, 0, -8, -8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10414134801210", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-10, 2, -8, 2, 4, -4, 4, 12, 5, -10, -12, 10],\n [2, -5, -6, -4, -6, -6, -12, -3, -3, 6, -9, -4],\n [-8, -6, 15, 6, -7, 2, 2, -6, -10, -8, 0, 2],\n [2, -4, 6, 15, 4, 6, -7, 2, -1, -2, -2, -10],\n [4, -6, -7, 4, 16, -2, -4, -2, 2, 2, 4, -2],\n [-4, -6, 2, 6, -2, 9, -2, 0, -8, -1, -7, 3],\n [4, -12, 2, -7, -4, -2, -16, 0, 14, 2, 4, -3],\n [12, -3, -6, 2, -2, 0, 0, 7, 7, 9, -8, 2],\n [5, -3, -10, -1, 2, -8, 14, 7, 10, 5, 0, 3],\n [-10, 6, -8, -2, 2, -1, 2, 9, 5, 14, 4, 9],\n [-12, -9, 0, -2, 4, -7, 4, -8, 0, 4, -13, -2],\n [10, -4, 2, -10, -2, 3, -3, 2, 3, 9, -2, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4296390796436410", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-4, -4, 4, 3, 0, 9, 14, 3, 7, 4, -5, 1],\n [-4, -4, -10, -2, 10, -7, 4, 0, -8, -8, -1, -8],\n [4, -10, 2, -7, 0, 0, 6, -6, 0, 6, -5, -4],\n [3, -2, -7, -4, -8, 8, -4, 4, 0, 5, 2, 10],\n [0, 10, 0, -8, 3, 4, 5, 0, 0, 4, 2, -2],\n [9, -7, 0, 8, 4, -5, -6, 10, -10, -2, 6, -2],\n [14, 4, 6, -4, 5, -6, -9, 8, -8, 6, 2, -8],\n [3, 0, -6, 4, 0, 10, 8, -7, -2, 5, -5, -2],\n [7, -8, 0, 0, 0, -10, -8, -2, 3, 2, 6, 6],\n [4, -8, 6, 5, 4, -2, 6, 5, 2, 1, 16, 2],\n [-5, -1, -5, 2, 2, 6, 2, -5, 6, 16, 11, -10],\n [1, -8, -4, 10, -2, -2, -8, -2, 6, 2, -10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2666849199613", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[12, 10, -3, -7, -6, -6, 2, 7, -16, -5, -3, -14],\n [15, -1, -7, 0, -13, -2, 16, -7, -10, 16, 0, -5],\n [0, -1, -3, -14, 13, 9, -5, 14, 0, -9, 2, 9],\n [-13, -2, -3, 13, 7, 2, -14, -13, -6, -4, 1, 2],\n [16, -14, -16, 8, -4, -13, -11, -6, -16, -9, -8, 4],\n [3, -16, 11, -10, -8, -16, 0, 15, -15, 8, 9, 9],\n [4, 1, 12, 7, 11, -5, -6, 10, 6, 16, -1, 11],\n [11, -11, 12, -14, -11, -4, -2, -11, 16, -5, -4, 16],\n [11, -12, 8, 0, 2, -11, 2, -16, -10, 2, 16, 9],\n [10, 9, 3, 7, 4, 9, 3, -11, -14, -7, -5, 16],\n [5, -1, 0, -7, -5, 2, 6, -7, -7, -7, 13, -13],\n [-16, 2, -12, 13, 9, -15, 7, -3, -4, 12, -16, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2000455396182", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (8, 5) of the matrix A^7 where A is:\n[[11, 2, -16, -4, -12, 16, -3, -1, 15, 10, -14, -13],\n [-10, -4, -14, 0, -7, -16, 11, -7, -10, -14, -10, -8],\n [9, -12, -4, 13, -7, 6, -6, -5, -4, -1, -8, -7],\n [12, -8, 16, 7, -6, -4, 6, 8, -1, 4, -7, 2],\n [11, -15, 13, -12, -2, -14, 7, -5, -9, -3, 1, 3],\n [6, -12, -16, -15, -1, -12, 5, -16, -5, 2, 5, 0],\n [-4, 11, -14, -12, -2, 0, 12, -13, 15, -13, -4, 3],\n [1, -5, 8, 13, -2, -9, 11, 5, -1, -12, -6, -15],\n [8, 8, -16, 14, -12, -13, -12, -12, -1, 1, 0, 1],\n [-13, 14, 14, -8, 14, -12, -1, -1, 3, 13, 9, 14],\n [-2, 3, 6, 8, 5, -9, -8, -2, 3, -14, -8, 13],\n [9, -5, 7, 2, -1, 9, 6, 16, 13, 6, -7, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7838758766", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[5, -15, 6, 15, -5, -14, 7, 0, -16, -9, -2, 8],\n [-9, 15, -4, -2, -11, 16, -10, 16, 12, 15, -14, 3],\n [-3, 11, -13, -2, 0, 7, -9, -14, 13, 5, 16, 8],\n [13, -14, -13, 12, 15, 6, 2, -2, -1, 6, -16, 2],\n [13, 0, 9, -4, 5, 6, 16, 10, -5, -8, -3, -14],\n [4, -10, 16, -6, 15, 5, 2, -6, -4, 11, -2, -4],\n [16, -9, 15, -13, 1, 6, 12, -15, -4, -1, -9, 2],\n [15, -14, 15, 4, 8, 0, 8, 16, 14, 6, 8, 13],\n [-4, 12, -1, 10, 9, -6, -14, 9, 16, -2, -15, 11],\n [3, -1, -13, -9, 3, 9, 15, -4, -12, -4, -6, 15],\n [1, 12, -2, 3, -12, 16, 1, 2, 15, 5, -16, 8],\n [3, -11, -11, -14, 14, -2, 0, -2, -12, 5, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2851084220174", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, -1, 4, 10, -12, 8, -2, -4, 2, -4, 0, -4],\n [-1, 6, 2, -7, 6, -6, -11, -7, 2, -12, 2, -8],\n [4, 2, 11, -10, -1, 2, -4, -2, -12, -9, -3, -6],\n [10, -7, -10, -9, -2, -11, 8, -14, 5, 0, -8, 8],\n [-12, 6, -1, -2, -3, -7, 2, -3, 14, 2, 8, -4],\n [8, -6, 2, -11, -7, -7, -6, 0, 2, 2, 4, -1],\n [-2, -11, -4, 8, 2, -6, -7, 2, -1, 6, -6, -16],\n [-4, -7, -2, -14, -3, 0, 2, -1, -2, 8, 5, 4],\n [2, 2, -12, 5, 14, 2, -1, -2, 12, 6, 5, -6],\n [-4, -12, -9, 0, 2, 2, 6, 8, 6, 14, 0, 10],\n [0, 2, -3, -8, 8, 4, -6, 5, 5, 0, 12, -4],\n [-4, -8, -6, 8, -4, -1, -16, 4, -6, 10, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2137977941813", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-5, -13, 8, -9, -2, 13, 15, 4, 14, 10, -9, 6],\n [6, 16, -4, -1, -5, 14, -12, 8, 4, -14, -7, 6],\n [0, 8, -15, 10, -8, -13, 9, 15, 12, 5, -4, 6],\n [14, 14, -2, -3, 7, 13, 13, 10, -3, -6, 9, 4],\n [-8, -16, -11, -16, 5, -4, 14, -2, -15, 14, 9, -15],\n [-6, 16, 1, 4, 14, 9, 13, 4, -1, -10, 5, -10],\n [-15, -3, -9, 12, -10, 5, 0, -1, 16, 15, -14, -14],\n [-9, 14, -8, -12, 11, -2, 10, 14, 1, -13, 4, 6],\n [5, -16, 8, 11, -6, 5, 8, 4, 3, -1, 11, 12],\n [9, -15, -7, -4, -2, -8, 10, -9, -11, 7, -14, 9],\n [4, -4, -6, -9, -3, 16, -15, -16, -6, -11, 15, -2],\n [-5, 12, 5, -3, 2, -12, 8, -8, -10, 1, -15, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1506127458620", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-15, -2, 2, -1, -8, -6, 3, -1, 6, 2, 11, -12],\n [-2, 15, -12, 8, -2, 4, 2, 3, -15, -14, 1, -4],\n [2, -12, 1, -8, -13, 5, 2, 0, 2, 10, 0, -4],\n [-1, 8, -8, -13, -11, 6, -12, 0, 0, -10, -10, 0],\n [-8, -2, -13, -11, 4, 10, -6, 6, -2, -7, -8, 0],\n [-6, 4, 5, 6, 10, 2, -4, 14, -8, -10, 7, -4],\n [3, 2, 2, -12, -6, -4, -6, 6, 0, 3, 2, -13],\n [-1, 3, 0, 0, 6, 14, 6, 12, -4, 10, 2, -8],\n [6, -15, 2, 0, -2, -8, 0, -4, -1, -3, 3, -6],\n [2, -14, 10, -10, -7, -10, 3, 10, -3, -14, 6, -3],\n [11, 1, 0, -10, -8, 7, 2, 2, 3, 6, -9, -6],\n [-12, -4, -4, 0, 0, -4, -13, -8, -6, -3, -6, 9]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-730314620407927", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-1, 5, 6, -14, -14, -5, 6, -6, 12, -11, -1, -6],\n [-6, 8, 2, 15, -9, -5, -11, 4, 9, -16, 0, 10],\n [-15, -16, -7, 14, -12, -4, 7, 10, -16, 3, -9, -14],\n [15, 8, 8, -3, 10, 15, 10, -13, -6, -14, 8, 7],\n [-8, -9, 14, 0, 14, -13, -13, -9, -11, -8, -9, 15],\n [-2, 1, 6, -12, 10, 16, -15, 11, 7, 4, 14, -6],\n [11, -13, -1, -5, 5, -1, 7, 11, 12, 4, 8, 14],\n [-2, 5, -12, -4, 15, -14, -2, 10, 10, 13, -11, 8],\n [11, 5, -13, -2, 9, 1, -8, -13, -12, -11, -5, 14],\n [-8, -10, 12, -3, 3, 15, 5, 1, 8, 14, 9, -13],\n [3, -5, -1, -12, 10, -16, 15, 16, 14, -4, -15, 13],\n [-7, 6, 16, 12, 13, 0, 5, -12, -6, 5, 15, 7]], determine the value at position (5, 8).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32448283793", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-6, -3, -6, 12, -2, -2, 10, 5, 10, 5, -1, -4],\n [-3, -16, 6, 9, 5, 1, -4, 4, -6, 0, -10, 6],\n [-6, 6, -1, -8, 10, 0, 4, 12, -4, 2, -9, 14],\n [12, 9, -8, 1, -12, -1, 6, -2, 0, 2, 0, -1],\n [-2, 5, 10, -12, -8, -4, -14, 8, -5, -4, 2, -4],\n [-2, 1, 0, -1, -4, -9, -4, -12, -4, 4, 12, -6],\n [10, -4, 4, 6, -14, -4, -2, 10, 3, -6, -7, 4],\n [5, 4, 12, -2, 8, -12, 10, -7, 8, 4, 0, -2],\n [10, -6, -4, 0, -5, -4, 3, 8, -13, 8, -6, -10],\n [5, 0, 2, 2, -4, 4, -6, 4, 8, 6, 12, -3],\n [-1, -10, -9, 0, 2, 12, -7, 0, -6, 12, 0, -6],\n [-4, 6, 14, -1, -4, -6, 4, -2, -10, -3, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3099190025850", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-9, 0, 0, -12, 4, -6, -10, 1, -6, 7, 14, 5],\n [0, -6, -14, 2, -7, 14, 2, -8, 4, -4, -1, 10],\n [0, -14, 6, -2, 4, -8, 9, -1, 15, -8, 13, 2],\n [-12, 2, -2, 16, 1, -4, -8, -8, 4, 4, -5, 6],\n [4, -7, 4, 1, -8, 2, -12, -2, 7, 9, -2, 2],\n [-6, 14, -8, -4, 2, 7, -10, 2, 4, -4, 2, 8],\n [-10, 2, 9, -8, -12, -10, 4, 4, -5, -2, 0, 6],\n [1, -8, -1, -8, -2, 2, 4, -5, -4, 4, 4, 12],\n [-6, 4, 15, 4, 7, 4, -5, -4, 8, -4, 2, -12],\n [7, -4, -8, 4, 9, -4, -2, 4, -4, -5, -4, -4],\n [14, -1, 13, -5, -2, 2, 0, 4, 2, -4, 13, 8],\n [5, 10, 2, 6, 2, 8, 6, 12, -12, -4, 8, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5939392065646", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[11, 7, -2, 0, -4, -10, -6, 2, -3, 1, -4, 2],\n [7, 16, -4, 4, -8, 2, 2, 8, -1, -2, 7, -6],\n [-2, -4, 0, 0, 0, -10, -2, 1, -4, 10, -4, -8],\n [0, 4, 0, -7, 0, 4, -9, 0, 8, 2, 4, 14],\n [-4, -8, 0, 0, 4, 2, 10, 10, 10, -1, 2, -6],\n [-10, 2, -10, 4, 2, 5, 1, 2, 13, 5, -12, 12],\n [-6, 2, -2, -9, 10, 1, 12, 10, 1, 4, 10, 0],\n [2, 8, 1, 0, 10, 2, 10, 1, 0, 14, -7, 4],\n [-3, -1, -4, 8, 10, 13, 1, 0, 12, -3, -3, -1],\n [1, -2, 10, 2, -1, 5, 4, 14, -3, -2, 6, 2],\n [-4, 7, -4, 4, 2, -12, 10, -7, -3, 6, 9, 2],\n [2, -6, -8, 14, -6, 12, 0, 4, -1, 2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11404353976003", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 7th power of the matrix:\n[[-11, 9, -3, -9, 7, 5, 4, 9, -7, -4, -3, -8],\n [-10, 14, -1, -9, -2, 8, -2, 8, -10, 9, -9, 1],\n [4, -1, -14, -16, -4, 15, -5, 14, -15, -9, 8, -12],\n [-15, -14, 5, 16, 15, 0, 1, -14, -11, -4, 14, 0],\n [4, -1, 0, 15, -16, -9, -16, -15, 7, 10, 3, 4],\n [-2, 13, -13, -2, 6, -2, 9, -5, 1, -11, 1, 7],\n [11, -2, 2, -12, -13, 0, -7, -5, -12, -10, 6, -15],\n [13, -12, 3, 9, -11, 12, -7, -1, 14, -12, 16, 2],\n [15, 6, -14, -16, 11, -12, -4, -6, 5, 6, -5, 4],\n [2, -12, 7, 13, -9, -15, 6, -14, 7, 1, 14, -3],\n [-16, -3, -12, 14, 14, 13, -16, -14, 3, 4, 13, 13],\n [-12, -7, 7, -11, -7, -7, 8, -3, -4, -6, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31336332066", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[16, 15, -7, -2, -1, 10, 15, -11, -9, 8, -10, 0],\n [13, -15, 0, -13, 9, -3, -9, -12, -12, -12, 10, -12],\n [-14, 13, -16, -9, -4, 3, -11, -9, 13, -2, -7, 16],\n [-8, 16, -8, -3, 15, -11, -12, -13, -1, -7, 14, 14],\n [-3, -4, -13, 9, 7, -8, -2, 7, 14, 2, -15, -15],\n [2, 6, -1, -11, 9, 5, 7, 4, 13, -6, -8, -5],\n [9, -14, 16, -2, -12, 7, -6, 16, 6, -7, 11, 0],\n [9, 8, -5, -14, 12, 7, 2, -4, -1, 10, -11, -7],\n [-9, 1, 15, 0, -15, 3, -7, -8, 8, 8, 7, -11],\n [13, -7, 14, 1, 16, 2, 6, -12, 9, 12, 7, -11],\n [-13, 9, -2, -4, 5, -4, 0, 8, 4, 8, 8, 5],\n [6, 8, -3, -3, 9, 13, 9, 5, 8, -4, 12, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4650655412718799", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-2, 15, -3, 3, -10, -8, 6, -6, 2, -6, 10, 9],\n [15, -13, 2, 12, 4, -3, -3, 4, 6, -14, 10, -1],\n [-3, 2, 9, 1, 4, -2, 2, 0, -4, 6, -8, -2],\n [3, 12, 1, 2, 4, -4, 5, 0, 4, 2, -6, -8],\n [-10, 4, 4, 4, 9, 8, 4, 6, 4, 1, 0, 1],\n [-8, -3, -2, -4, 8, 8, -11, -16, 1, 6, -4, 10],\n [6, -3, 2, 5, 4, -11, -6, -2, 0, 6, 4, 5],\n [-6, 4, 0, 0, 6, -16, -2, 14, -2, 0, 14, -5],\n [2, 6, -4, 4, 4, 1, 0, -2, -8, 2, 9, 8],\n [-6, -14, 6, 2, 1, 6, 6, 0, 2, 11, 0, 14],\n [10, 10, -8, -6, 0, -4, 4, 14, 9, 0, 3, -5],\n [9, -1, -2, -8, 1, 10, 5, -5, 8, 14, -5, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160998135184211", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (10, 1) of the result:\nA =\n[[-14, -9, -10, -2, 0, 4, -2, 8, -2, 6, 0, -4],\n [-9, 11, 6, -3, 6, 5, 6, -6, -4, -2, -3, -3],\n [-10, 6, 8, 10, 13, -8, 1, 10, -1, -3, 0, 5],\n [-2, -3, 10, 14, 6, -8, 8, -6, -6, 12, 2, -1],\n [0, 6, 13, 6, -6, 0, -7, 10, 3, 12, -9, 4],\n [4, 5, -8, -8, 0, -9, 13, 1, 0, -12, 0, 3],\n [-2, 6, 1, 8, -7, 13, 8, -12, 8, 5, 1, -6],\n [8, -6, 10, -6, 10, 1, -12, -13, 8, -3, 10, -4],\n [-2, -4, -1, -6, 3, 0, 8, 8, 14, -1, -4, 6],\n [6, -2, -3, 12, 12, -12, 5, -3, -1, 4, -2, -6],\n [0, -3, 0, 2, -9, 0, 1, 10, -4, -2, 11, 0],\n [-4, -3, 5, -1, 4, 3, -6, -4, 6, -6, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-283436415649", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[6, 7, 12, -12, -16, 1, -11, 6, -7, -10, -9, -4],\n [13, 1, -3, -6, -4, 16, -4, 8, 7, 12, -11, 1],\n [11, -12, 1, -10, -8, -5, 7, -8, -5, -8, 5, 0],\n [16, 7, -2, 12, 15, 16, 12, -2, 10, -13, 1, 4],\n [-9, -11, 3, -15, 5, 4, -11, 15, -11, -4, -16, 5],\n [7, 13, 5, -5, 9, -13, 2, -1, -5, 16, 4, -8],\n [-9, 3, -7, 15, 11, -7, -9, 16, -4, 12, -12, -14],\n [-11, -1, 1, -6, 6, -6, 12, 10, -8, -8, 1, 4],\n [-16, 10, 12, 2, 7, -16, 6, -4, 13, -6, -10, -6],\n [4, -14, 13, 7, -14, 16, 5, 14, -5, -3, -5, 10],\n [-4, 7, -8, -9, -2, -10, 7, -1, 7, -10, 11, -15],\n [-14, -16, 14, 6, 3, -1, 15, 0, 1, -13, 6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-59278851823320", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-4, -3, -3, -12, 5, 11, -13, 12, 3, 3, -15, 1],\n [13, 12, 5, 12, -7, 3, -1, -11, 0, -11, 5, 1],\n [15, 11, -7, 5, 11, -2, 12, -10, 15, -15, 9, -6],\n [8, 2, 3, 16, 0, 13, 1, 15, -13, 15, 2, -14],\n [11, -11, 0, -12, 2, 5, 7, -7, -15, 11, 0, -11],\n [-12, -10, 15, -13, 4, 15, 1, 16, -3, -11, -6, 3],\n [12, -1, -10, 14, -11, 12, 10, -15, 5, -8, -6, -1],\n [-4, 1, 8, 16, -7, 13, -16, 16, -2, 12, -15, -6],\n [2, -15, 3, 14, -13, 12, 13, -4, -2, 3, 11, 3],\n [8, 10, 13, 3, -16, 7, 8, -5, -6, 13, -4, 8],\n [8, 0, -5, -6, -7, 0, -1, 3, -12, 15, 10, -13],\n [-10, -3, 7, 1, -16, 0, 9, 5, 1, 11, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-100344163429", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[13, -9, 13, -8, 16, 12, 14, -14, -6, -12, 14, 3],\n [-13, -9, -4, -12, 2, 1, 16, -13, 1, 7, 12, 14],\n [11, -8, 9, -15, -11, 12, 9, 11, -10, -7, 5, 10],\n [5, 2, -8, 2, -15, 11, 5, -11, -10, -11, 16, -3],\n [-16, 8, -11, 11, 1, 10, -15, 4, 6, -15, -1, -13],\n [-12, 5, 3, -4, -11, 12, 16, -16, -10, 5, 15, -3],\n [7, 2, 10, 6, 4, 12, -16, 14, 10, 10, -2, 8],\n [-2, 2, -6, 16, 6, -5, -15, 4, -3, -2, 4, 6],\n [4, -3, 4, -5, -12, -15, 5, -11, -15, 12, -10, -1],\n [16, 16, -3, -5, -11, -5, 14, -5, -7, 10, -10, 16],\n [10, -9, -12, -9, 4, 7, -10, 2, 14, 10, 12, 6],\n [3, -11, -5, -5, -14, 2, -13, 14, 16, -11, -9, 11]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13088712917", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (8, 5) of the result:\nA =\n[[-2, 13, 3, 2, 10, -8, -10, 0, 4, 4, -8, -12],\n [13, -6, 2, 13, 6, 4, -5, -2, -14, 10, 0, 4],\n [3, 2, 9, -14, 4, -2, 12, 2, 10, 0, -9, 4],\n [2, 13, -14, -4, -2, -9, -4, 11, 1, -2, 3, -4],\n [10, 6, 4, -2, -14, -4, 6, -5, 2, 2, 0, -7],\n [-8, 4, -2, -9, -4, -14, -7, 8, -8, 6, 3, 8],\n [-10, -5, 12, -4, 6, -7, 9, 11, -8, -9, 0, 4],\n [0, -2, 2, 11, -5, 8, 11, 5, 2, 8, 3, 11],\n [4, -14, 10, 1, 2, -8, -8, 2, 0, 7, -6, -4],\n [4, 10, 0, -2, 2, 6, -9, 8, 7, 16, -2, 10],\n [-8, 0, -9, 3, 0, 3, 0, 3, -6, -2, 7, -2],\n [-12, 4, 4, -4, -7, 8, 4, 11, -4, 10, -2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15958490997964", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[3, 11, -10, -13, 11, 16, -10, -8, -4, 12, -7, 13],\n [9, 11, 12, -11, -14, 12, -15, 5, 10, 5, -7, 2],\n [7, 10, 0, -7, 0, -7, -7, 0, 9, 9, -13, 10],\n [4, 14, -10, 1, 7, -4, -4, 8, -12, 12, 16, 7],\n [-7, 8, -7, -1, 11, -5, 15, 12, 10, 9, -14, 9],\n [-16, 10, -13, 2, 5, -11, -8, -6, 5, -8, 12, -7],\n [14, 5, -13, -15, -12, -2, 2, -2, -9, 3, -5, -13],\n [-2, -16, 14, -8, 6, 9, 1, 16, -3, -16, -4, -2],\n [-12, -3, -3, -12, -6, 15, -12, -2, -10, -12, 13, -2],\n [13, -3, 7, 7, -12, -5, 3, -12, 4, -14, 12, 8],\n [10, 5, -16, -14, 7, -9, 1, -14, 1, -1, 15, -16],\n [9, -5, 4, -4, -5, -4, 1, 2, 2, -11, -10, -10]], determine the value at position (5, 12).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97064268810", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[11, 11, 2, -1, 0, 5, 2, 12, 2, 8, 3, 2],\n [-4, -5, -2, -13, -2, 0, 10, -6, 6, -2, 14, 9],\n [-10, -4, -4, 3, -7, 10, -1, 4, -1, 0, -2, -4],\n [16, -12, 10, -16, 13, 6, -2, 2, 13, -1, 1, 9],\n [0, -6, 12, -8, 0, 10, 5, -9, -14, 15, -9, 10],\n [15, 8, 14, -4, -2, -4, 16, 14, 8, 6, -14, -1],\n [-15, 6, 13, -7, -16, 5, 16, 8, 5, -1, 13, 1],\n [7, -12, 6, 10, -5, -7, 16, -1, 12, 1, 10, -10],\n [10, -7, -7, -6, 13, -14, 12, -3, -4, 2, 8, -7],\n [-2, 11, -10, -3, 13, -5, 11, -3, -16, -13, 1, 15],\n [11, 11, 15, -9, 8, 3, 16, 13, -1, 8, -7, -12],\n [-9, 16, -16, 14, -10, 6, 7, -3, 6, -8, -9, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99331499759052", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-14, 15, -13, -15, -8, -16, -6, 12, 9, 10, 12, 16],\n [11, 14, 2, 9, 12, -6, 15, 4, 5, 10, -9, 14],\n [-16, 7, 11, -13, 1, 12, 6, 10, -1, 10, -8, -12],\n [-9, 1, -11, 6, 9, 7, -7, -2, 3, 12, -11, -8],\n [-12, 2, -12, 3, -6, 10, 12, -10, -14, -12, -4, -1],\n [-5, 10, 16, -2, 4, 0, -2, 3, 2, -16, -13, -14],\n [-9, -12, -8, -16, 13, -10, 5, 3, 12, 10, 8, 10],\n [-6, 0, 14, 1, 2, 12, -2, -10, -10, 5, -5, -9],\n [1, 11, 1, 14, 0, 6, -6, -2, 13, 14, -11, -5],\n [6, -14, 11, -2, -4, 2, 1, 14, 4, -12, 0, 2],\n [-13, 9, 7, 2, 13, 9, -6, -14, 5, 0, -6, 10],\n [12, -5, -4, -6, 14, -6, -15, 6, -3, 10, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7948597111791", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-11, 6, -7, -5, 15, 9, -10, 15, 16, 1, 3, 14],\n [-12, 15, 2, -16, -10, 5, -7, 9, 15, 10, -5, 6],\n [-3, 0, -11, 10, -9, 16, 0, 9, -10, 7, 8, 9],\n [-12, 13, 8, 7, 13, 3, -14, 15, -9, 6, -1, 8],\n [-2, -9, 8, 2, -4, -5, -2, 6, -15, 6, -12, -7],\n [10, -13, -13, -9, -11, 8, 10, 3, 10, -10, 6, 3],\n [12, -12, 10, -5, 0, 13, -11, 15, 15, -8, 5, -7],\n [12, -6, 11, -15, 4, 14, 0, 10, 13, -9, -12, 9],\n [-11, -1, -16, -8, 4, -10, -2, 7, -12, 12, -6, -13],\n [-7, -13, -7, 16, 1, -5, 6, 8, -13, -4, 1, 12],\n [13, 11, -10, 7, -7, 10, 4, 12, -10, -4, 6, 8],\n [-4, 13, 9, -5, -16, 1, 4, 7, 0, -8, 11, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8535832606082", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-4, 11, 0, -8, 4, 13, -6, 13, 8, -10, 3, -7],\n [-16, -3, -12, 7, -13, 10, -12, -4, 4, 15, 14, 15],\n [-2, 13, -10, 14, 9, 9, -15, -8, -12, 10, -5, 12],\n [-1, 2, 10, 1, -4, 13, 9, -11, -14, 6, -5, -2],\n [-16, -9, 14, -6, 0, 10, 14, 10, -3, 6, -12, 13],\n [2, 14, -1, 10, 9, 12, 12, 14, -15, -11, -8, -2],\n [3, -15, -14, 13, -9, 4, -4, 15, -3, -16, 10, 7],\n [5, -3, -9, 10, -14, 16, 4, 15, 15, 7, -6, 4],\n [1, -6, 10, -16, 12, 4, 12, -8, -10, 14, 10, 15],\n [-12, 16, -2, -12, 3, 0, -13, 4, -12, -13, 5, -3],\n [-13, -9, -14, 12, 9, 13, -5, -2, -15, -16, 11, -13],\n [1, -5, 4, -7, 4, 8, 0, -11, -3, 1, 13, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1248239266966", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-3, 6, 2, 8, -2, -4, -1, -3, 3, -6, -9, 8],\n [6, -2, 4, -4, -12, 9, -6, -14, -16, -4, -10, 3],\n [2, 4, -11, 0, -7, 0, 2, -10, -6, -2, 8, 0],\n [8, -4, 0, 16, -2, 2, 1, 2, -4, 8, -4, -4],\n [-2, -12, -7, -2, 2, -2, -8, -4, -2, -3, 8, 2],\n [-4, 9, 0, 2, -2, 4, 0, 2, 2, 4, -6, 5],\n [-1, -6, 2, 1, -8, 0, -10, -10, 10, 10, 5, -6],\n [-3, -14, -10, 2, -4, 2, -10, -4, -6, 8, -4, -5],\n [3, -16, -6, -4, -2, 2, 10, -6, 16, 2, -1, 12],\n [-6, -4, -2, 8, -3, 4, 10, 8, 2, 11, 4, -6],\n [-9, -10, 8, -4, 8, -6, 5, -4, -1, 4, -7, -4],\n [8, 3, 0, -4, 2, 5, -6, -5, 12, -6, -4, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882223988228", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[15, -2, -6, -9, 1, 9, 0, -8, 6, 3, 4, 10],\n [-2, 12, 2, -4, 0, -10, 4, -2, 10, -7, -8, 2],\n [-6, 2, -2, 12, -14, -2, -6, 8, 10, 3, -3, 14],\n [-9, -4, 12, 1, 0, 2, -9, -3, 0, 0, 12, -8],\n [1, 0, -14, 0, 3, -4, 10, -1, -10, 11, 0, 4],\n [9, -10, -2, 2, -4, 5, -16, 10, 12, 8, -10, -12],\n [0, 4, -6, -9, 10, -16, 1, -8, 1, 6, -1, 5],\n [-8, -2, 8, -3, -1, 10, -8, 6, 10, 6, -6, 1],\n [6, 10, 10, 0, -10, 12, 1, 10, 7, -1, -1, -6],\n [3, -7, 3, 0, 11, 8, 6, 6, -1, -7, 4, 5],\n [4, -8, -3, 12, 0, -10, -1, -6, -1, 4, -9, 4],\n [10, 2, 14, -8, 4, -12, 5, 1, -6, 5, 4, 11]], determine the value at position (9, 8).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3350272945852", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[8, 2, -13, 15, 8, 5, 11, 1, -10, -6, -6, -8],\n [6, 16, -16, 3, -12, 12, 9, -14, 4, -4, 14, 0],\n [6, -14, -15, -14, 3, -8, -13, 8, -16, -5, 7, -8],\n [3, -12, 3, 4, -15, 4, 7, -8, 13, 1, -7, 4],\n [5, 0, -12, -11, -7, -15, -10, -13, 2, 11, 3, 13],\n [-15, -14, 8, -15, -2, -14, -12, 10, -12, 0, -5, 14],\n [16, 12, -14, 13, 5, 15, -7, 15, -13, 12, -9, 3],\n [-10, -16, 8, 9, -8, 6, -15, 9, -3, 14, 9, 2],\n [-12, -11, -1, 14, 1, -3, 8, -2, 9, -6, -10, 1],\n [3, -15, 9, 6, 15, -4, -4, 0, 8, 5, 10, 0],\n [9, -3, -3, -5, -12, -13, 12, 8, -13, -1, -15, 6],\n [-13, 3, 0, -11, 1, 3, 7, 1, 13, -16, 6, 12]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13916906897506", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[15, -6, 1, -12, -12, -4, -3, -2, 4, -14, -10, 0],\n [-6, 11, -12, -1, 4, 4, 2, 0, 1, 2, 11, -3],\n [1, -12, -16, 2, 2, -6, 8, 6, 7, 0, 2, -3],\n [-12, -1, 2, -16, 0, -6, 6, -8, -1, 8, 5, 0],\n [-12, 4, 2, 0, -13, -4, 0, 0, -2, -6, -10, 0],\n [-4, 4, -6, -6, -4, -1, -8, -6, 12, 6, 4, 14],\n [-3, 2, 8, 6, 0, -8, 4, 5, 10, 6, 0, -14],\n [-2, 0, 6, -8, 0, -6, 5, -14, -6, 0, 10, -2],\n [4, 1, 7, -1, -2, 12, 10, -6, 2, -8, 8, 2],\n [-14, 2, 0, 8, -6, 6, 6, 0, -8, 8, -1, 14],\n [-10, 11, 2, 5, -10, 4, 0, 10, 8, -1, -16, -12],\n [0, -3, -3, 0, 0, 14, -14, -2, 2, 14, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3409797494309203", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (10, 10) of the result:\nA =\n[[7, 9, 9, 0, 10, 12, -8, -3, -12, 13, 11, -9],\n [-2, 11, 16, -11, -5, -10, 11, -10, -16, 7, 2, 15],\n [13, -16, 15, 3, 4, 2, 13, 11, 15, 13, 6, 10],\n [9, -14, 14, -15, -7, 2, 14, 12, 8, 15, 0, 6],\n [1, -6, 3, -4, 7, 3, 11, 4, -11, -10, 12, 6],\n [-12, 5, -8, 15, -7, 11, -6, -10, 13, 11, 15, -1],\n [-16, 6, 3, 1, 1, 4, -9, -6, -7, -9, -9, 2],\n [-16, -14, 15, -1, 13, 11, 11, -1, 16, 8, 1, 9],\n [-11, -14, -11, -3, 1, -1, 7, -4, -16, -3, 0, -4],\n [-4, -8, -11, -11, 13, -3, -13, -15, 0, -3, 0, 13],\n [12, -10, -8, 6, -3, 3, 0, 15, 8, 13, 10, 10],\n [14, 9, -3, 4, 11, -2, 13, 8, -6, -6, 11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15600261266", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[11, -10, -2, -4, 4, 15, 6, -3, -7, 2, -4, -14],\n [-10, -4, 2, 2, 0, 8, 12, -8, -7, 2, 2, -1],\n [-2, 2, -2, -10, -6, 0, 14, 11, -4, 8, 6, -2],\n [-4, 2, -10, -4, -4, -4, -2, 4, 8, 12, 0, -3],\n [4, 0, -6, -4, -9, 4, 4, -2, 8, -1, 8, -2],\n [15, 8, 0, -4, 4, 11, -2, -9, -7, -6, 4, 3],\n [6, 12, 14, -2, 4, -2, 12, -2, 0, -7, -7, 10],\n [-3, -8, 11, 4, -2, -9, -2, -2, -6, -4, 1, 1],\n [-7, -7, -4, 8, 8, -7, 0, -6, 13, -9, 5, -10],\n [2, 2, 8, 12, -1, -6, -7, -4, -9, -16, 4, -1],\n [-4, 2, 6, 0, 8, 4, -7, 1, 5, 4, 3, 3],\n [-14, -1, -2, -3, -2, 3, 10, 1, -10, -1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42464539097246", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 5) of the 9th power of the matrix:\n[[-3, -14, 6, -3, -5, -6, -11, 3, -2, 12, 4, -13],\n [-14, -10, 8, -6, 2, -4, 16, -4, 4, 2, 3, 4],\n [6, 8, -10, 4, -2, 3, -4, 0, -6, 10, 0, -12],\n [-3, -6, 4, 14, 3, -4, 2, -8, 8, 7, -1, -5],\n [-5, 2, -2, 3, 5, 4, 7, -2, -8, -8, 7, 2],\n [-6, -4, 3, -4, 4, -14, 4, -4, 6, -11, 6, 4],\n [-11, 16, -4, 2, 7, 4, 15, -1, -9, -14, -3, 0],\n [3, -4, 0, -8, -2, -4, -1, -6, 6, 0, -1, 0],\n [-2, 4, -6, 8, -8, 6, -9, 6, -5, -6, 4, -8],\n [12, 2, 10, 7, -8, -11, -14, 0, -6, -14, 4, 4],\n [4, 3, 0, -1, 7, 6, -3, -1, 4, 4, -13, -2],\n [-13, 4, -12, -5, 2, 4, 0, 0, -8, 4, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10369173390789", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-16, -4, 2, -6, -6, -1, -8, -12, -10, -9, -8, 3],\n [-4, 16, 0, -4, 0, -6, -12, -3, -8, 4, 12, -1],\n [2, 0, -15, 8, 7, -10, -3, -5, 14, 10, 4, -12],\n [-6, -4, 8, -7, 0, 3, 4, -6, -6, 10, -2, 10],\n [-6, 0, 7, 0, 11, 3, -8, 12, -10, 5, -10, -2],\n [-1, -6, -10, 3, 3, -10, 10, 5, 7, 11, -4, 4],\n [-8, -12, -3, 4, -8, 10, 16, 4, -6, 8, 7, -3],\n [-12, -3, -5, -6, 12, 5, 4, 1, -6, 8, 0, -6],\n [-10, -8, 14, -6, -10, 7, -6, -6, 12, 2, 0, 9],\n [-9, 4, 10, 10, 5, 11, 8, 8, 2, -11, -6, 6],\n [-8, 12, 4, -2, -10, -4, 7, 0, 0, -6, -10, 6],\n [3, -1, -12, 10, -2, 4, -3, -6, 9, 6, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14103705331937039", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[0, -2, 4, -6, 12, -6, 10, 0, 0, -2, 10, -4],\n [-2, 9, -4, -14, -2, 6, -2, -8, 0, -10, 2, -2],\n [4, -4, 9, 8, -10, -1, 8, -2, 2, -14, -6, 5],\n [-6, -14, 8, 12, -4, -6, -7, 4, -7, -4, 0, 0],\n [12, -2, -10, -4, -2, 4, 8, 4, -8, 2, -7, 8],\n [-6, 6, -1, -6, 4, -13, 3, 3, 10, -4, 14, -10],\n [10, -2, 8, -7, 8, 3, 11, 6, 8, 8, -10, 0],\n [0, -8, -2, 4, 4, 3, 6, 15, -2, -2, 0, -5],\n [0, 0, 2, -7, -8, 10, 8, -2, 4, 6, 2, -8],\n [-2, -10, -14, -4, 2, -4, 8, -2, 6, 6, -2, 6],\n [10, 2, -6, 0, -7, 14, -10, 0, 2, -2, 7, -8],\n [-4, -2, 5, 0, 8, -10, 0, -5, -8, 6, -8, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50506246529243", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-5, -4, -2, 12, -4, 4, -6, -2, 8, 8, -2, -7],\n [-4, -3, 2, -4, 12, -6, 4, 0, 2, -4, 8, -4],\n [-2, 2, -14, 2, 6, 3, -9, -4, 2, 4, -3, -10],\n [12, -4, 2, -11, -2, -4, 10, 2, 4, 8, 2, -13],\n [-4, 12, 6, -2, -15, 4, 10, -6, 0, -11, -3, 2],\n [4, -6, 3, -4, 4, 13, -1, 0, 0, 2, -5, -7],\n [-6, 4, -9, 10, 10, -1, -12, 4, 13, 10, 8, 4],\n [-2, 0, -4, 2, -6, 0, 4, 1, -7, -1, -6, 2],\n [8, 2, 2, 4, 0, 0, 13, -7, -15, 0, 4, 13],\n [8, -4, 4, 8, -11, 2, 10, -1, 0, 2, 2, -5],\n [-2, 8, -3, 2, -3, -5, 8, -6, 4, 2, -16, -3],\n [-7, -4, -10, -13, 2, -7, 4, 2, 13, -5, -3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22325804705200", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-11, 8, 5, -6, 5, 12, 1, 0, 2, 5, 2, 12],\n [8, 14, -2, -10, 0, 10, 0, -4, -8, 4, 4, 10],\n [5, -2, 0, -10, 2, -12, 0, 12, -8, -5, -1, 0],\n [-6, -10, -10, -6, -4, -4, 3, -8, -2, -12, 8, 4],\n [5, 0, 2, -4, -7, 6, 0, 4, 8, 1, 0, 4],\n [12, 10, -12, -4, 6, 5, -6, -9, -8, 5, 5, 12],\n [1, 0, 0, 3, 0, -6, 7, 2, -4, 14, 8, 6],\n [0, -4, 12, -8, 4, -9, 2, 4, -6, -2, -1, 8],\n [2, -8, -8, -2, 8, -8, -4, -6, 10, 2, 4, 9],\n [5, 4, -5, -12, 1, 5, 14, -2, 2, 11, 16, 1],\n [2, 4, -1, 8, 0, 5, 8, -1, 4, 16, 16, -2],\n [12, 10, 0, 4, 4, 12, 6, 8, 9, 1, -2, -2]], determine the value at position (8, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-329889886481", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[-7, 5, 6, -6, -1, -1, -3, -11, 0, 14, -7, 3],\n [-8, -2, -15, -13, 7, 1, -6, 9, -9, 5, -12, -15],\n [-12, 15, 2, -13, 6, 2, 9, 9, -10, 15, 16, 9],\n [7, 6, 9, 14, -11, 14, -5, 0, 9, -14, -2, 7],\n [13, 10, 5, -15, -10, -1, 7, 13, -16, 10, -8, -10],\n [-12, 13, 10, -7, 8, 1, -10, 14, 15, -6, -7, 5],\n [14, -3, -14, 7, -3, -1, 11, -15, 1, -10, -10, -13],\n [-1, -11, 3, 14, 2, 5, 4, 1, 15, 10, 13, 16],\n [10, 6, 2, 14, -13, 2, 5, -8, 14, -7, -7, 13],\n [-7, 1, 2, 6, -13, -5, 7, -4, -13, 10, -9, 9],\n [-8, -7, -16, -9, -7, 8, 14, -14, -9, -16, -12, 10],\n [9, 9, -6, -15, 4, 9, -5, -8, 6, -12, -8, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "635503574669", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-7, 0, -6, 3, 10, -2, -10, -5, 0, -4, 2, 10],\n [0, 16, 8, 4, -8, 0, -11, -4, -16, -8, 0, 0],\n [-6, 8, -12, 1, -2, -4, 5, -6, 8, 5, -7, -9],\n [3, 4, 1, 4, 11, -4, 3, 0, -5, -3, -10, 7],\n [10, -8, -2, 11, 11, 6, 6, -6, -12, 2, -12, 1],\n [-2, 0, -4, -4, 6, 4, -8, -10, 12, -6, 8, -4],\n [-10, -11, 5, 3, 6, -8, 3, 12, -2, -14, -8, -4],\n [-5, -4, -6, 0, -6, -10, 12, 16, -5, -1, -10, -4],\n [0, -16, 8, -5, -12, 12, -2, -5, -5, 8, -6, -8],\n [-4, -8, 5, -3, 2, -6, -14, -1, 8, 16, -9, 10],\n [2, 0, -7, -10, -12, 8, -8, -10, -6, -9, -4, -7],\n [10, 0, -9, 7, 1, -4, -4, -4, -8, 10, -7, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7913775421210", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (8, 7) of the result:\nA =\n[[11, 14, 11, 10, 4, -8, 12, -2, 16, 11, -7, 6],\n [11, -12, 1, -11, 6, 11, -4, 8, -10, -15, -1, -15],\n [-15, -7, -3, 10, -2, 4, -5, 16, 5, 1, -15, 12],\n [-10, 14, 1, -8, -9, 16, -12, -3, -4, -6, 3, 6],\n [10, -2, 13, -1, 1, 6, -9, 12, -5, 1, 2, 16],\n [-12, 11, 9, 4, 6, 4, -6, -1, 16, 10, -16, -1],\n [-12, 1, 8, -2, -13, -13, 8, -4, 8, -14, -8, -3],\n [5, -8, 7, 6, -2, -3, 3, 10, 0, 9, -13, -14],\n [2, -10, 2, -5, 3, -5, 12, 13, 3, -13, -15, 13],\n [6, -11, 1, 5, -13, -6, -6, -8, 14, 15, -6, 0],\n [-15, 7, -2, 11, -14, 12, -4, 5, 14, -10, 9, 14],\n [-13, 16, -14, 2, -8, 2, 2, 9, -4, 5, -9, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3587619828224", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[9, -14, -10, -15, 16, -5, -5, -7, 10, 1, -13, 6],\n [4, 13, 4, 6, 4, -9, -4, 5, -10, 7, -12, 9],\n [-7, -6, -6, 13, -13, -15, -4, 0, 6, -7, -4, 12],\n [-1, -14, -13, -1, -11, 11, 6, -5, 14, -5, 15, 8],\n [12, 2, 5, 7, 16, -1, -15, -9, -4, 13, -16, -5],\n [-10, -3, 11, -5, 7, -16, 0, 11, 16, 7, -11, 4],\n [-13, 16, -7, -4, -8, 14, -13, 3, -9, 10, -8, 7],\n [13, 9, -13, -16, 3, 11, 7, 11, 11, -12, 15, 13],\n [4, -1, -9, -5, 15, 8, -14, 9, 0, 10, 5, -10],\n [-14, -11, -4, -2, 9, 16, -2, -3, 2, 11, 7, 16],\n [-5, -7, -10, -16, -2, -16, 3, -15, -14, -1, 12, -14],\n [-5, 3, 6, 5, 15, -10, 5, -15, -3, -1, 7, -10]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1627071991337361", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-13, -12, -4, -13, -13, 3, 4, -10, -6, 6, -2, -3],\n [-12, 10, -12, 8, -14, 7, 1, -12, -16, -4, 0, 6],\n [-4, -12, -4, 6, 0, -6, 6, -4, -8, -4, -5, 8],\n [-13, 8, 6, 5, -2, -8, -2, 4, 4, 8, 0, -7],\n [-13, -14, 0, -2, 3, -10, -8, -4, 3, -1, 4, 4],\n [3, 7, -6, -8, -10, -6, 4, -4, -10, -6, 11, -2],\n [4, 1, 6, -2, -8, 4, 15, 5, -4, 12, 0, 1],\n [-10, -12, -4, 4, -4, -4, 5, 11, -3, -1, 0, 0],\n [-6, -16, -8, 4, 3, -10, -4, -3, 9, -2, 8, -6],\n [6, -4, -4, 8, -1, -6, 12, -1, -2, -1, 4, 0],\n [-2, 0, -5, 0, 4, 11, 0, 0, 8, 4, -3, 8],\n [-3, 6, 8, -7, 4, -2, 1, 0, -6, 0, 8, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1143888681629", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[11, -5, 5, 7, 2, 7, 3, 10, 12, -16, -10, 3],\n [3, 8, 4, -8, 10, 11, 8, -15, -8, 2, -2, 4],\n [-1, -15, 9, 12, 16, 10, -10, -2, 0, -8, -4, 15],\n [-15, 15, 3, 2, 10, 13, -6, -1, 9, 13, -15, 5],\n [14, 4, 6, 9, 1, -2, 5, 11, -10, 7, -4, -4],\n [14, 2, 12, 5, 4, -1, 13, -12, -11, 4, -6, 7],\n [11, -2, 2, 0, -14, -14, 11, 14, -9, 0, 10, 16],\n [-6, 4, -11, 4, 11, 0, 1, -6, 8, 13, 8, -10],\n [10, 9, -4, 7, -5, -3, -8, 14, -13, 2, -16, 12],\n [-11, -16, 8, 10, 5, 0, 12, -14, 0, -15, 15, 5],\n [16, 5, -13, -4, 6, -4, 3, 16, 12, 15, -6, 1],\n [4, -5, 3, -10, 10, -10, -15, 16, 4, 12, 15, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56362298806871", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 4) of the 7th power of the matrix:\n[[-4, -14, -9, -15, -11, -2, -5, 15, -11, 10, -4, 6],\n [-7, -3, -14, -5, 8, -16, 15, 7, -8, -16, -7, 13],\n [-12, -13, -9, -1, -16, -2, 7, -2, -11, -15, -12, 15],\n [12, 12, 7, 14, 7, -2, -5, 3, -13, -4, -7, 6],\n [-10, -5, -2, -10, -9, -10, -13, -10, 13, 1, 13, -10],\n [6, -10, 12, 1, 8, 10, 10, -5, 6, 0, -10, 7],\n [-10, 12, 11, 6, -7, -1, 8, -15, -12, -3, 14, -11],\n [11, -8, -11, 0, -5, 1, -16, -2, 1, 5, 1, -16],\n [3, 8, -1, 3, 16, -10, 6, -6, 16, -12, -9, 0],\n [1, 10, 14, -13, -15, -12, 0, 15, 12, -1, -16, -5],\n [2, -8, -10, 13, -2, -13, -11, -15, -12, -9, 13, 2],\n [13, 14, -1, 5, 16, 5, -9, -5, -12, 8, 12, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24166104776", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[9, 6, 8, -6, 11, -12, -6, 4, 4, 0, -12, 7],\n [6, -12, -15, -4, 9, 8, 0, 4, -8, -2, 2, 6],\n [8, -15, -14, -8, 2, -6, 12, 4, 0, -5, -8, 12],\n [-6, -4, -8, 12, 2, 2, -2, 4, -3, 2, 0, 0],\n [11, 9, 2, 2, -5, -4, 7, 8, 2, 0, 10, -10],\n [-12, 8, -6, 2, -4, 12, -4, -5, -1, -7, -1, -8],\n [-6, 0, 12, -2, 7, -4, -9, -3, 0, 4, -8, 3],\n [4, 4, 4, 4, 8, -5, -3, 14, -1, 6, -14, 5],\n [4, -8, 0, -3, 2, -1, 0, -1, 9, -10, -13, -2],\n [0, -2, -5, 2, 0, -7, 4, 6, -10, 6, -3, 6],\n [-12, 2, -8, 0, 10, -1, -8, -14, -13, -3, 1, 4],\n [7, 6, 12, 0, -10, -8, 3, 5, -2, 6, 4, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-135860858385583", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[2, 2, -11, -9, -16, 6, -7, -15, -15, -2, 3, 4],\n [13, 7, -15, 5, 12, -3, -12, 7, 9, -15, 6, -2],\n [-14, -5, 0, 10, 2, 4, 7, 7, 2, 14, 3, -2],\n [16, 1, 0, -9, 3, -6, 13, 10, -3, -2, -5, 3],\n [0, 9, -3, 8, 9, 8, 8, 10, -5, 3, -1, 8],\n [10, 1, -7, 13, -16, -13, 6, -10, 13, 9, -16, 12],\n [8, 9, 0, 14, -9, -12, -16, -2, -10, 10, 10, 3],\n [1, -15, 13, 13, -10, -4, 16, 13, 13, 6, 7, 3],\n [11, 2, -4, -1, -2, -6, -5, 5, 8, -14, 7, 8],\n [-8, 11, 13, -10, -6, -7, -14, 2, -15, 0, 12, -15],\n [-1, -7, -13, 9, 7, -5, 4, -1, -8, -11, -16, -3],\n [7, -7, 1, -8, 10, 2, -14, -8, -7, -8, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91020417535", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-10, -13, -7, 4, -3, 8, 0, 11, -3, -4, -14, -13],\n [-2, 3, -9, -12, -15, 11, 5, -8, 11, -16, -15, 9],\n [14, 2, 14, -8, -14, -11, -10, 8, 8, -16, 5, 3],\n [-4, 4, 6, 16, -8, 12, 15, -6, 12, 14, -3, 8],\n [9, 5, -8, 16, 6, 3, 16, 13, 13, 5, -16, -2],\n [8, 3, -10, -1, 6, 4, -16, 3, 2, -11, 15, -16],\n [13, -1, 10, 1, -4, 11, -7, -3, 12, -6, 10, 0],\n [-14, 14, 4, 16, -16, -11, -13, 5, -4, 13, 9, -10],\n [-3, 9, 1, 7, 8, 15, -11, -1, -14, 4, 15, -15],\n [3, -6, 1, -6, -5, 14, 13, -13, -15, -4, 9, 12],\n [11, -9, -12, 15, 13, -3, -7, -7, -11, -1, 9, 4],\n [13, -12, -7, 14, -6, -10, -5, -9, 11, -1, -14, 15]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1094237429531", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[4, 6, -6, 0, -1, 0, 7, 0, -3, -4, -4, 3],\n [6, 8, -12, 8, 5, 8, -2, 0, 4, 6, -11, 3],\n [-6, -12, 4, 5, 8, -2, 10, 8, 10, -6, -3, -4],\n [0, 8, 5, 2, -5, -6, -2, -8, 8, 0, 16, 8],\n [-1, 5, 8, -5, 12, -4, -14, -10, -2, 5, 6, 2],\n [0, 8, -2, -6, -4, 15, 0, -7, 8, -14, -4, -10],\n [7, -2, 10, -2, -14, 0, -1, 6, -11, -5, -4, 2],\n [0, 0, 8, -8, -10, -7, 6, -1, -8, -6, 8, 0],\n [-3, 4, 10, 8, -2, 8, -11, -8, -11, 6, -4, -8],\n [-4, 6, -6, 0, 5, -14, -5, -6, 6, -2, 2, 2],\n [-4, -11, -3, 16, 6, -4, -4, 8, -4, 2, -6, -14],\n [3, 3, -4, 8, 2, -10, 2, 0, -8, 2, -14, -8]], determine the value at position (5, 7).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33471961479184", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[11, 12, -12, 0, 6, 14, -4, 0, -6, 1, 7, 4],\n [12, -8, 4, 0, -2, 10, 2, -12, 2, 0, -5, 2],\n [-12, 4, 2, -8, 6, -11, 2, 12, 8, 1, -1, 1],\n [0, 0, -8, 4, -4, -4, -2, 6, 14, -5, -2, -10],\n [6, -2, 6, -4, 6, -6, -3, 0, 0, -8, 3, 14],\n [14, 10, -11, -4, -6, -6, 2, 6, 6, 8, -7, 8],\n [-4, 2, 2, -2, -3, 2, 5, -2, 4, 3, -1, 2],\n [0, -12, 12, 6, 0, 6, -2, 4, 0, -2, -8, -13],\n [-6, 2, 8, 14, 0, 6, 4, 0, -9, -8, -9, 4],\n [1, 0, 1, -5, -8, 8, 3, -2, -8, -1, 6, 12],\n [7, -5, -1, -2, 3, -7, -1, -8, -9, 6, -1, 4],\n [4, 2, 1, -10, 14, 8, 2, -13, 4, 12, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3158556105225", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 12) of the 7th power of the matrix:\n[[-11, 4, -2, -8, 5, 5, 10, -2, 12, -4, -3, -9],\n [4, 8, 2, -2, -6, 0, -1, 4, 12, 1, -2, 10],\n [-2, 2, 12, 2, 6, -1, 1, 2, 4, 0, -7, -4],\n [-8, -2, 2, 10, 5, -2, -11, 0, 4, 4, -2, -2],\n [5, -6, 6, 5, 13, -12, -10, -7, -2, -6, 0, 2],\n [5, 0, -1, -2, -12, 3, 0, -8, -5, 5, 0, -9],\n [10, -1, 1, -11, -10, 0, 16, 6, -6, 0, -10, -12],\n [-2, 4, 2, 0, -7, -8, 6, -4, -12, -3, 14, 0],\n [12, 12, 4, 4, -2, -5, -6, -12, 4, -8, -3, 12],\n [-4, 1, 0, 4, -6, 5, 0, -3, -8, 7, -2, 2],\n [-3, -2, -7, -2, 0, 0, -10, 14, -3, -2, -6, 7],\n [-9, 10, -4, -2, 2, -9, -12, 0, 12, 2, 7, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41140329814", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-3, 6, 9, -5, -16, 2, 6, -10, -10, -16, 1, -9],\n [8, 12, 6, 12, -16, -2, -2, 11, 15, -4, 4, -8],\n [3, 3, -9, -3, 3, 4, 5, -11, 10, -13, -13, 11],\n [10, 0, 12, -10, -9, 16, 15, 1, -1, 1, 8, -13],\n [-12, -3, -16, 5, 4, -4, 12, -8, 16, 5, 0, 6],\n [-11, 12, 10, -12, -8, 7, 2, 16, 13, -13, 15, -16],\n [4, 14, -3, 9, 5, 16, -4, 15, -9, 5, 3, 4],\n [13, -11, 10, 3, -3, -7, -2, -14, -2, 14, -6, 2],\n [-2, 3, 5, -10, -3, -13, -8, 8, 10, 11, 7, 16],\n [16, -1, 6, -6, 2, 6, -7, -16, -15, 5, 0, 7],\n [4, 12, -3, -9, 13, 5, 6, -4, 11, 13, -12, -7],\n [-8, -3, -7, 16, -6, -11, 0, -11, -7, -12, 2, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32355882043436", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[7, 4, -2, -2, 6, -10, -2, 5, -11, 3, 0, 2],\n [4, 12, 2, -11, -6, 8, -10, 2, -1, 6, 15, -2],\n [-2, 2, 13, 0, -8, 1, -1, 6, -8, -2, -6, 1],\n [-2, -11, 0, -11, 8, -4, -1, -4, -2, -3, 6, -2],\n [6, -6, -8, 8, -4, 4, 3, 0, -8, 4, -10, 7],\n [-10, 8, 1, -4, 4, 6, 0, -2, -14, -9, 2, -13],\n [-2, -10, -1, -1, 3, 0, -8, 6, -2, -12, 6, -5],\n [5, 2, 6, -4, 0, -2, 6, 1, 7, 1, -2, -4],\n [-11, -1, -8, -2, -8, -14, -2, 7, -16, 4, 9, -6],\n [3, 6, -2, -3, 4, -9, -12, 1, 4, -11, 8, 4],\n [0, 15, -6, 6, -10, 2, 6, -2, 9, 8, -13, 0],\n [2, -2, 1, -2, 7, -13, -5, -4, -6, 4, 0, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2541233398468", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[3, -4, -5, -4, 0, -6, 1, 2, 3, 2, 0, -10],\n [-4, 7, -5, -12, 0, 0, -8, -10, -5, 7, -6, -9],\n [-5, -5, 12, 2, -2, 2, -2, -4, -5, 10, 10, 2],\n [-4, -12, 2, 8, -8, 2, 2, 4, -2, 9, -1, 8],\n [0, 0, -2, -8, 9, -14, -2, 1, 4, -10, -2, -6],\n [-6, 0, 2, 2, -14, -11, -3, -4, -7, 4, 4, -11],\n [1, -8, -2, 2, -2, -3, -15, -7, 2, 0, 10, 6],\n [2, -10, -4, 4, 1, -4, -7, 8, -9, 2, -10, 4],\n [3, -5, -5, -2, 4, -7, 2, -9, 7, -2, -4, 0],\n [2, 7, 10, 9, -10, 4, 0, 2, -2, 8, -8, 4],\n [0, -6, 10, -1, -2, 4, 10, -10, -4, -8, -13, 6],\n [-10, -9, 2, 8, -6, -11, 6, 4, 0, 4, 6, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1685814563474", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[10, -10, 10, 14, -1, -4, 2, -2, -4, 6, 4, 7],\n [-10, 10, -2, 2, -2, 0, 2, 3, -1, -5, -4, 2],\n [10, -2, 11, 16, -2, 4, -12, 5, -4, 0, 4, 1],\n [14, 2, 16, -5, 0, 0, 7, -9, -14, -6, 0, -4],\n [-1, -2, -2, 0, 9, 8, -6, 11, -2, 8, 0, 8],\n [-4, 0, 4, 0, 8, -11, 4, -10, -4, -16, -3, 12],\n [2, 2, -12, 7, -6, 4, -16, 2, -4, 5, 14, -13],\n [-2, 3, 5, -9, 11, -10, 2, 8, 4, 4, 5, 2],\n [-4, -1, -4, -14, -2, -4, -4, 4, -6, -2, -8, -2],\n [6, -5, 0, -6, 8, -16, 5, 4, -2, 11, -5, 4],\n [4, -4, 4, 0, 0, -3, 14, 5, -8, -5, 6, 2],\n [7, 2, 1, -4, 8, 12, -13, 2, -2, 4, 2, -3]], determine the value at position (9, 7).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-864685095121", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-7, -4, 4, -4, 2, 0, 14, -7, -1, 8, 3, 10],\n [-4, 7, -10, 2, -7, 6, -6, -6, -5, 2, 4, -6],\n [4, -10, -5, 4, -1, -12, -10, 7, 0, 2, 8, -6],\n [-4, 2, 4, 4, -12, 0, 0, -15, -12, 0, -3, -6],\n [2, -7, -1, -12, 15, 0, 8, -10, 2, -3, -1, -12],\n [0, 6, -12, 0, 0, -9, 13, -11, 0, 1, 5, 10],\n [14, -6, -10, 0, 8, 13, -15, -1, -1, 2, 0, -2],\n [-7, -6, 7, -15, -10, -11, -1, -2, 1, 8, 0, -2],\n [-1, -5, 0, -12, 2, 0, -1, 1, 6, 3, -2, -2],\n [8, 2, 2, 0, -3, 1, 2, 8, 3, 3, -12, 8],\n [3, 4, 8, -3, -1, 5, 0, 0, -2, -12, 12, 2],\n [10, -6, -6, -6, -12, 10, -2, -2, -2, 8, 2, -9]], determine the value at position (4, 10).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3352678159", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[2, 12, -11, 12, 7, -7, -3, -11, -13, -2, 11, -15],\n [-4, -15, 15, -12, -14, -15, -3, 12, -11, -9, -15, 9],\n [0, 7, 14, -1, 4, 9, 0, -13, -13, 2, 8, -9],\n [1, 1, -10, 0, -14, 5, -2, 14, 9, -3, 0, -8],\n [-10, 10, 11, -5, 0, -8, -9, 10, -5, 3, -16, -8],\n [7, -13, 12, 6, -1, -9, 10, -5, -13, 8, -11, -14],\n [7, 4, -11, 16, -9, 16, -14, -15, 7, 4, 1, -6],\n [-6, -14, 6, -16, 6, 5, 13, -15, 0, 3, -8, -6],\n [0, -3, 1, 1, -9, 12, -9, 9, 11, -9, 3, -9],\n [-3, -4, 0, 9, -11, 0, -13, 8, -10, 0, 5, 11],\n [-11, 13, -7, -3, 5, 9, -7, -15, -14, -6, -7, -5],\n [-3, 13, -4, 13, -6, -16, 10, -8, 9, 8, 0, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9043620192623", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-2, -12, 14, 6, -8, 6, 11, -6, -6, -4, 4, -6],\n [-12, -6, -1, -6, 1, -4, -6, -8, -11, 8, 12, 2],\n [14, -1, 9, 9, 4, -4, 2, 0, -6, -10, -6, 3],\n [6, -6, 9, -7, 0, -9, -1, -5, 6, 11, 6, -6],\n [-8, 1, 4, 0, 6, 2, -6, 5, 2, -2, -5, -2],\n [6, -4, -4, -9, 2, 6, -1, 5, 11, 9, -6, -10],\n [11, -6, 2, -1, -6, -1, 5, 13, -10, -3, -10, 4],\n [-6, -8, 0, -5, 5, 5, 13, -9, -11, -14, 6, -2],\n [-6, -11, -6, 6, 2, 11, -10, -11, 14, 10, 10, -8],\n [-4, 8, -10, 11, -2, 9, -3, -14, 10, 3, -7, -10],\n [4, 12, -6, 6, -5, -6, -10, 6, 10, -7, -16, 2],\n [-6, 2, 3, -6, -2, -10, 4, -2, -8, -10, 2, -13]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15204081673896178", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[13, 15, 10, 15, -6, -4, 0, 13, 1, 13, 9, -1],\n [-6, -13, -2, -5, 10, -13, 4, -15, 11, 16, -9, -9],\n [5, 10, 11, -6, 10, -16, 11, 10, -9, 7, 7, 5],\n [-7, -13, -9, -2, -9, 12, -3, 15, -10, 16, 10, -16],\n [-11, -15, -10, -9, 12, -1, 12, 14, 5, -7, -13, 8],\n [-4, 0, -9, 6, -10, 15, 7, -16, 10, -11, 14, -5],\n [9, 8, -13, -11, -4, 8, 14, 5, 4, -2, -14, 9],\n [0, -9, -6, 7, -9, 13, -16, 3, -4, -11, 8, 10],\n [14, -14, 11, -13, 0, 3, -4, -12, 7, 0, 14, 11],\n [-16, -15, 16, 12, -13, 1, 7, 15, -8, -1, 4, 13],\n [-14, 16, 14, -3, -11, -12, 12, 4, -5, 6, -3, -7],\n [10, -15, -3, -10, 0, 3, -9, 3, -12, -4, 0, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2916559238175", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 0, 1, 3, 6, -1, -6, -5, -2, 0, -8, -12],\n [0, 13, 4, 9, 3, 2, 6, 6, -8, 13, 6, -6],\n [1, 4, -5, 0, -2, -7, 0, -8, 0, 0, 0, 4],\n [3, 9, 0, -14, -4, -2, -4, 2, 9, -2, 6, -5],\n [6, 3, -2, -4, -12, 8, 3, -3, 4, 3, 6, 6],\n [-1, 2, -7, -2, 8, 0, -1, -3, 7, -11, 1, 8],\n [-6, 6, 0, -4, 3, -1, 2, 2, 7, -4, -2, -2],\n [-5, 6, -8, 2, -3, -3, 2, 11, 8, 7, -4, -2],\n [-2, -8, 0, 9, 4, 7, 7, 8, 6, -10, 2, -1],\n [0, 13, 0, -2, 3, -11, -4, 7, -10, -13, -5, -6],\n [-8, 6, 0, 6, 6, 1, -2, -4, 2, -5, 13, 9],\n [-12, -6, 4, -5, 6, 8, -2, -2, -1, -6, 9, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553104259263", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 7) of the 7th power of the matrix:\n[[-4, -4, -2, -10, 2, 6, 10, 4, -2, 0, 10, -10],\n [-4, 11, 0, 0, -1, -4, -8, 1, 0, 4, -4, 2],\n [-2, 0, 5, -8, 0, -14, -8, -10, 4, 1, -2, -8],\n [-10, 0, -8, -15, -1, 6, 8, -4, 6, 3, -10, 12],\n [2, -1, 0, -1, -5, -4, -9, -8, 8, -2, -2, 6],\n [6, -4, -14, 6, -4, 14, 6, -6, -4, -2, 0, 4],\n [10, -8, -8, 8, -9, 6, 2, -1, -1, -2, 0, -7],\n [4, 1, -10, -4, -8, -6, -1, -5, -7, 12, 6, -2],\n [-2, 0, 4, 6, 8, -4, -1, -7, -8, -10, 2, 3],\n [0, 4, 1, 3, -2, -2, -2, 12, -10, -13, 12, -6],\n [10, -4, -2, -10, -2, 0, 0, 6, 2, 12, -12, -6],\n [-10, 2, -8, 12, 6, 4, -7, -2, 3, -6, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16074636973", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[16, 13, 4, 0, -6, 13, 1, 3, 11, -8, 14, -1],\n [14, 12, -4, 6, -3, -15, -5, 11, 15, 7, 12, 1],\n [-14, -4, -4, 12, -15, 11, -13, -12, -12, -9, 8, 10],\n [-10, 15, 4, 1, -15, -12, 11, 14, 7, 16, -5, -8],\n [-2, 6, 5, -7, 11, 12, -12, -13, -2, 13, 9, 6],\n [12, 5, 1, 16, -10, -7, 7, 8, 10, -11, -9, 4],\n [2, 6, -4, 11, -11, -5, -14, 3, -9, 9, 11, -15],\n [-10, 8, 15, -5, -6, -7, -13, -15, 11, -3, 12, -15],\n [16, 3, 13, 9, 3, -16, -16, 8, 16, 6, -6, -2],\n [-3, -16, 16, -11, 6, 9, -14, -11, 8, 0, 11, 15],\n [12, 6, -1, 15, 9, 16, 2, 0, -3, 1, 4, 11],\n [3, -11, 9, -11, 9, 0, -15, 4, -10, 3, -14, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48401402646736", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[13, -10, -4, 0, 0, -5, -6, 13, 0, -6, 12, 10],\n [-10, -16, -7, -9, 2, -4, 2, 3, 3, 10, 4, 2],\n [-4, -7, 3, 3, -2, -6, 6, -13, -4, -4, 0, 0],\n [0, -9, 3, 11, 2, 2, 0, -6, 4, -12, 8, -15],\n [0, 2, -2, 2, 13, -1, 6, -4, 10, 0, 8, -6],\n [-5, -4, -6, 2, -1, 16, -2, 16, -5, 7, -5, 2],\n [-6, 2, 6, 0, 6, -2, 15, -4, -14, 8, 4, -9],\n [13, 3, -13, -6, -4, 16, -4, -6, -3, 7, -6, -8],\n [0, 3, -4, 4, 10, -5, -14, -3, -4, 4, 8, 2],\n [-6, 10, -4, -12, 0, 7, 8, 7, 4, 0, 3, 0],\n [12, 4, 0, 8, 8, -5, 4, -6, 8, 3, 2, 14],\n [10, 2, 0, -15, -6, 2, -9, -8, 2, 0, 14, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40520403348941", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (12, 8) of the result:\nA =\n[[-4, 3, 0, 10, -5, 2, 10, -4, 3, -8, -6, 6],\n [3, -6, 2, -7, 8, -4, -6, 1, -7, 1, 9, 6],\n [0, 2, 3, 4, -2, -12, -8, -4, 3, 3, 6, -2],\n [10, -7, 4, -15, 4, -10, 12, 1, -8, 0, -7, 6],\n [-5, 8, -2, 4, -11, -12, 13, -8, -4, -2, 10, 11],\n [2, -4, -12, -10, -12, 11, -7, -12, 12, 0, 10, -4],\n [10, -6, -8, 12, 13, -7, 9, -4, 6, 2, 1, -2],\n [-4, 1, -4, 1, -8, -12, -4, 10, 0, 3, -12, 12],\n [3, -7, 3, -8, -4, 12, 6, 0, -16, -5, -3, -8],\n [-8, 1, 3, 0, -2, 0, 2, 3, -5, -12, 7, 1],\n [-6, 9, 6, -7, 10, 10, 1, -12, -3, 7, -3, 6],\n [6, 6, -2, 6, 11, -4, -2, 12, -8, 1, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393214838608", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 5) of the 7th power of the matrix:\n[[9, 3, -11, -2, -13, -11, -15, -2, -5, -10, 5, -9],\n [-6, -15, 13, -13, 8, 4, 8, -8, -9, -12, 11, -15],\n [4, -9, 6, -2, 10, -15, 11, -6, 4, 15, 15, -10],\n [5, -3, -4, 4, 5, -7, -16, -16, 7, -14, 14, -4],\n [-13, 6, -11, 1, 9, 16, 16, 8, 0, -14, 5, -13],\n [11, -4, 13, -5, -14, 4, -16, 1, -4, -10, -4, 0],\n [15, 12, 13, -6, -3, -7, -9, 14, -11, 2, 2, -5],\n [1, -14, -8, -11, -16, 12, 13, 5, 11, 1, 15, -12],\n [14, 16, -13, -3, -2, 3, 3, -13, 1, 7, 10, 16],\n [8, -12, 1, 3, -11, 10, 11, -6, -8, 11, 2, 4],\n [14, -10, 8, 11, 0, 9, 11, 0, 0, 16, 6, 13],\n [10, -8, 3, 6, 2, -13, -4, -5, -8, -2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28470113579", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-12, -12, 8, 7, 14, -3, 10, -13, 6, -12, 10, -3],\n [-10, 1, 15, -15, 3, 12, 9, -16, -12, -3, 8, -8],\n [13, 2, -9, -1, -9, 6, -8, 15, 1, -2, -2, 12],\n [6, 6, -16, 5, -10, 15, 11, 15, 16, -4, 11, -8],\n [-14, 0, 15, -8, -16, 3, -12, 4, -12, -13, -9, 8],\n [-10, 15, 0, 11, -11, -15, 14, -16, -14, -4, 14, 12],\n [16, -7, -8, -16, 15, 16, -15, -15, -12, -7, -15, 8],\n [1, 10, 3, -9, -13, 13, -8, -5, -3, -11, 6, -13],\n [-16, -8, -8, -2, 7, -9, 11, 0, 14, -13, -3, 8],\n [-10, 14, 3, -1, 5, 2, -15, -13, -10, -3, 15, 0],\n [-3, 0, 15, -15, -13, 13, 13, 16, -16, 16, 14, -3],\n [-11, -10, 7, -13, 8, -14, 11, 6, -4, 5, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6073129224865", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (5, 1) of the result:\nA =\n[[16, 5, 2, 7, 2, -12, -5, -8, 4, 12, -6, 6],\n [5, -10, -4, -13, -11, -8, -4, 2, 6, 10, 0, -2],\n [2, -4, -11, -8, 4, -7, -1, 4, -2, 6, -14, 4],\n [7, -13, -8, -14, 5, -4, 7, 6, 2, 5, -10, -6],\n [2, -11, 4, 5, -2, -7, 1, -8, -13, 6, 7, -3],\n [-12, -8, -7, -4, -7, 11, 4, -9, -8, -4, -2, 11],\n [-5, -4, -1, 7, 1, 4, -12, -8, 0, 4, 4, -3],\n [-8, 2, 4, 6, -8, -9, -8, 5, -7, 2, -9, -5],\n [4, 6, -2, 2, -13, -8, 0, -7, -12, 3, 11, -4],\n [12, 10, 6, 5, 6, -4, 4, 2, 3, -14, 6, 7],\n [-6, 0, -14, -10, 7, -2, 4, -9, 11, 6, -3, 1],\n [6, -2, 4, -6, -3, 11, -3, -5, -4, 7, 1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1462377016", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[0, 12, 9, -4, -2, 3, 10, -8, 11, -4, -10, 2],\n [12, -8, 4, -6, 8, 6, 0, -8, -4, -4, 3, 10],\n [9, 4, -8, -6, 7, 4, -10, 0, -10, -14, -2, 0],\n [-4, -6, -6, 12, 8, 4, 6, -2, 13, 13, -3, 0],\n [-2, 8, 7, 8, 3, -10, -3, -4, 5, 0, -5, 2],\n [3, 6, 4, 4, -10, 11, -11, 6, -6, 4, -5, 10],\n [10, 0, -10, 6, -3, -11, -2, -2, 8, -2, 8, 6],\n [-8, -8, 0, -2, -4, 6, -2, 3, 9, 13, -6, 9],\n [11, -4, -10, 13, 5, -6, 8, 9, 7, 8, 3, -11],\n [-4, -4, -14, 13, 0, 4, -2, 13, 8, 14, 10, -1],\n [-10, 3, -2, -3, -5, -5, 8, -6, 3, 10, -11, -6],\n [2, 10, 0, 0, 2, 10, 6, 9, -11, -1, -6, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5832210475438", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-11, -10, 10, 8, 0, 12, 6, 2, -2, 8, 5, -8],\n [-10, 5, -2, 3, 6, -4, 2, -1, 0, -14, -4, -2],\n [10, -2, 4, 6, -4, 13, 2, 4, 0, 2, -16, 4],\n [8, 3, 6, 2, -4, -9, -8, 6, -8, 2, -8, 8],\n [0, 6, -4, -4, 4, 7, -12, 4, -8, -11, -10, 2],\n [12, -4, 13, -9, 7, 4, -7, -8, 4, 0, 8, 4],\n [6, 2, 2, -8, -12, -7, -1, 0, 12, -6, 4, 9],\n [2, -1, 4, 6, 4, -8, 0, -16, -11, 13, 0, -6],\n [-2, 0, 0, -8, -8, 4, 12, -11, 4, -5, 2, -12],\n [8, -14, 2, 2, -11, 0, -6, 13, -5, -2, -4, 6],\n [5, -4, -16, -8, -10, 8, 4, 0, 2, -4, -8, 8],\n [-8, -2, 4, 8, 2, 4, 9, -6, -12, 6, 8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3592186811687", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 3) of the 9th power of the matrix:\n[[6, 14, 0, -4, -2, 6, -1, -6, -2, -2, -14, 11],\n [14, 0, -4, -12, 6, 4, 6, 4, -2, 8, 0, 4],\n [0, -4, -2, -2, -8, 2, 2, 15, 0, -6, 6, 6],\n [-4, -12, -2, 12, -3, 0, 2, 5, 6, 2, 0, -2],\n [-2, 6, -8, -3, 11, -10, 6, 2, -8, 8, -2, 3],\n [6, 4, 2, 0, -10, -10, -4, 6, -8, 7, -2, 0],\n [-1, 6, 2, 2, 6, -4, 15, 0, -12, 1, 1, -4],\n [-6, 4, 15, 5, 2, 6, 0, 1, -2, 6, -8, -12],\n [-2, -2, 0, 6, -8, -8, -12, -2, -15, -10, 2, 2],\n [-2, 8, -6, 2, 8, 7, 1, 6, -10, -16, 4, 3],\n [-14, 0, 6, 0, -2, -2, 1, -8, 2, 4, 12, 0],\n [11, 4, 6, -2, 3, 0, -4, -12, 2, 3, 0, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4681813274589", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[2, 6, 3, -11, 7, 5, -11, 7, 5, 1, -1, -4],\n [7, 2, 3, 10, 0, -1, -16, 4, 10, -16, 13, 3],\n [7, -15, -2, 12, -4, 2, -16, -1, -14, -11, 14, -12],\n [9, 11, -2, -8, 5, 4, 12, 9, -11, -6, 3, 3],\n [10, -11, 16, 13, -12, -1, -5, -5, -6, 4, -10, 12],\n [-11, -9, -7, -1, -15, 2, -10, -15, 6, 14, -13, -1],\n [-7, 4, 11, -5, -4, 0, 1, -7, 11, -4, -11, -5],\n [12, -4, 9, -13, -2, -1, 2, 9, 15, -11, -11, -12],\n [-15, -15, -14, -11, 14, -12, -7, 10, 7, 5, 8, -14],\n [-1, 13, -13, -1, -9, 7, -1, 10, -15, 3, 3, 3],\n [2, 1, -4, 0, 16, 11, -12, 11, 8, 3, 4, -4],\n [-11, 12, -8, 12, -16, 13, 15, 6, -7, 4, 9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551871945814026", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[0, 9, -4, 7, -10, -1, -3, 12, 8, 4, -8, -2],\n [9, 4, -2, -2, -6, -4, 10, 8, 12, -11, 0, 0],\n [-4, -2, -13, 2, 6, 13, -8, -1, 7, -5, 12, 2],\n [7, -2, 2, 10, -6, -1, 5, -12, 6, -8, 8, 10],\n [-10, -6, 6, -6, -1, -10, -6, -2, 2, 14, -6, -2],\n [-1, -4, 13, -1, -10, 13, -8, 0, -2, -2, -8, -13],\n [-3, 10, -8, 5, -6, -8, -16, -4, 2, 5, 6, 6],\n [12, 8, -1, -12, -2, 0, -4, -14, -4, -2, 10, 16],\n [8, 12, 7, 6, 2, -2, 2, -4, -15, 7, 4, 8],\n [4, -11, -5, -8, 14, -2, 5, -2, 7, -14, -2, 9],\n [-8, 0, 12, 8, -6, -8, 6, 10, 4, -2, -13, 14],\n [-2, 0, 2, 10, -2, -13, 6, 16, 8, 9, 14, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "873882918657311", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-15, -2, 14, 7, -4, 5, -6, -2, -2, 6, 7, 4],\n [-2, -7, -5, -2, 6, 0, 12, -4, 2, -4, -2, 11],\n [14, -5, -3, -15, 0, 2, -4, 2, -4, -2, -6, 12],\n [7, -2, -15, -6, -8, -6, 12, -15, -3, -14, -8, -3],\n [-4, 6, 0, -8, 12, 0, -1, -12, 4, 6, 3, 4],\n [5, 0, 2, -6, 0, 7, -4, 14, -14, 6, -11, -2],\n [-6, 12, -4, 12, -1, -4, -13, 8, 2, -12, 10, -4],\n [-2, -4, 2, -15, -12, 14, 8, 11, -2, 8, -10, -2],\n [-2, 2, -4, -3, 4, -14, 2, -2, 9, -11, -8, -6],\n [6, -4, -2, -14, 6, 6, -12, 8, -11, -16, 4, 2],\n [7, -2, -6, -8, 3, -11, 10, -10, -8, 4, -6, -12],\n [4, 11, 12, -3, 4, -2, -4, -2, -6, 2, -12, 12]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16177368345443220", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[15, 1, -6, 11, -4, 3, -10, 8, 6, 10, 12, 6],\n [1, -4, -6, 3, 5, 4, 14, -8, -2, 0, 2, -5],\n [-6, -6, -7, -2, 9, 1, 3, -4, 7, -4, 7, 2],\n [11, 3, -2, 8, -8, 2, -2, 4, 2, 16, 4, -2],\n [-4, 5, 9, -8, 0, -6, -2, 12, 2, 4, 4, -6],\n [3, 4, 1, 2, -6, -16, 0, -4, 1, -6, 5, -1],\n [-10, 14, 3, -2, -2, 0, -4, 0, -5, 1, -7, -4],\n [8, -8, -4, 4, 12, -4, 0, -5, 1, -2, 14, 0],\n [6, -2, 7, 2, 2, 1, -5, 1, 3, 0, 11, -10],\n [10, 0, -4, 16, 4, -6, 1, -2, 0, -9, -2, 10],\n [12, 2, 7, 4, 4, 5, -7, 14, 11, -2, -7, -4],\n [6, -5, 2, -2, -6, -1, -4, 0, -10, 10, -4, 16]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1482673611747778", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-5, 3, 4, 12, 2, 4, -2, 10, -8, -1, 13, 8],\n [3, -4, -12, 1, -12, 2, 2, 10, 0, 4, 2, -2],\n [4, -12, -12, 3, 12, -10, -2, -2, 4, -10, 0, 6],\n [12, 1, 3, -6, -2, 0, -14, -10, 0, -2, -2, 0],\n [2, -12, 12, -2, 8, -6, 1, -10, -14, 0, 10, 4],\n [4, 2, -10, 0, -6, 13, 4, 15, 2, -6, -6, 13],\n [-2, 2, -2, -14, 1, 4, 9, 2, -6, 2, 1, 10],\n [10, 10, -2, -10, -10, 15, 2, -10, -3, 2, 2, 10],\n [-8, 0, 4, 0, -14, 2, -6, -3, -2, -3, -4, -9],\n [-1, 4, -10, -2, 0, -6, 2, 2, -3, -4, 0, 6],\n [13, 2, 0, -2, 10, -6, 1, 2, -4, 0, 14, -6],\n [8, -2, 6, 0, 4, 13, 10, 10, -9, 6, -6, 5]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45864617479090", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[14, 1, -5, -13, -8, 8, 0, 2, -1, -10, -10, -11],\n [1, 11, 4, -4, 4, -3, -2, -2, 13, 6, 2, -3],\n [-5, 4, -7, -2, 4, 8, -6, 7, -1, -14, -12, 4],\n [-13, -4, -2, 2, -12, 10, 8, -4, 2, -6, 8, 2],\n [-8, 4, 4, -12, -16, -14, -3, 12, 8, -8, -6, -4],\n [8, -3, 8, 10, -14, 2, 0, 9, -4, 0, 2, -9],\n [0, -2, -6, 8, -3, 0, 16, -5, 9, 2, 1, 0],\n [2, -2, 7, -4, 12, 9, -5, -3, -9, 0, 4, 9],\n [-1, 13, -1, 2, 8, -4, 9, -9, -5, 4, -4, 4],\n [-10, 6, -14, -6, -8, 0, 2, 0, 4, 9, -9, -14],\n [-10, 2, -12, 8, -6, 2, 1, 4, -4, -9, -16, 4],\n [-11, -3, 4, 2, -4, -9, 0, 9, 4, -14, 4, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9151988615994124", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[4, -14, -2, 0, 10, -2, 10, -2, 0, 7, 0, -2],\n [-14, 6, 2, -4, 7, 13, 9, -10, 8, 2, 6, -2],\n [-2, 2, -1, 4, -6, 6, 8, -11, 2, 10, -6, 2],\n [0, -4, 4, -1, 0, -2, 4, 4, 2, 4, 8, -4],\n [10, 7, -6, 0, -14, -5, -2, -4, 10, 1, 0, 0],\n [-2, 13, 6, -2, -5, 10, 11, -12, 4, 6, -8, 2],\n [10, 9, 8, 4, -2, 11, -12, -1, -11, -2, -8, -4],\n [-2, -10, -11, 4, -4, -12, -1, -8, 4, -2, 6, -12],\n [0, 8, 2, 2, 10, 4, -11, 4, 11, -14, -10, -14],\n [7, 2, 10, 4, 1, 6, -2, -2, -14, -16, -8, -4],\n [0, 6, -6, 8, 0, -8, -8, 6, -10, -8, -8, 0],\n [-2, -2, 2, -4, 0, 2, -4, -12, -14, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196444630983929", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[4, 6, -8, 0, 0, -9, 5, 4, -2, -1, -4, 10],\n [6, 3, -6, 11, 2, -2, 3, -4, 2, -6, 4, 1],\n [-8, -6, 11, 10, 2, 3, 6, -2, 0, 6, 8, -10],\n [0, 11, 10, -10, 10, 0, 8, -7, -6, -6, 4, 2],\n [0, 2, 2, 10, 11, 6, 6, 12, 8, 2, 2, 0],\n [-9, -2, 3, 0, 6, -10, -3, -6, -10, -4, 6, -9],\n [5, 3, 6, 8, 6, -3, 12, -3, -7, 0, 14, -9],\n [4, -4, -2, -7, 12, -6, -3, 14, -4, -2, -10, 7],\n [-2, 2, 0, -6, 8, -10, -7, -4, 8, -12, -8, -2],\n [-1, -6, 6, -6, 2, -4, 0, -2, -12, -12, -4, 11],\n [-4, 4, 8, 4, 2, 6, 14, -10, -8, -4, 3, -2],\n [10, 1, -10, 2, 0, -9, -9, 7, -2, 11, -2, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20997008770379", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-8, 0, -8, -1, 2, -8, -2, -4, -1, 6, -12, 8],\n [0, -7, 1, 0, 10, -5, -6, 4, -14, -8, 14, -2],\n [-8, 1, 11, -6, -6, -1, 0, 4, -6, -2, -7, 6],\n [-1, 0, -6, 0, -10, 10, 10, 2, 0, 8, -1, -6],\n [2, 10, -6, -10, -2, 0, 8, -1, -5, -2, -8, 10],\n [-8, -5, -1, 10, 0, -8, 0, 12, 9, -5, 2, -6],\n [-2, -6, 0, 10, 8, 0, 6, 3, -9, 9, 6, 2],\n [-4, 4, 4, 2, -1, 12, 3, -2, -12, 4, 4, 2],\n [-1, -14, -6, 0, -5, 9, -9, -12, 7, 8, -6, -13],\n [6, -8, -2, 8, -2, -5, 9, 4, 8, -16, 10, -7],\n [-12, 14, -7, -1, -8, 2, 6, 4, -6, 10, 13, 0],\n [8, -2, 6, -6, 10, -6, 2, 2, -13, -7, 0, -15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5279461082806438", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (7, 5) of the result:\nA =\n[[12, 1, 0, 2, 4, -10, -8, -4, 12, 9, -6, 11],\n [1, -16, 5, 0, -1, -9, 6, -14, -7, 0, 4, 8],\n [0, 5, -16, 6, 5, 12, -13, -12, 1, -2, -12, -2],\n [2, 0, 6, 2, -10, 0, 6, -13, -7, 10, 4, -1],\n [4, -1, 5, -10, 12, 3, 0, 1, 10, -4, -8, -2],\n [-10, -9, 12, 0, 3, 5, -5, -3, 10, 10, -14, -12],\n [-8, 6, -13, 6, 0, -5, 3, 2, -1, 2, 0, -6],\n [-4, -14, -12, -13, 1, -3, 2, 16, -9, 2, 4, -4],\n [12, -7, 1, -7, 10, 10, -1, -9, -5, 4, -14, -2],\n [9, 0, -2, 10, -4, 10, 2, 2, 4, -10, 3, -2],\n [-6, 4, -12, 4, -8, -14, 0, 4, -14, 3, -5, 5],\n [11, 8, -2, -1, -2, -12, -6, -4, -2, -2, 5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27476416952", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 5) of the 9th power of the matrix:\n[[-10, -7, 5, 8, 12, -2, 2, 1, -14, -11, 5, 14],\n [4, -9, -16, -14, 12, -11, 16, 1, -16, 5, 14, 6],\n [-9, 12, 2, -1, 2, 5, 2, -13, -12, -12, 8, 7],\n [-16, 11, 4, 2, 6, -3, -11, 15, 15, -9, 5, -9],\n [-7, -14, -4, 13, -13, -11, -1, 5, 10, 4, 12, -16],\n [13, 7, -4, 13, 9, 3, -11, -8, -1, -13, 15, 3],\n [12, 14, 0, 8, -1, 3, -7, 6, 16, -4, 8, 7],\n [-11, -2, -13, -3, -13, 11, 12, 1, 3, 15, -9, -4],\n [-8, 16, -5, 8, 8, -1, -1, 6, -9, -14, 7, 5],\n [-3, 5, 14, 4, -12, 2, 4, -15, -14, 13, 8, 12],\n [-5, 6, 11, 0, -1, -8, -14, 5, 14, -3, -14, 6],\n [4, 7, 15, -12, 16, 2, -14, 11, -6, -7, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25908742539377", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 10) of the matrix A^7 where A is:\n[[-8, -10, 8, 14, -4, 12, -4, -6, -5, 8, -6, -1],\n [-10, 9, 0, -10, 4, -1, 6, 3, -5, 12, -4, 0],\n [8, 0, -13, 2, 8, 0, -12, -10, 0, 4, -4, 5],\n [14, -10, 2, -2, 0, 4, -8, 0, -4, 0, -8, 6],\n [-4, 4, 8, 0, -6, 0, -5, -8, -12, 6, -6, -6],\n [12, -1, 0, 4, 0, -5, -12, 13, -8, 4, -3, 12],\n [-4, 6, -12, -8, -5, -12, -8, 3, -12, -6, 2, 4],\n [-6, 3, -10, 0, -8, 13, 3, -15, -8, -3, -4, -9],\n [-5, -5, 0, -4, -12, -8, -12, -8, 14, 2, -10, -1],\n [8, 12, 4, 0, 6, 4, -6, -3, 2, 1, -4, -2],\n [-6, -4, -4, -8, -6, -3, 2, -4, -10, -4, 10, -15],\n [-1, 0, 5, 6, -6, 12, 4, -9, -1, -2, -15, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8986563938", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[0, -13, -3, 4, -9, 16, 11, -14, -3, 2, -11, 3],\n [-16, -7, -4, -5, -6, 0, 12, -14, 12, -7, 2, -13],\n [-5, 14, -15, -16, 0, 8, -12, -3, -7, 4, 8, -14],\n [1, 16, 0, -11, 9, 14, 11, -4, 4, 9, 14, -1],\n [14, -4, 13, 15, -12, -5, -13, 12, -12, -6, 13, -8],\n [11, 5, -6, 4, -11, 9, -1, -3, 5, -15, -4, -6],\n [-5, 16, 5, -8, -10, 0, -7, 8, 10, 13, 13, 16],\n [15, -5, 6, 12, -16, 3, -7, 2, 6, 4, 15, -7],\n [-15, -11, 0, -2, 7, 12, -3, -15, 5, -11, -8, -5],\n [-12, -16, -7, -6, 10, 6, 3, -12, -4, -7, -1, -10],\n [15, 8, 9, 11, -5, 9, -13, 6, 7, 14, 13, -14],\n [-1, 11, -10, -9, -10, -10, 1, 4, 10, -9, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37986654562617", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[5, -4, -9, 6, 10, -4, 4, 12, 5, 4, 2, -2],\n [-4, -10, 0, 12, 1, 9, -4, 3, -2, -7, -8, 4],\n [-9, 0, 2, 2, 2, -6, 7, -11, -6, -1, 13, -13],\n [6, 12, 2, -10, 10, -10, -1, -2, 2, -6, 0, -4],\n [10, 1, 2, 10, 14, -8, -2, -13, 10, 7, -4, 3],\n [-4, 9, -6, -10, -8, -11, -12, 2, -7, -7, 2, -8],\n [4, -4, 7, -1, -2, -12, -15, 5, -5, -14, 14, 4],\n [12, 3, -11, -2, -13, 2, 5, 3, 2, -2, 4, 8],\n [5, -2, -6, 2, 10, -7, -5, 2, 5, 8, -2, 4],\n [4, -7, -1, -6, 7, -7, -14, -2, 8, -5, 6, 8],\n [2, -8, 13, 0, -4, 2, 14, 4, -2, 6, -5, 6],\n [-2, 4, -13, -4, 3, -8, 4, 8, 4, 8, 6, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31511780482264", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-16, 11, 9, 9, -12, -15, 15, 13, 7, 11, -14, -7],\n [-11, 14, -4, 3, 15, -7, 9, 2, 12, -4, 3, 1],\n [-9, -1, 6, 15, -4, 9, -16, -15, -4, 10, -13, 3],\n [-14, 6, -15, -1, -7, 11, 1, -15, -3, 3, 6, -10],\n [-3, -9, -12, 6, -7, 10, -16, -10, -9, -6, 11, 3],\n [11, -14, -8, 5, 8, -15, 6, 0, 8, -5, 10, 3],\n [-8, 6, 11, 12, 15, -5, 13, -6, 3, -6, -1, -16],\n [8, 10, 15, -11, 6, 12, 13, 5, -6, 9, 6, -14],\n [-11, -10, 5, 16, -14, 13, 7, -14, -15, 2, 7, 3],\n [14, 14, 12, -13, -7, 4, -16, -5, 7, -15, 3, -1],\n [-4, 1, 12, -3, 13, -8, -5, 4, 1, -6, 10, 7],\n [3, -4, -9, -12, -10, -5, -13, 2, -16, -4, 8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2062634384259", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[9, 0, 4, 2, -6, 4, 9, 2, 2, 0, -4, -5],\n [0, 7, 0, -8, -9, -12, 5, 8, 6, -1, -10, 0],\n [4, 0, 9, 4, 4, -4, 6, 10, 4, -8, 0, 4],\n [2, -8, 4, 9, -1, -4, -5, 10, 10, 10, 4, -4],\n [-6, -9, 4, -1, -15, -8, 4, 16, -1, -4, -10, -4],\n [4, -12, -4, -4, -8, -6, -7, 8, -6, -6, -6, -10],\n [9, 5, 6, -5, 4, -7, -7, -12, -9, -4, -8, 8],\n [2, 8, 10, 10, 16, 8, -12, 4, 6, -10, -8, 8],\n [2, 6, 4, 10, -1, -6, -9, 6, 15, 0, -4, 11],\n [0, -1, -8, 10, -4, -6, -4, -10, 0, -5, 2, 8],\n [-4, -10, 0, 4, -10, -6, -8, -8, -4, 2, 7, -4],\n [-5, 0, 4, -4, -4, -10, 8, 8, 11, 8, -4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-157734050270", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^9 where A is:\n[[4, -2, -4, 10, -2, -6, -8, 0, 4, 6, 13, -5],\n [-2, 15, 12, -3, 6, 2, 0, -10, 14, -2, 4, -6],\n [-4, 12, 12, 2, 6, 12, 8, 0, -8, -2, 2, 12],\n [10, -3, 2, -14, 11, -9, 6, 11, 8, 0, 5, -2],\n [-2, 6, 6, 11, 13, 4, -14, -9, -7, 10, -8, 12],\n [-6, 2, 12, -9, 4, 3, 8, 4, -4, 2, 1, -12],\n [-8, 0, 8, 6, -14, 8, -1, 15, 4, 0, 2, -5],\n [0, -10, 0, 11, -9, 4, 15, 13, -10, -6, 6, 10],\n [4, 14, -8, 8, -7, -4, 4, -10, 14, -8, 0, -15],\n [6, -2, -2, 0, 10, 2, 0, -6, -8, 12, 3, -1],\n [13, 4, 2, 5, -8, 1, 2, 6, 0, 3, -10, -8],\n [-5, -6, 12, -2, 12, -12, -5, 10, -15, -1, -8, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123952696693918", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[16, 0, -1, 6, -2, -4, 0, -14, 0, 0, 0, 4],\n [0, 11, -7, -8, -2, 8, 2, -1, 10, 0, -4, 8],\n [-1, -7, 7, 4, -6, 7, 16, -10, 8, -6, 2, 15],\n [6, -8, 4, -3, -4, 4, -4, -2, -9, -4, 9, 12],\n [-2, -2, -6, -4, -7, 2, -2, -1, -5, 4, 2, 12],\n [-4, 8, 7, 4, 2, 1, -8, -2, 4, -8, -11, -11],\n [0, 2, 16, -4, -2, -8, -14, 2, 7, -4, -2, 2],\n [-14, -1, -10, -2, -1, -2, 2, 8, -4, -9, 4, -6],\n [0, 10, 8, -9, -5, 4, 7, -4, -16, -12, -3, 8],\n [0, 0, -6, -4, 4, -8, -4, -9, -12, 7, 8, 6],\n [0, -4, 2, 9, 2, -11, -2, 4, -3, 8, 13, -2],\n [4, 8, 15, 12, 12, -11, 2, -6, 8, 6, -2, 13]], determine the value at position (6, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3303020485", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[15, -4, 1, 5, -13, 6, -10, -6, -12, 8, 11, -3],\n [10, -1, 10, -15, 2, 6, -3, 9, -9, 10, 11, -13],\n [-6, 7, 11, 1, 4, 9, -14, -4, 11, -3, -16, 11],\n [-6, -13, -16, -7, 0, -10, -4, 5, -16, 11, 16, -4],\n [-16, 8, 4, 16, -14, 13, -14, 1, 6, -9, -8, -15],\n [-15, 10, -12, -16, 5, -7, 7, -2, 16, 6, -3, 1],\n [8, 5, -10, 9, 7, -4, -11, 4, -10, 1, -2, -9],\n [-1, -14, -8, 9, 9, 13, 10, -1, -13, 2, -11, -2],\n [-7, -11, -11, -2, 12, 8, 2, -3, -14, -3, 4, -6],\n [-7, -2, 13, 0, 12, 0, 16, 4, -3, -7, 6, -3],\n [5, 11, -8, 6, -10, 7, -8, -10, 6, 8, 5, -10],\n [-11, 5, 16, 4, -6, -4, -14, -4, 11, 15, 6, 7]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9985562518", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-16, 4, -12, -8, -4, 4, -2, 1, -1, 3, 2, -2],\n [4, -8, 7, -6, -4, 6, -1, -10, 10, -10, 6, 8],\n [-12, 7, 14, 8, -12, 10, 0, -3, 4, 7, -2, -4],\n [-8, -6, 8, -5, 10, 0, -2, -2, 14, 6, 1, -4],\n [-4, -4, -12, 10, 5, -8, -2, 3, -9, -2, -4, -10],\n [4, 6, 10, 0, -8, -16, -13, -4, -2, -14, 2, -4],\n [-2, -1, 0, -2, -2, -13, 13, 4, 12, 8, -6, -2],\n [1, -10, -3, -2, 3, -4, 4, 4, 2, 11, -1, 0],\n [-1, 10, 4, 14, -9, -2, 12, 2, 6, 3, 10, -2],\n [3, -10, 7, 6, -2, -14, 8, 11, 3, -9, -7, -1],\n [2, 6, -2, 1, -4, 2, -6, -1, 10, -7, -13, -4],\n [-2, 8, -4, -4, -10, -4, -2, 0, -2, -1, -4, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1425485153608", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-13, 12, 0, 8, 0, -12, -8, 0, 0, -4, 2, -10],\n [12, -10, 3, 8, 8, -6, -6, 3, -6, -8, -5, 6],\n [0, 3, 7, 10, 10, -2, -12, -2, 2, -2, -6, -2],\n [8, 8, 10, 8, -6, -8, -4, 6, 12, -3, 4, 1],\n [0, 8, 10, -6, 4, -6, -5, 2, -2, 6, 2, 1],\n [-12, -6, -2, -8, -6, 3, 4, 0, 2, -6, -4, -1],\n [-8, -6, -12, -4, -5, 4, 8, -14, -7, 12, 12, 2],\n [0, 3, -2, 6, 2, 0, -14, -14, -6, -3, 6, -10],\n [0, -6, 2, 12, -2, 2, -7, -6, -13, -5, -4, 2],\n [-4, -8, -2, -3, 6, -6, 12, -3, -5, 11, 0, 4],\n [2, -5, -6, 4, 2, -4, 12, 6, -4, 0, 1, -6],\n [-10, 6, -2, 1, 1, -1, 2, -10, 2, 4, -6, 14]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27229666012737", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-9, 4, -12, -2, 9, 8, -10, 8, 10, 3, 1, 2],\n [4, 1, -6, 1, 0, -9, 7, 4, 14, -10, -10, 0],\n [-12, -6, -15, 1, 5, -12, 8, 4, -7, 3, -9, 5],\n [-2, 1, 1, 9, -8, -1, 6, -8, -2, 6, 6, 3],\n [9, 0, 5, -8, 11, 2, -12, 0, 1, 2, -4, 4],\n [8, -9, -12, -1, 2, 4, 7, -12, 0, 2, -7, -9],\n [-10, 7, 8, 6, -12, 7, -5, 10, 12, -4, -4, 0],\n [8, 4, 4, -8, 0, -12, 10, -16, -5, -2, -8, 14],\n [10, 14, -7, -2, 1, 0, 12, -5, 0, -11, -3, -2],\n [3, -10, 3, 6, 2, 2, -4, -2, -11, 15, 5, 1],\n [1, -10, -9, 6, -4, -7, -4, -8, -3, 5, 1, 2],\n [2, 0, 5, 3, 4, -9, 0, 14, -2, 1, 2, 3]], determine the value at position (11, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8972649283946", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (4, 8) of the result:\nA =\n[[-9, 6, 12, -4, -8, -8, 0, -3, -2, -2, -1, -7],\n [6, 7, 0, 2, 3, -4, 2, -8, -8, -8, 11, 2],\n [12, 0, -16, 2, 2, 1, -10, -1, -9, 4, -2, 2],\n [-4, 2, 2, -16, 1, 1, 0, -13, -1, -11, 10, -1],\n [-8, 3, 2, 1, -6, -9, -4, 6, 2, 0, 0, -8],\n [-8, -4, 1, 1, -9, 14, 0, -12, -2, -8, 1, 2],\n [0, 2, -10, 0, -4, 0, -5, 12, 13, 14, 10, 2],\n [-3, -8, -1, -13, 6, -12, 12, 4, 14, 1, -5, 5],\n [-2, -8, -9, -1, 2, -2, 13, 14, -9, 2, 8, -7],\n [-2, -8, 4, -11, 0, -8, 14, 1, 2, 7, -11, 12],\n [-1, 11, -2, 10, 0, 1, 10, -5, 8, -11, -9, 13],\n [-7, 2, 2, -1, -8, 2, 2, 5, -7, 12, 13, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-49535883443", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[11, 11, 10, -7, 6, 8, 2, -10, 2, 8, -4, -6],\n [11, 11, 0, 4, 0, -2, 0, 8, -6, 6, -12, 11],\n [10, 0, -2, -12, 1, 4, -8, -11, -6, 14, 3, -2],\n [-7, 4, -12, 12, -2, -4, 2, 10, 15, -2, 12, -1],\n [6, 0, 1, -2, -1, -4, -7, -12, -12, -10, -14, -2],\n [8, -2, 4, -4, -4, 13, 8, 2, -6, -8, -2, 3],\n [2, 0, -8, 2, -7, 8, -5, 6, 13, 2, 8, -2],\n [-10, 8, -11, 10, -12, 2, 6, 4, 12, 8, 4, -4],\n [2, -6, -6, 15, -12, -6, 13, 12, 8, 0, -6, -6],\n [8, 6, 14, -2, -10, -8, 2, 8, 0, -2, 0, 10],\n [-4, -12, 3, 12, -14, -2, 8, 4, -6, 0, 8, -4],\n [-6, 11, -2, -1, -2, 3, -2, -4, -6, 10, -4, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1904022434233595", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[3, 10, 0, -4, 1, 2, -14, -2, -5, -2, -3, -2],\n [10, -16, 0, 0, 13, -7, 2, 1, -12, -5, 2, 0],\n [0, 0, -8, -7, -8, -11, 1, -4, 10, 12, -9, -9],\n [-4, 0, -7, 0, 0, -1, -4, -8, 0, 4, 4, 11],\n [1, 13, -8, 0, 16, 7, -1, -6, 4, -8, 3, -6],\n [2, -7, -11, -1, 7, -8, 4, 10, 4, -2, 4, -2],\n [-14, 2, 1, -4, -1, 4, -13, 3, -2, -6, 8, -1],\n [-2, 1, -4, -8, -6, 10, 3, -9, 2, 6, 0, 1],\n [-5, -12, 10, 0, 4, 4, -2, 2, -7, -2, -2, -10],\n [-2, -5, 12, 4, -8, -2, -6, 6, -2, 8, 0, -4],\n [-3, 2, -9, 4, 3, 4, 8, 0, -2, 0, 13, -2],\n [-2, 0, -9, 11, -6, -2, -1, 1, -10, -4, -2, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1241998285974884", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[12, -3, 8, 9, -7, -3, -12, 5, -6, 12, -10, 1],\n [14, 3, -10, 13, -13, 13, 13, 13, 1, -7, -3, 6],\n [-5, -5, 9, -11, -2, 2, 6, -4, 14, 9, 1, 16],\n [15, -13, 2, -10, 9, 6, -10, -6, -9, -4, 15, 1],\n [-2, 7, 4, 1, -3, 2, -4, -1, -15, 9, 5, 3],\n [12, 1, 12, 10, 12, -11, 8, 4, 14, -1, -3, -11],\n [-6, 10, -12, -2, -1, 1, 16, 7, -10, -3, 13, 7],\n [-2, -4, 2, 12, 5, -15, -4, 1, -2, 0, -4, 5],\n [4, 9, -13, -10, -7, -2, 9, -1, 0, -1, 12, 1],\n [-6, -5, -15, 1, 16, -8, -2, 11, -9, -9, 2, -13],\n [10, -4, 4, 9, 6, 13, 14, 14, -1, -10, 0, 7],\n [3, 10, -15, -16, 10, -11, 10, -1, 10, 11, -14, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17286804121", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-14, 11, 6, 5, -10, 4, -1, 12, 0, -9, 3, 4],\n [11, 3, -8, -13, 4, -3, -3, 6, 2, -8, -6, 4],\n [6, -8, -10, -16, -2, 7, 10, -2, -6, 14, 14, -1],\n [5, -13, -16, -4, 0, 6, -11, 2, -5, -4, 0, -7],\n [-10, 4, -2, 0, 5, 2, 6, 8, -9, -8, -3, 9],\n [4, -3, 7, 6, 2, -12, 6, -2, -8, 2, -4, 3],\n [-1, -3, 10, -11, 6, 6, -12, 0, 0, -4, -4, 8],\n [12, 6, -2, 2, 8, -2, 0, -13, -6, 0, -2, -2],\n [0, 2, -6, -5, -9, -8, 0, -6, 6, -3, 0, 12],\n [-9, -8, 14, -4, -8, 2, -4, 0, -3, 1, 9, 8],\n [3, -6, 14, 0, -3, -4, -4, -2, 0, 9, -4, -2],\n [4, 4, -1, -7, 9, 3, 8, -2, 12, 8, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2840471854258", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[16, 1, -12, -16, -10, -14, -5, -2, -13, 16, -1, 12],\n [-11, 6, -4, -16, -5, 10, 8, 5, 1, -1, 12, 13],\n [13, 3, 5, -13, 14, -3, -9, -12, -9, -6, 12, 4],\n [-4, 2, -14, 2, 15, -3, -10, 3, 15, 14, 5, -12],\n [14, -2, 0, 2, -7, 8, 11, -2, 3, -4, 3, 14],\n [1, 11, -13, 7, -8, 15, 15, 4, 10, -9, 2, 12],\n [2, -12, 5, -7, -2, -15, 5, 2, -5, 3, -10, 7],\n [-14, -11, 16, 16, 12, 6, -13, -12, -1, -14, -3, 16],\n [11, -2, -13, 3, 8, 5, 11, -7, -1, 6, 2, -16],\n [-16, 9, -15, 11, 3, 10, 11, 14, -10, -9, 15, -6],\n [9, 8, -10, 3, 13, -16, 1, -9, 12, 5, 15, -3],\n [-15, -10, -14, -2, 5, 1, 1, 1, 12, -5, 1, 14]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44020592395918", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-2, 8, 3, -4, 1, -5, -10, 4, 0, 10, 6, -2],\n [8, 3, -6, 0, 14, -6, -4, 4, -2, 8, -1, -12],\n [3, -6, -1, -9, 8, 7, -5, 8, -2, 2, -3, -4],\n [-4, 0, -9, 9, -6, 7, -2, 0, -4, -1, 0, -10],\n [1, 14, 8, -6, 6, 6, 4, -3, -2, -9, -4, 8],\n [-5, -6, 7, 7, 6, 5, 0, -12, 8, -11, 4, -2],\n [-10, -4, -5, -2, 4, 0, 15, 12, 13, -10, 1, -2],\n [4, 4, 8, 0, -3, -12, 12, -6, 4, -8, -1, 2],\n [0, -2, -2, -4, -2, 8, 13, 4, -15, -5, -2, -1],\n [10, 8, 2, -1, -9, -11, -10, -8, -5, 2, 12, -2],\n [6, -1, -3, 0, -4, 4, 1, -1, -2, 12, -15, 2],\n [-2, -12, -4, -10, 8, -2, -2, 2, -1, -2, 2, 11]], determine the value at position (12, 12).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371285506313", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-14, -12, 12, -4, -13, -11, -11, -6, 10, -13, 10, -1],\n [1, -10, -6, -9, -11, -12, -11, -15, 14, 15, -8, -2],\n [4, 11, 10, -12, 0, 7, 14, -13, 3, 0, -7, 4],\n [4, -1, 16, -7, 1, 16, 12, 14, 7, -5, 3, -11],\n [-9, -3, -12, -14, 5, -9, -3, -10, -13, 2, 7, -1],\n [-11, -9, 8, 15, 8, -7, 0, -14, -8, 1, 13, -12],\n [15, 10, 4, 7, -14, -1, -2, 8, -9, -13, 15, 13],\n [13, 0, 2, 14, 0, -15, 12, 13, 5, -6, 16, 2],\n [-14, 5, 1, 13, -16, 3, -12, -5, -6, 7, 1, -9],\n [12, 5, -15, 6, -1, -9, -13, -3, -8, -6, -1, -4],\n [0, -3, 12, 0, -16, 3, 16, -15, 0, 6, 5, -16],\n [-5, -4, -3, -7, -5, 5, 1, 2, 13, -2, -3, -8]], determine the value at position (2, 8).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12437512413", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-12, 0, -12, 6, -3, 1, -6, -8, 2, -3, 6, -2],\n [0, -6, 7, 8, -4, -10, 6, -3, 8, 7, 6, 6],\n [-12, 7, 7, -1, -8, 14, -4, -6, -12, 0, -6, 6],\n [6, 8, -1, 5, -8, 4, 0, -4, -1, 0, -15, 0],\n [-3, -4, -8, -8, -8, 6, 0, 6, 12, -2, -2, -7],\n [1, -10, 14, 4, 6, -4, 8, 4, -2, -8, -3, 6],\n [-6, 6, -4, 0, 0, 8, -4, -12, 6, -10, 4, -4],\n [-8, -3, -6, -4, 6, 4, -12, 13, 1, 3, 6, -4],\n [2, 8, -12, -1, 12, -2, 6, 1, 4, 0, 6, -2],\n [-3, 7, 0, 0, -2, -8, -10, 3, 0, 15, 0, 0],\n [6, 6, -6, -15, -2, -3, 4, 6, 6, 0, 8, -3],\n [-2, 6, 6, 0, -7, 6, -4, -4, -2, 0, -3, 11]], determine the value at position (6, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17057130076", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-8, 10, 5, 5, -2, 1, -8, 0, -12, 4, -1, 2],\n [10, 3, -6, -14, 5, -5, 8, -11, -10, -4, 16, 2],\n [5, -6, 9, -4, -2, -4, 8, -12, 0, 8, 9, 12],\n [5, -14, -4, -1, 11, 4, 12, 1, 5, 3, -2, -7],\n [-2, 5, -2, 11, 11, 0, -1, 2, 16, 2, -10, -6],\n [1, -5, -4, 4, 0, -11, -13, -6, -6, -8, -2, -2],\n [-8, 8, 8, 12, -1, -13, 14, -16, -9, -1, -11, 4],\n [0, -11, -12, 1, 2, -6, -16, -8, 4, 4, -4, -4],\n [-12, -10, 0, 5, 16, -6, -9, 4, -1, -12, -10, 0],\n [4, -4, 8, 3, 2, -8, -1, 4, -12, -12, -3, 6],\n [-1, 16, 9, -2, -10, -2, -11, -4, -10, -3, -1, -1],\n [2, 2, 12, -7, -6, -2, 4, -4, 0, 6, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6176696881516", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-11, 14, 0, -2, 9, -10, -4, -6, 9, 4, 4, 12],\n [14, -15, -9, 10, -4, -1, 2, -8, -14, 10, -6, 9],\n [0, -9, 4, -8, 2, 15, 2, 5, -8, 2, -2, -2],\n [-2, 10, -8, 10, 3, 2, 9, -2, 1, -4, 7, -5],\n [9, -4, 2, 3, -7, -8, 0, 6, 0, 1, -7, 2],\n [-10, -1, 15, 2, -8, 14, 0, 9, -4, -2, 0, 8],\n [-4, 2, 2, 9, 0, 0, 4, 10, 4, -2, -8, -2],\n [-6, -8, 5, -2, 6, 9, 10, -15, -10, -6, -2, 2],\n [9, -14, -8, 1, 0, -4, 4, -10, 11, -14, 12, 6],\n [4, 10, 2, -4, 1, -2, -2, -6, -14, 10, -10, 8],\n [4, -6, -2, 7, -7, 0, -8, -2, 12, -10, 12, -10],\n [12, 9, -2, -5, 2, 8, -2, 2, 6, 8, -10, 11]], determine the value at position (6, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44268805933374", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[15, 4, 2, -2, 8, 10, -2, -2, -2, 4, -6, 10],\n [4, 0, 3, 0, -10, 8, -6, 0, -2, -14, 4, -12],\n [2, 3, 14, 10, 12, 5, 8, -9, -11, 12, 1, 14],\n [-2, 0, 10, 0, 2, 8, -6, -4, -8, -8, -4, -2],\n [8, -10, 12, 2, 4, 9, 6, -6, 0, 8, -4, 9],\n [10, 8, 5, 8, 9, 12, 13, 12, 9, 8, -12, -2],\n [-2, -6, 8, -6, 6, 13, 0, 8, -1, 1, 10, 6],\n [-2, 0, -9, -4, -6, 12, 8, 4, 4, 14, 2, -4],\n [-2, -2, -11, -8, 0, 9, -1, 4, -4, -2, -6, 6],\n [4, -14, 12, -8, 8, 8, 1, 14, -2, -10, -4, 2],\n [-6, 4, 1, -4, -4, -12, 10, 2, -6, -4, -8, -13],\n [10, -12, 14, -2, 9, -2, 6, -4, 6, 2, -13, -14]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4613769145235", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-4, -5, -11, -2, 1, -14, 5, 11, -5, -16, 13, 6],\n [11, -12, -7, -12, -3, 7, 11, 4, -5, 3, 15, 4],\n [0, -16, 11, -15, 0, -3, -3, 1, -16, 1, 6, -1],\n [2, -11, 7, 0, -1, -11, -1, -8, 12, -13, 9, 9],\n [-3, 7, -9, 8, -13, -2, -1, -6, 11, -10, 7, 14],\n [-13, -11, 16, 15, 0, 15, -3, 2, 7, -6, -10, 7],\n [7, -3, 7, -6, -9, -2, -15, 7, -7, 15, 0, -7],\n [5, -11, 10, 3, -16, 0, -16, -2, -16, 0, -15, 1],\n [-5, 12, 6, -8, -9, -1, 6, 12, -7, -5, -5, 13],\n [-7, -3, -13, 3, -10, 13, 7, -7, 0, 4, -14, -16],\n [1, -15, -13, 15, 2, 3, -10, -8, -10, 10, 4, 7],\n [15, -5, 6, 12, -14, -9, -3, 15, -10, -7, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-184265695027398", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-6, -4, -5, -10, -7, -10, 10, -10, 7, 6, 8, 16],\n [-10, 13, 14, 4, 4, 3, -9, 15, 13, 12, -12, 13],\n [-5, 10, -4, -7, 14, -1, 9, 3, -9, -13, 12, 14],\n [-15, 8, -14, -12, 5, -1, -8, -8, -5, -13, 1, 1],\n [16, -14, 0, -5, -6, 0, -11, -11, 15, -6, -4, -4],\n [-14, 15, -13, -16, -8, -10, 10, -14, 5, -1, -9, -12],\n [13, 11, 10, 5, 13, -10, 13, -4, 5, -6, -12, 5],\n [-2, 14, 12, 0, -11, 0, 6, 13, -4, 13, 3, -11],\n [14, 2, -11, 11, -4, -7, -10, 1, 5, -3, -9, -5],\n [16, 7, -3, -12, 2, -14, -16, 16, 0, -8, 14, -14],\n [-4, -3, -11, 12, -8, 6, -2, -10, 8, 6, -6, -9],\n [-16, -4, -1, -4, -3, -4, -5, 11, 5, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49103917731160", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 10) of the 7th power of the matrix:\n[[13, 9, -2, 13, 12, 15, 13, -1, 1, 11, 2, -6],\n [0, 4, 16, 12, -13, 15, -6, 9, 1, 15, 10, -1],\n [-7, 16, -7, 9, 8, -15, 9, 3, -14, 15, -16, 7],\n [16, 0, 16, -6, 6, 15, 2, -5, 11, -15, -7, 2],\n [11, -9, 6, 13, 11, -4, -5, -7, 0, -16, 5, -2],\n [-1, 3, -7, 9, 6, 0, 5, -13, -10, -12, 14, 2],\n [-13, 5, -14, 6, -13, 7, -3, -14, 4, 9, -16, 13],\n [-13, -3, 1, -5, -1, -16, -14, -2, -1, 0, -7, -6],\n [11, 10, 1, 13, -4, -1, -15, 3, -5, 12, -9, 3],\n [14, -1, 6, 15, 0, 7, 6, -9, 6, 4, 2, 14],\n [-10, 7, -9, -4, -14, -4, 15, 4, -16, -15, 9, -14],\n [7, 9, -9, -9, 1, 1, -5, -15, 3, -14, -11, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17910610810", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[7, 1, 16, -10, 12, 2, 8, 0, -14, 7, 1, 9],\n [4, -6, 0, 4, -13, 15, 1, 11, 9, 7, -7, -9],\n [-15, 4, 10, 6, 15, 9, -10, 16, 0, -9, 0, 1],\n [6, -5, 6, 16, 11, 6, -10, -15, -16, -13, -9, 12],\n [1, 14, -11, 7, -2, -5, -3, 10, -4, -14, -1, -5],\n [-3, 14, -12, -5, 9, 0, -6, 16, -13, 15, 14, -6],\n [0, 10, -9, 4, 16, -12, 15, 8, -9, 10, 9, 12],\n [-8, 1, -10, 4, -1, -14, 15, -7, 15, -9, 15, -13],\n [12, -5, 2, 14, 9, -11, 12, 0, 3, -7, -11, 15],\n [-15, -7, 10, 2, -1, 3, -12, 1, -9, -4, -7, 2],\n [14, 12, 6, 15, -6, -15, 15, -12, 14, -4, 5, 2],\n [12, 6, 2, -1, 14, -1, 9, -14, 6, -8, 7, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284073430173", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-3, 4, -4, 2, -4, -5, -1, 8, 6, -4, 0, 0],\n [4, -16, 2, -10, -10, -3, -4, 2, -2, 6, -1, -4],\n [-4, 2, -13, -8, 8, -2, -8, -2, -8, 2, -6, 6],\n [2, -10, -8, -14, 7, -4, 1, 4, -12, 6, 12, 4],\n [-4, -10, 8, 7, -8, 14, 8, -1, -3, 2, 8, -6],\n [-5, -3, -2, -4, 14, 0, 1, -2, -12, -6, 4, 7],\n [-1, -4, -8, 1, 8, 1, -1, 8, 0, 2, -9, 8],\n [8, 2, -2, 4, -1, -2, 8, -14, -5, 7, -7, 6],\n [6, -2, -8, -12, -3, -12, 0, -5, -1, 2, -12, -6],\n [-4, 6, 2, 6, 2, -6, 2, 7, 2, 15, -6, 4],\n [0, -1, -6, 12, 8, 4, -9, -7, -12, -6, -15, -6],\n [0, -4, 6, 4, -6, 7, 8, 6, -6, 4, -6, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-440930172474", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (1, 3) of the result:\nA =\n[[11, 4, -11, -15, -7, -8, -14, -15, -9, -8, 9, 13],\n [-9, -14, -6, 8, -12, -5, 13, 10, -12, 3, 4, -14],\n [-13, 7, -10, 7, -6, -15, -11, -10, 1, -8, 11, 2],\n [-13, -13, -4, 11, -6, -15, -11, -5, 7, -8, 9, -13],\n [-13, 5, -4, -2, -15, -15, -9, 1, 12, -6, -11, -8],\n [5, 8, 14, 4, 2, -7, -5, 2, -15, -2, -9, 13],\n [-8, 13, 2, 12, -15, 11, -9, 8, -7, 5, 7, 9],\n [14, 6, -15, 16, 7, -5, -8, -14, 6, 7, 16, 13],\n [-15, 5, -6, -5, 2, 3, -8, 1, 1, 10, -4, -9],\n [6, -4, -10, -15, -14, 6, -10, -13, -9, 15, 2, -5],\n [-7, -3, 10, 4, 3, -13, 2, 12, -10, 16, -9, -6],\n [16, 8, 16, 9, -6, 13, 16, -7, 12, 8, 15, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-59199672235", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 1) of the 7th power of the matrix:\n[[5, 2, -6, 0, 4, 6, 0, -11, -3, 1, -13, -3],\n [2, -2, 10, -8, 0, 0, 3, 6, 1, 12, 10, 4],\n [-6, 10, 7, -2, -1, 7, 0, 0, -6, -6, 4, -8],\n [0, -8, -2, -3, 2, -16, 8, -6, -12, -10, 5, 4],\n [4, 0, -1, 2, 14, 6, -1, 4, 12, -4, 6, 1],\n [6, 0, 7, -16, 6, 2, -9, 8, 0, -2, -10, -10],\n [0, 3, 0, 8, -1, -9, 1, 0, 4, 6, -1, 5],\n [-11, 6, 0, -6, 4, 8, 0, -4, 14, 6, 8, -6],\n [-3, 1, -6, -12, 12, 0, 4, 14, 0, 10, -3, -5],\n [1, 12, -6, -10, -4, -2, 6, 6, 10, -13, 2, -1],\n [-13, 10, 4, 5, 6, -10, -1, 8, -3, 2, -2, -15],\n [-3, 4, -8, 4, 1, -10, 5, -6, -5, -1, -15, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8681500989", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[0, 2, 6, 13, 2, 7, 9, 4, 2, 6, 6, 1],\n [2, 7, -4, 2, -2, 2, 2, -2, -4, 7, -9, 2],\n [6, -4, 2, -8, 3, 8, 10, -4, -2, -4, -4, 6],\n [13, 2, -8, 6, 8, 0, -2, -2, -4, -1, -6, 2],\n [2, -2, 3, 8, 16, 0, 8, -8, -4, 1, 2, 6],\n [7, 2, 8, 0, 0, -6, -6, -2, 2, -2, -9, -3],\n [9, 2, 10, -2, 8, -6, 7, 4, 6, 2, 8, 7],\n [4, -2, -4, -2, -8, -2, 4, 12, 2, -5, 0, -10],\n [2, -4, -2, -4, -4, 2, 6, 2, -9, -10, 0, 6],\n [6, 7, -4, -1, 1, -2, 2, -5, -10, 14, -2, -4],\n [6, -9, -4, -6, 2, -9, 8, 0, 0, -2, 15, 2],\n [1, 2, 6, 2, 6, -3, 7, -10, 6, -4, 2, -9]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244795909385", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-3, 12, 13, -13, -10, 9, 15, 16, 7, -16, 12, 4],\n [6, -12, 13, 1, -11, -12, 1, -4, 3, 4, -13, -4],\n [1, -4, -4, 10, 9, -5, -15, 3, -7, -9, 14, -2],\n [1, -2, 2, 7, -15, -4, -8, -15, -1, -15, -1, -9],\n [-16, 1, 9, -12, 4, 11, 9, 15, 4, -13, 7, 16],\n [-12, -14, -6, 15, 5, -6, 5, -13, -14, -7, 2, 1],\n [11, 14, 0, 7, -16, -12, 15, 0, 4, 5, -3, -1],\n [-12, 1, -13, 11, 10, -11, -6, 4, 0, 14, -4, 6],\n [-16, -13, 13, 14, -1, -14, -5, -5, -6, -1, 12, 4],\n [-12, -4, 0, -5, 0, -16, -9, -1, -2, 2, 8, 14],\n [-15, 8, 14, -13, -13, -5, 0, 4, 12, 5, -1, -2],\n [13, -6, -4, 6, 3, -15, -9, 1, -10, 14, 5, 11]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41717705754565", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[8, -1, 11, 0, -6, -2, 1, 8, -2, -2, 12, 6],\n [-1, 10, -8, -4, 6, 0, 6, -11, -10, -2, 6, -3],\n [11, -8, 11, -4, 6, 2, 11, 10, -10, -3, -12, -13],\n [0, -4, -4, 10, 11, 2, 0, -10, 2, 14, -3, 8],\n [-6, 6, 6, 11, -7, 6, -10, -6, 0, -11, -7, 13],\n [-2, 0, 2, 2, 6, -3, 8, 12, 2, 0, 1, -10],\n [1, 6, 11, 0, -10, 8, -8, 5, 0, 6, 0, 3],\n [8, -11, 10, -10, -6, 12, 5, 7, -4, -2, -8, -8],\n [-2, -10, -10, 2, 0, 2, 0, -4, 16, -2, 0, 0],\n [-2, -2, -3, 14, -11, 0, 6, -2, -2, -4, 4, -8],\n [12, 6, -12, -3, -7, 1, 0, -8, 0, 4, -14, 4],\n [6, -3, -13, 8, 13, -10, 3, -8, 0, -8, 4, 1]], determine the value at position (10, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "134674745103", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[5, -11, 2, -6, 7, 6, -13, 1, 13, -2, 6, -5],\n [-13, -13, -3, -9, 6, -16, -6, 10, -13, 12, 0, 2],\n [7, 15, 14, -1, 15, -1, 4, -4, 1, -15, 16, 1],\n [11, -5, -9, 8, -10, -15, 16, 16, 6, -12, -3, -9],\n [3, 1, 6, 12, -10, 7, 8, -3, -14, -3, -14, -8],\n [-10, 9, -10, -10, -4, -14, 3, -8, 5, 16, 6, 6],\n [9, 15, 11, 13, 0, 1, 8, -13, 9, 14, -5, 1],\n [-7, -15, 8, -8, 15, -12, -14, 0, -4, -14, 11, -13],\n [1, -3, -1, -5, -6, -15, 16, -4, 13, 9, 1, -4],\n [-13, 16, -2, 0, -11, -12, 16, -1, 7, -12, -14, 10],\n [-5, 8, 0, 3, 11, -2, 16, -14, -10, -7, 9, -11],\n [16, -1, 7, 13, -7, -6, 5, -14, 6, 2, -4, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12630676721327", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[5, 2, 2, 6, 0, 5, 5, 2, -5, -2, 0, 8],\n [2, 9, 14, 8, 12, -6, 6, 7, -4, 2, 0, -6],\n [2, 14, -2, -9, -2, 4, -8, 6, -8, -7, -1, 4],\n [6, 8, -9, -9, -6, 14, -4, -8, 0, 4, -7, 14],\n [0, 12, -2, -6, 0, -9, -4, -7, -3, 2, 9, 10],\n [5, -6, 4, 14, -9, -16, 10, -6, -4, -6, 4, 6],\n [5, 6, -8, -4, -4, 10, 16, 2, 5, 9, -3, -4],\n [2, 7, 6, -8, -7, -6, 2, 13, 6, 4, -10, 10],\n [-5, -4, -8, 0, -3, -4, 5, 6, 13, 10, -2, -2],\n [-2, 2, -7, 4, 2, -6, 9, 4, 10, 8, -8, 10],\n [0, 0, -1, -7, 9, 4, -3, -10, -2, -8, -7, -2],\n [8, -6, 4, 14, 10, 6, -4, 10, -2, 10, -2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451677592549199", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -5, 10, 3, 8, 6, -7, -12, 9, 2, 10, -2],\n [-5, -11, 2, 2, -5, 10, -5, -12, 0, 1, -2, -4],\n [10, 2, 5, 8, -4, -12, 7, 0, -12, -8, -10, 3],\n [3, 2, 8, -8, -4, -6, 8, 6, -7, 6, 10, 0],\n [8, -5, -4, -4, -2, 3, -1, -10, 1, 0, 10, 4],\n [6, 10, -12, -6, 3, -16, 2, -10, 9, 2, -7, 6],\n [-7, -5, 7, 8, -1, 2, 4, 2, 9, -4, -10, 2],\n [-12, -12, 0, 6, -10, -10, 2, 6, 3, -5, 10, 2],\n [9, 0, -12, -7, 1, 9, 9, 3, 5, 12, 4, 6],\n [2, 1, -8, 6, 0, 2, -4, -5, 12, -5, 2, 10],\n [10, -2, -10, 10, 10, -7, -10, 10, 4, 2, 8, 6],\n [-2, -4, 3, 0, 4, 6, 2, 2, 6, 10, 6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71153018584960", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 11, 0, 4, 12, -2, -12, 15, 2, 0, 0, -2],\n [11, -2, -2, 2, 12, -6, 0, 0, 0, -9, 2, 6],\n [0, -2, 12, 12, 10, 1, 9, 4, -2, -1, 9, -2],\n [4, 2, 12, 14, -8, 3, -2, 5, 10, -14, -6, 0],\n [12, 12, 10, -8, -10, -7, -2, 4, 12, 2, 10, 4],\n [-2, -6, 1, 3, -7, -1, 12, 0, 2, 5, -1, 4],\n [-12, 0, 9, -2, -2, 12, 3, -8, -1, -12, -1, 13],\n [15, 0, 4, 5, 4, 0, -8, 14, 0, -8, -2, 3],\n [2, 0, -2, 10, 12, 2, -1, 0, 9, -8, -8, -6],\n [0, -9, -1, -14, 2, 5, -12, -8, -8, -4, 2, 0],\n [0, 2, 9, -6, 10, -1, -1, -2, -8, 2, 12, -9],\n [-2, 6, -2, 0, 4, 4, 13, 3, -6, 0, -9, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4539358625338082", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 2) of the 8th power of the matrix:\n[[3, -2, -14, -14, 6, -8, -6, -4, -9, 5, 10, 9],\n [6, 14, 12, -16, -7, -13, 14, -13, 12, -8, -2, -14],\n [-2, -6, -11, -10, -13, 4, -16, 6, -4, 11, 12, 1],\n [6, 11, -8, -11, -1, -16, 5, 6, 4, 14, 11, 10],\n [-4, 15, -10, 16, -4, 15, -10, -5, -2, 4, -5, -4],\n [-15, 12, 12, -10, 13, 6, 11, 6, 12, -13, 3, -12],\n [-6, -15, 7, 16, 5, -11, 7, 12, 15, 13, -14, 8],\n [11, -2, 0, -15, 10, -3, 15, -5, 6, -1, -15, -10],\n [4, 14, 6, 8, -10, -12, 15, -12, 8, 14, 3, 5],\n [-4, -15, 5, -8, -15, 15, -9, -1, 16, -6, 15, -9],\n [15, 4, 8, 3, -16, 4, -10, 8, -8, 5, -15, 2],\n [-11, -12, -7, -16, 9, 9, 1, 4, -5, -3, 15, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-678783625445", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 9) of the matrix A^9 where A is:\n[[-7, -4, -8, -6, 0, 12, -9, 4, -13, -6, -3, -4],\n [-4, 6, 6, 2, 10, 0, -5, -5, -12, 10, 2, 8],\n [-8, 6, -5, -1, -10, 8, 1, -5, -10, -7, -13, 2],\n [-6, 2, -1, 15, 6, -11, 1, -8, -6, -2, 0, 6],\n [0, 10, -10, 6, -9, 2, -6, -12, -2, -8, -4, 5],\n [12, 0, 8, -11, 2, 11, 8, 7, 2, -4, 2, 8],\n [-9, -5, 1, 1, -6, 8, -6, -5, 5, -2, 1, -3],\n [4, -5, -5, -8, -12, 7, -5, -15, 2, -2, -6, 8],\n [-13, -12, -10, -6, -2, 2, 5, 2, -14, 10, 4, -12],\n [-6, 10, -7, -2, -8, -4, -2, -2, 10, -13, 4, -6],\n [-3, 2, -13, 0, -4, 2, 1, -6, 4, 4, -16, -4],\n [-4, 8, 2, 6, 5, 8, -3, 8, -12, -6, -4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10786244269359", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[13, 14, 3, 12, 0, 2, 2, -8, 5, 12, 8, 11],\n [14, -14, 1, -1, -2, 0, 8, -2, 0, 0, -11, 11],\n [3, 1, 13, -4, -13, -10, 3, 1, -2, 0, 6, -4],\n [12, -1, -4, 1, 0, 3, 5, -14, 0, 0, 4, -10],\n [0, -2, -13, 0, -12, 0, -10, -12, 0, -6, -10, -1],\n [2, 0, -10, 3, 0, -11, 2, -6, -12, 4, -12, -10],\n [2, 8, 3, 5, -10, 2, 16, 9, 0, -1, 2, 2],\n [-8, -2, 1, -14, -12, -6, 9, -6, -8, -3, -11, -5],\n [5, 0, -2, 0, 0, -12, 0, -8, -2, 5, -4, 4],\n [12, 0, 0, 0, -6, 4, -1, -3, 5, 1, 2, 8],\n [8, -11, 6, 4, -10, -12, 2, -11, -4, 2, 13, 11],\n [11, 11, -4, -10, -1, -10, 2, -5, 4, 8, 11, 8]], determine the value at position (5, 8).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31608599082968", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[2, 0, -1, -1, -13, 13, -12, 16, -8, 0, -5, 7],\n [-5, -2, -1, 6, 1, 5, 14, -2, 4, -9, -11, 0],\n [11, 6, 14, -6, 3, 15, 0, -11, -16, -13, 14, -6],\n [0, -10, -15, -7, -5, 0, 9, -12, -12, 10, -12, -9],\n [14, 16, 4, 4, -2, -15, 13, 11, 0, 3, 12, -12],\n [8, -7, 2, -16, -3, 8, 9, 4, -1, -7, 15, 3],\n [-8, 14, 2, 14, 13, 7, 16, 1, 4, 14, -13, 9],\n [16, 16, 3, -9, -9, 14, 5, 2, 3, 6, 7, 7],\n [-8, -1, 10, -4, -15, -5, 16, 6, -3, 13, -8, -2],\n [7, 8, 15, 4, -11, 8, -15, 14, 13, -2, 1, 15],\n [-3, 1, 5, -3, -3, 5, -1, -1, -1, 1, 6, 1],\n [5, 13, 1, 1, -16, -2, -12, 10, 0, 15, 9, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-79963446606651", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[11, 9, 2, -6, 0, 6, 4, -6, 2, -7, -2, 4],\n [9, 6, -6, 5, 0, 9, 0, 0, 4, 1, -6, -6],\n [2, -6, -3, -9, -13, 2, -2, -10, 10, -13, 11, -12],\n [-6, 5, -9, 12, -14, 10, 4, -11, -2, 13, -8, -2],\n [0, 0, -13, -14, -12, -10, 13, 6, 4, -4, 1, -6],\n [6, 9, 2, 10, -10, -10, -10, -1, -3, 0, -6, 11],\n [4, 0, -2, 4, 13, -10, -10, 10, 2, 6, 6, -2],\n [-6, 0, -10, -11, 6, -1, 10, 16, -4, 4, -6, 4],\n [2, 4, 10, -2, 4, -3, 2, -4, 9, 0, 4, 0],\n [-7, 1, -13, 13, -4, 0, 6, 4, 0, -14, -8, 2],\n [-2, -6, 11, -8, 1, -6, 6, -6, 4, -8, -12, 9],\n [4, -6, -12, -2, -6, 11, -2, 4, 0, 2, 9, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13807564091897", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-7, 2, 1, -5, 1, 1, 8, 0, 0, -4, 6, 12],\n [2, -1, -2, -8, 6, -3, 2, -6, 10, -6, -4, 8],\n [1, -2, -12, 14, 11, 0, 2, 5, -4, -6, 0, -12],\n [-5, -8, 14, -10, -4, -5, -10, -3, 6, 2, -4, 3],\n [1, 6, 11, -4, -9, 3, -14, -8, -2, -2, 0, -4],\n [1, -3, 0, -5, 3, 11, 2, -4, 8, -5, -5, -12],\n [8, 2, 2, -10, -14, 2, -10, 0, -5, 12, 3, 2],\n [0, -6, 5, -3, -8, -4, 0, -2, -10, -2, -8, 12],\n [0, 10, -4, 6, -2, 8, -5, -10, -10, -10, 4, -5],\n [-4, -6, -6, 2, -2, -5, 12, -2, -10, -14, -8, 6],\n [6, -4, 0, -4, 0, -5, 3, -8, 4, -8, 1, 2],\n [12, 8, -12, 3, -4, -12, 2, 12, -5, 6, 2, -14]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154965433804855", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-16, -10, -8, -16, -12, -7, -15, 6, 12, 2, 3, -5],\n [-6, -10, 6, 0, -15, -12, 4, -4, -6, 7, 16, 10],\n [1, 4, -13, 15, -6, -14, 4, -3, -11, 12, 14, 11],\n [11, 2, -14, -5, 7, -5, 7, -16, 11, -1, 4, 13],\n [9, 14, -1, 12, 12, -8, -3, -9, -15, -6, -15, 1],\n [-12, -10, 6, 2, 2, 2, 11, -6, -6, -8, -3, 12],\n [4, -12, 16, -8, -14, -3, 1, -5, 6, -3, -1, 3],\n [3, -2, 8, 0, -5, -10, -9, 7, 8, 4, 16, -7],\n [5, 2, 12, -14, -13, 14, -11, 11, -7, -5, -15, -14],\n [-16, 7, 3, -1, 13, 8, -12, 12, 11, 6, 15, 1],\n [7, 11, 4, -12, 9, 6, 16, 9, 5, 3, -15, 1],\n [-12, 15, -6, 4, 5, -14, -8, -15, 11, -7, 2, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50366242030950", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-15, -14, -1, -6, 6, 4, 2, -1, 11, -4, -6, 8],\n [-14, -14, -4, -10, -2, 0, 7, 5, -4, 2, -8, 16],\n [-1, -4, 14, -4, -6, -10, -2, -4, 4, 8, 4, 1],\n [-6, -10, -4, -9, -2, -3, 4, -3, 5, 4, -8, -12],\n [6, -2, -6, -2, 9, 1, 4, 6, 10, -8, 0, -6],\n [4, 0, -10, -3, 1, 16, -8, 1, 6, 0, 4, -3],\n [2, 7, -2, 4, 4, -8, 7, -6, 10, -8, 8, 0],\n [-1, 5, -4, -3, 6, 1, -6, -11, -10, 6, -1, 6],\n [11, -4, 4, 5, 10, 6, 10, -10, -11, -6, 7, -13],\n [-4, 2, 8, 4, -8, 0, -8, 6, -6, -5, 1, -12],\n [-6, -8, 4, -8, 0, 4, 8, -1, 7, 1, 6, 8],\n [8, 16, 1, -12, -6, -3, 0, 6, -13, -12, 8, -16]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4762385307543", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[7, 0, 15, -3, 0, 15, 16, 13, 11, 7, -3, -16],\n [5, 16, 1, -5, -7, -15, -15, -11, 3, 11, -14, 8],\n [6, -4, 7, -14, 11, 9, 3, 10, -16, -7, -7, -16],\n [15, 15, 10, -4, 0, 11, 8, -15, 15, 15, -11, 14],\n [-8, -1, 8, 11, 0, 14, 6, 14, 9, -13, -2, 6],\n [-12, 8, 13, 9, -14, -13, 1, -6, -6, -1, 8, -16],\n [9, 13, -11, 10, 2, 2, 15, -16, 8, -4, -7, 1],\n [5, -11, 10, -9, 7, 3, 5, -8, 2, -16, -6, -7],\n [-16, 10, 0, 0, -15, 6, -7, 13, 8, 0, 2, 1],\n [1, -7, 6, 5, -8, 15, 9, 12, 2, 12, -5, -9],\n [8, 10, -11, -4, -6, -11, -12, -10, 2, -11, 8, -8],\n [3, 8, -9, -15, 5, -13, -16, 16, 7, -12, 9, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299479156450", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 6) of the 7th power of the matrix:\n[[-12, 6, 2, 4, 4, 4, -12, -8, 6, 0, 9, -6],\n [6, -12, -5, -4, 2, -2, 8, 0, 2, 14, 2, 2],\n [2, -5, -14, 0, -4, -1, -6, -6, 4, -12, 7, 4],\n [4, -4, 0, -15, -8, -10, -16, -10, -8, 0, 8, -2],\n [4, 2, -4, -8, 13, -2, 7, 4, -2, 6, -10, 0],\n [4, -2, -1, -10, -2, 16, -15, 2, -4, 2, 6, 8],\n [-12, 8, -6, -16, 7, -15, 0, -2, 2, -6, 3, 4],\n [-8, 0, -6, -10, 4, 2, -2, 10, 4, -6, 12, 4],\n [6, 2, 4, -8, -2, -4, 2, 4, -13, 11, -3, 4],\n [0, 14, -12, 0, 6, 2, -6, -6, 11, 4, 2, 5],\n [9, 2, 7, 8, -10, 6, 3, 12, -3, 2, -1, 10],\n [-6, 2, 4, -2, 0, 8, 4, 4, 4, 5, 10, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8896211890", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (9, 6) of the result:\nA =\n[[-8, 3, -3, 9, 10, 12, 15, -12, -13, 6, 4, 16],\n [7, -1, 15, 2, 9, -14, 1, -10, 15, 7, -1, 7],\n [-13, 15, 2, -3, -4, 5, 14, 13, 6, -5, -3, -9],\n [7, -14, -3, -6, 11, 6, 1, 3, 16, -15, 9, -15],\n [-14, 3, -7, 4, -8, -15, 11, -14, -1, -13, 6, 13],\n [-4, -11, -7, 0, -9, -8, 0, 5, -14, 12, 10, -14],\n [2, -3, 4, -15, -7, 0, -15, 10, -16, 16, 5, 1],\n [-14, -1, -6, -7, 4, 8, -11, -9, -16, -14, 10, -4],\n [2, 2, -11, -3, -12, -8, 6, 15, 12, 11, -6, 2],\n [-16, -8, -15, -13, 12, -13, -16, 11, 1, -4, -11, 5],\n [13, 10, -9, 11, -15, 3, -6, -3, 7, -4, -9, 4],\n [5, -8, -6, -1, -8, -14, -4, -16, -6, 7, -12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21993748306351", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (7, 12) of the result:\nA =\n[[0, 0, 2, -3, -6, -7, 0, -3, -7, -4, 12, 4],\n [0, -6, -11, 6, 12, 4, 0, 14, -12, -8, 8, -12],\n [2, -11, -1, -9, -1, -10, -13, -6, -6, 3, 0, 4],\n [-3, 6, -9, -13, 10, -1, -4, 4, 0, 10, 5, 12],\n [-6, 12, -1, 10, -13, -2, 3, -4, 1, 2, -1, 14],\n [-7, 4, -10, -1, -2, -2, 6, -3, -3, 6, 2, 6],\n [0, 0, -13, -4, 3, 6, -16, 2, -6, -3, 10, 4],\n [-3, 14, -6, 4, -4, -3, 2, 10, -2, 2, 4, 2],\n [-7, -12, -6, 0, 1, -3, -6, -2, -11, -7, -9, -10],\n [-4, -8, 3, 10, 2, 6, -3, 2, -7, -2, -8, 6],\n [12, 8, 0, 5, -1, 2, 10, 4, -9, -8, -8, 10],\n [4, -12, 4, 12, 14, 6, 4, 2, -10, 6, 10, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1267399124510", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[1, 13, -9, -11, 6, 8, 9, -8, -15, -8, 3, 0],\n [13, -10, -1, 14, -4, -12, -2, 16, -4, -6, 1, -2],\n [-9, -1, 10, -6, 0, -4, 1, -2, 4, -4, 6, 4],\n [-11, 14, -6, -12, -1, -2, -14, -2, -5, -4, -9, -2],\n [6, -4, 0, -1, 11, -2, -6, 10, -1, -3, 12, -2],\n [8, -12, -4, -2, -2, 5, 5, -2, 8, -8, 7, -2],\n [9, -2, 1, -14, -6, 5, 15, 10, -1, 10, -6, -9],\n [-8, 16, -2, -2, 10, -2, 10, -14, -8, -2, 6, 2],\n [-15, -4, 4, -5, -1, 8, -1, -8, -11, 0, -4, 0],\n [-8, -6, -4, -4, -3, -8, 10, -2, 0, 10, -7, -4],\n [3, 1, 6, -9, 12, 7, -6, 6, -4, -7, 2, 2],\n [0, -2, 4, -2, -2, -2, -9, 2, 0, -4, 2, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15075381640907128", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-14, -7, -12, 7, 3, 14, 0, 7, 1, 9, -10, -3],\n [-15, 13, 0, 3, -7, 7, -5, 10, -2, -8, 1, -10],\n [11, -14, -1, -13, -8, -5, -7, -15, 2, -4, 16, -16],\n [11, -11, -14, 8, -1, -13, -9, -1, 6, -11, -1, -1],\n [6, -1, -5, -8, 1, -8, 4, -16, 6, -12, 2, 16],\n [1, -3, 3, -4, -1, 14, 3, -16, -4, -10, 5, -10],\n [3, -13, -11, -14, -14, -14, -8, -1, -1, -5, 3, 14],\n [13, 4, -14, 4, 11, 11, -12, -10, -12, -8, 4, 3],\n [0, 11, 14, 16, 15, 15, 6, 4, 8, 16, -14, -11],\n [11, -15, 15, 9, -12, -6, -7, -2, 1, -3, 11, 13],\n [-4, 3, -15, 8, -5, 8, -13, -5, -10, 15, -11, 10],\n [4, 3, 2, 16, -13, 2, 11, 5, 7, 13, 12, -7]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7006255071079", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[15, -8, 8, -1, -2, 1, 6, -14, -10, -6, 7, 8],\n [11, -5, 6, 0, 1, -8, 1, 3, 4, 3, -11, -8],\n [12, 12, -4, 10, -11, 15, 11, -16, 14, 13, 1, 12],\n [6, 5, -15, -12, -2, 15, -11, -3, 7, 4, -3, -5],\n [-13, 4, 0, 12, -1, 1, -6, 15, 11, -1, 13, 5],\n [-12, -8, -4, 6, 10, 15, 14, 16, 9, 1, -5, -14],\n [-12, -3, -5, -13, -1, -6, -15, -4, -9, 4, 9, -2],\n [13, -15, -1, -4, -16, 11, -16, -4, -15, -13, 8, -4],\n [15, 4, 9, -2, 12, 9, 4, -5, -5, -12, 9, 15],\n [-15, -9, 10, -9, 7, -4, 12, -4, 6, -2, 7, 6],\n [-7, -12, -12, 14, -16, -15, 12, -10, 12, -8, -10, 11],\n [-7, -1, -7, 9, -3, 1, -16, 0, 5, -1, -10, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1961827609015", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (4, 7) of the result:\nA =\n[[4, -15, 8, -8, 3, -7, 4, -13, 13, 13, -3, 5],\n [-16, -9, -6, -16, -12, -7, -4, 4, 16, 11, -8, -6],\n [12, -10, 10, 5, 14, 13, 11, 3, -2, -2, -5, 0],\n [6, -11, -1, 10, 6, -16, -10, 1, 5, -15, 9, 15],\n [6, 1, 2, 7, -13, -15, 13, 14, -1, 16, -14, 1],\n [-7, -15, 13, 13, 8, 7, -7, 13, 9, 7, 3, -7],\n [10, -2, -2, -14, 12, -13, -1, -12, 4, 4, -15, -3],\n [-12, -10, -6, 13, -16, -1, -16, 5, -4, 10, -2, 0],\n [-8, -12, 6, -6, 7, -9, 14, 5, -3, -12, 0, 1],\n [2, -10, 9, 8, 1, -2, 12, -16, -13, -8, 15, 7],\n [1, -2, 3, -15, 8, -4, 10, -4, 11, -2, 12, 4],\n [14, 6, -14, -3, -15, -4, -15, -5, 10, -12, 8, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-605265432584", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-4, 2, 6, 1, 8, 5, 3, -2, 0, -10, 5, -10],\n [2, -3, 2, 0, -2, 8, 4, 2, -10, 3, -4, -2],\n [6, 2, 7, 6, -8, 12, 11, 8, 1, -4, 2, 14],\n [1, 0, 6, -9, -4, 8, -6, 8, 10, 3, -5, -6],\n [8, -2, -8, -4, -4, -2, 5, -6, -14, 2, -12, -2],\n [5, 8, 12, 8, -2, -13, -5, 6, -6, 7, -4, 0],\n [3, 4, 11, -6, 5, -5, 14, 1, 0, 0, 8, -5],\n [-2, 2, 8, 8, -6, 6, 1, -4, -6, -2, 2, 10],\n [0, -10, 1, 10, -14, -6, 0, -6, -8, 6, -3, -1],\n [-10, 3, -4, 3, 2, 7, 0, -2, 6, -11, -2, 6],\n [5, -4, 2, -5, -12, -4, 8, 2, -3, -2, -15, -4],\n [-10, -2, 14, -6, -2, 0, -5, 10, -1, 6, -4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19260145236", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-12, -1, 10, 4, -8, 6, -5, -1, -8, -2, 0, 6],\n [-1, 3, 8, -5, 3, -2, 12, -4, -6, 3, -13, 0],\n [10, 8, 14, -2, 0, -3, -8, 6, 6, 0, -2, 8],\n [4, -5, -2, 3, -4, -6, -8, 11, -1, -4, -16, -8],\n [-8, 3, 0, -4, -9, 2, 6, 7, -8, 4, 6, 8],\n [6, -2, -3, -6, 2, -1, 0, 4, -8, 9, 4, 0],\n [-5, 12, -8, -8, 6, 0, 7, -4, 2, 4, 2, -4],\n [-1, -4, 6, 11, 7, 4, -4, -13, 4, 1, -5, -6],\n [-8, -6, 6, -1, -8, -8, 2, 4, 10, -12, -12, -4],\n [-2, 3, 0, -4, 4, 9, 4, 1, -12, 14, 11, 8],\n [0, -13, -2, -16, 6, 4, 2, -5, -12, 11, -12, -4],\n [6, 0, 8, -8, 8, 0, -4, -6, -4, 8, -4, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135411355916662", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (11, 7) of the result:\nA =\n[[12, -7, 3, -2, -16, 9, 15, -15, 15, 12, 3, 6],\n [-5, -7, 2, -7, 2, 9, 7, -8, 12, 12, 11, -14],\n [6, -13, -3, -4, 11, 3, 11, 15, -3, -4, -6, -2],\n [-8, -14, -12, 11, -2, -14, -10, 13, 7, 14, -3, -1],\n [-13, -14, -8, -13, 2, 7, -6, -2, 14, -9, -15, -14],\n [-14, 4, -5, -3, 6, -4, -1, 0, 1, -4, 9, 14],\n [0, 15, -16, 2, 11, -15, 12, 12, 2, 11, 14, 2],\n [15, 12, -8, -10, -5, 14, 1, 11, 4, -8, 7, -1],\n [11, -11, -6, -13, -3, -4, -2, -9, 7, -6, 8, 6],\n [-10, -12, 15, 11, -14, 13, -12, 16, 3, 13, 5, 5],\n [12, 4, 1, -6, -7, 9, -13, -7, -1, 13, -14, 8],\n [-13, -7, -4, -11, -10, 11, -2, 13, -7, -5, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2543573146", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the 9th power of the matrix:\n[[-16, 7, 4, 15, 1, -4, 4, 1, 9, -12, -12, 14],\n [11, -4, -6, -16, 7, -4, 1, 7, 12, 11, 5, 3],\n [-6, 3, -4, 7, 7, 0, -12, 13, -3, -2, -8, -3],\n [-7, 5, 14, -4, 0, -16, -3, -16, 10, 5, -8, 15],\n [3, 10, -14, -6, 7, 12, -12, 16, -9, 2, -13, 13],\n [-12, -14, -1, -9, -12, -9, 8, -9, 4, -8, 15, -4],\n [6, -9, 11, -2, 12, -13, 7, 4, -15, -10, -6, -5],\n [-13, 9, 1, -1, -5, 2, -2, 5, 3, -4, 6, 14],\n [9, 15, 4, 0, 12, 12, 5, 2, -3, 6, -15, 15],\n [16, -10, -13, 6, 3, 5, 12, -14, 5, 3, 8, 12],\n [-7, 3, 6, -6, -9, 12, 8, 15, 6, 4, 2, 8],\n [6, 2, -12, 2, -5, 8, -12, -5, 10, -13, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-694932408405", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[11, 4, 2, 2, 6, 4, 2, 4, -6, -4, -4, -4],\n [4, 2, -4, -4, 2, 11, -2, -4, 6, -3, 0, 6],\n [2, -4, -15, 0, 0, -12, 8, 11, -9, 15, 10, 10],\n [2, -4, 0, -11, 8, -12, -8, 0, 8, -8, -1, -8],\n [6, 2, 0, 8, -5, -2, 14, 4, -15, 0, -4, -1],\n [4, 11, -12, -12, -2, 13, -2, -8, -2, -6, -2, -4],\n [2, -2, 8, -8, 14, -2, -9, 10, 6, -4, -4, 6],\n [4, -4, 11, 0, 4, -8, 10, 2, -8, 6, -5, -7],\n [-6, 6, -9, 8, -15, -2, 6, -8, 16, 4, -2, -6],\n [-4, -3, 15, -8, 0, -6, -4, 6, 4, -14, 10, 6],\n [-4, 0, 10, -1, -4, -2, -4, -5, -2, 10, 12, -1],\n [-4, 6, 10, -8, -1, -4, 6, -7, -6, 6, -1, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "134651000667733", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-3, -5, -11, 3, 4, -1, -5, 3, 16, -15, 9, 16],\n [13, -16, -9, -16, -7, 15, -15, 14, -13, -5, 14, 6],\n [16, -9, -1, -2, 9, -3, -5, 10, 14, -13, 13, -13],\n [14, -13, 3, 1, -9, -15, -8, -1, 5, -5, -12, -2],\n [-9, 7, 2, 1, 4, -3, -2, -14, -6, -14, 13, -11],\n [-11, 14, 5, 4, -11, 12, -6, 5, -11, 13, 8, -16],\n [5, -8, -9, -1, 2, -9, -5, 14, 16, 2, 10, 7],\n [11, -13, -5, 6, 3, 11, -16, -6, 14, -8, -11, -11],\n [-14, 15, -1, -15, -10, 13, 12, -16, -16, -10, -14, 14],\n [8, 7, -16, 14, -6, -14, -5, 3, 13, -7, -2, 4],\n [1, 15, 2, 13, 16, 5, 12, 7, -13, -5, -13, -12],\n [2, 14, -10, -5, -7, 12, 4, -4, 6, -11, 14, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95250242052412", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[7, -1, -6, -16, 4, -11, -3, 12, -16, -9, 2, 6],\n [-6, 10, 3, -9, 9, -14, -13, 12, 11, 2, 11, 1],\n [-3, -3, 12, -14, -8, -12, 12, -12, -4, 9, -8, -13],\n [14, -12, -10, 11, -3, 7, -12, 11, -9, 4, 7, 7],\n [-4, -2, 8, 11, -9, 14, -10, 0, 5, -10, -7, 11],\n [12, 5, -8, -9, 13, 13, 14, 5, 14, 11, -12, 0],\n [-6, 5, 8, -4, -6, -12, -3, 5, -14, 15, 7, 11],\n [4, 16, 11, -7, 8, 0, -13, -7, 8, 15, -9, -5],\n [4, 10, 13, -7, 4, -16, -8, -14, 2, -11, -10, -1],\n [-13, 1, 15, 15, 1, 11, -15, -15, 2, -12, -4, 5],\n [-10, -15, -3, 8, 9, -12, 3, -5, 14, 0, -1, -7],\n [16, 10, -10, 10, -5, 16, -4, -15, -14, -6, -12, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-106035729714", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[11, -4, -4, -5, 1, 1, 0, 5, -4, 2, 7, 2],\n [4, 7, 13, 11, 0, -8, -4, -3, 9, 4, 3, -6],\n [14, 1, -3, -12, 0, 4, -3, -14, 14, 8, 0, 9],\n [0, 2, 10, -10, 9, -12, -15, -1, -6, 6, -11, -16],\n [16, 1, -14, 2, -7, 3, -6, 15, 3, 15, 5, -13],\n [-4, -11, 12, -15, 8, 15, 9, 9, 5, -7, 6, -13],\n [-1, 16, -4, -4, 16, -3, -9, 9, 5, -16, -1, 12],\n [6, -12, 4, 3, -9, 9, 8, -10, 5, 16, -12, -5],\n [-3, -10, 11, -1, -15, 14, -3, 11, 15, 11, -5, -4],\n [5, 12, 13, -2, -13, 16, -8, -1, 9, 10, -6, 9],\n [-3, -16, -6, 13, 7, -13, 5, -9, -1, 16, 16, -7],\n [-15, -13, 6, 10, 16, 16, 3, -4, -6, 2, 15, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89901592778657", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-4, 14, 10, -2, 6, -6, 10, 0, 1, 3, 2, 6],\n [14, -15, -2, 7, 6, 6, -2, 4, -10, 8, -9, 6],\n [10, -2, -3, 0, -10, 2, 2, -4, 2, -6, -11, -8],\n [-2, 7, 0, 3, -5, -11, -4, 0, 0, 14, 2, -5],\n [6, 6, -10, -5, -14, 12, 7, 0, -7, -14, -14, 0],\n [-6, 6, 2, -11, 12, -15, 4, -6, 1, 4, 4, -5],\n [10, -2, 2, -4, 7, 4, -12, 6, 5, 10, 0, 6],\n [0, 4, -4, 0, 0, -6, 6, -11, -10, 2, -8, 10],\n [1, -10, 2, 0, -7, 1, 5, -10, -7, 8, -4, -5],\n [3, 8, -6, 14, -14, 4, 10, 2, 8, 1, 2, -10],\n [2, -9, -11, 2, -14, 4, 0, -8, -4, 2, -12, -3],\n [6, 6, -8, -5, 0, -5, 6, 10, -5, -10, -3, -12]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19433272317038322", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[13, -5, 9, -2, -10, 2, 4, -4, 5, -1, 0, 0],\n [-5, -15, 6, 10, 2, -2, 2, 6, -8, -10, 2, 8],\n [9, 6, -5, -10, 8, 2, -2, -2, 0, 0, 13, 0],\n [-2, 10, -10, 11, -1, 9, 12, 4, -6, -8, 4, -4],\n [-10, 2, 8, -1, -11, 14, 0, 4, 11, 4, 11, 11],\n [2, -2, 2, 9, 14, 1, -1, -4, 6, 2, -1, -7],\n [4, 2, -2, 12, 0, -1, -13, -6, -1, 13, 8, -2],\n [-4, 6, -2, 4, 4, -4, -6, -11, -13, 0, -3, 0],\n [5, -8, 0, -6, 11, 6, -1, -13, -9, -1, -2, 2],\n [-1, -10, 0, -8, 4, 2, 13, 0, -1, 3, -5, 2],\n [0, 2, 13, 4, 11, -1, 8, -3, -2, -5, 1, 2],\n [0, 8, 0, -4, 11, -7, -2, 0, 2, 2, 2, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34171309175962", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 7, 13, 3, -11, 16, -2, -2, 15, -3, -9, 5],\n [3, 7, 4, 11, 6, 7, 6, -13, -13, 13, 11, 14],\n [16, 2, -7, 8, -4, -11, 13, 6, -1, -9, -1, -6],\n [-16, 5, 1, -6, 3, -7, -7, 5, -6, -8, -2, 2],\n [-11, -12, -14, -7, -4, -13, 16, 16, 4, -12, -4, 0],\n [-7, -7, -15, 4, -16, 13, 1, 5, -14, -11, -1, -14],\n [-6, 0, 2, -9, -3, 9, 8, -7, 15, -2, -13, 11],\n [-13, -4, -5, -2, 12, 6, -4, -5, 13, -12, -15, 13],\n [-7, -8, 0, 13, -10, -5, -14, 16, -4, -6, 3, 14],\n [16, -8, -10, -8, 9, -15, -12, -15, -7, 14, 16, -11],\n [-3, -3, -2, 16, 14, 0, -2, 3, 4, 12, -8, 12],\n [-8, 13, 0, -13, 15, 15, -10, 15, -12, -14, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75260153001863", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 8) of the matrix A^9 where A is:\n[[-1, -2, -9, 4, 6, -10, 10, 8, 12, -8, 1, 3],\n [-2, 13, 2, 4, -1, 8, -6, -7, 2, 3, 0, 0],\n [-9, 2, 9, -9, 4, -3, 6, -14, 14, 0, 2, 0],\n [4, 4, -9, 3, -5, -4, -2, -4, -6, 6, -5, -4],\n [6, -1, 4, -5, -12, -2, 10, -13, -2, 0, 10, 11],\n [-10, 8, -3, -4, -2, 11, 2, -10, -2, 8, 12, 12],\n [10, -6, 6, -2, 10, 2, -8, -9, 8, 0, 0, 8],\n [8, -7, -14, -4, -13, -10, -9, 7, -5, -6, 4, 4],\n [12, 2, 14, -6, -2, -2, 8, -5, 9, 2, -4, -6],\n [-8, 3, 0, 6, 0, 8, 0, -6, 2, 16, 10, 8],\n [1, 0, 2, -5, 10, 12, 0, 4, -4, 10, 0, 0],\n [3, 0, 0, -4, 11, 12, 8, 4, -6, 8, 0, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-172855707092949", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 16, 9, -7, 12, 11, -5, -10, -1, 3, 12, 11],\n [-10, 5, -3, -7, -15, 5, -1, -6, 16, 16, 2, 3],\n [-7, 2, -5, -7, -10, -6, -1, 16, 0, 8, 14, -16],\n [3, -8, -15, -16, -12, -5, -3, 15, -8, 16, 8, -3],\n [-8, 10, 2, 8, 15, 5, 12, 11, -4, 11, -14, 13],\n [-6, -15, -8, 16, 9, -1, 8, -16, 4, 3, -12, 0],\n [-16, -4, 1, -13, -3, -12, 16, 9, -13, 13, 0, 11],\n [-11, 10, -10, -16, -7, -4, 15, -3, 16, 13, -8, -11],\n [-7, -6, 3, 8, -5, 5, -5, -3, -3, -15, -15, -11],\n [8, -14, 6, -8, 14, 11, 8, -16, -15, -2, -1, 6],\n [-9, -10, 4, 16, 1, 2, -7, -13, 13, 16, -13, -8],\n [0, 7, -4, 9, 2, 0, 13, 9, -4, 1, 4, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1885473536750", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[13, 12, 12, 2, -9, 0, -5, -2, -12, -14, -12, -8],\n [7, -12, 10, 3, -15, 6, 12, 13, -14, -7, -16, -11],\n [-11, -1, -16, -12, 8, 10, 9, -1, 9, 11, 11, 13],\n [-4, 8, 2, -4, -6, 6, -3, -7, 6, 4, 3, 15],\n [-3, 7, 1, 13, 11, -3, 4, -12, 14, -14, 6, 13],\n [13, -10, -12, -11, -3, -6, -15, 14, 10, -1, -15, 9],\n [-1, -8, -8, -12, -10, 15, 12, -14, 13, 14, 10, -11],\n [12, -8, 3, -6, 2, -7, -12, 6, -11, 14, 1, 4],\n [-2, 14, -7, -11, 7, 16, 11, 11, -7, 6, -2, -3],\n [-3, -10, 1, -2, 16, 5, 0, 9, -2, 1, -9, -14],\n [-3, 16, -16, -7, 2, -6, -15, -14, -2, 11, -15, 13],\n [-12, -11, -12, -5, -13, 7, 8, 9, 16, 4, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1754554163328", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[4, -4, 16, -11, -5, 13, 1, -1, -10, -16, 11, -14],\n [-7, -3, -2, -11, -1, 1, 8, 16, 16, 2, -6, -14],\n [-16, 8, 15, -13, 6, -1, -6, 5, 16, -4, 4, -5],\n [9, -16, 5, 10, 15, -9, 1, -13, -16, -1, 13, 6],\n [14, 11, -1, -8, -15, -15, 15, -1, -4, 10, 14, 16],\n [4, 2, -4, 2, 16, -14, 4, 6, -6, -13, -13, -2],\n [11, -9, 7, -2, 6, 10, -3, -15, -10, -1, 5, 11],\n [15, -10, 5, -15, -9, -10, 4, 5, 1, -8, -15, 0],\n [3, -11, -6, -12, -7, 6, 16, 0, 9, 10, -14, 2],\n [-9, 0, -16, -10, -14, 2, 10, -14, -12, -1, -3, 13],\n [15, -5, 10, 9, 12, 6, 5, 3, -1, 14, -14, 4],\n [-12, 3, 6, 15, -8, -14, 10, 10, -7, -1, 7, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37991107913374", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-8, -15, -11, -10, -2, 4, 6, 12, -4, -12, -16, 3],\n [-16, -10, -12, 12, 10, -10, -16, -8, -16, 10, 0, 15],\n [13, -2, 11, -14, 11, -12, -15, -1, 0, -5, 9, -10],\n [7, -1, 1, -9, 10, 9, 14, 1, -15, 6, 5, 16],\n [1, -2, -14, 6, -15, -13, 9, 2, -7, 5, -11, -16],\n [-1, -10, 7, -3, -13, -2, 6, 2, -3, 10, 5, -6],\n [-13, 15, 7, -14, -15, 6, 3, -9, -14, 15, 14, 14],\n [-16, -5, 1, 7, 12, 8, 6, -14, 13, 0, 13, 2],\n [-12, -8, 9, -12, 7, 14, 7, 4, 5, 5, 4, 13],\n [-7, -14, 12, 8, -15, -4, 10, 12, -3, -13, -9, -12],\n [10, 7, 11, 7, -12, -4, 1, 0, 13, 2, 5, 1],\n [9, -2, 11, 13, 11, 3, -13, -13, -2, -6, 6, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1222673580178", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-15, -2, 11, 14, 15, 5, 12, -9, 5, -5, 6, -15],\n [-5, 4, -5, 14, -8, -2, 15, -8, 7, -9, 11, 1],\n [15, 4, 12, 1, 6, 16, -8, -13, -1, -14, -9, -1],\n [-15, 2, 7, -1, -15, 15, -16, 1, 15, -8, -14, 7],\n [-6, 11, -1, 12, -5, -13, 9, -13, -6, -15, 14, -14],\n [8, -16, -12, 14, -14, -5, -1, -9, -6, -3, 10, 1],\n [-9, 16, -13, 13, 3, 13, 10, 8, -11, -12, -3, -3],\n [8, 1, 3, -9, 9, 4, 10, 15, 0, -16, 10, -6],\n [-7, -16, 5, 0, -5, -4, 8, 9, 16, -9, -4, 9],\n [0, 7, 7, -5, 14, -1, -1, 13, 11, -14, 16, 7],\n [13, 11, -15, -4, -7, -4, 2, -11, 1, -8, 0, -13],\n [-11, -6, 9, -6, -9, -14, -15, 1, -15, 9, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4347195879270", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -1, -6, 2, -1, -8, -1, -2, 2, 0, -2, 1],\n [-1, 13, 13, 4, -6, -5, -4, 6, 8, -6, 8, -2],\n [-6, 13, -12, 4, 0, 6, 4, 10, 0, 8, 0, 10],\n [2, 4, 4, -10, -11, 9, 0, 1, -4, 15, 6, -6],\n [-1, -6, 0, -11, -9, -4, -10, 6, 0, -6, -2, -3],\n [-8, -5, 6, 9, -4, -6, 5, 0, 5, -2, -4, -7],\n [-1, -4, 4, 0, -10, 5, 8, 4, 2, -4, -13, 8],\n [-2, 6, 10, 1, 6, 0, 4, 13, 5, 2, 2, -2],\n [2, 8, 0, -4, 0, 5, 2, 5, -12, 2, -12, 2],\n [0, -6, 8, 15, -6, -2, -4, 2, 2, -4, 4, -12],\n [-2, 8, 0, 6, -2, -4, -13, 2, -12, 4, 14, 8],\n [1, -2, 10, -6, -3, -7, 8, -2, 2, -12, 8, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1806225078625", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-15, -8, -8, 10, -6, 2, 4, 8, -14, 0, -8, -2],\n [-8, -15, -6, 0, 12, 0, -16, -7, 10, 4, -4, -8],\n [-8, -6, 11, -8, -4, 5, 8, -12, 2, -6, 1, -8],\n [10, 0, -8, 2, 0, 3, 13, -2, 3, -11, -10, 8],\n [-6, 12, -4, 0, -1, -8, 4, -12, 0, -8, -2, 2],\n [2, 0, 5, 3, -8, 10, 12, 8, 10, 8, 4, 1],\n [4, -16, 8, 13, 4, 12, -14, 12, -8, -2, -16, 10],\n [8, -7, -12, -2, -12, 8, 12, -3, 6, 2, 2, 0],\n [-14, 10, 2, 3, 0, 10, -8, 6, 15, -9, -5, -11],\n [0, 4, -6, -11, -8, 8, -2, 2, -9, -3, -7, 10],\n [-8, -4, 1, -10, -2, 4, -16, 2, -5, -7, 12, -4],\n [-2, -8, -8, 8, 2, 1, 10, 0, -11, 10, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4357210917018", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[8, -14, 6, 6, -4, 8, -13, 4, -6, 0, -6, 3],\n [-14, 6, -4, -12, -1, 12, 10, -3, -12, 1, -5, 0],\n [6, -4, -11, -8, 8, 0, -10, -4, 5, -8, -10, -10],\n [6, -12, -8, 10, -11, 3, -2, 6, 1, -5, 8, 1],\n [-4, -1, 8, -11, -4, 10, 2, 4, 10, -13, -10, -2],\n [8, 12, 0, 3, 10, 4, 1, 12, -6, 4, 6, 2],\n [-13, 10, -10, -2, 2, 1, 12, -10, 8, 0, 14, 2],\n [4, -3, -4, 6, 4, 12, -10, -7, -8, 8, 2, 8],\n [-6, -12, 5, 1, 10, -6, 8, -8, -16, -2, 7, 1],\n [0, 1, -8, -5, -13, 4, 0, 8, -2, -15, 2, -2],\n [-6, -5, -10, 8, -10, 6, 14, 2, 7, 2, -14, 0],\n [3, 0, -10, 1, -2, 2, 2, 8, 1, -2, 0, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5462909104756488", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[16, 10, -14, 4, 0, -4, 0, 4, -4, -1, 4, 4],\n [10, -10, -1, -10, -8, -6, 8, 0, -6, -13, 4, 6],\n [-14, -1, -14, 13, 2, -3, -6, -3, -4, -4, 2, -1],\n [4, -10, 13, -16, 0, -11, -5, 5, 6, 4, -4, -2],\n [0, -8, 2, 0, 5, -7, 6, 8, -4, 5, -4, 8],\n [-4, -6, -3, -11, -7, -9, 8, -14, -12, -10, -4, -12],\n [0, 8, -6, -5, 6, 8, 6, 7, -6, 1, 2, 2],\n [4, 0, -3, 5, 8, -14, 7, -8, -2, -4, 2, 1],\n [-4, -6, -4, 6, -4, -12, -6, -2, 8, -8, -11, -8],\n [-1, -13, -4, 4, 5, -10, 1, -4, -8, 10, -2, 3],\n [4, 4, 2, -4, -4, -4, 2, 2, -11, -2, 4, -5],\n [4, 6, -1, -2, 8, -12, 2, 1, -8, 3, -5, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48428878436728", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[6, 9, -6, 7, -8, -3, 7, -10, -7, 16, 16, 10],\n [-9, -3, -10, 1, 9, -2, 16, -6, 2, 1, 5, 1],\n [1, 5, 8, 14, -8, 2, 8, -2, -12, -6, -4, -9],\n [8, 10, -6, 1, -7, 16, 0, -12, 6, -14, -7, 10],\n [-10, 12, -11, -8, -9, -3, -8, -6, -6, -6, -14, 2],\n [-9, 11, -16, 13, -6, 12, 14, -7, 12, -15, -16, 15],\n [7, -15, -14, -8, 7, -5, 6, 2, 15, 11, 9, -5],\n [14, -6, -13, 1, 12, 14, 11, 10, 13, -6, -3, -13],\n [-16, 16, 4, 7, -4, 12, -12, 3, 12, -6, -9, 11],\n [1, 13, -3, -8, -7, 8, 10, -15, -14, 12, 10, -13],\n [10, 2, -7, 9, -10, 10, 13, -5, -12, -4, -13, -15],\n [-11, 9, -6, -16, 4, -7, -12, 9, 2, 4, 12, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-715153819310", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -4, -3, -7, 7, 2, 1, 1, 1, -2, 0, -4],\n [-4, -5, -2, -4, -3, 0, -3, -2, -12, 9, 9, 7],\n [-3, -2, 7, 0, 10, 6, 4, -2, -14, -2, 12, -10],\n [-7, -4, 0, 13, 4, -6, -2, -3, 2, 8, 12, -6],\n [7, -3, 10, 4, -5, -2, 2, 4, 2, 4, 2, -5],\n [2, 0, 6, -6, -2, 2, 10, -4, 3, -4, -11, 4],\n [1, -3, 4, -2, 2, 10, -10, 2, -2, 0, -5, 12],\n [1, -2, -2, -3, 4, -4, 2, 8, 0, 0, 7, 4],\n [1, -12, -14, 2, 2, 3, -2, 0, 14, -14, -6, -4],\n [-2, 9, -2, 8, 4, -4, 0, 0, -14, -14, 10, 3],\n [0, 9, 12, 12, 2, -11, -5, 7, -6, 10, -11, 2],\n [-4, 7, -10, -6, -5, 4, 12, 4, -4, 3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1358266764291", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (7, 9) of the result:\nA =\n[[-5, 5, -1, 16, -3, 1, -1, -14, 9, -2, 10, 0],\n [-3, -15, 10, 7, -13, 9, -13, -4, -16, -16, -8, -6],\n [-1, 12, -2, -15, -7, -6, 13, 6, 5, 12, 15, 16],\n [-8, -16, 1, 5, -3, 5, 16, -11, 10, -11, -1, -15],\n [12, 6, 4, -4, -16, 12, -10, 14, 5, -1, 11, 8],\n [-3, 4, 2, -4, -15, -3, 1, 7, 13, 2, 4, 2],\n [9, -13, 4, -14, -12, 12, 2, 0, 3, 11, -8, -14],\n [-7, 4, -13, 5, -10, -5, -6, 5, 12, 10, 3, -3],\n [-10, -2, 11, -7, -14, -5, -4, -16, 8, 2, 8, -11],\n [-13, 9, 9, 9, -3, 15, 11, -15, 4, -3, -15, -12],\n [-15, -16, 5, 8, 13, -8, -7, -2, -14, -9, 8, 4],\n [10, -8, -7, 10, 8, -4, -13, -1, -5, 8, -1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1749519172158", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 4) of the matrix A^8 where A is:\n[[-8, -4, 0, 0, 8, 2, -10, 8, -12, -12, 6, -3],\n [-4, 2, 2, -8, 9, 0, -5, 6, -2, -9, -2, 5],\n [0, 2, 16, -6, 8, -1, 0, -7, -2, 2, 5, 10],\n [0, -8, -6, 15, -8, -10, 8, 2, 7, -2, 14, -1],\n [8, 9, 8, -8, -3, 4, 2, -10, 4, -3, -1, 6],\n [2, 0, -1, -10, 4, 8, -2, 0, -1, 2, -2, -10],\n [-10, -5, 0, 8, 2, -2, 15, 0, -3, -10, -4, -10],\n [8, 6, -7, 2, -10, 0, 0, -6, 2, 14, 6, 7],\n [-12, -2, -2, 7, 4, -1, -3, 2, 3, 0, -5, -2],\n [-12, -9, 2, -2, -3, 2, -10, 14, 0, 4, -2, -8],\n [6, -2, 5, 14, -1, -2, -4, 6, -5, -2, -15, 2],\n [-3, 5, 10, -1, 6, -10, -10, 7, -2, -8, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-673240004156", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 2) of the 7th power of the matrix:\n[[8, 6, 11, 9, -5, -14, -8, -2, -9, 11, 9, -1],\n [3, -16, 7, 12, -13, -13, -14, -15, 12, 11, -5, -2],\n [14, 15, 5, -14, 0, 12, -5, -3, -9, -15, 7, 3],\n [-7, -10, -16, -7, -12, 4, -8, 12, 14, 10, -11, 14],\n [-15, 4, 5, -4, 2, 16, -14, 2, -10, -2, 8, 5],\n [6, -7, -10, 8, 7, -12, 4, 3, 12, 3, 1, -13],\n [-6, 5, -3, 11, -13, -1, 6, -4, 3, -12, 2, 4],\n [-12, -3, -11, -12, 7, 12, 12, -15, -11, -5, 5, -13],\n [-11, -14, -4, 6, 9, -8, 6, -13, -9, -11, -10, -12],\n [-14, 0, 2, -16, -8, -13, -7, 15, -16, 6, 0, 13],\n [10, -2, -10, 16, -12, -14, 15, -15, -1, 0, -5, -12],\n [-13, -1, 1, 3, -8, -1, 12, 13, 3, 5, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6234395573", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 3) of the 8th power of the matrix:\n[[-16, 10, 1, -4, -13, 8, -6, -1, -8, 6, -7, -6],\n [10, 7, 6, 2, 5, 9, -6, 8, 0, 12, 3, 10],\n [1, 6, 3, -7, -8, 4, 0, 8, 3, 0, 6, 6],\n [-4, 2, -7, 12, 4, 2, 6, -4, 11, 2, -2, 9],\n [-13, 5, -8, 4, -2, -6, 1, 4, -10, 6, 8, 13],\n [8, 9, 4, 2, -6, -8, -8, 9, 8, 6, 12, 4],\n [-6, -6, 0, 6, 1, -8, -16, -10, -7, 9, -6, 2],\n [-1, 8, 8, -4, 4, 9, -10, 9, 12, -2, -6, 6],\n [-8, 0, 3, 11, -10, 8, -7, 12, 1, -1, 0, -10],\n [6, 12, 0, 2, 6, 6, 9, -2, -1, 14, 14, -4],\n [-7, 3, 6, -2, 8, 12, -6, -6, 0, 14, -16, 6],\n [-6, 10, 6, 9, 13, 4, 2, 6, -10, -4, 6, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60832122406", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-14, 9, -13, -15, 2, 6, 8, -10, -9, -14, 6, 16],\n [11, 5, 13, -3, -8, 5, 11, -3, -2, 7, -14, 6],\n [3, -2, -1, -10, 16, 2, 1, 1, -14, -14, -1, 6],\n [6, -2, -8, 1, -11, -11, 4, 13, 11, 3, 2, -3],\n [-16, 10, 15, 12, 14, 8, -10, -1, -6, 1, -12, -15],\n [-7, 9, 7, 9, -1, 8, -11, -5, -8, -9, 14, 15],\n [-10, 15, 8, 16, 11, -6, 14, -7, -15, -13, 5, 11],\n [-7, -15, 14, 6, -1, -8, -11, 8, -13, -5, 7, 10],\n [-14, -5, 13, -5, 5, -2, 11, 0, 8, -14, 14, -2],\n [11, 14, 3, 4, 10, 2, -5, 16, 6, -4, 13, -7],\n [3, -11, 14, 2, -14, -7, -7, 4, -15, 13, 11, 1],\n [-3, 2, -5, 3, 4, 2, -9, 5, 1, -9, -15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "877501798925", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-12, 13, 1, 6, -15, 15, -16, -16, 14, -9, -14, -5],\n [8, -10, -2, 4, 8, -1, -16, -3, -15, 14, 2, 2],\n [6, 13, 0, -15, -6, -3, 12, 2, 11, -16, -12, -3],\n [2, 7, 0, -15, 14, 0, -9, 0, 9, -10, 7, 13],\n [9, 13, -15, -13, -12, -15, 14, 10, 7, -13, 11, -12],\n [10, -12, -12, -8, 10, -13, 7, 10, -16, 15, -1, 6],\n [11, 3, 0, -9, 1, -4, -8, 13, 11, 1, 3, 2],\n [-12, 0, 11, 13, 1, -11, 9, -2, -16, 0, 14, -15],\n [10, -14, 3, -9, 12, -9, 10, 9, -7, 13, 16, 3],\n [-13, 6, 12, 15, 9, -12, 7, -15, -2, -9, -3, -12],\n [-8, 5, 13, 16, -10, -14, 15, 2, 14, 13, 8, -4],\n [-5, -8, -8, 10, 14, -11, 12, 13, -6, -11, 14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121726278796392", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-11, 9, 15, -13, -14, -15, 3, 2, -5, 11, -8, -6],\n [13, -15, 16, -10, 4, -5, 4, 6, -11, -3, 15, -4],\n [10, -6, 15, -14, -15, 13, -15, 12, 5, 8, 2, -1],\n [0, 10, 2, 13, -3, 15, 6, -7, 12, -6, -2, 15],\n [10, -16, -3, -14, 13, 14, -16, -3, -2, 8, -3, 7],\n [-15, 6, -9, -12, 12, 16, 3, -1, 7, 12, -8, 5],\n [3, -13, -5, 6, -9, -7, 6, 12, 15, -3, -1, 0],\n [3, -5, -8, -9, 4, 15, 1, 12, -10, -11, 3, -8],\n [-8, -9, 0, 7, 6, 16, 5, 5, 10, -15, 14, -4],\n [-15, -10, -6, 9, 4, -2, -1, -8, 4, -11, -16, 14],\n [-12, 9, -16, -16, 12, 5, 2, 11, -12, 4, 5, 3],\n [-5, -11, 12, -6, 16, 8, -3, 12, -4, -2, -9, 16]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3912885404846556", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (11, 11) of the matrix A^9 where A is:\n[[-6, 0, 2, -3, -4, -4, 12, 9, -14, 0, 10, 0],\n [0, 8, 9, 4, 12, 4, 4, 8, -2, 6, 1, 8],\n [2, 9, 2, -9, -12, -4, 12, -10, -4, -9, -8, -2],\n [-3, 4, -9, 12, -2, -2, -10, -6, 10, -6, -10, 1],\n [-4, 12, -12, -2, 4, -2, -2, 4, -5, 10, -4, 0],\n [-4, 4, -4, -2, -2, 16, 8, -2, 0, 8, 4, 6],\n [12, 4, 12, -10, -2, 8, -6, 2, -6, -10, 6, 9],\n [9, 8, -10, -6, 4, -2, 2, -16, 5, 12, 4, -7],\n [-14, -2, -4, 10, -5, 0, -6, 5, 12, 6, 6, -1],\n [0, 6, -9, -6, 10, 8, -10, 12, 6, 13, 4, 0],\n [10, 1, -8, -10, -4, 4, 6, 4, 6, 4, -9, -10],\n [0, 8, -2, 1, 0, 6, 9, -7, -1, 0, -10, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31017296596544", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[4, -12, 13, 2, 2, 1, -11, -6, 4, -8, -3, 3],\n [-12, 4, 3, -8, -1, -2, -9, -2, 6, -10, 0, 5],\n [13, 3, -8, -3, 10, -4, 6, -8, -6, 0, 2, -1],\n [2, -8, -3, 10, 4, -6, -8, -14, -2, -8, -4, -2],\n [2, -1, 10, 4, -12, -6, 9, -4, -6, 8, -9, 4],\n [1, -2, -4, -6, -6, -11, -2, 7, 7, -6, 4, 0],\n [-11, -9, 6, -8, 9, -2, 0, -4, -8, 1, 0, 0],\n [-6, -2, -8, -14, -4, 7, -4, -9, -2, -11, 8, -10],\n [4, 6, -6, -2, -6, 7, -8, -2, -16, 2, 4, -4],\n [-8, -10, 0, -8, 8, -6, 1, -11, 2, 8, -14, -2],\n [-3, 0, 2, -4, -9, 4, 0, 8, 4, -14, 10, -1],\n [3, 5, -1, -2, 4, 0, 0, -10, -4, -2, -1, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1714662764690", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (5, 5) of the result:\nA =\n[[9, -1, 10, -4, -2, -4, 2, -12, -3, 2, -6, 9],\n [-1, 8, 2, 10, 4, 0, -6, -4, -4, -9, 8, 9],\n [10, 2, 5, -10, -12, 2, 4, 5, 10, -2, -14, 1],\n [-4, 10, -10, 14, -6, 5, -2, -1, -2, 5, 11, 0],\n [-2, 4, -12, -6, 11, -3, -12, -3, -4, 4, 4, -8],\n [-4, 0, 2, 5, -3, 3, 3, 6, -4, 4, 5, -4],\n [2, -6, 4, -2, -12, 3, -13, 2, 0, 8, -2, 0],\n [-12, -4, 5, -1, -3, 6, 2, 6, -2, 0, 1, 6],\n [-3, -4, 10, -2, -4, -4, 0, -2, 8, -5, 3, 9],\n [2, -9, -2, 5, 4, 4, 8, 0, -5, 14, -2, -10],\n [-6, 8, -14, 11, 4, 5, -2, 1, 3, -2, -3, -1],\n [9, 9, 1, 0, -8, -4, 0, 6, 9, -10, -1, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1815125381692", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[-8, 0, 6, 10, -8, 10, 4, -8, -2, 4, 10, -8],\n [0, 13, 6, 6, 11, -11, 8, 6, 10, 6, -4, 0],\n [6, 6, 7, 0, -3, 10, 12, 14, -2, -4, -2, 0],\n [10, 6, 0, 13, -6, 2, -8, -5, 2, 1, 8, -2],\n [-8, 11, -3, -6, -5, 10, -4, 6, -4, -1, 4, -9],\n [10, -11, 10, 2, 10, -9, 1, 8, 2, 5, 4, 2],\n [4, 8, 12, -8, -4, 1, 9, -7, -4, 5, 8, -1],\n [-8, 6, 14, -5, 6, 8, -7, -13, 0, 7, 7, -9],\n [-2, 10, -2, 2, -4, 2, -4, 0, -2, -4, -6, -11],\n [4, 6, -4, 1, -1, 5, 5, 7, -4, -10, -10, 11],\n [10, -4, -2, 8, 4, 4, 8, 7, -6, -10, -13, 10],\n [-8, 0, 0, -2, -9, 2, -1, -9, -11, 11, 10, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-309364754910035", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-3, 2, -2, -4, -2, 3, -4, 10, -8, -12, 4, 11],\n [2, 15, -4, -12, -6, -8, -8, 0, 0, -2, 6, 2],\n [-2, -4, 9, -11, -6, -6, 1, 4, 4, -12, 0, -4],\n [-4, -12, -11, 5, 14, 6, 0, 0, 5, -12, 6, -5],\n [-2, -6, -6, 14, -9, 10, -14, 4, -10, -3, -3, -8],\n [3, -8, -6, 6, 10, 7, 4, 0, -3, 8, 8, -8],\n [-4, -8, 1, 0, -14, 4, 0, -6, 0, -6, 3, -4],\n [10, 0, 4, 0, 4, 0, -6, 3, 4, 4, 0, 4],\n [-8, 0, 4, 5, -10, -3, 0, 4, 12, 4, 9, 6],\n [-12, -2, -12, -12, -3, 8, -6, 4, 4, -9, -6, 7],\n [4, 6, 0, 6, -3, 8, 3, 0, 9, -6, -5, -3],\n [11, 2, -4, -5, -8, -8, -4, 4, 6, 7, -3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10360571872399", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-10, -4, 3, 2, -3, -8, 10, -6, 2, -7, -10, -8],\n [-4, -9, -8, -13, -4, -2, 2, -10, 4, -4, -6, -6],\n [3, -8, -6, 12, 7, -10, 0, 0, -2, 2, -8, 11],\n [2, -13, 12, 9, -2, -2, -2, -9, 0, -10, 12, -1],\n [-3, -4, 7, -2, 13, -2, -1, 0, 3, 8, 2, 2],\n [-8, -2, -10, -2, -2, 9, 6, 3, -1, 5, 5, -4],\n [10, 2, 0, -2, -1, 6, 2, 6, 0, -10, 4, 0],\n [-6, -10, 0, -9, 0, 3, 6, -2, 4, -12, -4, -2],\n [2, 4, -2, 0, 3, -1, 0, 4, -7, -4, 0, 0],\n [-7, -4, 2, -10, 8, 5, -10, -12, -4, -3, 10, -2],\n [-10, -6, -8, 12, 2, 5, 4, -4, 0, 10, -6, -14],\n [-8, -6, 11, -1, 2, -4, 0, -2, 0, -2, -14, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35315263005814", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (9, 12) of the result:\nA =\n[[15, -9, 4, -2, 1, 4, 10, 6, 0, 5, -6, 10],\n [-9, -6, -2, 10, -4, -10, 2, 6, -4, -7, -11, 7],\n [4, -2, -14, -5, 0, -7, -2, 2, 6, -2, 14, 2],\n [-2, 10, -5, 1, -8, 10, -6, -11, -12, 16, 12, -2],\n [1, -4, 0, -8, -2, -4, -4, -10, 12, -13, 9, -1],\n [4, -10, -7, 10, -4, 6, 6, 0, 2, 0, 0, 5],\n [10, 2, -2, -6, -4, 6, -13, 0, 11, -8, -8, 10],\n [6, 6, 2, -11, -10, 0, 0, -4, 10, -1, 4, 0],\n [0, -4, 6, -12, 12, 2, 11, 10, -15, -2, 10, 6],\n [5, -7, -2, 16, -13, 0, -8, -1, -2, 9, 0, 10],\n [-6, -11, 14, 12, 9, 0, -8, 4, 10, 0, -3, -3],\n [10, 7, 2, -2, -1, 5, 10, 0, 6, 10, -3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "269659142216", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[9, -4, 2, -4, 8, -3, 2, -6, 4, -8, -4, 2],\n [-4, 11, 8, -6, 0, -12, -4, 13, -10, 0, -10, 4],\n [2, 8, -1, -8, -3, -4, -14, 8, 1, -8, -3, -8],\n [-4, -6, -8, -13, 8, 2, -2, 6, -10, 0, -3, 7],\n [8, 0, -3, 8, 2, 0, 8, 0, -5, 0, 0, -2],\n [-3, -12, -4, 2, 0, -16, -1, 4, -2, -6, -13, 12],\n [2, -4, -14, -2, 8, -1, 4, -6, -2, 4, -4, -3],\n [-6, 13, 8, 6, 0, 4, -6, -4, 2, -4, -6, -2],\n [4, -10, 1, -10, -5, -2, -2, 2, 13, 0, 8, 4],\n [-8, 0, -8, 0, 0, -6, 4, -4, 0, 16, -8, -11],\n [-4, -10, -3, -3, 0, -13, -4, -6, 8, -8, 5, -2],\n [2, 4, -8, 7, -2, 12, -3, -2, 4, -11, -2, 1]], determine the value at position (4, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32833374256143", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-8, 5, 4, -10, -5, -6, -14, 10, -10, -15, -7, -14],\n [0, -16, -4, -3, 0, 0, 8, 13, -6, 4, 3, 12],\n [-13, 0, -5, -13, -3, -13, 1, -4, -7, -3, -8, 3],\n [-16, 12, 0, -9, 0, 4, 8, 3, 8, 4, -4, -4],\n [13, -4, -10, -5, -15, -3, 0, -4, -16, -16, 9, -4],\n [-8, 2, 6, 11, 13, -10, -3, -15, -5, -15, 11, 11],\n [-5, 13, 5, 1, -3, 8, -7, -8, -6, 10, -4, -16],\n [-6, -14, -15, 7, 3, -2, -11, 3, 5, -15, -2, 14],\n [13, 11, 16, 4, 6, -4, 9, 2, 10, -10, 8, -10],\n [3, 7, 11, -12, 14, 16, 7, -7, -12, 14, -8, 15],\n [-12, 10, 11, -5, -12, -9, 0, -9, 6, 1, -7, -12],\n [0, -6, 2, 4, -14, -16, 7, -11, -7, 7, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1475480653070", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-1, 10, -12, -6, 6, 8, -12, 12, 10, -2, -9, 8],\n [10, 10, -2, -2, 9, -14, -12, -4, -7, -10, 10, 9],\n [-12, -2, 6, -4, 2, -4, 4, -12, 0, -2, 1, -1],\n [-6, -2, -4, -1, -6, -10, 6, 6, -12, -6, -6, -14],\n [6, 9, 2, -6, 12, 6, -2, -9, -4, 8, 0, -9],\n [8, -14, -4, -10, 6, -12, 1, -12, 3, 6, -6, -4],\n [-12, -12, 4, 6, -2, 1, 9, -1, -8, -2, 3, -3],\n [12, -4, -12, 6, -9, -12, -1, -2, -14, -6, -2, -7],\n [10, -7, 0, -12, -4, 3, -8, -14, 15, -3, 0, -5],\n [-2, -10, -2, -6, 8, 6, -2, -6, -3, -13, 2, 10],\n [-9, 10, 1, -6, 0, -6, 3, -2, 0, 2, -12, 8],\n [8, 9, -1, -14, -9, -4, -3, -7, -5, 10, 8, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-584343381389809", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 8) of the 7th power of the matrix:\n[[-1, -4, -13, 8, -4, 11, -5, 7, 11, -16, -14, 5],\n [4, 10, 4, 5, -4, -1, 7, 0, -12, 10, 15, 9],\n [-10, -10, 10, 7, 7, 12, 10, 4, -16, -7, 13, 11],\n [13, 11, 12, 14, -13, 2, -7, 14, 14, -6, 15, 6],\n [-14, 11, 8, 11, 2, 2, 12, 2, 1, 7, -1, 1],\n [-4, -13, -4, -13, 2, 7, 16, 16, -8, -14, -14, 13],\n [1, -15, 15, -8, -15, 3, 10, 2, -1, 9, -3, 1],\n [11, 2, 13, 4, 4, 13, 15, 13, 5, 7, -7, 7],\n [-16, -1, -12, 14, 8, 8, -14, 15, 3, 13, -15, -12],\n [2, 3, 5, -6, 1, 10, 14, 4, 3, -8, 14, -8],\n [-10, 16, -16, 2, -14, -5, 13, -1, -4, 7, 0, 10],\n [12, -3, -12, -11, 7, 16, -8, -14, 6, 4, 5, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9204645488", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[3, 1, 8, -8, -5, -6, 3, 14, 2, -9, 2, 10],\n [1, -16, 2, 4, 3, -2, 0, 8, 13, 1, -12, -10],\n [8, 2, 14, 0, -6, 0, 0, -8, -2, -6, 12, 1],\n [-8, 4, 0, -14, 4, -6, 2, -12, 0, -6, -10, -8],\n [-5, 3, -6, 4, -7, 3, -2, 2, -10, -6, -4, -4],\n [-6, -2, 0, -6, 3, 2, 14, -2, 0, -2, -8, 9],\n [3, 0, 0, 2, -2, 14, 13, 4, -2, -6, -4, 2],\n [14, 8, -8, -12, 2, -2, 4, -10, 2, 4, -2, 7],\n [2, 13, -2, 0, -10, 0, -2, 2, 4, 4, 3, 3],\n [-9, 1, -6, -6, -6, -2, -6, 4, 4, -9, -5, -4],\n [2, -12, 12, -10, -4, -8, -4, -2, 3, -5, 10, 0],\n [10, -10, 1, -8, -4, 9, 2, 7, 3, -4, 0, 10]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37286019879144", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 1) of the matrix A^8 where A is:\n[[-12, 5, 8, 4, -2, 3, 0, 4, 6, 8, -4, 10],\n [5, 2, 12, 6, -8, -10, 10, 8, 8, -8, 8, -4],\n [8, 12, 9, 0, 3, -8, -1, 4, -12, -8, -2, 0],\n [4, 6, 0, -9, -8, 14, 0, 2, 9, 8, 8, -7],\n [-2, -8, 3, -8, 8, -6, 4, -11, 2, -4, -10, 2],\n [3, -10, -8, 14, -6, 6, 2, 0, 1, -1, 0, 6],\n [0, 10, -1, 0, 4, 2, -15, 10, 4, 4, -2, 0],\n [4, 8, 4, 2, -11, 0, 10, 12, 1, 2, 5, 3],\n [6, 8, -12, 9, 2, 1, 4, 1, 13, -3, 14, -7],\n [8, -8, -8, 8, -4, -1, 4, 2, -3, -6, 8, -1],\n [-4, 8, -2, 8, -10, 0, -2, 5, 14, 8, 15, 15],\n [10, -4, 0, -7, 2, 6, 0, 3, -7, -1, 15, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-202435834868", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[5, -14, 6, -14, -11, 6, -5, -12, -12, -14, -13, 7],\n [-12, 14, 2, -9, 11, 6, -10, -4, 4, -11, -7, 10],\n [9, 11, -1, 11, -14, -16, -14, 13, 2, 16, -9, 2],\n [-12, 10, 7, 14, 5, 6, 7, 15, 16, 11, 0, 9],\n [1, -2, 5, 1, 4, 2, -15, 13, 8, 9, 0, -1],\n [10, -14, 12, -15, -3, -5, 7, 11, 1, 8, -11, 13],\n [14, 2, 11, -9, -6, -1, 9, -16, 14, 10, -8, 9],\n [-11, -10, -4, -7, 14, 1, -6, -7, 11, 4, 8, -11],\n [-6, 16, -12, 15, 7, -4, -11, 8, 6, -4, 11, -4],\n [-10, 0, -8, -3, 13, 13, 16, 8, 14, 6, 10, 16],\n [3, 11, -9, 5, 14, 7, -2, 14, -12, 5, 0, 11],\n [-14, 2, 10, 0, 15, 4, -6, -16, 13, 9, 9, 10]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111468619183673", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 10) of the 8th power of the matrix:\n[[9, 4, 6, 10, -6, -2, 0, 1, 2, -2, -10, 2],\n [4, -4, -4, 1, -12, -4, 8, -7, -1, -6, 5, 6],\n [6, -4, -1, -4, -2, 6, 6, 0, -6, -10, -2, 4],\n [10, 1, -4, 4, 10, -10, 2, 2, -4, -6, -4, 2],\n [-6, -12, -2, 10, -12, -6, 8, 14, 14, 7, 4, -10],\n [-2, -4, 6, -10, -6, 3, 9, 2, 4, 0, 4, -4],\n [0, 8, 6, 2, 8, 9, 14, -2, -4, -4, -4, 2],\n [1, -7, 0, 2, 14, 2, -2, 1, 4, -6, -8, 2],\n [2, -1, -6, -4, 14, 4, -4, 4, 15, 4, 12, 12],\n [-2, -6, -10, -6, 7, 0, -4, -6, 4, 4, -3, -9],\n [-10, 5, -2, -4, 4, 4, -4, -8, 12, -3, 16, 0],\n [2, 6, 4, 2, -10, -4, 2, 2, 12, -9, 0, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "638890518795", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (11, 3) of the matrix A^7 where A is:\n[[-9, 7, 4, 9, 4, 7, 0, 2, 4, 9, -2, 0],\n [7, -3, -2, -8, 11, -10, 4, 2, 0, -1, 1, -4],\n [4, -2, -5, -6, 0, 4, 2, -12, 0, -12, -1, -2],\n [9, -8, -6, 8, 0, -6, 2, 0, 12, -12, 5, -8],\n [4, 11, 0, 0, 16, 4, -4, 6, 14, 2, 0, -8],\n [7, -10, 4, -6, 4, -1, 4, -8, -1, -12, 4, -3],\n [0, 4, 2, 2, -4, 4, -9, -6, 11, 9, -6, 8],\n [2, 2, -12, 0, 6, -8, -6, 16, 4, -12, 2, 1],\n [4, 0, 0, 12, 14, -1, 11, 4, 1, 2, 0, -8],\n [9, -1, -12, -12, 2, -12, 9, -12, 2, 8, -8, 2],\n [-2, 1, -1, 5, 0, 4, -6, 2, 0, -8, -3, 4],\n [0, -4, -2, -8, -8, -3, 8, 1, -8, 2, 4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5279157306", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 7) of the 9th power of the matrix:\n[[8, 10, 5, -9, -10, 5, -4, -4, -6, -2, 5, -4],\n [10, 12, 8, -6, -8, 0, 12, 5, 5, -6, 12, -10],\n [5, 8, 11, -7, -12, -3, 2, -12, -2, 6, 3, -5],\n [-9, -6, -7, -7, 0, 12, 4, -7, -4, 7, 2, -9],\n [-10, -8, -12, 0, 7, -6, -2, -6, 10, -2, -6, 1],\n [5, 0, -3, 12, -6, 0, 4, -4, 6, 1, -7, -12],\n [-4, 12, 2, 4, -2, 4, -12, -2, -3, -4, 8, 12],\n [-4, 5, -12, -7, -6, -4, -2, -16, -4, -12, 7, 2],\n [-6, 5, -2, -4, 10, 6, -3, -4, 6, 12, -8, -8],\n [-2, -6, 6, 7, -2, 1, -4, -12, 12, -5, 7, -13],\n [5, 12, 3, 2, -6, -7, 8, 7, -8, 7, -13, 1],\n [-4, -10, -5, -9, 1, -12, 12, 2, -8, -13, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33578198842469", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (7, 11) of the matrix A^8 where A is:\n[[-5, -11, 4, 15, 15, 10, -6, 5, 6, 6, 10, 3],\n [-2, -13, 12, -6, -10, -6, 16, 13, 15, -4, -10, 7],\n [-6, 14, -3, 9, -16, -11, 14, -5, -16, -11, 12, 13],\n [-4, 13, -5, -7, -7, 1, -11, -9, 3, -1, -15, -6],\n [7, 2, -13, -14, -2, -13, 0, -8, 8, -16, -15, 16],\n [5, -5, 10, -6, -3, -3, 5, -8, -2, 16, 2, 14],\n [1, -5, -16, -10, -15, 5, -13, 3, -14, -8, 1, -1],\n [-8, 2, -11, -2, -11, -12, 12, 10, 9, 11, 15, 8],\n [-10, 13, 14, -5, -8, -14, 11, 5, 9, 2, 4, -7],\n [-1, 7, 8, 9, -16, -13, -3, 7, 10, 10, 7, -16],\n [-4, 3, -5, -12, -12, 0, -7, -1, 7, 12, -3, -7],\n [12, 11, 0, -12, -15, -8, -12, -2, -8, 8, 11, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-70820273181", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (12, 11) of the result:\nA =\n[[16, 16, -9, -13, 14, -7, -9, 13, -3, -14, 12, -1],\n [-7, -13, -13, -15, -6, -2, -6, 6, 13, -16, 16, 6],\n [1, -7, 0, -10, -2, 10, -8, 4, 12, 16, -11, 8],\n [0, 10, 8, -5, 8, -15, -16, -14, 12, -3, 5, -2],\n [-7, -8, 0, 1, 8, -1, 8, -1, 7, -5, -8, 15],\n [2, 5, 2, -5, 1, -12, 9, 10, 3, -9, -1, -15],\n [-16, -12, 14, 6, 4, -5, -13, -6, -8, 9, 10, 12],\n [8, 1, 13, -9, -15, 5, 4, 9, 12, -12, -3, -11],\n [6, 0, 7, 12, 13, 7, -15, 4, -12, 2, -1, 8],\n [-1, 14, 16, 0, 4, 6, -1, -3, 16, 4, 0, -13],\n [-1, 13, 5, 12, -12, -16, 8, -11, 6, 16, -3, 1],\n [-7, -5, 6, -10, 8, -4, 2, 5, -6, -14, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8749954068286", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-10, 4, 2, 2, 2, -3, -6, 13, 4, 12, 14, -2],\n [4, 3, 10, -3, 4, 12, 10, -9, -5, -6, -2, -8],\n [2, 10, 10, -3, 0, 5, -8, 6, -9, -2, 4, 4],\n [2, -3, -3, 12, 2, -11, 3, -7, 0, -6, -4, -8],\n [2, 4, 0, 2, 11, 10, 4, 6, 8, 0, -6, -12],\n [-3, 12, 5, -11, 10, 5, 6, 10, -13, -5, 0, 6],\n [-6, 10, -8, 3, 4, 6, -7, -4, 2, 10, 2, 0],\n [13, -9, 6, -7, 6, 10, -4, 3, -9, 4, 6, -2],\n [4, -5, -9, 0, 8, -13, 2, -9, -8, 4, 4, 9],\n [12, -6, -2, -6, 0, -5, 10, 4, 4, -14, 4, -4],\n [14, -2, 4, -4, -6, 0, 2, 6, 4, 4, -13, -2],\n [-2, -8, 4, -8, -12, 6, 0, -2, 9, -4, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3802044769462581", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[4, -8, -13, -14, -8, -12, 10, -6, -14, 2, -10, 5],\n [-8, -6, 4, -4, 2, 4, -4, 14, 1, -7, 0, 6],\n [-13, 4, 8, -6, 5, 2, 7, 2, -1, 9, 2, 2],\n [-14, -4, -6, -8, 6, -2, 2, -1, 4, 12, 2, -11],\n [-8, 2, 5, 6, 7, 2, 4, 4, -7, -4, 10, -13],\n [-12, 4, 2, -2, 2, -5, -8, -2, -14, 4, -2, -2],\n [10, -4, 7, 2, 4, -8, -16, 8, 0, -1, 3, 8],\n [-6, 14, 2, -1, 4, -2, 8, -3, -6, -2, 4, 2],\n [-14, 1, -1, 4, -7, -14, 0, -6, 3, -8, 11, 4],\n [2, -7, 9, 12, -4, 4, -1, -2, -8, -16, 4, -3],\n [-10, 0, 2, 2, 10, -2, 3, 4, 11, 4, 11, -8],\n [5, 6, 2, -11, -13, -2, 8, 2, 4, -3, -8, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23008096587663", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[4, -16, 0, 7, 14, 3, -1, 0, -12, -2, -2, -4],\n [-16, -14, 1, 10, -16, -8, 8, -6, -8, -4, 6, -12],\n [0, 1, 12, 6, -1, -2, 12, -5, 3, 12, -2, -7],\n [7, 10, 6, 13, 13, -4, 5, -4, 2, -12, 7, 2],\n [14, -16, -1, 13, -12, -6, -4, 1, -2, -4, -6, 8],\n [3, -8, -2, -4, -6, -1, 6, 2, 4, 0, -15, 0],\n [-1, 8, 12, 5, -4, 6, -13, 3, -6, 8, -7, 0],\n [0, -6, -5, -4, 1, 2, 3, -13, 10, -7, 9, 1],\n [-12, -8, 3, 2, -2, 4, -6, 10, -1, -8, -4, -6],\n [-2, -4, 12, -12, -4, 0, 8, -7, -8, -4, 0, -11],\n [-2, 6, -2, 7, -6, -15, -7, 9, -4, 0, 2, 4],\n [-4, -12, -7, 2, 8, 0, 0, 1, -6, -11, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47605987870551", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-3, 13, 1, -4, -3, 8, 10, 6, -10, -7, 8, 7],\n [-6, 3, -7, 4, 11, 11, 10, 16, -13, 3, -11, -11],\n [0, 2, 0, -14, -13, 6, 1, 12, -2, -6, -8, -7],\n [12, -11, 2, 9, -8, -4, 9, 3, -15, -13, -10, 2],\n [-6, 2, 15, -3, -12, 8, -3, -5, 3, 1, -16, -13],\n [-5, 9, 15, -2, 9, -2, -9, 11, 13, -14, -11, 14],\n [9, -9, 12, 0, -1, -13, -7, -1, 2, -4, -13, 15],\n [1, -1, 8, -1, 5, 7, 11, 6, 4, -8, -15, 11],\n [9, 10, 8, 4, 8, -6, 11, -13, 2, 7, 5, 8],\n [-9, 3, -16, -13, -5, 8, 4, 2, -11, -14, 16, -8],\n [-10, 10, -16, 1, 0, -6, -6, -14, -4, 11, 11, -15],\n [-15, -1, -9, -6, -2, -13, 6, -9, -1, -1, 7, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25873371408", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (12, 9) of the result:\nA =\n[[1, -1, -9, 3, 6, -3, -1, 1, 13, -16, 0, 11],\n [-10, 3, 7, -16, 1, 9, -3, 2, 1, -10, -15, -10],\n [11, 11, 0, 13, 4, -8, 5, -2, -3, 10, 1, -7],\n [5, 6, -12, 8, -16, 7, 16, -10, 7, -2, -6, 0],\n [6, -13, 14, -7, -7, -6, 14, -7, -9, -6, 3, 7],\n [-10, 4, -11, 14, -5, -4, 14, -8, 10, 0, -9, 10],\n [-2, -11, 15, -9, 14, 9, 7, -15, -16, -7, 6, 16],\n [-6, 3, 9, -15, 8, -13, 2, -4, 2, -4, -5, -15],\n [6, 2, -14, 7, 6, -13, 1, -5, 10, -3, 14, -14],\n [-12, 12, 0, 2, 16, -9, 3, 0, -4, -13, 13, -11],\n [-15, -2, 3, -1, 12, 10, -16, -4, 15, -14, -3, 11],\n [9, 4, -6, 10, -16, 16, 1, -15, -13, -13, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2086161434212", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-8, 4, -4, -1, 1, 13, 8, 3, 6, 10, -2, -2],\n [4, -1, 6, 2, 1, -9, 1, -5, -7, -6, 1, -3],\n [-4, 6, -10, 0, -6, 3, 14, 4, -8, 4, 5, -5],\n [-1, 2, 0, 9, 4, 0, -3, -8, 10, -4, 14, 6],\n [1, 1, -6, 4, 6, -10, 0, -2, 8, 3, 5, 4],\n [13, -9, 3, 0, -10, -14, 3, 5, -10, -11, -4, -10],\n [8, 1, 14, -3, 0, 3, 8, -5, -2, 5, 2, 4],\n [3, -5, 4, -8, -2, 5, -5, 10, 6, -5, -8, 4],\n [6, -7, -8, 10, 8, -10, -2, 6, 11, 10, 0, -4],\n [10, -6, 4, -4, 3, -11, 5, -5, 10, -6, 4, 6],\n [-2, 1, 5, 14, 5, -4, 2, -8, 0, 4, -4, 6],\n [-2, -3, -5, 6, 4, -10, 4, 4, -4, 6, 6, 7]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110537015289075", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[13, -12, -13, -8, 16, 12, 14, 2, -15, 3, -5, 4],\n [14, 3, 3, 1, -11, 16, -7, 1, -2, -14, -9, -6],\n [15, 0, 13, -9, -10, 3, -5, 4, 11, 11, -1, -7],\n [5, -10, -13, 7, -3, 0, -9, -4, -10, -14, 7, 7],\n [-10, 13, -12, 4, -9, -10, -15, -5, 11, 2, 11, -5],\n [11, 9, -11, 2, 10, -8, -7, -7, 16, 1, -7, -10],\n [15, -11, 2, -12, 2, -3, -7, -6, 14, -15, -7, 4],\n [-16, 14, -6, -7, 3, 4, -3, -12, -11, 7, -1, 6],\n [-1, -4, -9, 15, 5, 0, -12, -9, 13, 2, -5, 8],\n [-4, -13, -7, 11, -12, 11, 14, -1, 6, 12, 4, -15],\n [6, -1, -6, -8, -15, 1, -4, -9, -7, 10, 0, 7],\n [4, -16, -1, 16, -11, -5, 15, -6, 1, -15, 15, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122090647727", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[4, 0, 2, 8, 7, 10, 1, 12, 5, -6, -6, -8],\n [0, 5, 13, 16, -9, 3, 6, -2, -8, 11, 2, 10],\n [2, 13, -7, -6, -6, 5, -14, -4, 6, -6, -8, -7],\n [8, 16, -6, 1, 2, -4, 4, 10, -10, 8, -10, 0],\n [7, -9, -6, 2, -15, 6, 7, -6, 15, -3, -9, -12],\n [10, 3, 5, -4, 6, 13, -12, -4, 2, 10, -3, 4],\n [1, 6, -14, 4, 7, -12, -6, 6, 2, 1, -8, 10],\n [12, -2, -4, 10, -6, -4, 6, 15, -4, -2, 12, -7],\n [5, -8, 6, -10, 15, 2, 2, -4, -7, 2, 9, -5],\n [-6, 11, -6, 8, -3, 10, 1, -2, 2, 0, -12, 6],\n [-6, 2, -8, -10, -9, -3, -8, 12, 9, -12, -2, 0],\n [-8, 10, -7, 0, -12, 4, 10, -7, -5, 6, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3604916162475", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-6, 6, 14, 1, 7, 5, -16, -11, 12, -6, -1, -11],\n [-16, 7, -14, -15, -2, 5, -13, 7, 2, 13, 5, 10],\n [-2, -16, -5, -8, 2, 1, -6, -6, 13, 3, -2, 8],\n [-14, 9, 11, -11, 15, -6, -4, 0, 13, -13, -3, 11],\n [-10, -1, -3, 10, 13, -2, 1, -6, 5, -13, -14, 7],\n [-3, -14, 14, 14, -5, -7, 3, 1, 2, 0, -6, -12],\n [-3, 11, -8, 12, 8, -9, 2, -15, -11, 13, -15, 2],\n [-4, -9, -8, 6, -9, -8, -1, -1, -5, 8, -6, 1],\n [-4, 1, 13, 13, -14, 12, 8, -15, -12, 14, -12, 4],\n [9, -10, 13, 11, -3, 1, 0, 8, -11, -12, 4, 3],\n [-6, -12, 8, 13, -15, 3, -15, 10, 15, -13, 10, 13],\n [-14, 10, -16, -5, 1, 6, 16, -3, -16, 10, 7, -15]], determine the value at position (5, 12).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108637498206", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[-5, -4, 10, 3, -11, -9, 4, 4, -11, 13, -7, -6],\n [-16, -7, 8, -1, 2, -7, -3, -14, -13, 16, 3, -2],\n [-10, -14, 10, 12, 9, 10, 8, 13, 3, -10, 12, 9],\n [10, -8, 5, -5, -11, -11, 10, 2, -11, 0, 12, 6],\n [0, 4, -7, -9, -3, 14, 1, 13, 1, 8, 8, 13],\n [13, -6, 10, -1, 15, 12, -7, 13, -6, -2, 6, 6],\n [-10, -3, -8, 11, -11, 5, 1, 5, -8, 1, 4, -2],\n [-8, -15, -3, 4, -10, -2, -5, -10, -12, 6, 11, 8],\n [-15, -8, 15, -5, 2, -7, -7, 15, -10, -7, 10, 15],\n [-10, 9, 5, -5, 7, 12, 15, -1, 9, -11, -16, -4],\n [-11, -5, -8, 3, 10, -14, 7, -2, 15, 4, -16, 16],\n [-6, -14, 5, -7, 7, -10, -16, -16, 9, 0, -6, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13711932073253", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-7, -10, 6, -4, -2, -5, 7, -10, -2, -13, -10, 2],\n [-10, -1, -4, -4, 5, -2, 6, -2, -6, -10, 8, 4],\n [6, -4, 10, 2, 10, 2, 9, 4, -2, 4, -10, -4],\n [-4, -4, 2, -4, 10, -7, 2, 13, 1, 12, -1, -16],\n [-2, 5, 10, 10, 9, 5, -8, -12, 1, 6, 6, -5],\n [-5, -2, 2, -7, 5, 9, 5, 0, 0, 6, -2, 8],\n [7, 6, 9, 2, -8, 5, 6, -10, -2, -2, -8, -5],\n [-10, -2, 4, 13, -12, 0, -10, -11, 4, -10, -6, 1],\n [-2, -6, -2, 1, 1, 0, -2, 4, 16, 4, 2, 5],\n [-13, -10, 4, 12, 6, 6, -2, -10, 4, 2, -6, -7],\n [-10, 8, -10, -1, 6, -2, -8, -6, 2, -6, -11, 11],\n [2, 4, -4, -16, -5, 8, -5, 1, 5, -7, 11, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2465395834589", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[12, 14, 4, 8, 2, 4, 2, -6, 2, 8, 10, 4],\n [14, -10, 1, -10, 8, -1, -6, 0, 11, 12, 9, 12],\n [4, 1, 5, 6, -3, 4, 7, -14, -2, 10, -8, -1],\n [8, -10, 6, 1, 9, -6, 0, 12, 14, 7, 2, 15],\n [2, 8, -3, 9, 15, -2, -7, 0, -1, -6, 0, -10],\n [4, -1, 4, -6, -2, 5, -12, -1, 0, -4, -2, -12],\n [2, -6, 7, 0, -7, -12, -6, -6, 5, 0, 5, 4],\n [-6, 0, -14, 12, 0, -1, -6, 13, 1, 5, -4, 2],\n [2, 11, -2, 14, -1, 0, 5, 1, -2, 4, -7, 1],\n [8, 12, 10, 7, -6, -4, 0, 5, 4, 6, -2, -1],\n [10, 9, -8, 2, 0, -2, 5, -4, -7, -2, 11, 0],\n [4, 12, -1, 15, -10, -12, 4, 2, 1, -1, 0, -14]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232018377218116", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (3, 5) of the result:\nA =\n[[12, 6, -16, -11, 0, 2, -15, -2, 6, 2, 16, -11],\n [2, 13, 5, -14, -12, 13, -14, 11, -16, 5, 0, 11],\n [13, -9, 10, 8, -4, -10, 5, 16, 14, 16, 5, 10],\n [10, 4, -7, 11, 16, -9, 16, 2, 13, -3, -3, -10],\n [15, 16, -3, 8, 11, 13, 14, 7, -13, -3, -8, -11],\n [7, 9, -16, 6, 0, 3, 9, -6, 3, -16, -4, -4],\n [-3, -5, 10, -5, -16, 9, 4, 15, 8, -5, 8, 9],\n [-1, -3, 7, -9, 10, -4, 12, 14, 2, -7, -16, 2],\n [-16, 7, 8, -13, 7, 3, 16, 11, 7, -15, 6, 16],\n [-3, -2, 15, 6, -13, 3, 14, -10, -16, -12, -3, 13],\n [6, -10, -1, -8, 14, -10, -15, -11, 0, 9, -5, 3],\n [12, 14, -4, 9, 5, -9, -10, -12, -16, -6, 15, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1537381912", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (2, 12) of the result:\nA =\n[[12, 14, -4, -5, 2, 12, -1, -8, -10, -14, -4, 10],\n [14, 16, 7, -2, -12, -8, 10, 0, 11, 0, 0, 2],\n [-4, 7, 2, -4, 12, 3, -1, -10, 6, 0, 8, -2],\n [-5, -2, -4, 5, 6, -4, 12, 11, -8, 6, 6, -4],\n [2, -12, 12, 6, 13, 0, -2, 8, 8, -4, 8, 2],\n [12, -8, 3, -4, 0, -16, -8, 8, 0, -4, 11, 0],\n [-1, 10, -1, 12, -2, -8, -8, 1, -6, -5, 11, -7],\n [-8, 0, -10, 11, 8, 8, 1, 11, -5, 0, -1, 10],\n [-10, 11, 6, -8, 8, 0, -6, -5, 16, -9, -4, -12],\n [-14, 0, 0, 6, -4, -4, -5, 0, -9, 16, 6, -8],\n [-4, 0, 8, 6, 8, 11, 11, -1, -4, 6, -3, -4],\n [10, 2, -2, -4, 2, 0, -7, 10, -12, -8, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607516717965", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-1, -4, -11, 2, -6, 3, 11, 1, 3, -4, 8, 2],\n [-4, -9, -4, -5, -1, 0, 3, -16, -5, 2, 12, 4],\n [-11, -4, -11, -12, 12, 6, 6, -1, 6, -2, 4, -1],\n [2, -5, -12, -7, 0, 8, 8, 7, 6, -4, 4, 10],\n [-6, -1, 12, 0, 5, -4, -6, 2, 6, 3, 10, -6],\n [3, 0, 6, 8, -4, -6, 2, 4, 8, -4, -2, -8],\n [11, 3, 6, 8, -6, 2, -4, -4, 10, 6, 0, 2],\n [1, -16, -1, 7, 2, 4, -4, 5, -2, 6, -4, 2],\n [3, -5, 6, 6, 6, 8, 10, -2, 14, -10, 12, 2],\n [-4, 2, -2, -4, 3, -4, 6, 6, -10, 15, 10, 6],\n [8, 12, 4, 4, 10, -2, 0, -4, 12, 10, -8, 10],\n [2, 4, -1, 10, -6, -8, 2, 2, 2, 6, 10, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113708498900", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-16, -2, 1, -5, -4, -2, -6, -4, -3, -10, 11, -5],\n [-2, -5, -2, -1, 1, 6, 0, -12, 0, -6, 0, 4],\n [1, -2, -12, -10, -10, -3, -2, 5, 8, -2, -8, 2],\n [-5, -1, -10, 5, -7, -2, -4, 2, 0, 7, 6, 8],\n [-4, 1, -10, -7, -3, 4, 6, -2, 3, -1, -5, 1],\n [-2, 6, -3, -2, 4, 8, 12, -6, 12, -7, -6, 4],\n [-6, 0, -2, -4, 6, 12, 9, 1, 6, 6, -4, -6],\n [-4, -12, 5, 2, -2, -6, 1, -1, -10, -2, -8, 12],\n [-3, 0, 8, 0, 3, 12, 6, -10, -11, 0, -3, -2],\n [-10, -6, -2, 7, -1, -7, 6, -2, 0, 7, 6, 7],\n [11, 0, -8, 6, -5, -6, -4, -8, -3, 6, 12, -12],\n [-5, 4, 2, 8, 1, 4, -6, 12, -2, 7, -12, 9]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28000333335122", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[13, -8, 16, 9, -7, 15, 16, 10, 12, 2, 1, 11],\n [-7, -14, 12, -1, -16, 1, -13, -12, 4, -13, 3, 2],\n [7, 3, 11, 7, 3, 7, -11, 8, 15, 0, 0, -12],\n [0, -8, 3, -15, 2, -8, 2, -13, -11, -6, 4, 8],\n [13, 1, 8, 4, 6, 13, 1, 16, 5, 7, 6, -16],\n [-2, 11, 3, -1, -12, -2, -15, 7, -4, 6, -5, 16],\n [8, -16, -13, 14, 11, -6, 15, -15, -4, 0, -13, 14],\n [-14, -5, 1, 13, -6, 7, 4, -13, 9, -9, 7, -5],\n [-12, -1, 15, 12, 16, -3, 8, -9, 10, 5, -10, -5],\n [-8, 2, 11, 12, -9, 10, -12, 12, 16, 15, 4, -7],\n [-1, -6, 2, -4, -2, 15, 2, -2, 5, -4, 3, -2],\n [-10, 5, 3, 2, 10, -9, 1, -7, -2, 6, -5, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779334481030", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-11, 7, 5, -8, -7, -14, -11, 9, -3, 2, 6, -12],\n [-2, 13, 16, 2, -12, -8, -10, 7, -1, -7, 4, 4],\n [-2, -4, -10, -9, -15, 5, -13, -10, -16, 2, 13, -15],\n [-4, 11, -3, -14, -1, 8, -14, -14, 12, 2, 3, 4],\n [3, 11, 10, 8, -15, 7, 16, 2, 9, -14, 10, -3],\n [3, 6, 8, -13, -15, -15, 8, 6, 4, 8, 10, -6],\n [-3, 0, -2, 14, -4, 1, 0, 11, 9, -3, -6, 15],\n [7, 14, -9, -9, 14, 2, 15, 4, 6, -2, -15, -5],\n [-11, -16, 9, 6, -16, 4, 2, 12, 9, 0, 1, 15],\n [-13, 13, 14, 1, -12, 15, 12, -5, -2, -2, -3, 1],\n [5, -6, -14, -3, 8, -3, 14, 8, 2, -5, -10, -3],\n [12, -3, 6, -3, 6, -9, -4, -16, 9, -13, -1, 8]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-403408107988", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 5, -3, 10, -1, -2, 5, 1, 10, 0, 8, 6],\n [5, -16, -2, 8, 0, 4, 6, 6, 4, -2, 9, -10],\n [-3, -2, 11, -4, -10, -7, -7, 2, 6, -10, 10, -10],\n [10, 8, -4, 12, 6, 0, 1, -7, 1, 1, -3, 8],\n [-1, 0, -10, 6, 16, 7, -8, -8, -2, 8, 10, 6],\n [-2, 4, -7, 0, 7, 14, -4, 8, 8, 6, 0, -2],\n [5, 6, -7, 1, -8, -4, -13, 0, 8, 0, -8, 12],\n [1, 6, 2, -7, -8, 8, 0, 3, -2, 8, -12, -2],\n [10, 4, 6, 1, -2, 8, 8, -2, -15, 10, -14, 12],\n [0, -2, -10, 1, 8, 6, 0, 8, 10, -4, 2, 7],\n [8, 9, 10, -3, 10, 0, -8, -12, -14, 2, -13, -1],\n [6, -10, -10, 8, 6, -2, 12, -2, 12, 7, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6590710331656", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[13, 2, 8, 2, 4, 3, -4, 6, 2, -11, 0, 8],\n [2, -16, -6, 2, -6, 0, 8, -2, 10, -2, 3, -14],\n [8, -6, 16, 0, 4, 6, 2, -6, 12, -2, -10, 4],\n [2, 2, 0, -2, 0, -14, -2, 0, -9, 2, 6, 10],\n [4, -6, 4, 0, -1, 2, -8, -2, -5, 12, -4, 6],\n [3, 0, 6, -14, 2, -5, -1, 9, 12, -14, 12, 10],\n [-4, 8, 2, -2, -8, -1, -8, 0, -12, 1, 2, 6],\n [6, -2, -6, 0, -2, 9, 0, 12, -5, 14, -14, 1],\n [2, 10, 12, -9, -5, 12, -12, -5, -10, -4, -16, -3],\n [-11, -2, -2, 2, 12, -14, 1, 14, -4, -16, 5, -4],\n [0, 3, -10, 6, -4, 12, 2, -14, -16, 5, 6, -6],\n [8, -14, 4, 10, 6, 10, 6, 1, -3, -4, -6, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "313444270162", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 3) of the 9th power of the matrix:\n[[5, 10, -2, 4, -13, 1, -10, -1, -5, -10, -7, -16],\n [-5, 10, 11, 1, -16, 6, 0, -16, -13, -2, 4, 4],\n [5, -3, -13, 15, 11, -5, 13, -8, 2, -1, 13, -16],\n [6, -5, -12, 3, -14, -15, 3, -15, -13, -11, -3, -2],\n [16, 2, -5, -8, 2, 15, 11, 11, 14, -4, 16, 1],\n [12, -9, 5, -16, 14, 3, 6, 0, -7, -8, 0, -14],\n [16, -16, 3, -15, -1, -8, -3, -16, 1, -16, -12, -6],\n [7, 15, -1, -14, -9, 15, 5, 0, 10, -14, 9, -4],\n [0, 13, 12, -3, 13, -8, 15, -13, -11, -16, 8, -14],\n [4, -3, 13, -15, 5, -4, 8, -6, -7, 8, 2, 11],\n [-7, -2, 15, -14, 7, -7, 13, 16, 8, 8, -5, -13],\n [11, 3, -7, 14, 2, -15, -13, -2, 16, 1, 15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19072668794912", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-4, -1, 16, -3, -15, -4, 12, 0, -14, 13, -13, 14],\n [-12, -15, -13, 10, 10, -2, -3, 1, 12, -10, 7, -11],\n [3, -7, 5, 16, 6, -13, 4, -4, -4, -5, 7, 2],\n [-8, -4, 5, 11, -10, 13, 14, -6, 13, -2, -4, 3],\n [6, 3, 2, 1, -13, -9, 13, 3, -9, -12, -10, 5],\n [-8, -6, -5, -9, 15, 0, 9, 16, 9, 5, -14, 14],\n [-3, 1, 0, -5, 16, 15, 4, -3, -15, -10, -2, 14],\n [11, -9, -10, -7, 13, -12, 4, -11, -1, -1, 7, 2],\n [2, 16, -12, -8, 4, -10, 8, 4, -4, 4, -7, 7],\n [10, 16, 9, 0, 4, -15, -2, -15, -10, 15, -14, -14],\n [16, 8, 2, 2, 16, 1, 10, 13, 14, -14, 5, -7],\n [-9, 1, -5, 15, -15, 0, -5, -10, -2, -15, 10, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43438644472877", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (1, 2) of the result:\nA =\n[[8, -6, -8, -10, 10, -10, 8, 7, -12, -6, 0, -3],\n [-6, 0, 2, 0, -6, 4, 14, 12, 2, 4, -12, 2],\n [-8, 2, -7, 9, 8, -15, -7, -8, -2, -10, 6, 5],\n [-10, 0, 9, -15, 2, -7, 5, 4, 1, 7, -10, 6],\n [10, -6, 8, 2, 10, 2, -10, 8, 2, 2, 2, 3],\n [-10, 4, -15, -7, 2, -1, -6, -4, 9, -1, -1, -8],\n [8, 14, -7, 5, -10, -6, -2, -4, 2, -6, -9, 6],\n [7, 12, -8, 4, 8, -4, -4, -16, 3, -8, -4, -2],\n [-12, 2, -2, 1, 2, 9, 2, 3, 15, -6, -3, 10],\n [-6, 4, -10, 7, 2, -1, -6, -8, -6, 7, 5, 6],\n [0, -12, 6, -10, 2, -1, -9, -4, -3, 5, 14, -3],\n [-3, 2, 5, 6, 3, -8, 6, -2, 10, 6, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-378374678696", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[12, -2, 0, 0, -14, 4, -7, 8, 3, -2, 10, 2],\n [-2, 2, -2, 10, 2, -5, -10, -6, -4, -9, 2, -4],\n [0, -2, -13, 3, 5, 4, 0, -1, -14, 10, -8, -4],\n [0, 10, 3, -4, -4, 4, -11, 3, 8, 3, -2, -6],\n [-14, 2, 5, -4, 4, -3, 0, 4, -11, 2, 10, 10],\n [4, -5, 4, 4, -3, -10, -6, 4, -2, 0, 2, -10],\n [-7, -10, 0, -11, 0, -6, -11, -8, 6, -9, -4, -10],\n [8, -6, -1, 3, 4, 4, -8, 10, -6, -8, 6, -2],\n [3, -4, -14, 8, -11, -2, 6, -6, 7, 0, -6, 9],\n [-2, -9, 10, 3, 2, 0, -9, -8, 0, 14, 12, -7],\n [10, 2, -8, -2, 10, 2, -4, 6, -6, 12, 12, 1],\n [2, -4, -4, -6, 10, -10, -10, -2, 9, -7, 1, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-137366415129", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[-1, 9, 16, -13, 9, -8, -6, -12, 15, 12, 11, 7],\n [2, -16, -12, 6, 2, -15, -15, -8, 1, -1, -8, 6],\n [16, 9, 0, -3, -4, 5, 1, 3, 13, 16, 0, -5],\n [-15, -5, 9, 15, 4, -12, 11, 6, 15, -12, -11, 2],\n [-11, -3, -14, -6, 7, 1, 14, -7, 9, 12, -15, 13],\n [-7, -5, 3, 2, -11, 6, 2, 14, 16, -15, -2, -6],\n [9, 1, -16, 15, -13, 5, 12, 16, -3, -12, 5, -12],\n [-2, 10, -16, 12, -9, 16, -10, 12, 14, -9, 14, -2],\n [15, 9, -6, 6, 16, 0, 16, -15, -13, -5, 12, 2],\n [-15, -10, 5, -6, 16, 3, -12, -13, -3, -14, 1, 10],\n [-13, -14, 10, 11, 5, 12, -1, 2, 13, -2, -12, 14],\n [14, -8, -4, 4, 14, -16, -4, -1, -7, 8, -16, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10060515122561", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[5, 5, -15, -9, 16, -12, -7, -14, -6, 13, 11, -12],\n [-5, 12, 9, 12, 12, -3, -9, -1, -12, -1, -4, -9],\n [9, -12, -8, -15, -10, 13, 0, 14, -16, 11, 13, 14],\n [7, 14, -6, -1, -8, 13, -5, -1, 16, -11, -16, -4],\n [9, -8, 0, 8, -10, 14, 15, 2, 0, -11, 8, 16],\n [2, -2, 15, 15, 15, -7, 16, -7, 5, 6, -10, 4],\n [-16, -4, -8, 3, -7, 9, -16, 0, 0, -5, -2, -16],\n [15, -6, -12, 1, 1, 6, -10, 9, -16, 11, 3, 6],\n [15, 1, 16, 8, 15, 11, -4, 2, -14, 10, 0, 12],\n [16, 11, 3, -1, -15, 11, 0, 3, 1, 11, 11, -1],\n [16, 4, -12, 1, -12, -6, 5, 6, 9, 10, -14, -15],\n [0, -14, -14, -1, -5, -16, -13, 0, 2, -13, 3, -13]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33889028407", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[0, 0, 1, 2, -8, 4, 13, 5, 0, -2, 4, -6],\n [0, 6, -2, -10, -6, 4, 2, 10, 6, -12, -6, -6],\n [1, -2, 8, 6, -2, 2, 16, -14, -5, -10, 6, 4],\n [2, -10, 6, -1, 7, -4, -3, -12, -2, -2, -6, 4],\n [-8, -6, -2, 7, -9, 9, -1, 8, -4, 4, -2, 2],\n [4, 4, 2, -4, 9, -16, 7, -14, -8, -12, -3, 1],\n [13, 2, 16, -3, -1, 7, -15, -2, 4, 2, -8, 4],\n [5, 10, -14, -12, 8, -14, -2, 13, 7, -6, 8, 6],\n [0, 6, -5, -2, -4, -8, 4, 7, -6, 1, -6, 13],\n [-2, -12, -10, -2, 4, -12, 2, -6, 1, 9, -6, -12],\n [4, -6, 6, -6, -2, -3, -8, 8, -6, -6, 15, 5],\n [-6, -6, 4, 4, 2, 1, 4, 6, 13, -12, 5, 10]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12995882871", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 4) of the 9th power of the matrix:\n[[0, -7, -12, -13, -2, -15, -9, -1, 3, 7, 0, -12],\n [-3, -3, 14, 3, -4, -8, -5, -1, -16, -1, -11, 3],\n [-11, -14, 4, -10, -3, 13, 5, -3, 8, -14, -12, -12],\n [-8, -13, 3, 4, 7, -10, -9, -6, -8, -11, 0, -4],\n [0, -15, 13, 15, -10, -1, 2, -2, -3, -10, 16, 7],\n [4, 7, -1, 0, 12, 1, -6, -14, 1, -1, -16, 10],\n [14, 11, 10, -8, 10, 9, 10, -13, -5, -2, 13, -3],\n [-9, 11, 14, -15, -2, -9, -12, -13, -5, -7, -13, -7],\n [12, 11, 12, 2, -4, 3, 1, -16, 9, -14, -14, 4],\n [1, 14, 14, -9, 8, 3, -6, -16, 4, 0, 11, 1],\n [12, -7, -8, 3, 14, -14, -16, 16, -9, 1, 13, 16],\n [5, 0, -8, 5, -7, 16, -14, 0, -8, 2, -15, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5992211040152", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[2, 2, -2, 2, 2, 10, 10, 2, -6, -8, 0, -1],\n [2, -9, -14, 8, 2, -6, 6, 4, 0, 6, -2, 6],\n [-2, -14, 6, -4, 0, 10, -9, -3, 5, -6, 4, -12],\n [2, 8, -4, -15, -2, 6, -8, -6, 6, 0, 13, 12],\n [2, 2, 0, -2, 11, 8, 8, 4, -3, 2, 8, 3],\n [10, -6, 10, 6, 8, -6, 1, -1, 0, -4, 12, 4],\n [10, 6, -9, -8, 8, 1, -14, 10, 7, -2, 8, 2],\n [2, 4, -3, -6, 4, -1, 10, 11, 8, 7, -8, 6],\n [-6, 0, 5, 6, -3, 0, 7, 8, 5, 2, 10, 3],\n [-8, 6, -6, 0, 2, -4, -2, 7, 2, 3, -2, -10],\n [0, -2, 4, 13, 8, 12, 8, -8, 10, -2, 0, -2],\n [-1, 6, -12, 12, 3, 4, 2, 6, 3, -10, -2, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15822757222704", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[7, -1, 15, -13, -3, 12, 5, 6, 9, 9, 5, -14],\n [0, -3, 13, -4, 9, 15, 6, -5, 6, 11, 2, -9],\n [-1, -10, 10, 3, 0, 11, -9, -13, 16, 5, 14, -16],\n [-3, -10, -9, -9, 7, -16, -9, -12, 15, -16, -15, -2],\n [-8, -5, -7, 7, 2, 0, -15, -7, -12, -11, -15, -9],\n [-13, 14, -9, 14, 0, -3, -9, 8, -3, 6, 0, -5],\n [3, -6, 10, -8, 1, 11, 3, 12, -13, -2, 11, 7],\n [-1, 5, 0, -16, 14, 8, -5, 3, 2, -12, -2, 8],\n [-14, 1, 5, -1, -2, -12, -4, 11, -7, -1, -15, 8],\n [-12, 11, 0, -15, -2, 12, 6, 1, -3, 15, -11, 11],\n [1, -13, 14, -6, -6, 12, 2, 0, -13, -13, -5, -10],\n [4, 16, -5, -10, -2, -8, 16, -1, 14, -2, -15, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1310151302689310", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-12, 16, 15, 4, -15, 16, -6, 6, 16, -9, 16, 12],\n [14, 13, -9, 9, 6, 9, -15, 9, 1, 10, 0, -2],\n [-10, 0, 2, 10, 0, 15, -1, 13, -3, 1, 5, -1],\n [-1, 9, -11, -10, -8, 9, -15, -14, 4, -14, -8, -5],\n [-9, 4, -14, 4, 9, 7, 15, 10, 13, -13, -15, 6],\n [-13, -6, -2, -14, 13, 6, 16, -16, -16, -14, -8, 15],\n [-4, 14, 4, 6, -4, 9, 8, -9, 13, -12, 7, -7],\n [2, 5, -10, 3, 15, -15, -2, -7, 4, -2, -12, 2],\n [-10, 1, -11, -13, -12, -3, 16, 4, -4, -15, -2, -1],\n [3, -16, -14, 0, 0, 3, 3, -13, -6, -2, 10, 7],\n [3, -2, -11, 1, 5, 4, 7, 0, -6, 1, 14, 11],\n [7, 7, 16, 13, -4, -1, -8, -4, -10, 9, -8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "695582689360133", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[16, 4, 5, 2, 15, -12, -5, -11, 1, -10, 2, -2],\n [-8, 3, 3, -13, -7, -16, 7, -10, 5, 6, -16, 7],\n [3, 15, 14, 16, 1, 16, 16, -12, 1, -8, 14, -10],\n [-2, -13, -9, 7, -9, -12, 6, -2, 2, 8, -13, -9],\n [12, -4, 14, 2, 8, -16, 4, 9, -14, -12, 12, 16],\n [-15, 1, -3, 13, 12, 12, 2, 9, -8, -4, 14, -3],\n [14, -2, -7, 4, 8, 3, -10, 1, 9, 0, -10, 11],\n [4, 6, -7, 0, -16, -6, 16, 14, 7, 3, -12, 9],\n [-10, 10, 1, 14, -8, -15, 12, -2, -8, -1, -15, -16],\n [-8, 3, -15, -16, -7, 6, 2, 1, 7, 5, 3, -6],\n [-8, -2, -1, -4, -11, 8, -2, 1, 16, -3, -15, 3],\n [-1, -14, 13, 6, 6, -14, -4, 12, 6, 0, 4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43093077832259", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-12, 8, -12, 11, 2, 1, -4, -8, -8, -4, -6, 0],\n [8, -8, 0, 6, -2, 0, -6, 4, 2, 0, -2, 9],\n [-12, 0, -11, -14, -10, -14, 6, -4, 10, -2, -1, 4],\n [11, 6, -14, 3, -12, -4, 5, 14, -5, -9, 6, -4],\n [2, -2, -10, -12, 15, 10, 0, 0, 12, 4, 4, 4],\n [1, 0, -14, -4, 10, 10, 6, 2, 5, -10, 10, -8],\n [-4, -6, 6, 5, 0, 6, 8, -2, 0, 0, -2, 4],\n [-8, 4, -4, 14, 0, 2, -2, 0, 6, 8, -4, 0],\n [-8, 2, 10, -5, 12, 5, 0, 6, 15, 2, 12, -6],\n [-4, 0, -2, -9, 4, -10, 0, 8, 2, 7, 5, 5],\n [-6, -2, -1, 6, 4, 10, -2, -4, 12, 5, 15, 12],\n [0, 9, 4, -4, 4, -8, 4, 0, -6, 5, 12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119984594888089", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-5, -8, 7, -4, 6, 6, -4, 12, 4, 10, -5, 4],\n [-8, -10, -6, -6, -6, -12, 7, 6, -5, 0, 9, 12],\n [7, -6, -5, 10, 0, 4, 0, -2, 4, 5, -4, 6],\n [-4, -6, 10, 9, 6, 4, 12, 12, -6, -10, 0, 12],\n [6, -6, 0, 6, -12, -2, -5, 7, -1, -10, 1, 10],\n [6, -12, 4, 4, -2, 15, -8, 0, 4, 6, -4, 14],\n [-4, 7, 0, 12, -5, -8, 7, -10, -4, -4, -4, 2],\n [12, 6, -2, 12, 7, 0, -10, -1, -10, -6, -4, -3],\n [4, -5, 4, -6, -1, 4, -4, -10, 16, 5, 2, -4],\n [10, 0, 5, -10, -10, 6, -4, -6, 5, 10, 6, -6],\n [-5, 9, -4, 0, 1, -4, -4, -4, 2, 6, 12, -1],\n [4, 12, 6, 12, 10, 14, 2, -3, -4, -6, -1, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3661188341924", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (6, 3) of the result:\nA =\n[[4, 0, 9, 0, -10, 8, 9, -11, -7, 0, -3, -14],\n [-1, -12, 6, 10, -12, 1, -5, 4, -10, 0, -8, 7],\n [-6, 8, -10, 0, 2, 4, -8, -9, 10, 6, -7, -15],\n [-10, -15, -1, -11, -1, 8, -7, -8, 15, 15, -15, 4],\n [-14, 12, 3, 6, -9, -3, 6, 10, -2, 5, -2, 15],\n [1, 14, 8, -7, -3, 9, 2, 13, -5, 14, 1, -15],\n [-3, 3, 3, -14, 16, 2, 14, 5, 10, 11, 4, 3],\n [-4, 12, 4, 16, 15, 11, -3, 5, 0, 16, 16, 9],\n [-10, 8, 13, 16, 11, 1, -7, -15, -3, -4, -16, 15],\n [8, -7, -2, 12, 0, 6, -10, -11, -15, 15, -12, 2],\n [-15, 6, -13, -13, -6, 3, -3, -3, -14, -2, 4, -15],\n [4, -7, 10, 2, -5, -1, -9, 8, 7, 1, 4, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3307757319310", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[2, 11, 2, 8, -2, 6, 12, -10, -2, 4, 3, 6],\n [11, -6, 5, -12, -6, 6, -8, -7, -4, 0, 4, -4],\n [2, 5, 15, 8, -3, -14, 8, 6, 1, 1, 3, 1],\n [8, -12, 8, -16, 2, 10, -8, 0, 2, 4, -6, 4],\n [-2, -6, -3, 2, -3, 11, -2, -5, 9, 9, -12, 4],\n [6, 6, -14, 10, 11, 3, 4, -2, 1, 10, 2, -14],\n [12, -8, 8, -8, -2, 4, -2, -4, 3, 2, -1, 0],\n [-10, -7, 6, 0, -5, -2, -4, 4, -2, 12, 1, 6],\n [-2, -4, 1, 2, 9, 1, 3, -2, -4, 0, -6, 0],\n [4, 0, 1, 4, 9, 10, 2, 12, 0, 5, 2, -6],\n [3, 4, 3, -6, -12, 2, -1, 1, -6, 2, 11, -14],\n [6, -4, 1, 4, 4, -14, 0, 6, 0, -6, -14, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4311107067709948", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-11, -5, 2, -4, 6, 8, 15, 4, -8, -4, -2, -6],\n [-5, -8, -10, -6, -4, 4, -7, 2, 2, 3, 4, -2],\n [2, -10, 14, 4, -1, 6, 8, -3, 2, -10, 10, 10],\n [-4, -6, 4, 7, -2, -15, 6, 6, 6, 12, 0, -1],\n [6, -4, -1, -2, 15, -11, 0, -1, 8, 14, 8, -2],\n [8, 4, 6, -15, -11, 5, -2, -4, 1, -14, 5, -2],\n [15, -7, 8, 6, 0, -2, -6, 2, -4, -10, 6, -3],\n [4, 2, -3, 6, -1, -4, 2, -9, 0, -2, 2, -1],\n [-8, 2, 2, 6, 8, 1, -4, 0, 0, -14, -9, -7],\n [-4, 3, -10, 12, 14, -14, -10, -2, -14, -4, -8, -2],\n [-2, 4, 10, 0, 8, 5, 6, 2, -9, -8, 1, -2],\n [-6, -2, 10, -1, -2, -2, -3, -1, -7, -2, -2, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4717239028135860", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (8, 1) of the matrix A^7 where A is:\n[[15, -11, -16, -13, 8, -9, 3, -3, 16, -14, -2, 10],\n [2, -16, 16, 0, -4, -5, 9, 10, 7, 0, -6, 5],\n [-9, 15, 12, 15, -12, -4, 8, -7, 9, 9, 4, 6],\n [-5, 8, -5, 15, 1, 3, -15, 16, 0, 13, -8, 14],\n [4, 5, 0, -14, 15, 16, -7, -12, -13, 15, 3, -8],\n [-2, -9, 13, -7, -3, 5, -4, 12, 12, -10, -11, -13],\n [-3, -11, 0, 7, -4, -5, 12, 7, -3, 10, -12, -8],\n [-1, -4, -2, 8, -1, 14, 16, 3, 9, -10, 14, 0],\n [-9, 6, 1, -5, 13, -2, 1, 8, -4, 7, 0, -16],\n [10, 3, 1, -8, -7, 8, -16, 1, -2, 16, 5, 7],\n [-16, -6, 9, 9, -11, 16, -3, 7, 0, -3, 2, -9],\n [6, -15, -14, -4, -12, 1, -16, 4, 2, -15, 3, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14915972036", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-4, -3, -5, -4, 7, 14, -3, 13, 10, -11, -11, -2],\n [7, -4, -10, 4, -3, -14, -5, 4, 3, 10, -12, -6],\n [-11, -12, 5, -16, 3, 7, 3, 12, 7, -9, 5, 16],\n [13, -11, -4, 2, 9, 0, 10, 7, -3, -14, -12, -3],\n [-9, 8, -2, -14, -6, -8, -13, -2, 10, 14, -1, 15],\n [-11, -12, 7, 2, 13, -5, -12, 11, -5, 6, -12, -1],\n [-8, 16, 16, -16, -8, 1, 4, -3, -11, -14, 1, 3],\n [12, -1, -13, -3, 0, 15, -7, 12, -5, -8, 9, 4],\n [-16, 2, -11, 1, -9, -6, -12, 4, 4, 3, -8, -15],\n [-13, 9, -5, 2, 2, 2, 12, -9, -11, 15, 11, -6],\n [11, 15, -9, 3, 7, 10, -6, 6, 5, -12, 14, 9],\n [6, 15, -12, 8, 16, -10, -1, 12, -2, 3, 5, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96022502227", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-9, 4, 2, 0, 8, 9, 4, 14, -6, -6, 0, -4],\n [4, -8, -2, -12, -2, 0, -6, -6, -2, -6, -3, -6],\n [2, -2, -8, 12, -8, 4, 2, 6, 0, -10, -4, -6],\n [0, -12, 12, 8, 2, -7, 6, -8, 3, 4, -2, 2],\n [8, -2, -8, 2, -7, -8, -2, 11, 6, -10, -4, -4],\n [9, 0, 4, -7, -8, 14, -5, 0, 13, -6, 6, 0],\n [4, -6, 2, 6, -2, -5, 15, -10, 8, -6, 2, 12],\n [14, -6, 6, -8, 11, 0, -10, -5, 14, 0, 6, 7],\n [-6, -2, 0, 3, 6, 13, 8, 14, 14, -6, -4, -10],\n [-6, -6, -10, 4, -10, -6, -6, 0, -6, -13, 1, 2],\n [0, -3, -4, -2, -4, 6, 2, 6, -4, 1, 9, 2],\n [-4, -6, -6, 2, -4, 0, 12, 7, -10, 2, 2, 11]], determine the value at position (7, 9).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1080851267535", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 5) of the matrix A^7 where A is:\n[[-7, -3, 3, -4, -2, -6, -2, -4, -7, 4, 4, -3],\n [-3, -8, 5, -2, 11, 4, -8, 2, -10, -9, -4, 8],\n [3, 5, -10, -9, 0, -5, -7, 2, 2, -5, 1, 8],\n [-4, -2, -9, -14, -8, -6, -4, 0, 11, -10, 2, -4],\n [-2, 11, 0, -8, -7, 4, 10, -3, 10, 6, -2, 0],\n [-6, 4, -5, -6, 4, -15, 3, 6, 4, 12, 4, 3],\n [-2, -8, -7, -4, 10, 3, 8, 4, 10, -10, 2, -2],\n [-4, 2, 2, 0, -3, 6, 4, 10, 8, -8, 6, 10],\n [-7, -10, 2, 11, 10, 4, 10, 8, -9, 0, 11, 6],\n [4, -9, -5, -10, 6, 12, -10, -8, 0, -15, -6, -5],\n [4, -4, 1, 2, -2, 4, 2, 6, 11, -6, -12, -14],\n [-3, 8, 8, -4, 0, 3, -2, 10, 6, -5, -14, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22260636572", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-12, -12, 3, -4, -8, -12, 15, 13, 11, 11, -11, 12],\n [-13, 1, -2, 8, -13, -3, 0, 2, 12, 5, -3, -15],\n [-10, 11, -9, 12, -7, 4, -13, 4, 8, 3, -10, -10],\n [15, 15, 5, 8, -11, 10, 1, -5, 11, 2, 0, -2],\n [-12, 16, 4, 10, 13, 13, 4, 9, 7, 5, 9, 5],\n [16, 7, -12, 7, 5, 16, 0, -5, 13, 9, -4, -11],\n [-14, -6, -7, -6, -1, 3, 2, -8, -2, 6, 4, -12],\n [5, 14, -2, 11, -2, 2, 1, -7, -2, 7, 3, -6],\n [-8, -12, -6, 10, -15, 3, 4, 13, -16, 9, 15, -8],\n [4, -1, -5, 10, -10, 13, 7, 13, 3, 11, -13, -5],\n [-14, -13, -2, 11, -8, -3, 15, -14, 1, -3, 8, 9],\n [-11, 9, -16, 4, -3, -9, 8, 1, -2, 3, -1, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "855377921135446", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[12, 14, 12, 0, -12, 1, -3, 14, 1, 8, -6, 9],\n [-12, -1, -9, -4, 15, 10, 9, -8, -10, -9, -15, 1],\n [7, -6, -7, 12, -11, -7, 13, 11, 12, 8, 10, 15],\n [-13, -1, -6, -2, 13, 10, -1, -16, 8, 11, -3, -13],\n [-3, -1, -2, -4, 0, 11, -7, 0, -9, -15, -16, -12],\n [5, -1, -8, -8, -3, -7, 5, -1, -14, 11, 13, 12],\n [-16, 11, 5, 15, -6, 9, 14, 3, 3, 16, -12, -14],\n [14, -10, 13, 1, -1, -4, 16, -10, 13, -6, -11, 4],\n [15, -12, 12, -5, 5, -6, 6, -7, 7, -1, -5, 15],\n [7, -13, 16, 1, 0, 4, -16, 8, 14, 3, 9, 2],\n [13, 8, 1, -13, 10, 16, -11, -10, -16, 6, -1, 14],\n [14, -6, -9, 7, 6, 15, -2, 11, 3, -3, 9, -15]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145029678024828", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-8, -4, 13, 2, 14, -2, 11, 4, 9, 8, -2, 1],\n [-4, 2, -10, -7, 11, -7, -4, -7, -8, -4, -10, -4],\n [13, -10, -11, 2, -1, -13, -4, 2, 0, -7, -9, 4],\n [2, -7, 2, -5, 2, 3, -3, 13, 9, -8, -9, 3],\n [14, 11, -1, 2, 14, 8, -3, 1, 8, 0, -2, 4],\n [-2, -7, -13, 3, 8, 9, 0, -3, 4, 0, -13, 2],\n [11, -4, -4, -3, -3, 0, -15, 4, -7, -5, 4, 0],\n [4, -7, 2, 13, 1, -3, 4, -8, 4, 2, 12, 10],\n [9, -8, 0, 9, 8, 4, -7, 4, 5, 12, 3, 0],\n [8, -4, -7, -8, 0, 0, -5, 2, 12, 7, 3, 4],\n [-2, -10, -9, -9, -2, -13, 4, 12, 3, 3, -14, -6],\n [1, -4, 4, 3, 4, 2, 0, 10, 0, 4, -6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109106949186438", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-3, -2, 6, -7, -4, -6, -3, -3, 6, -10, 11, 3],\n [-2, 15, -3, 0, 10, -4, 2, 0, 6, 0, 3, 3],\n [6, -3, -13, 2, 6, 2, 0, -10, 4, 12, -2, -3],\n [-7, 0, 2, 5, 2, 4, 0, -1, 4, -2, 0, 0],\n [-4, 10, 6, 2, -13, 0, -6, 12, 6, 8, 10, -1],\n [-6, -4, 2, 4, 0, 16, 14, -8, 6, 4, -2, 2],\n [-3, 2, 0, 0, -6, 14, 4, 2, 6, 1, 14, -1],\n [-3, 0, -10, -1, 12, -8, 2, 14, 6, 8, -6, -6],\n [6, 6, 4, 4, 6, 6, 6, 6, 3, -6, -8, -4],\n [-10, 0, 12, -2, 8, 4, 1, 8, -6, 5, -6, -13],\n [11, 3, -2, 0, 10, -2, 14, -6, -8, -6, 5, 11],\n [3, 3, -3, 0, -1, 2, -1, -6, -4, -13, 11, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2407441616930039", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-13, 6, 3, 7, 14, 12, -2, -10, -1, -4, -6, 0],\n [6, -10, 4, 0, 3, -10, 3, -3, -1, 0, -6, -10],\n [3, 4, 11, -3, 0, 6, -5, -4, 7, -8, -10, -6],\n [7, 0, -3, 0, 0, 9, 14, 7, 12, -10, -7, 1],\n [14, 3, 0, 0, 9, 0, 9, 6, -6, -1, 10, 6],\n [12, -10, 6, 9, 0, -15, 6, 4, -12, -2, 12, 5],\n [-2, 3, -5, 14, 9, 6, 4, -4, 4, 13, -10, 3],\n [-10, -3, -4, 7, 6, 4, -4, 7, -2, -2, -2, 2],\n [-1, -1, 7, 12, -6, -12, 4, -2, -16, -4, 4, -11],\n [-4, 0, -8, -10, -1, -2, 13, -2, -4, -7, -9, -4],\n [-6, -6, -10, -7, 10, 12, -10, -2, 4, -9, 9, -6],\n [0, -10, -6, 1, 6, 5, 3, 2, -11, -4, -6, 12]], determine the value at position (7, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22891692485", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[14, -9, -5, -12, 13, -13, 4, -1, 1, 14, 15, 16],\n [2, 3, -7, 9, 1, -2, 1, 14, -2, 12, -2, -16],\n [6, -6, -1, 13, 12, -14, 0, 9, -8, 0, 14, 14],\n [-6, 5, -14, 11, 15, -13, -6, -16, -1, 15, 16, -6],\n [-4, 3, 8, -11, 9, -13, 9, 1, -4, -9, 16, -1],\n [14, 6, -1, -7, 14, 15, 4, -1, 12, -1, -2, -9],\n [-2, 4, 4, -10, 2, 5, -4, 9, 5, -10, -14, -1],\n [-1, -15, 0, 7, 5, 6, 2, 5, 0, -15, -3, 11],\n [-4, 0, -8, -3, -15, 4, 13, 0, 8, -11, -14, -16],\n [-16, 9, 1, -11, -6, 13, -3, -7, 14, -2, 13, -3],\n [6, 0, 10, -4, -3, 9, -6, -16, 7, 3, -9, -9],\n [13, 1, -4, 2, -4, 9, -8, 14, -10, -8, 9, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2542909922184041", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[16, -13, 11, -13, -11, 16, -12, 2, 1, -14, -15, -16],\n [-13, -9, 12, -3, 13, -10, -4, 5, -15, -9, 4, 3],\n [-6, -12, 13, 16, -5, -12, -16, 8, -13, -8, -14, 13],\n [3, -7, 3, -14, -6, -2, 11, -10, 16, 2, 12, -15],\n [2, -8, -11, 0, -15, -11, -3, 9, 1, -11, -5, 5],\n [-3, -4, -8, 15, -7, 10, -3, -8, -8, 9, 15, 9],\n [-14, 13, 12, 3, -13, -3, 4, -10, -11, -11, 8, -13],\n [8, 1, 8, 5, -3, -6, 10, 9, -1, 3, -2, -3],\n [-9, 7, 16, -1, 10, 11, -3, -8, -4, 5, 13, 15],\n [-1, 8, 6, 11, -14, 6, 16, 8, 8, 4, 14, 13],\n [-10, 10, -4, 12, 6, -9, 4, -4, 9, -7, 12, 10],\n [-13, 14, 0, -9, 3, -7, -6, -5, -7, -4, 13, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2248601328963", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 7) of the 8th power of the matrix:\n[[-9, -1, -12, 2, -2, 8, -16, -6, -2, 2, -10, -8],\n [-1, 5, 8, -11, -10, 10, 12, 2, 8, 0, 7, 6],\n [-12, 8, 0, -6, 0, -12, 4, 4, 2, 2, -4, 3],\n [2, -11, -6, -9, 3, 8, -5, 0, 13, 3, 5, 11],\n [-2, -10, 0, 3, -4, -2, 0, 8, -2, 1, -6, 2],\n [8, 10, -12, 8, -2, 8, 6, -2, -3, 1, -1, 2],\n [-16, 12, 4, -5, 0, 6, -10, -6, 0, -12, -7, -8],\n [-6, 2, 4, 0, 8, -2, -6, -15, 6, 6, -8, -2],\n [-2, 8, 2, 13, -2, -3, 0, 6, 8, -9, 10, 0],\n [2, 0, 2, 3, 1, 1, -12, 6, -9, 10, 5, -12],\n [-10, 7, -4, 5, -6, -1, -7, -8, 10, 5, -10, -4],\n [-8, 6, 3, 11, 2, 2, -8, -2, 0, -12, -4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2259399029304", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-7, 0, -2, 3, 0, 1, -8, 11, 10, 8, 2, 12],\n [0, 12, 0, -4, -10, -1, 11, 2, 14, -6, -6, 15],\n [-2, 0, 3, 6, -4, -10, 2, -12, -8, -8, -4, 8],\n [3, -4, 6, -12, -11, 2, 6, -3, -8, 4, 12, -6],\n [0, -10, -4, -11, 10, -1, -3, -7, 0, 6, 16, 4],\n [1, -1, -10, 2, -1, 13, 3, -10, -10, -10, 9, 5],\n [-8, 11, 2, 6, -3, 3, -12, 6, -8, -4, -8, -6],\n [11, 2, -12, -3, -7, -10, 6, -8, 9, 4, 1, 10],\n [10, 14, -8, -8, 0, -10, -8, 9, 11, 10, -10, -3],\n [8, -6, -8, 4, 6, -10, -4, 4, 10, -5, 3, 8],\n [2, -6, -4, 12, 16, 9, -8, 1, -10, 3, 12, -8],\n [12, 15, 8, -6, 4, 5, -6, 10, -3, 8, -8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419059341084602", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[3, -9, 12, -6, 3, 4, 4, 8, 3, -6, 8, 4],\n [-9, -4, -2, 5, -12, -8, -2, 2, -5, -4, -4, -2],\n [12, -2, 14, -10, -9, -4, 2, 0, 14, 4, 0, -1],\n [-6, 5, -10, -4, 4, -2, -2, -6, -6, -6, 1, 6],\n [3, -12, -9, 4, -10, 3, 16, 6, 10, 0, 12, -4],\n [4, -8, -4, -2, 3, 10, 0, 12, 0, -4, -7, 0],\n [4, -2, 2, -2, 16, 0, -5, -10, 4, 4, 8, -2],\n [8, 2, 0, -6, 6, 12, -10, -4, -2, -12, -10, 0],\n [3, -5, 14, -6, 10, 0, 4, -2, 14, -2, 0, -14],\n [-6, -4, 4, -6, 0, -4, 4, -12, -2, 3, 0, -4],\n [8, -4, 0, 1, 12, -7, 8, -10, 0, 0, 2, -2],\n [4, -2, -1, 6, -4, 0, -2, 0, -14, -4, -2, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4709803902758478", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (11, 7) of the matrix A^7 where A is:\n[[-3, -9, -5, -10, -14, 9, -14, -13, 15, -3, -14, -4],\n [-9, -15, 14, 10, 0, 7, -16, 12, 9, 7, 16, 9],\n [9, -6, 12, 12, -14, -8, -11, -8, -9, 10, 7, -12],\n [-7, 3, 5, -5, 12, 14, -11, -10, 16, -2, -4, 7],\n [13, 16, 3, 2, 2, 7, -12, 5, 5, 11, 0, 14],\n [-10, 0, -5, -10, 12, -9, -13, -1, -1, 5, -6, -6],\n [-12, -5, 8, -4, 9, -6, 6, -4, 16, 11, -13, 11],\n [-7, -9, -8, 1, -15, 1, -15, 5, -1, 15, -7, -1],\n [-4, -5, -2, 13, 14, 12, 15, 6, -7, -9, 4, -6],\n [-5, 2, 9, -1, 2, 12, 4, -7, 6, -10, -12, 2],\n [16, 7, 6, 5, 4, 1, 10, 8, 13, -3, 15, 14],\n [-15, 6, -11, 4, 9, 13, 13, -9, 16, -7, 1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2000080656", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-9, -16, -9, -12, -16, -14, 10, 6, -6, -6, 14, 7],\n [2, 15, 0, -5, -2, -4, 13, 2, -8, 11, 8, -13],\n [-10, -13, 6, -11, -8, -8, 4, -14, -4, 1, 14, 12],\n [-15, 14, -10, -7, -4, -16, 8, 13, -15, 7, -5, -12],\n [-2, -10, -15, -14, -13, -1, 10, 5, -14, 0, 5, -10],\n [13, -9, 2, -10, -16, -1, 14, 10, -7, -3, -15, 5],\n [9, -12, -1, -5, 0, 8, 7, -6, 1, -14, 2, -11],\n [6, -10, -8, -15, -6, -14, 13, -9, 4, -9, -6, -1],\n [-10, -13, 15, 5, -10, -4, 1, -4, 12, -12, 14, -6],\n [-13, -10, 6, 14, 0, -7, 5, 13, 12, 0, 4, 5],\n [5, 10, 6, -13, 9, 0, -14, 0, 2, 1, 11, -2],\n [9, -1, -2, -12, 7, -15, 14, 13, -5, 4, -5, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-731542864305", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-9, 10, 10, -10, -14, -13, 7, -9, -4, -8, 3, 3],\n [-12, -12, -16, -2, 0, -5, -2, -3, 10, 5, -8, 4],\n [-14, 14, -4, -15, -3, -10, 12, -13, -13, 7, 4, 11],\n [-9, 0, -8, 3, -12, 12, -5, 15, 14, 14, -16, -12],\n [-5, -1, -1, 4, 16, 9, -14, 6, 8, 3, 16, -12],\n [-13, -9, -6, 10, -7, 3, 15, 10, 1, 9, 11, -16],\n [9, -11, 8, 0, 9, 4, 15, 8, 15, 2, -15, -1],\n [-1, 16, 7, 14, 6, 0, 16, 2, 4, 2, -9, 9],\n [1, -3, 1, 11, 16, -11, -10, -12, 10, -9, 16, -5],\n [-2, 0, 12, -14, -6, 9, -11, 7, 7, 2, -4, -8],\n [2, 15, 4, 15, -5, 12, 16, -16, -13, -4, 6, 11],\n [-5, 2, 16, 1, 13, -11, -13, -5, 6, 11, -6, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184852459969", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 12, 10, 0, 3, -2, -8, 0, 4, 3, 4, 10],\n [12, 3, -4, 6, 0, 0, 14, 4, -3, -7, -6, 10],\n [10, -4, -4, 3, 0, -6, 3, -7, 6, 0, 2, 10],\n [0, 6, 3, 7, 0, -4, -10, 4, 0, 6, 4, 8],\n [3, 0, 0, 0, 4, 6, -6, 11, -4, 0, 3, 13],\n [-2, 0, -6, -4, 6, 6, 0, 2, 11, -4, 12, 4],\n [-8, 14, 3, -10, -6, 0, -5, -2, 4, 4, 4, 5],\n [0, 4, -7, 4, 11, 2, -2, -9, 1, -8, -6, 1],\n [4, -3, 6, 0, -4, 11, 4, 1, 11, 2, -8, 4],\n [3, -7, 0, 6, 0, -4, 4, -8, 2, -3, -10, 7],\n [4, -6, 2, 4, 3, 12, 4, -6, -8, -10, 10, 8],\n [10, 10, 10, 8, 13, 4, 5, 1, 4, 7, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37219804197113", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-7, 11, -5, 16, 11, 1, 11, 11, -3, -9, 13, -14],\n [-7, -8, -4, 5, 7, -10, -4, -11, -7, -6, 12, -1],\n [3, 4, 12, -3, -1, -8, -11, 12, 1, 7, 0, 4],\n [2, 6, 10, -6, 9, -6, 5, 2, -9, 6, 6, -8],\n [7, -5, -5, 15, -15, -11, -13, -4, 1, -2, 16, 13],\n [8, -13, 1, 16, 3, 4, -16, -8, -16, 10, -2, 7],\n [8, -7, 13, 8, -14, 5, 7, 10, 9, -1, -13, 6],\n [2, -2, 14, 7, -6, -7, -9, -14, 2, -13, 12, 4],\n [-8, 1, 2, 0, 7, -11, 14, 10, 10, 10, -5, 12],\n [-11, -10, -11, 2, -3, 4, -3, -3, 15, 9, -14, -2],\n [4, 13, -3, 11, -15, 5, -10, 15, -1, -15, 0, -14],\n [6, 11, -9, 16, -13, -10, -6, -9, 3, 11, -6, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4505498442092450", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-11, -2, -2, -14, -6, 6, 16, -6, -6, -1, -1, -12],\n [-2, -4, -3, 10, 9, -2, -5, 0, -4, 4, 6, 8],\n [-2, -3, 4, -6, 5, 0, 8, -8, -3, -2, 1, 0],\n [-14, 10, -6, -12, 6, 4, 15, -4, -3, 2, 2, 10],\n [-6, 9, 5, 6, -12, 6, -5, -6, -6, 7, 7, -2],\n [6, -2, 0, 4, 6, -6, -7, -10, 14, 1, 4, 3],\n [16, -5, 8, 15, -5, -7, 6, 4, 2, 5, -6, -8],\n [-6, 0, -8, -4, -6, -10, 4, -8, -10, 2, 10, -2],\n [-6, -4, -3, -3, -6, 14, 2, -10, 11, -2, -1, -14],\n [-1, 4, -2, 2, 7, 1, 5, 2, -2, 10, 8, -6],\n [-1, 6, 1, 2, 7, 4, -6, 10, -1, 8, 4, 0],\n [-12, 8, 0, 10, -2, 3, -8, -2, -14, -6, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28503764167510", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[7, -16, 2, -5, -4, 4, 7, 0, -2, -6, -1, -8],\n [-16, -8, 6, 6, 13, 2, -3, 5, 6, 3, -12, -7],\n [2, 6, -2, 0, 8, -4, 4, 7, 1, 10, -6, -1],\n [-5, 6, 0, 5, -4, 8, 2, 4, -2, -1, 12, 12],\n [-4, 13, 8, -4, 8, -6, 12, 8, 0, -3, -1, 6],\n [4, 2, -4, 8, -6, -7, 0, -2, 11, -6, 7, -6],\n [7, -3, 4, 2, 12, 0, 10, 2, -4, -7, 5, -1],\n [0, 5, 7, 4, 8, -2, 2, -2, -2, 8, 10, -2],\n [-2, 6, 1, -2, 0, 11, -4, -2, -2, 3, -1, -4],\n [-6, 3, 10, -1, -3, -6, -7, 8, 3, -12, -1, 10],\n [-1, -12, -6, 12, -1, 7, 5, 10, -1, -1, 6, -7],\n [-8, -7, -1, 12, 6, -6, -1, -2, -4, 10, -7, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59496074561547", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[7, 7, -13, -5, 6, 5, 9, -13, -10, 6, 14, -10],\n [5, 2, 13, 9, 5, -8, 12, 15, 1, 14, 15, -8],\n [13, 15, -9, 7, -13, 0, 4, -8, -12, -12, 13, -11],\n [-9, 16, -2, -8, -14, 14, -10, -1, 11, -2, -10, 14],\n [-9, -1, -16, 2, -3, 2, 6, -13, -15, -5, 6, 1],\n [15, 0, 14, 9, -5, -1, -13, 11, 16, -7, 14, -3],\n [-12, -7, 8, 0, 3, 16, -8, 14, -12, 12, -13, 14],\n [-13, 1, 1, -3, 9, 6, 16, 0, 15, 13, -2, -10],\n [-11, -8, -4, 1, -16, 7, -1, 1, -14, -9, 1, 12],\n [10, 12, -13, -5, -4, -3, -3, -7, 5, -8, 7, 0],\n [7, -12, -16, 10, -9, -11, -12, 1, -10, 16, 15, -14],\n [-16, 4, -4, -9, 13, -9, 10, 6, -9, -2, -10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-481164873876", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[13, -8, 2, -2, -2, -2, 12, -11, 2, 4, -4, -13],\n [-8, -9, 4, -4, 12, 1, -5, 2, -4, -2, -8, -2],\n [2, 4, 11, -12, -10, -4, 1, 7, -4, -2, 0, 0],\n [-2, -4, -12, -2, 2, -3, -3, -2, -10, 0, -1, -4],\n [-2, 12, -10, 2, 11, 1, 2, 6, 6, 2, 4, -4],\n [-2, 1, -4, -3, 1, -16, 2, 2, 9, -5, 8, -8],\n [12, -5, 1, -3, 2, 2, -14, 4, 3, -4, -7, 1],\n [-11, 2, 7, -2, 6, 2, 4, -4, 4, 7, 0, 4],\n [2, -4, -4, -10, 6, 9, 3, 4, -1, 12, -7, -4],\n [4, -2, -2, 0, 2, -5, -4, 7, 12, 6, -8, -4],\n [-4, -8, 0, -1, 4, 8, -7, 0, -7, -8, -7, 15],\n [-13, -2, 0, -4, -4, -8, 1, 4, -4, -4, 15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1284964083625760", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (8, 4) of the matrix A^8 where A is:\n[[-6, 6, 4, 2, -12, 2, -6, -1, -1, 10, 12, 1],\n [6, -15, -7, 12, -6, -6, -10, 2, 10, 9, 4, 10],\n [4, -7, 5, -2, 2, 6, 0, 2, -3, 8, -7, 0],\n [2, 12, -2, -13, -6, 4, 8, 9, 6, 10, 2, -4],\n [-12, -6, 2, -6, -2, 6, 0, -10, 0, -6, 4, 9],\n [2, -6, 6, 4, 6, 2, -9, 2, -2, -14, 8, 2],\n [-6, -10, 0, 8, 0, -9, 9, 10, -4, 6, 0, -2],\n [-1, 2, 2, 9, -10, 2, 10, 5, 4, -1, -5, 12],\n [-1, 10, -3, 6, 0, -2, -4, 4, -2, -1, 7, -10],\n [10, 9, 8, 10, -6, -14, 6, -1, -1, -7, 2, 8],\n [12, 4, -7, 2, 4, 8, 0, -5, 7, 2, 8, -4],\n [1, 10, 0, -4, 9, 2, -2, 12, -10, 8, -4, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-79032210935", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[12, -4, 7, -4, 1, -2, 4, 2, -10, 1, 8, -10],\n [-4, -7, -12, -8, 10, 6, -2, -2, 2, -12, 0, -6],\n [7, -12, 11, -10, 3, 12, 6, 1, 6, 14, 8, -1],\n [-4, -8, -10, -2, -1, 0, -4, -3, -12, 8, -2, -5],\n [1, 10, 3, -1, 14, 12, -4, -7, 0, -15, 6, -4],\n [-2, 6, 12, 0, 12, 8, 11, -1, -4, 0, 4, -4],\n [4, -2, 6, -4, -4, 11, -15, -6, -3, 2, -8, -12],\n [2, -2, 1, -3, -7, -1, -6, 14, -8, -8, 7, -6],\n [-10, 2, 6, -12, 0, -4, -3, -8, 6, 1, 9, -4],\n [1, -12, 14, 8, -15, 0, 2, -8, 1, -15, -10, -6],\n [8, 0, 8, -2, 6, 4, -8, 7, 9, -10, -4, 3],\n [-10, -6, -1, -5, -4, -4, -12, -6, -4, -6, 3, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-318911236892", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-14, 8, 12, 4, -11, 6, -6, -11, 10, 10, -4, -8],\n [-9, 10, 15, 12, 16, -12, -8, -4, 16, 13, 8, -11],\n [-7, 2, -6, 0, -15, -10, 14, 14, 0, -2, -10, 13],\n [-3, 14, -8, -8, -15, 5, -1, -15, -2, -11, 6, 11],\n [0, 2, -12, 6, 2, -16, 10, 8, -11, 0, -5, 8],\n [-7, 7, -6, 7, -14, 3, 6, -12, -4, -11, -15, 12],\n [-12, -2, -9, 9, -8, -9, -3, 8, -14, 15, -12, -2],\n [11, 1, -6, -7, -13, 3, -12, -16, -4, 5, -4, -2],\n [-8, -14, -15, -5, 7, 1, 8, -2, -16, -9, -10, -1],\n [0, 13, 1, -5, 11, -6, -11, 9, -1, -8, 1, 16],\n [2, -8, -8, -12, 6, 5, -12, -16, 9, 1, 9, -2],\n [-15, -2, -6, 3, 0, -12, 16, 8, -10, -2, -4, 15]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2062676238880", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-3, 3, -1, 13, 2, 5, -7, -9, 12, -3, -6, 13],\n [16, -12, -12, 0, 2, 9, -15, -3, 11, -13, -14, -2],\n [5, 2, -7, -1, 5, 15, 0, -8, 16, 16, -15, -3],\n [16, -16, 5, 13, 10, 16, -1, -7, 10, -15, 13, 2],\n [2, -6, 15, -1, 0, 12, 3, 7, -13, -12, 2, 7],\n [-16, -15, -7, -11, 3, 2, 12, 7, -8, 15, -12, 4],\n [0, 7, 10, 1, 5, -11, 11, 3, -1, 2, -9, 1],\n [14, -15, 15, -2, -6, -12, 12, 3, 3, 1, -5, 0],\n [-13, 2, 6, 10, -3, -13, -13, 7, 6, -6, 16, -12],\n [10, 10, 14, -5, -11, -5, -3, 5, -6, -4, -11, 3],\n [-15, -6, -9, 13, 10, -13, -10, 7, 15, 2, -14, 1],\n [5, 16, 6, 12, -15, -3, -9, -16, 11, -14, -10, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3754008768715407", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the 9th power of the matrix:\n[[-8, 2, -2, 14, -1, -10, 12, -15, 14, -5, -16, 12],\n [-16, -16, -2, -14, -3, -7, -14, 3, 10, -6, -14, 7],\n [-7, 9, 15, -9, -4, -14, -2, 4, 12, 10, 13, -3],\n [-2, -3, 8, 10, -15, 0, -2, 10, -7, -8, -14, 7],\n [-16, -11, -12, -13, -14, 13, 6, -10, 15, -7, 16, 9],\n [14, 13, 6, 12, -9, -1, -8, -13, 2, -4, -5, -8],\n [-5, 7, -4, 15, -3, -15, 4, 14, -1, 9, -14, -15],\n [5, -14, 9, 10, -9, 6, -11, 8, -1, 9, -2, 15],\n [2, -3, 9, -4, -9, -3, 9, 13, -4, -6, -15, 13],\n [7, 1, 6, -11, -6, -10, 16, -7, 4, -8, 13, 8],\n [8, 7, -5, -10, -14, -11, 10, 2, -9, 1, -10, -16],\n [-12, -3, -16, -5, 2, -15, -3, -14, -4, -14, -3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7871304959233", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 2) of the 8th power of the matrix:\n[[-7, -9, 12, 16, 6, -9, 6, 3, -5, -8, 16, -11],\n [15, -16, 7, 12, -9, -4, 8, 12, 7, 10, 9, 3],\n [-13, 5, -10, 1, -7, 14, 9, 9, 8, 1, 7, -2],\n [-9, 8, 7, 4, -16, 9, -7, 9, -15, -3, 16, -16],\n [13, 1, 13, 10, 13, 4, -1, 0, 1, 4, -5, 14],\n [-7, -13, -2, 11, -10, -6, 12, 13, 10, 8, 6, 12],\n [-6, -13, 14, -7, -1, 13, 0, -12, -14, -1, -13, -8],\n [-13, 4, -7, 14, 0, -1, -11, 13, -2, 14, 13, -1],\n [-15, 11, 0, 15, 8, -4, -3, 8, 12, -2, -2, 0],\n [8, 6, 15, 14, 6, 0, 12, -15, -6, -1, 0, 4],\n [4, -11, 6, 15, 12, 14, 8, -15, 5, -2, -11, 16],\n [-6, -5, 7, -14, 13, 2, -10, -5, 12, -9, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112761082771", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[10, -13, 15, 7, -8, -7, -6, 16, -10, -6, 11, 13],\n [-9, 10, 5, 15, -3, 9, -6, -10, 13, -15, 9, 8],\n [-16, 12, 7, -16, 8, -12, -5, -9, -3, 3, -8, -12],\n [-16, -6, -13, 0, -13, 15, -12, 5, -3, 4, 1, -14],\n [-6, 10, 8, -2, 4, -14, 7, -12, 16, 7, -11, -10],\n [2, 4, -11, -14, -3, 3, -3, -15, 8, -13, 16, -15],\n [6, 4, -2, 7, 3, 8, 5, -13, -1, -10, 7, 12],\n [9, -3, 3, -10, 1, -7, 13, -14, -16, 13, -15, -2],\n [-6, 15, -11, -11, 11, 8, 6, -5, -7, 0, -15, 0],\n [-8, -10, -4, -7, 5, 11, -3, 2, -16, 10, -13, 7],\n [-3, 6, -12, 3, 5, -12, 16, 7, 8, 8, 5, -12],\n [-9, 10, -16, 3, -10, -14, -8, -3, 2, 10, -11, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3061993380589", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 8) of the 9th power of the matrix:\n[[9, -8, 16, 4, 2, 6, 2, 0, -8, 0, -4, 6],\n [-8, 6, -7, -2, 7, 14, 4, -2, 8, -6, 0, 10],\n [16, -7, 7, 4, -11, 6, 14, -12, 1, -11, -7, -3],\n [4, -2, 4, -16, -14, -2, 4, 0, 7, -8, -5, 0],\n [2, 7, -11, -14, 2, -10, 6, -16, -14, 2, -2, 0],\n [6, 14, 6, -2, -10, -14, 0, 8, 6, 2, -6, 0],\n [2, 4, 14, 4, 6, 0, -8, 12, -3, -2, 2, 4],\n [0, -2, -12, 0, -16, 8, 12, -7, -2, 9, 11, 10],\n [-8, 8, 1, 7, -14, 6, -3, -2, -11, -1, -3, 5],\n [0, -6, -11, -8, 2, 2, -2, 9, -1, -10, 6, 6],\n [-4, 0, -7, -5, -2, -6, 2, 11, -3, 6, -1, -10],\n [6, 10, -3, 0, 0, 0, 4, 10, 5, 6, -10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44130903697244", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-7, 11, 15, 15, -2, -11, -8, 13, -1, 8, -7, 13],\n [-8, -10, -5, 0, 8, -10, 2, 0, 15, 6, 15, 9],\n [-9, 5, -9, -12, -5, 10, 3, -6, -15, -7, -10, -5],\n [-1, 14, 10, 15, 10, 8, -12, -13, -2, -4, 16, -12],\n [-11, 8, 8, -7, -5, -14, 12, 12, 7, 7, 8, -12],\n [-6, 5, -2, -8, -11, 9, -11, 15, 3, -14, 1, -7],\n [13, 9, 13, 14, -13, 7, -16, 9, 12, -8, 15, 1],\n [7, 1, -9, -6, 7, -4, 14, 13, 12, -11, -14, 11],\n [-7, -16, -5, 15, -6, -16, -11, 10, -2, -7, 7, -9],\n [0, 7, -4, -8, -11, 12, 6, 5, 4, 0, 9, 8],\n [-14, -14, -3, -7, -15, -10, -3, 0, -7, 10, -14, 8],\n [-10, -4, 8, 12, 2, 5, -15, 5, -12, 10, 1, -14]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "949032793821", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[4, 0, 3, 4, 4, -13, 0, 6, -4, 4, -6, -6],\n [0, 3, -4, 3, 7, -1, -8, -9, 8, -6, -6, 0],\n [3, -4, 4, -6, -2, -4, -6, -4, 0, -7, 2, -4],\n [4, 3, -6, 15, 4, 1, 14, 12, -2, 0, 2, 7],\n [4, 7, -2, 4, 13, -4, 12, -4, -12, 2, 2, 0],\n [-13, -1, -4, 1, -4, 4, -5, -6, 10, -8, -10, 8],\n [0, -8, -6, 14, 12, -5, 15, 10, -6, 12, -14, 6],\n [6, -9, -4, 12, -4, -6, 10, -12, -2, -10, 2, -2],\n [-4, 8, 0, -2, -12, 10, -6, -2, -7, -8, -8, 2],\n [4, -6, -7, 0, 2, -8, 12, -10, -8, 4, -1, 6],\n [-6, -6, 2, 2, 2, -10, -14, 2, -8, -1, 7, -5],\n [-6, 0, -4, 7, 0, 8, 6, -2, 2, 6, -5, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18344474968924025", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[15, 8, -3, -8, 13, 12, 14, -3, 0, 8, 10, 1],\n [12, 1, -13, 3, -16, 7, 7, -12, 9, 1, -16, -7],\n [0, -13, 10, -6, -14, 11, -6, -14, -14, 8, -5, -5],\n [15, -7, 2, -10, 7, 15, 6, 2, -14, 8, 8, -11],\n [16, 16, -2, 3, 15, 7, -14, -13, -11, 2, 9, 8],\n [8, -7, 3, -12, -12, -14, 15, 13, 12, 9, 8, -5],\n [1, 9, -2, -12, 16, -8, 15, -4, 11, 6, 7, 14],\n [-12, -15, 13, -12, -7, -10, 12, 15, 10, -16, 3, 9],\n [6, 16, -16, -14, -4, 16, -4, 5, -12, 0, -7, 10],\n [-2, -8, -10, -7, -4, -1, -9, 14, 11, -10, 16, -13],\n [9, -15, 15, -15, 9, 10, -2, 4, 10, -6, 6, 5],\n [6, -16, -5, 8, -11, 11, 8, 1, -16, 15, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3145420896507", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 6) of the 8th power of the matrix:\n[[-4, 1, -10, -2, 3, -2, 8, 14, 1, 10, 11, -2],\n [1, 4, -7, -4, 4, -8, -3, 10, -10, 6, -12, 11],\n [-10, -7, 6, 2, 6, -5, -2, 4, 6, 4, -14, 6],\n [-2, -4, 2, 14, -3, -4, -4, -14, 1, -10, 14, -4],\n [3, 4, 6, -3, 14, -2, -6, 1, 4, -10, 0, -14],\n [-2, -8, -5, -4, -2, 11, -2, 11, -10, 9, 12, 10],\n [8, -3, -2, -4, -6, -2, 16, -8, -8, 4, -2, -8],\n [14, 10, 4, -14, 1, 11, -8, -16, -11, -4, -2, 8],\n [1, -10, 6, 1, 4, -10, -8, -11, 4, 3, -6, -1],\n [10, 6, 4, -10, -10, 9, 4, -4, 3, 16, 1, 10],\n [11, -12, -14, 14, 0, 12, -2, -2, -6, 1, 14, 14],\n [-2, 11, 6, -4, -14, 10, -8, 8, -1, 10, 14, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6553740474076", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[11, -13, -2, -15, 6, 6, 10, 9, -4, -7, 9, -13],\n [1, 0, 10, -9, -4, 5, 13, -13, -4, -11, 1, -9],\n [3, 4, 15, 15, -15, -15, 15, 5, 9, -7, -12, -5],\n [15, 1, -7, 6, -16, 1, 13, 2, 0, 11, 5, 15],\n [8, -8, -16, 12, -2, 12, 4, -5, 9, 14, -3, -10],\n [-14, -13, -15, 16, -4, -10, 10, -14, 0, 8, 13, -3],\n [12, -12, -10, 2, 16, 4, 4, 0, 6, 10, 14, -2],\n [-16, 3, -16, 15, 5, 12, -6, 16, -16, -8, -4, 7],\n [3, -16, 3, -16, -11, 9, 12, -2, 2, -8, 0, 15],\n [11, -2, 11, -8, 10, 2, -10, 8, 13, -4, -15, 1],\n [-9, 3, -8, -4, 4, 11, -10, 14, 6, -4, -15, -12],\n [-15, -15, 3, -9, 6, -1, 5, -9, 9, 6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "898659705123", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[12, 3, -5, 9, -14, 1, -16, 2, -4, 16, 13, 5],\n [10, -4, -9, -15, 2, 7, -12, -9, 3, -15, -11, -1],\n [-15, -3, 9, 3, 12, -13, 3, 7, -16, 8, -3, 4],\n [6, 3, 9, 10, -3, -13, 9, -1, 3, 7, -7, -15],\n [-8, 1, 13, -14, 12, -10, 8, 7, -11, -2, -2, 10],\n [4, 15, 15, -5, -8, 3, -2, -4, -9, 4, 8, 13],\n [14, -11, -6, -9, -9, -5, -14, -1, 10, -1, -12, -5],\n [-14, -14, 14, 7, 12, 16, -1, 16, -7, 13, -10, -11],\n [-2, 15, -15, 15, 11, 4, 0, 2, -3, 3, 4, -14],\n [-3, 4, 10, -10, 12, -8, -2, 11, -2, -2, 13, 15],\n [-5, 3, 10, -15, 5, 9, -9, 9, 0, -10, -16, 10],\n [9, 15, -3, 2, -8, -16, 4, 3, 16, 16, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-122381644448858", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-4, -8, -16, 6, -3, 4, 4, 11, 15, 13, -5, 12],\n [-16, 9, -1, 1, 16, 6, -12, 4, -16, 14, 1, 4],\n [-10, -16, 6, 10, -15, -1, -7, 3, 8, -13, 15, 11],\n [-4, -12, 0, -10, -7, 10, 6, -1, 10, -2, -11, 7],\n [6, -12, -10, 5, 12, 14, 2, 13, 2, 1, -16, -1],\n [11, -6, 15, 9, -7, 6, 16, -3, -8, -3, -15, -6],\n [-3, 8, 16, -8, -4, -7, 16, -8, -4, 7, 0, 16],\n [6, 10, 9, 7, -6, 12, -12, 7, -8, -7, -6, 14],\n [-14, 8, 10, -16, -1, -2, -6, -8, 7, 5, -10, 13],\n [12, -8, -16, -14, -12, -6, -13, 16, 16, 3, 3, 4],\n [-10, -1, 15, -6, 12, -7, -14, 5, 15, 3, -15, -9],\n [8, -6, 7, 9, -12, -2, -3, 1, -5, -14, 16, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1460327185306", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[9, 6, 4, 10, 7, -6, 2, 12, 12, -7, -3, -2],\n [6, -7, 4, -1, 3, 15, 14, 0, 6, -7, 14, 3],\n [4, 4, 6, 2, 10, 2, 1, -2, -3, -2, 0, 9],\n [10, -1, 2, -7, 13, 1, 6, -2, -3, -8, -4, -12],\n [7, 3, 10, 13, 2, 2, -6, 3, -4, -16, 0, -8],\n [-6, 15, 2, 1, 2, 2, -2, 7, -6, 14, -9, 2],\n [2, 14, 1, 6, -6, -2, -15, -12, 2, 0, 6, 1],\n [12, 0, -2, -2, 3, 7, -12, 5, 0, 8, -13, 0],\n [12, 6, -3, -3, -4, -6, 2, 0, 6, -7, -3, 16],\n [-7, -7, -2, -8, -16, 14, 0, 8, -7, 16, 1, 8],\n [-3, 14, 0, -4, 0, -9, 6, -13, -3, 1, -1, -2],\n [-2, 3, 9, -12, -8, 2, 1, 0, 16, 8, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8160175233923673", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 5) of the 7th power of the matrix:\n[[-7, -10, 6, 12, 5, -8, -5, 8, 9, -8, -4, 4],\n [-10, 5, 6, 2, -8, 4, -4, -2, 9, -6, 6, 7],\n [6, 6, -16, -7, -5, -2, -10, -4, -12, -10, -6, 2],\n [12, 2, -7, 8, 2, -10, -5, -2, 6, 4, -4, 6],\n [5, -8, -5, 2, -8, 2, 14, -10, -4, 3, 4, 4],\n [-8, 4, -2, -10, 2, -8, 6, 0, 0, -6, -2, 4],\n [-5, -4, -10, -5, 14, 6, 8, 10, 16, -8, 1, 9],\n [8, -2, -4, -2, -10, 0, 10, 5, 10, -2, 4, -4],\n [9, 9, -12, 6, -4, 0, 16, 10, -8, -6, 3, 11],\n [-8, -6, -10, 4, 3, -6, -8, -2, -6, 9, 14, -10],\n [-4, 6, -6, -4, 4, -2, 1, 4, 3, 14, 3, -5],\n [4, 7, 2, 6, 4, 4, 9, -4, 11, -10, -5, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11389906901", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 9) of the 9th power of the matrix:\n[[14, -2, 12, 5, 0, 0, -2, 2, 12, 10, -8, 2],\n [-2, 3, -8, 1, -3, -8, 2, -6, -8, -10, -10, -5],\n [12, -8, 3, 6, -10, 2, -6, 7, 8, 3, -1, 4],\n [5, 1, 6, 10, -2, 4, 0, 10, -4, 4, -1, 12],\n [0, -3, -10, -2, 7, 2, 0, 12, 6, 10, -9, 8],\n [0, -8, 2, 4, 2, 9, 0, -6, 0, 8, 2, 7],\n [-2, 2, -6, 0, 0, 0, 16, -6, -6, 4, 2, 6],\n [2, -6, 7, 10, 12, -6, -6, 14, -6, 12, -4, -1],\n [12, -8, 8, -4, 6, 0, -6, -6, -13, -2, 2, -6],\n [10, -10, 3, 4, 10, 8, 4, 12, -2, -15, 4, 2],\n [-8, -10, -1, -1, -9, 2, 2, -4, 2, 4, -9, 9],\n [2, -5, 4, 12, 8, 7, 6, -1, -6, 2, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29530520719108", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 12) of the matrix A^7 where A is:\n[[-2, -14, -1, 2, -10, 5, -2, -8, 0, 16, -15, -10],\n [14, -3, -13, -7, 5, 7, 1, -6, -16, 15, -1, -3],\n [16, -10, 2, 8, -12, -7, -13, 7, -11, -5, 3, 9],\n [-5, 16, -5, -13, 0, -7, 2, 16, 11, -15, 4, 6],\n [16, 9, 13, -13, -11, 3, -2, 6, -8, 10, -1, -13],\n [11, 0, -5, -12, 13, -3, -3, -15, 11, 4, -2, 6],\n [-7, 9, -15, 14, -12, 2, 13, 0, 12, -5, -9, -2],\n [11, 4, 0, 1, 7, 7, -5, -16, 15, -12, 9, -14],\n [16, 3, -5, 3, 0, -9, -4, -8, 2, 9, -12, 8],\n [-12, 6, 15, -11, -3, 12, 5, 3, -9, 10, -10, 11],\n [14, 4, -7, -4, 9, 2, -11, -2, 1, 3, -16, 5],\n [1, -7, 3, -11, 5, -13, -13, 2, 12, 11, -4, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-719913656", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[13, 5, 6, 1, 0, 14, 11, -9, 15, -11, -9, 5],\n [14, -11, -13, -10, 10, -15, -3, 12, 5, -12, 1, -1],\n [-11, -16, -5, 7, -6, 12, 15, 4, 16, 16, 11, -16],\n [-5, 16, -12, -15, 7, 4, 13, -2, -8, 15, -9, 6],\n [10, -9, 12, -6, 4, 13, 16, -14, -4, 6, 9, -7],\n [6, -9, -3, 7, 1, 8, 3, 8, 0, -13, 4, 3],\n [0, 6, 4, 4, 7, 1, 2, -12, 10, -11, -3, -14],\n [-16, 14, -7, 14, 0, -1, 10, -1, -13, 10, -8, 8],\n [7, 11, 1, 9, -7, -6, -3, -16, 0, 0, -7, 13],\n [16, -15, 3, 15, -14, -12, 3, -14, -14, -11, 7, -9],\n [-1, -16, -3, -7, -7, 5, 14, -13, 6, -5, -9, 7],\n [-16, 9, 5, 8, 14, -6, -13, -9, 8, 14, 6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94965802060", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-10, -6, -4, 14, -14, 2, -1, 6, -2, -9, 6, 2],\n [-6, 14, 15, 4, 4, 0, -6, -6, -6, -1, 4, 2],\n [-4, 15, -2, 0, -10, -6, -5, -3, 4, -4, -10, 2],\n [14, 4, 0, -12, -2, 1, 0, 2, -8, 10, 4, -4],\n [-14, 4, -10, -2, -11, 2, -1, 2, -2, 14, -10, -4],\n [2, 0, -6, 1, 2, -3, 2, 13, 4, 1, 4, -4],\n [-1, -6, -5, 0, -1, 2, 16, -7, 2, -5, 0, 1],\n [6, -6, -3, 2, 2, 13, -7, 14, 4, 14, -12, -4],\n [-2, -6, 4, -8, -2, 4, 2, 4, -15, -3, 4, -2],\n [-9, -1, -4, 10, 14, 1, -5, 14, -3, -6, -6, -2],\n [6, 4, -10, 4, -10, 4, 0, -12, 4, -6, 3, 10],\n [2, 2, 2, -4, -4, -4, 1, -4, -2, -2, 10, 7]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-49797329950576", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (9, 5) of the matrix A^8 where A is:\n[[4, -16, 4, 7, -13, -11, -14, 8, 10, 1, -12, 7],\n [15, 4, 12, -12, 11, -11, -6, -9, -6, 3, 5, -5],\n [-12, 13, 6, 8, -11, 12, 4, -10, -8, -16, 14, 3],\n [11, 2, -16, 12, -7, 6, 1, 12, 11, -10, 14, -15],\n [-2, 5, -6, 2, -11, -8, 12, -14, -4, -2, -12, -12],\n [-15, 13, 11, 15, 3, 3, 12, 15, 0, -9, 4, 6],\n [10, -11, -9, -12, 16, -16, 7, 15, 16, -15, 0, -7],\n [-15, -5, 13, -2, 6, 1, 14, 12, -3, 6, 8, 11],\n [13, 10, -9, 2, -16, 3, 13, 12, -9, -3, -14, -14],\n [-3, 4, 10, 11, 11, -12, -7, -8, 3, 12, 12, 11],\n [-6, 4, 6, 12, -2, 0, 7, 3, -6, 13, 3, 5],\n [7, -3, -4, -16, 10, -4, -9, 1, -11, 10, 1, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2398481884007", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-2, 6, -8, -3, 0, -1, 1, -10, 0, -8, -8, -1],\n [6, -13, -12, -10, 6, 5, 10, 10, -12, -6, -14, -10],\n [-8, -12, -6, 14, -8, 6, 1, 2, -8, -14, 6, -4],\n [-3, -10, 14, -4, -10, -10, -9, 8, -7, -2, -6, -7],\n [0, 6, -8, -10, 6, -4, 4, 2, 2, 7, -2, -10],\n [-1, 5, 6, -10, -4, -16, 8, 5, 2, 0, 2, 6],\n [1, 10, 1, -9, 4, 8, 2, 7, 10, -16, 4, 2],\n [-10, 10, 2, 8, 2, 5, 7, -2, -8, 2, 12, 12],\n [0, -12, -8, -7, 2, 2, 10, -8, 3, 4, 3, -6],\n [-8, -6, -14, -2, 7, 0, -16, 2, 4, 8, 6, 2],\n [-8, -14, 6, -6, -2, 2, 4, 12, 3, 6, 12, -2],\n [-1, -10, -4, -7, -10, 6, 2, 12, -6, 2, -2, 2]], determine the value at position (7, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10545252960", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[4, 1, -2, -15, 14, -11, 2, -2, 16, 9, 13, -6],\n [-16, -3, -7, 0, -6, -2, -5, -14, 5, 9, 6, -1],\n [-14, 13, -4, -9, 7, -12, -10, 10, -5, 8, 16, -2],\n [14, -6, -11, 9, -9, 13, -1, -2, -9, -8, 4, -12],\n [2, -1, 1, -5, -1, -12, -14, -10, 15, 14, -3, 7],\n [16, -12, -9, -15, 13, 6, -13, -3, 5, 13, -14, -6],\n [-7, -14, -12, -2, -11, -13, 6, -16, -2, -13, 10, -4],\n [15, -8, 8, -14, -1, 0, 10, -7, -16, 12, 1, 15],\n [16, 5, -6, 12, 3, 5, 15, -9, 5, -2, -1, 12],\n [3, -4, -4, 14, 4, 13, 8, 13, -7, -10, -13, 5],\n [12, -13, -16, 6, 6, -11, -12, 6, -10, -12, 16, 9],\n [4, 9, -7, -15, 3, -3, -10, -7, 14, -9, -16, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8328365356513", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[14, -8, -4, 0, 4, -6, 3, -2, 12, -4, -2, 2],\n [-8, -3, -6, 4, 4, -5, -5, 6, 4, 10, -12, 8],\n [-4, -6, -16, -9, 0, -12, -3, -6, -7, 2, 4, -4],\n [0, 4, -9, -9, 0, -2, -7, -1, 0, -11, 9, 12],\n [4, 4, 0, 0, -15, 0, 6, 0, 0, 1, 0, 7],\n [-6, -5, -12, -2, 0, -2, -14, 8, 7, 8, -16, -8],\n [3, -5, -3, -7, 6, -14, -10, 9, -10, 3, -12, 7],\n [-2, 6, -6, -1, 0, 8, 9, -10, -12, 4, 12, -7],\n [12, 4, -7, 0, 0, 7, -10, -12, -11, 1, -3, 0],\n [-4, 10, 2, -11, 1, 8, 3, 4, 1, -12, 4, 2],\n [-2, -12, 4, 9, 0, -16, -12, 12, -3, 4, 16, -12],\n [2, 8, -4, 12, 7, -8, 7, -7, 0, 2, -12, 9]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234821027008945", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 6) of the matrix A^8 where A is:\n[[1, 14, 1, -8, 9, -15, 15, -11, 3, -9, -13, 8],\n [14, 2, -10, 13, 10, 0, 15, 2, 8, 12, 8, 15],\n [-6, -13, 14, -13, -15, 16, 10, 9, 2, 16, -7, -16],\n [-6, -3, -11, 8, 6, -12, 9, 1, 15, 4, 9, -7],\n [11, 14, -2, -9, -7, -7, 1, 11, 11, 3, 7, -11],\n [15, -11, -6, 13, -14, -9, 16, 2, -7, 2, -8, -10],\n [-3, -15, 5, 3, 9, -13, 6, -1, 8, -8, -6, 8],\n [14, 10, -3, 6, -1, 3, -14, -11, 12, -13, -16, -9],\n [3, -1, 14, 15, 12, -5, -13, -11, -8, -12, -1, -16],\n [3, -7, 8, 11, 16, -2, 4, -7, -1, 3, -9, 14],\n [-9, -4, 7, -5, 0, -5, -4, -12, -4, -9, -6, -9],\n [14, -5, -6, 0, 10, -4, -4, 5, 7, 13, -4, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-179262236508", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[-12, -8, 0, 9, 2, 4, 9, 12, 0, -2, 2, -4],\n [-8, -6, -2, 3, 1, 14, 9, -2, -6, -6, -4, 2],\n [0, -2, -6, 12, -10, 0, 4, 12, 2, 10, -6, -4],\n [9, 3, 12, 7, -4, -12, 10, -8, 4, 6, -1, -4],\n [2, 1, -10, -4, 12, -2, 14, 8, -10, 8, -4, 14],\n [4, 14, 0, -12, -2, 5, 2, -5, 10, -4, 4, -3],\n [9, 9, 4, 10, 14, 2, 13, 6, 4, -13, 2, -4],\n [12, -2, 12, -8, 8, -5, 6, 12, -2, -2, 10, -10],\n [0, -6, 2, 4, -10, 10, 4, -2, -16, 2, -2, 5],\n [-2, -6, 10, 6, 8, -4, -13, -2, 2, 5, 12, 8],\n [2, -4, -6, -1, -4, 4, 2, 10, -2, 12, 8, -6],\n [-4, 2, -4, -4, 14, -3, -4, -10, 5, 8, -6, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16213730081042", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[11, 1, -9, -5, 13, 5, -11, 13, -9, 12, 14, -12],\n [-6, 0, -4, 3, 14, 9, 11, 8, 1, 15, 12, -14],\n [-2, -14, 4, -14, -9, -14, -6, -15, 16, -9, -5, 2],\n [1, 4, 5, 13, 1, -11, -16, -8, -1, 12, 12, -12],\n [2, 5, -9, 1, -3, -13, 10, 7, 13, -5, -4, -13],\n [9, -16, 10, 6, -6, 4, 5, 11, -11, 8, -13, 9],\n [10, 4, 4, 12, 10, 9, -12, 3, -9, 1, -12, -13],\n [-12, -1, -8, 8, -9, -16, 14, 16, -12, 1, 3, 7],\n [2, 11, 13, -2, -8, 14, -16, -4, -15, -6, 1, 3],\n [-15, 7, -1, 6, 12, 13, -13, 12, 10, 16, 1, -11],\n [15, 14, -5, 6, 12, -14, 16, 11, 1, 5, 3, -1],\n [-10, -13, 1, 16, -16, 8, -3, -6, -9, -1, 14, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12847510554721", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-10, -13, 15, 14, -7, 13, 14, 14, 16, -12, -7, 6],\n [-10, 11, 4, 14, 10, 12, -7, -9, -8, -6, 5, 9],\n [-15, 2, -1, -13, -10, -3, -5, 4, 4, -10, 4, -7],\n [4, -1, 8, -4, 10, -9, 13, 14, -10, 13, 1, 6],\n [13, 13, -9, -5, -7, -10, 0, 15, -12, 4, 14, -2],\n [-4, -10, 7, -13, 2, 12, -9, -15, -13, -15, 13, 12],\n [-13, 4, -8, -15, 3, 16, -11, 12, -1, -12, -8, 15],\n [12, 14, -14, 8, -4, 2, -1, 13, -15, -16, -14, 9],\n [11, 10, -3, 7, 7, -11, 14, 12, 12, -4, -9, -2],\n [16, 8, -1, 4, 0, -4, -2, 5, -13, 6, -4, -9],\n [-16, 0, 0, -9, -14, 12, 5, -15, -15, 0, -8, 16],\n [12, 12, -11, -11, -16, -1, -6, 5, -16, -4, 11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125234907980671", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[13, -13, -3, 6, -12, -2, 6, -9, -6, -10, 6, 10],\n [14, -15, 14, -9, -16, 8, 0, 13, 7, 14, -4, -2],\n [9, 15, -1, -8, 2, -14, 9, -9, -11, -12, 4, 10],\n [-9, 5, 6, 8, -10, -3, 12, 0, -11, 15, 2, 10],\n [13, 16, -6, -7, 12, 5, 3, 2, 7, 11, -15, 1],\n [1, -15, 6, -2, 8, 1, 4, 15, 2, 1, 7, 13],\n [12, 4, 4, -15, -16, 5, 2, 2, -15, 12, 6, 10],\n [6, 11, 11, -12, 1, 13, 7, -1, 12, 13, 8, -16],\n [14, 14, 16, -5, 8, 6, 11, 16, 9, 7, -12, 0],\n [-2, -15, 3, 13, -1, -13, 14, 9, -5, -15, -9, -3],\n [7, 8, -10, 15, 6, 9, -10, -13, 8, 1, -10, 5],\n [-13, 12, 7, -5, -8, -2, -4, 13, 9, 2, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268420458727", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-4, 4, 10, -2, 4, 8, 7, 9, 14, 10, -4, -8],\n [4, 6, -1, -6, -9, -2, 8, -4, 1, -1, -2, 2],\n [10, -1, -11, 6, 0, 7, -4, -10, -5, 12, -10, 6],\n [-2, -6, 6, -1, -7, 6, -7, 5, -6, 8, -8, -10],\n [4, -9, 0, -7, -9, 0, -5, 10, 14, -10, -5, -4],\n [8, -2, 7, 6, 0, 4, 6, -2, -1, 10, -4, 11],\n [7, 8, -4, -7, -5, 6, -7, -10, -2, -8, -4, 1],\n [9, -4, -10, 5, 10, -2, -10, 6, 0, -3, 4, 0],\n [14, 1, -5, -6, 14, -1, -2, 0, 8, -5, 1, 14],\n [10, -1, 12, 8, -10, 10, -8, -3, -5, -10, 5, -4],\n [-4, -2, -10, -8, -5, -4, -4, 4, 1, 5, -8, 2],\n [-8, 2, 6, -10, -4, 11, 1, 0, 14, -4, 2, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3993581115287782", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 6) of the 8th power of the matrix:\n[[-3, -8, -10, -3, -1, -7, -12, -10, 5, 7, 5, -14],\n [-10, 2, -9, 6, 3, 16, -11, -2, -12, -3, -8, 9],\n [15, 14, -11, -16, 2, -2, 2, -6, 1, 7, -8, -6],\n [-13, 1, 6, -16, 8, -8, -16, 0, -14, 6, -16, 7],\n [-4, 3, 3, -5, 0, 4, 7, 13, 6, 6, 0, -15],\n [7, 16, -2, 15, 5, 14, -2, 3, 6, 14, -15, -4],\n [15, -1, -2, 8, -5, 11, -5, 4, -5, -1, -7, -7],\n [-15, 10, 13, 16, -1, -7, -2, 9, -2, -11, 0, -16],\n [6, 8, -16, 8, -1, -5, -7, 10, -10, -11, -6, 7],\n [8, -14, -13, -13, -16, 13, -2, 14, -12, 4, -13, -10],\n [12, 15, -6, 16, 0, -5, -16, 6, -10, -3, -10, -3],\n [-15, 3, 0, -7, -12, 16, -6, 4, -13, 8, 16, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "388209698486", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (8, 8) of the matrix A^8 where A is:\n[[-13, 13, 10, 11, -9, 9, 12, -15, -11, -1, -10, -6],\n [-1, -11, -8, -14, 12, -9, 0, -11, -6, -7, -15, 12],\n [-11, -8, -15, -13, 13, -13, -16, -6, -10, 1, -9, 13],\n [-2, -7, -15, -2, 5, -14, -13, 8, -12, -5, 7, 2],\n [15, -5, 10, 1, 8, 6, -14, -15, -6, 13, -4, -11],\n [-5, -9, -8, -13, 15, -5, 1, 14, 12, 12, 10, -6],\n [16, 1, 3, 11, 5, 15, 4, 10, 9, 6, -5, -6],\n [15, -1, 14, -11, -4, -6, -6, 3, 12, 2, 13, -11],\n [0, 1, 1, -5, -14, 1, -1, 11, -8, 3, 1, 8],\n [4, 9, 6, -7, -4, -5, -14, -3, 12, 13, -10, -15],\n [1, 9, 0, -5, 15, 12, -7, -15, -3, -7, -16, 4],\n [-12, -8, -8, 1, -12, -1, -13, 4, -3, 10, -5, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "411728786151", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-13, 0, 13, -2, 8, -3, 6, 1, 4, -4, 2, 0],\n [0, -2, -4, 10, 9, -14, 0, 5, 12, 4, -8, -8],\n [13, -4, 14, -6, -8, 4, -2, -7, -6, 12, -5, -2],\n [-2, 10, -6, 14, 4, -10, 3, -4, 6, 5, 8, 7],\n [8, 9, -8, 4, -9, 0, 8, 8, 3, 8, 0, -11],\n [-3, -14, 4, -10, 0, 15, -2, 6, 6, -13, -14, 5],\n [6, 0, -2, 3, 8, -2, -14, 8, 4, 6, 16, 4],\n [1, 5, -7, -4, 8, 6, 8, -16, -10, 0, 1, -4],\n [4, 12, -6, 6, 3, 6, 4, -10, -4, -4, -6, -9],\n [-4, 4, 12, 5, 8, -13, 6, 0, -4, -13, 1, 2],\n [2, -8, -5, 8, 0, -14, 16, 1, -6, 1, 12, -4],\n [0, -8, -2, 7, -11, 5, 4, -4, -9, 2, -4, -16]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "302318695973", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-13, 4, -3, 7, -8, -11, -7, -8, -8, 0, 0, 6],\n [4, 4, 13, 2, 14, 7, -8, -4, -2, 14, 6, -2],\n [-3, 13, 3, -3, 4, 1, -8, -1, 16, -10, 8, 12],\n [7, 2, -3, 5, -2, -10, 7, 10, -8, 2, 0, 10],\n [-8, 14, 4, -2, 13, -2, -8, -4, 6, -4, -2, -10],\n [-11, 7, 1, -10, -2, 2, -3, -8, 5, -8, -2, -10],\n [-7, -8, -8, 7, -8, -3, -14, 8, 7, 6, 13, 4],\n [-8, -4, -1, 10, -4, -8, 8, -12, 0, -5, -10, -6],\n [-8, -2, 16, -8, 6, 5, 7, 0, 6, -1, 0, -4],\n [0, 14, -10, 2, -4, -8, 6, -5, -1, -2, -5, 10],\n [0, 6, 8, 0, -2, -2, 13, -10, 0, -5, 6, 16],\n [6, -2, 12, 10, -10, -10, 4, -6, -4, 10, 16, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17457318820", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-9, -13, -15, -10, 8, -10, 8, -15, 9, -14, 12, -6],\n [4, -13, -12, -11, 5, -11, -3, 5, -1, 15, -10, 6],\n [-3, -11, 8, -14, -4, -14, 14, -14, 0, -15, -12, -8],\n [12, 13, -2, 12, 8, -6, -13, -5, 15, -12, 8, -13],\n [7, -15, -9, -8, 11, -7, -12, 14, 12, -14, 9, 14],\n [-15, -2, -4, 11, -3, -5, -2, 4, 12, 3, 1, -2],\n [-5, -12, 0, -4, -4, -1, -14, -15, 8, -14, -6, -6],\n [-7, 11, -6, -10, 12, -16, -2, -10, -13, -14, 3, -14],\n [12, 3, -7, 9, 13, 9, 3, -8, -6, 16, 13, 13],\n [6, 7, 14, 6, 4, 9, -10, 8, -14, 1, -11, -4],\n [-15, -4, -16, -15, -13, -4, 13, -5, 16, -14, -8, -10],\n [-13, 11, 15, -16, -4, 9, -4, 5, 7, -6, 8, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1587512278767", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[15, 2, -14, 4, 4, -10, 9, -6, 2, 9, 7, 1],\n [2, 5, 2, -2, 6, -9, -10, 10, 2, -7, 4, -4],\n [-14, 2, -11, 4, -4, 6, 1, -16, 5, 6, -8, 8],\n [4, -2, 4, -11, 2, -4, 13, -10, 10, 3, 2, 2],\n [4, 6, -4, 2, 8, 4, 2, 0, 3, 2, 10, 1],\n [-10, -9, 6, -4, 4, 10, 1, -4, 2, -7, 10, 14],\n [9, -10, 1, 13, 2, 1, 8, 0, 8, 6, -4, 2],\n [-6, 10, -16, -10, 0, -4, 0, -15, 2, 4, 4, 8],\n [2, 2, 5, 10, 3, 2, 8, 2, -5, 0, 0, -10],\n [9, -7, 6, 3, 2, -7, 6, 4, 0, -9, 5, -2],\n [7, 4, -8, 2, 10, 10, -4, 4, 0, 5, 4, -9],\n [1, -4, 8, 2, 1, 14, 2, 8, -10, -2, -9, 9]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-372031919757", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 7) of the matrix A^8 where A is:\n[[-14, -6, -3, -10, 9, 16, 15, 3, -7, -2, -2, -11],\n [8, -16, -11, -4, -6, 7, 3, 9, 8, -5, -8, -8],\n [16, 7, 16, 16, 12, -4, 1, -15, 8, -11, 8, 3],\n [-3, -13, -9, 11, -15, 0, -13, 10, 2, 11, 15, 14],\n [-11, -11, 11, -9, -16, -1, 2, 1, 13, -1, 16, 11],\n [-1, -6, -11, -3, 5, 6, 14, 11, 2, 5, -16, -14],\n [-9, -4, -16, 12, -4, 12, 13, -1, -14, 12, 13, -13],\n [-9, 1, 5, -7, -3, 14, -15, -15, 12, -11, -13, -16],\n [9, 12, -6, -13, 5, 16, 14, -7, 11, 6, -5, 12],\n [-15, -4, 9, 0, 16, 5, -15, -7, 9, 13, 5, -6],\n [5, 7, 12, -7, 8, 4, -4, -15, -11, -16, 11, 5],\n [-6, -12, 1, 3, -5, 4, 10, 1, -15, -3, -16, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1228699025774", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[10, 13, 5, -5, -16, 16, -16, -12, -12, -10, 3, 9],\n [-11, 9, -14, -3, -3, 3, -8, -11, -15, 16, -12, -4],\n [-2, -8, 9, 13, 5, 8, -13, 11, -7, -8, -16, 13],\n [-6, 8, -6, -12, 10, 6, 2, -14, -9, -2, -4, 13],\n [-7, 13, 8, -11, 0, 15, 5, 16, 5, 1, 11, -4],\n [1, 6, 1, -7, -15, -3, 15, 13, 2, -12, 15, -7],\n [-12, -3, 2, -6, 5, 13, 13, -6, 5, -7, 2, -2],\n [-16, 1, 9, 1, 1, 1, 15, 10, 12, 3, 6, -5],\n [11, 3, -10, -11, 2, -9, 13, -15, -1, 7, 8, -4],\n [-8, 13, -8, -10, -1, 15, 12, -2, -6, -8, -1, 8],\n [15, -7, -7, 13, 3, -16, 15, 14, -6, 2, -10, 12],\n [16, 9, 12, 12, -14, -12, 16, -6, -11, -15, -4, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4997987253937", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[10, -2, 0, -12, 0, 16, 1, 1, 0, 4, 0, 16],\n [-2, 15, 4, -1, -2, -2, -4, -11, 5, -2, 9, -5],\n [0, 4, 5, 2, -10, -10, 11, 0, -1, -4, -2, 10],\n [-12, -1, 2, 5, 12, -10, -2, 5, -11, -6, 6, -12],\n [0, -2, -10, 12, 11, 16, -8, -10, -14, -8, 8, -5],\n [16, -2, -10, -10, 16, 13, -10, 4, 2, 0, -14, 9],\n [1, -4, 11, -2, -8, -10, 10, 2, 8, -7, -4, 11],\n [1, -11, 0, 5, -10, 4, 2, -4, 1, 2, 2, 4],\n [0, 5, -1, -11, -14, 2, 8, 1, 6, -4, 0, 0],\n [4, -2, -4, -6, -8, 0, -7, 2, -4, 1, 4, 8],\n [0, 9, -2, 6, 8, -14, -4, 2, 0, 4, -8, -2],\n [16, -5, 10, -12, -5, 9, 11, 4, 0, 8, -2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49625369851498339", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[6, -2, 0, 1, -6, 10, 8, -12, 1, -2, 1, 0],\n [-2, 2, -8, 4, 6, -3, 8, 2, -4, -2, 8, 3],\n [0, -8, 11, 3, 10, -2, 4, 8, 4, 2, -2, 1],\n [1, 4, 3, 8, 2, -6, -5, 7, 10, -10, -8, -2],\n [-6, 6, 10, 2, -11, 3, 11, -1, -8, 9, -5, 9],\n [10, -3, -2, -6, 3, -14, 6, 3, -1, 10, 14, -2],\n [8, 8, 4, -5, 11, 6, 15, -9, 8, -11, 16, 4],\n [-12, 2, 8, 7, -1, 3, -9, 14, -10, 16, 0, -12],\n [1, -4, 4, 10, -8, -1, 8, -10, 13, 0, -4, 5],\n [-2, -2, 2, -10, 9, 10, -11, 16, 0, -13, -2, 0],\n [1, 8, -2, -8, -5, 14, 16, 0, -4, -2, -10, -3],\n [0, 3, 1, -2, 9, -2, 4, -12, 5, 0, -3, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8076085351118145", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-13, -16, -14, 11, -6, -15, -8, 0, 15, 14, 4, 0],\n [0, 10, 11, -16, -1, -14, -2, -13, 13, 12, 6, -12],\n [-6, 2, -9, -6, -8, 8, 8, -3, 14, -4, -16, 13],\n [-8, 12, 14, 1, -14, -15, -13, -2, 0, 9, 14, 13],\n [6, 13, -6, 16, -12, -16, -13, -10, -7, 16, -3, 13],\n [9, 14, 2, -4, 6, 2, -1, 8, 9, 4, 1, -8],\n [7, 0, 13, -13, 11, -8, -9, 5, 8, -11, 9, -15],\n [14, -5, 2, -16, -7, -1, -10, -4, -13, 14, -7, -5],\n [11, -12, 11, -6, -2, -12, 4, 14, -10, 4, -12, -3],\n [-7, 1, 0, 15, 0, 5, 8, -1, 13, -12, 16, -12],\n [-14, -4, -9, 13, -12, 14, -15, -10, -1, -7, 12, 13],\n [3, -9, -10, -3, 3, 16, 14, 16, 9, 9, -1, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17139029441", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 3) of the 8th power of the matrix:\n[[-16, 4, -12, 9, 0, -4, -10, -6, -4, -5, 7, 7],\n [4, -16, -6, -2, -8, -4, 0, 9, 0, 0, 3, 0],\n [-12, -6, 1, -12, 8, -2, 8, -4, -4, -14, 3, 0],\n [9, -2, -12, -11, 8, 10, 0, 12, 7, 0, 10, 4],\n [0, -8, 8, 8, -3, 2, 1, 0, -5, 8, 2, 8],\n [-4, -4, -2, 10, 2, -10, -10, 0, -7, 3, 6, 6],\n [-10, 0, 8, 0, 1, -10, -10, 8, 0, -13, 10, -2],\n [-6, 9, -4, 12, 0, 0, 8, -7, -2, 12, 2, 0],\n [-4, 0, -4, 7, -5, -7, 0, -2, -12, 6, -5, -11],\n [-5, 0, -14, 0, 8, 3, -13, 12, 6, 16, 8, 4],\n [7, 3, 3, 10, 2, 6, 10, 2, -5, 8, 16, 8],\n [7, 0, 0, 4, 8, 6, -2, 0, -11, 4, 8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-541392759080", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[11, 2, -8, 5, 3, -4, 0, -4, 2, 3, 4, 4],\n [2, -16, 2, 1, -2, 0, -4, 0, 7, 10, 3, -2],\n [-8, 2, -10, 6, -6, 2, -1, 6, -3, -12, 1, 6],\n [5, 1, 6, -10, -14, 6, 7, 10, 0, -6, 8, 9],\n [3, -2, -6, -14, 5, -1, 0, 8, 0, -7, -2, 8],\n [-4, 0, 2, 6, -1, -14, 6, 10, 14, 8, 8, 0],\n [0, -4, -1, 7, 0, 6, -11, -11, 10, -10, 9, 14],\n [-4, 0, 6, 10, 8, 10, -11, -7, 12, 10, -2, 1],\n [2, 7, -3, 0, 0, 14, 10, 12, 16, -9, -7, -12],\n [3, 10, -12, -6, -7, 8, -10, 10, -9, -8, -3, 2],\n [4, 3, 1, 8, -2, 8, 9, -2, -7, -3, -9, -6],\n [4, -2, 6, 9, 8, 0, 14, 1, -12, 2, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-168301171495201", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[5, 8, 14, -12, 5, 8, 1, -8, 8, 12, 16, -9],\n [-4, -9, 10, -14, 16, 14, 11, 4, 12, 12, -8, 5],\n [-9, 0, 6, 13, -2, -3, 8, -1, 1, 15, -2, 16],\n [-4, -10, 2, 4, -8, -13, 14, -10, -4, -9, 9, 10],\n [9, -3, 3, 11, -9, -12, -4, -15, -3, -14, -1, -8],\n [-15, -6, 7, 12, -3, 5, 16, 1, 5, 8, -12, 15],\n [-8, -3, 15, -8, 6, -8, 4, 15, -7, 12, 5, -12],\n [-6, 11, 7, -7, 9, -10, -10, -2, -14, 9, -10, -15],\n [-7, 13, -14, 12, 8, -13, -12, -11, 2, 1, -5, 7],\n [13, -3, -15, 3, 6, 4, -9, 13, 3, 3, 6, 3],\n [6, -13, -7, -12, 15, 1, 8, 0, -12, 4, 2, 6],\n [-12, 16, -13, 16, 9, 5, -6, 9, -4, -3, -10, -1]], determine the value at position (6, 8).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-107745350", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 6) of the matrix A^9 where A is:\n[[3, 10, 5, -14, 10, -10, 6, -15, 7, -15, 0, -6],\n [-10, -15, -2, 14, -11, 12, -13, -5, 10, 8, -5, 0],\n [-5, 14, -8, 2, 12, 8, -2, -8, -4, -14, -7, 1],\n [-7, 11, -14, 3, 1, 3, -7, 5, 4, 16, -1, -16],\n [-5, -4, -9, 14, -12, 8, -4, 15, -9, 5, -11, -6],\n [-10, -2, -13, 5, 13, 2, 13, 15, 2, 8, 6, -5],\n [-8, 0, 13, -13, -13, 7, -14, -8, -6, 15, 12, 4],\n [8, 4, 3, 7, -12, -15, -8, -9, 15, -10, 3, -2],\n [11, 14, 5, 7, -8, -15, 8, -5, -13, -4, 12, 15],\n [10, 13, -16, -6, 6, 0, -2, 10, -7, -1, 11, -15],\n [-2, -6, 16, -1, -6, 3, 2, 6, -7, -9, -15, -10],\n [9, 2, -11, 16, -6, -5, 11, -8, 6, -11, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28106649357139", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (12, 5) of the matrix A^8 where A is:\n[[1, 10, 16, 12, -8, 10, -6, -9, -3, -4, -10, -2],\n [1, 14, -13, -4, 13, 2, -13, -16, 15, -5, -5, 3],\n [-6, 13, 14, 11, 12, 5, 12, -16, 4, 14, 10, -9],\n [-9, -11, -2, 4, -11, 12, 8, 6, 10, 6, 2, 11],\n [-10, -4, -13, -6, 4, 4, 9, 14, -13, -14, 4, 1],\n [16, 15, -6, 14, 13, 3, 9, -6, -15, 0, 7, 13],\n [-11, 6, 9, 8, 4, 6, -16, -7, 8, 5, -9, 16],\n [-5, -5, -5, -6, -9, -9, -1, 1, 4, -13, -10, 13],\n [9, -5, -6, 12, -14, -6, -8, 9, -9, 4, -9, -11],\n [1, -11, 4, 6, 1, 10, -14, -5, 3, 2, 6, -12],\n [2, -5, 11, -1, -13, -11, -10, -13, -2, -4, -8, 0],\n [-3, 14, -15, 2, 2, -4, 4, 14, 11, -16, -7, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-353990194239", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (5, 8) of the result:\nA =\n[[-4, 2, -6, -14, 2, 6, 6, -1, 8, -4, 2, -1],\n [2, -3, -2, 10, 5, 12, 2, 10, -8, -2, 0, -8],\n [-6, -2, -3, 6, -8, -10, 7, -2, 14, 2, -2, -3],\n [-14, 10, 6, -13, 0, -6, -13, 0, 11, -10, -8, 8],\n [2, 5, -8, 0, -10, 4, -2, 2, -2, 8, -5, -3],\n [6, 12, -10, -6, 4, -14, 0, -5, 12, -8, -6, 2],\n [6, 2, 7, -13, -2, 0, -4, 10, -7, 4, 5, -10],\n [-1, 10, -2, 0, 2, -5, 10, 13, 13, 4, 4, -4],\n [8, -8, 14, 11, -2, 12, -7, 13, 13, -8, 2, -12],\n [-4, -2, 2, -10, 8, -8, 4, 4, -8, 11, 2, -8],\n [2, 0, -2, -8, -5, -6, 5, 4, 2, 2, -5, 4],\n [-1, -8, -3, 8, -3, 2, -10, -4, -12, -8, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2491763850037", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 7) of the matrix A^8 where A is:\n[[13, 10, 10, 14, -7, -6, 2, 3, -1, 4, 0, -4],\n [10, 4, -6, -15, -8, -2, 0, -5, -6, 3, 4, -14],\n [10, -6, -7, -6, -4, -5, -4, 6, -9, -9, -2, 0],\n [14, -15, -6, -6, 11, -11, -8, 10, -3, 2, 12, -2],\n [-7, -8, -4, 11, 14, -2, 0, 16, -10, -10, 2, 4],\n [-6, -2, -5, -11, -2, 2, -4, 4, -11, 9, -12, 4],\n [2, 0, -4, -8, 0, -4, 15, 6, -16, -6, -14, 6],\n [3, -5, 6, 10, 16, 4, 6, -8, 1, 11, 3, -3],\n [-1, -6, -9, -3, -10, -11, -16, 1, 6, -4, 6, 0],\n [4, 3, -9, 2, -10, 9, -6, 11, -4, 8, 5, 0],\n [0, 4, -2, 12, 2, -12, -14, 3, 6, 5, -3, 8],\n [-4, -14, 0, -2, 4, 4, 6, -3, 0, 0, 8, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "865941215512", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[12, -5, -1, 14, -2, 16, -2, 15, 5, -11, 13, 0],\n [-15, -1, -5, -5, 0, -11, 9, -16, -1, -1, -1, 12],\n [9, 13, 16, 3, -4, -9, 15, 1, -6, -3, 16, 6],\n [-10, -2, -2, -8, 4, 11, -11, -7, -2, 7, -13, -2],\n [-15, 11, -12, 6, -8, -10, -13, 2, -9, 14, -3, 12],\n [-8, -11, 11, -7, -14, -5, -6, -8, -11, -5, -9, -4],\n [-8, 3, -7, 10, -13, -7, 2, -7, 6, -8, -15, 2],\n [-9, 9, -6, -14, 13, 1, 0, -8, 13, -1, -9, 9],\n [-12, -12, 7, -3, -12, 8, 0, -11, -10, -2, -11, 15],\n [10, -12, -1, -6, 8, -15, 11, -10, -16, 1, -5, -9],\n [3, -1, 16, 8, 2, -1, -1, 8, 15, 11, -8, 1],\n [6, 13, 15, 7, -6, 9, -6, 3, 1, -13, 4, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "962624711173352", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-3, 9, -4, 9, -2, 10, 6, 5, -7, -12, -13, -1],\n [15, -6, 16, -13, 6, -14, 3, -16, 16, -7, -14, 15],\n [14, 4, 7, 7, -7, -11, 11, -16, -7, 13, -2, -3],\n [7, -7, 9, -16, 3, 12, -15, -15, -15, -9, 8, 1],\n [0, 13, -9, 12, 2, 7, 1, -7, -1, -12, -2, 6],\n [14, 13, -10, 3, -14, -14, 14, -10, -16, 10, -16, -11],\n [3, -14, -15, 15, 3, 10, 3, 2, 4, 3, -12, 3],\n [-5, -7, 5, 11, -5, -7, 0, 10, 12, 9, -8, -5],\n [9, 16, 15, -6, 12, -9, 8, 3, 4, -13, 12, 2],\n [9, 8, 6, 11, -6, 12, 3, -8, 7, -4, -15, 0],\n [10, -15, 16, -12, -3, 10, 10, -3, -2, 10, -9, 4],\n [11, 7, 0, -11, 2, -16, 9, -12, -13, 8, 5, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-95752985657600", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[6, 16, 8, -7, 1, 10, 9, -15, -7, 3, -14, -7],\n [11, 2, 0, 6, 11, 10, 15, -5, 3, -11, -14, -14],\n [6, -8, 16, -5, 9, -7, -6, 2, -12, 7, 11, 13],\n [2, -11, 2, 14, -6, 0, 0, -2, -11, 15, -6, -4],\n [0, 11, 1, 11, -1, 3, 10, 16, -15, -4, -15, -12],\n [-11, 15, 7, 0, -8, -15, -8, -11, 2, 16, 2, 16],\n [13, -4, 1, -15, -14, -11, 11, -4, 3, 15, 14, -8],\n [-14, 14, -2, -13, 0, 14, 12, -6, 15, -14, -16, -9],\n [0, -9, 16, 9, -15, 12, -2, 13, -5, -15, 4, 12],\n [12, -1, 14, 16, -15, -13, -12, -15, -9, -11, -7, -13],\n [-3, -5, 0, 4, -4, 16, -4, -8, 3, -16, -4, 5],\n [-4, -16, 16, -12, 13, -12, 8, 9, 2, -5, -9, -7]], determine the value at position (12, 10).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-76337615304150", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[1, -6, 13, -12, 7, -4, 10, 15, -3, -15, -13, -6],\n [-4, -8, 10, -15, 10, -5, -5, -14, 9, -2, 10, -4],\n [-12, 0, 2, 3, 6, -5, 15, 12, -12, -15, -11, 4],\n [-2, 1, -15, -12, -11, 2, -1, -5, 7, -8, -14, 0],\n [13, 10, 7, -10, -8, -1, -6, -8, -16, 3, -9, -10],\n [3, -12, -5, 4, 3, -12, 6, -10, -16, 8, 2, -15],\n [-5, 8, 15, 1, 14, -8, 4, -10, -4, 3, -4, 11],\n [8, 9, 16, 10, -2, -14, 12, 14, 1, 7, -9, 12],\n [-8, 13, -2, -5, 10, 14, -4, -2, -12, 8, -5, -8],\n [9, -8, -12, -10, 14, -10, -12, 0, -6, 10, -16, -16],\n [-3, 11, -16, -9, 9, 12, -13, -15, 13, 3, 13, 1],\n [13, -16, -14, 6, 5, -2, -1, 10, 15, -5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271105489755594", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-13, 2, 14, 14, 3, 3, 15, 3, -1, 2, 14, -4],\n [3, -5, 9, -7, -5, 7, -8, -12, 14, -6, -8, 5],\n [11, -1, -7, -2, 1, 14, -12, 16, 12, -14, 6, -7],\n [15, 10, 7, 3, -14, -12, -14, -11, -2, -11, 6, 13],\n [4, 5, -15, -3, 1, -2, -15, 3, -7, -12, 15, -15],\n [-12, 4, 1, -13, 15, -13, 0, 16, 5, 1, 10, -2],\n [8, -7, -1, -13, 14, 15, 7, 1, 15, 11, -6, -9],\n [-16, -15, 4, 2, 13, 8, -8, 11, 15, -6, 4, 7],\n [-16, -1, 7, -7, 15, 11, 16, 5, -16, -5, 8, 11],\n [0, -1, 15, -13, -6, 3, 9, -10, 14, -10, -13, -9],\n [-3, 5, 6, 8, 9, 7, 1, 4, -12, -2, 14, 9],\n [-13, -13, 2, 9, 16, -13, 7, 14, -15, -9, 4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169687468954", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-16, -7, -8, 0, -10, 0, 1, 0, -6, -2, -4, -4],\n [-7, 8, 2, -7, -4, 6, -12, -4, 10, 3, 0, -10],\n [-8, 2, -12, -4, -6, -4, 0, -10, -9, -2, 8, 2],\n [0, -7, -4, -7, 10, 10, 0, 4, 2, -6, 0, 12],\n [-10, -4, -6, 10, -14, -5, 0, 4, -4, 3, 12, -10],\n [0, 6, -4, 10, -5, 0, -6, -2, -4, 2, -3, 12],\n [1, -12, 0, 0, 0, -6, -4, 6, -10, 4, -1, 8],\n [0, -4, -10, 4, 4, -2, 6, -10, 2, 10, -4, 10],\n [-6, 10, -9, 2, -4, -4, -10, 2, 10, 2, 1, -6],\n [-2, 3, -2, -6, 3, 2, 4, 10, 2, 0, -1, 3],\n [-4, 0, 8, 0, 12, -3, -1, -4, 1, -1, -7, 1],\n [-4, -10, 2, 12, -10, 12, 8, 10, -6, 3, 1, 11]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17788965461045", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (10, 8) of the result:\nA =\n[[-2, -9, 15, 5, -12, -7, 14, 6, 15, 7, -13, -2],\n [-6, 8, 9, 16, 3, -5, -13, -4, -14, 0, -10, -3],\n [15, 9, 14, 14, -1, -16, 9, 13, -12, 7, -7, -15],\n [12, 2, -3, 11, -13, 8, -11, 11, -8, 1, 14, 5],\n [-13, 16, -4, -2, 16, 11, -16, 14, 0, 5, 15, 12],\n [-16, 11, -15, 8, 4, 9, -16, 15, -8, -12, 0, 12],\n [2, 12, -5, -9, 14, -2, 9, 12, 16, 16, 4, 13],\n [2, 15, -16, 16, 9, 10, 11, 3, -9, 9, 14, -12],\n [-6, 4, -9, 9, -5, -4, -7, 12, -9, -16, -8, -13],\n [16, 4, -10, 15, 11, 9, -8, -11, 5, -8, -2, -16],\n [15, 1, -6, 16, -13, 2, -5, 5, -5, 11, -2, -13],\n [-9, 14, 9, -14, -10, -2, 3, 0, 15, -7, -1, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208277659413", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[5, -2, -5, -14, 7, -15, -13, 6, 6, -9, -5, -8],\n [-6, 14, -16, -2, -10, 11, -11, 3, 7, -5, -14, 11],\n [-5, -1, -2, 14, 4, 1, -11, 0, 6, 1, -6, 6],\n [0, -11, 7, -1, 12, 12, 11, -1, -14, 7, 1, 0],\n [-7, 8, 6, 2, -7, -6, -12, -11, -14, -6, 7, 9],\n [9, 7, -13, -7, 12, 9, 2, 4, 2, 2, 1, -3],\n [1, 11, 2, 8, -2, -14, 6, -5, 15, 11, -16, -7],\n [10, -5, 16, -13, 4, 3, 0, -3, -7, 3, -2, 10],\n [-2, 2, 9, -5, 7, 16, -12, -8, -3, 8, -10, -10],\n [14, 15, 4, -2, 13, -13, -8, -5, 13, 7, 12, 5],\n [3, -8, 5, -1, -15, 6, 12, -6, 5, -14, -5, -16],\n [9, 12, 16, 15, 8, -15, -2, -4, -2, -11, 4, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15562885761319", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[1, -12, -10, 8, 0, -3, 8, 10, -6, -3, -4, 14],\n [-12, -7, 11, 6, 4, -11, 4, 6, -2, 2, 0, 8],\n [-10, 11, -5, 6, 6, -8, -4, 13, -8, 0, -3, 4],\n [8, 6, 6, 12, 1, -2, 6, -12, 1, -2, -8, -2],\n [0, 4, 6, 1, 16, -8, -7, -8, 10, -8, 9, 0],\n [-3, -11, -8, -2, -8, 1, 10, -6, -4, -4, -11, -11],\n [8, 4, -4, 6, -7, 10, -3, 0, 12, 10, 0, 2],\n [10, 6, 13, -12, -8, -6, 0, 12, 3, -4, 0, -10],\n [-6, -2, -8, 1, 10, -4, 12, 3, -12, 14, 6, -4],\n [-3, 2, 0, -2, -8, -4, 10, -4, 14, -14, 0, -6],\n [-4, 0, -3, -8, 9, -11, 0, 0, 6, 0, 8, -4],\n [14, 8, 4, -2, 0, -11, 2, -10, -4, -6, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6036768853777403", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 9) of the matrix A^8 where A is:\n[[-16, 15, 4, 14, 0, 8, 16, -5, 11, 9, -9, 15],\n [9, -12, -4, 2, -11, -11, -1, 12, 1, 15, 12, 0],\n [-12, 15, 12, 12, -14, -13, 8, 5, -6, -9, 10, 5],\n [-14, 10, -6, 10, -10, 10, -6, 8, -1, 4, 9, 10],\n [0, 14, -3, 6, -15, 9, 9, 5, 11, -11, 2, 4],\n [3, 14, 10, -2, 14, -8, 0, 2, 15, -7, -12, -4],\n [10, -15, -16, -9, -7, 11, -12, -15, 0, 16, 8, -12],\n [11, 1, 6, 1, -6, -7, -7, -8, -4, 6, -16, -1],\n [2, -5, -12, -12, -10, -3, 16, -11, 1, -11, 13, -5],\n [-6, -13, -4, -16, 12, -3, 4, 14, -10, -2, -8, 12],\n [7, -2, 4, 7, -10, 7, 6, 8, -9, 5, 11, -16],\n [13, 8, -15, 11, 11, 6, 7, -9, 1, 3, -13, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36739875632", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[9, -6, 7, 3, -2, 4, 16, 2, 0, -4, 4, -12],\n [-6, 14, -2, 2, 1, -2, 0, 0, -4, 8, 7, 0],\n [7, -2, 0, 3, -8, 0, -8, -4, 0, 2, 8, 1],\n [3, 2, 3, -5, 3, -5, -9, 2, -7, -6, -9, 7],\n [-2, 1, -8, 3, 14, 4, 4, -4, -6, 0, -10, 2],\n [4, -2, 0, -5, 4, -12, 12, 0, -6, 7, 8, 0],\n [16, 0, -8, -9, 4, 12, 0, 0, 6, 10, -2, -1],\n [2, 0, -4, 2, -4, 0, 0, -14, 4, -6, 5, 1],\n [0, -4, 0, -7, -6, -6, 6, 4, 0, 2, 4, 4],\n [-4, 8, 2, -6, 0, 7, 10, -6, 2, 4, 4, 6],\n [4, 7, 8, -9, -10, 8, -2, 5, 4, 4, 5, 4],\n [-12, 0, 1, 7, 2, 0, -1, 1, 4, 6, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451900896686709", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 4) of the matrix A^8 where A is:\n[[-7, -16, 10, 5, 11, -14, 9, -12, -7, -10, 13, 8],\n [4, 12, 0, 4, -1, -8, -14, 6, -4, 13, 9, 15],\n [3, -8, -1, -13, -5, 9, -7, -1, -16, -5, 5, 12],\n [2, 13, 11, 4, 1, 7, 9, -1, 15, -15, -8, 1],\n [2, -5, -4, -7, 5, -7, -1, -6, 0, 8, -16, -5],\n [-14, -8, 2, 2, 3, -6, 7, 5, -16, -7, -6, -9],\n [0, -11, -10, 14, -13, -10, -1, 8, -3, -8, -6, -16],\n [-8, 8, -2, 7, -9, 12, -10, 1, -14, 7, 3, 14],\n [9, -9, 15, -9, -12, -1, 10, -16, -12, -14, 0, 16],\n [2, -13, -4, 9, 14, -1, 7, 13, 0, -4, -10, -8],\n [4, 13, 5, 14, -13, -7, 13, 13, -10, -2, 2, -7],\n [10, -14, 1, 7, -4, 0, 0, -6, 0, 2, -10, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76314438426", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[12, 6, 4, 0, -4, -2, -1, -2, 5, 6, -6, -2],\n [6, 3, -8, 1, 16, 1, -2, 6, 1, 6, -8, 10],\n [4, -8, -1, 8, -7, -5, 4, -2, 2, -6, -6, -10],\n [0, 1, 8, -7, 14, -3, 2, 12, 8, 7, -2, 5],\n [-4, 16, -7, 14, 14, -2, 4, 7, 2, -5, -2, 8],\n [-2, 1, -5, -3, -2, -14, -2, 9, 3, -1, 8, -6],\n [-1, -2, 4, 2, 4, -2, 12, 4, 14, -10, 4, -10],\n [-2, 6, -2, 12, 7, 9, 4, -13, 2, -7, 2, -2],\n [5, 1, 2, 8, 2, 3, 14, 2, -4, 10, -8, -8],\n [6, 6, -6, 7, -5, -1, -10, -7, 10, 16, -3, 10],\n [-6, -8, -6, -2, -2, 8, 4, 2, -8, -3, -16, 1],\n [-2, 10, -10, 5, 8, -6, -10, -2, -8, 10, 1, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1132228307872305", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[8, -2, -2, 9, -6, -7, -13, -3, 3, 2, 1, -12],\n [-2, 15, -12, 0, 10, -5, 6, 0, 13, -12, 8, 2],\n [-2, -12, 5, -4, 7, -1, -7, 0, -2, -14, 4, 2],\n [9, 0, -4, 10, -12, -6, 12, 6, 0, -6, -10, 8],\n [-6, 10, 7, -12, -11, 10, 0, 15, -14, -1, 1, 9],\n [-7, -5, -1, -6, 10, -9, -4, -5, 0, -10, 8, 0],\n [-13, 6, -7, 12, 0, -4, 0, 4, -3, -2, 12, -6],\n [-3, 0, 0, 6, 15, -5, 4, -1, 5, -2, -6, 10],\n [3, 13, -2, 0, -14, 0, -3, 5, 6, 4, 4, -1],\n [2, -12, -14, -6, -1, -10, -2, -2, 4, -15, -5, 2],\n [1, 8, 4, -10, 1, 8, 12, -6, 4, -5, -5, 0],\n [-12, 2, 2, 8, 9, 0, -6, 10, -1, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132765704719442", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[12, 0, -5, 0, 4, 10, 5, -4, -4, 5, -4, 16],\n [0, 6, 0, 4, -7, -1, 4, 10, -12, 6, 0, 0],\n [-5, 0, 9, 8, -4, 2, -6, 5, 10, -4, -6, 4],\n [0, 4, 8, 15, 2, -3, 4, 2, 0, -6, -3, 4],\n [4, -7, -4, 2, 0, 9, -8, 5, -10, -4, -6, 9],\n [10, -1, 2, -3, 9, 12, -3, -14, 0, 4, -10, 6],\n [5, 4, -6, 4, -8, -3, -9, 2, 0, 14, -6, -4],\n [-4, 10, 5, 2, 5, -14, 2, 9, 6, -2, -2, -3],\n [-4, -12, 10, 0, -10, 0, 0, 6, 1, -14, 6, -9],\n [5, 6, -4, -6, -4, 4, 14, -2, -14, -3, 1, -4],\n [-4, 0, -6, -3, -6, -10, -6, -2, 6, 1, 7, -4],\n [16, 0, 4, 4, 9, 6, -4, -3, -9, -4, -4, -11]], determine the value at position (11, 9).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35183031255", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[-15, -1, -1, -2, 6, 0, 0, 0, 12, 2, 0, -5],\n [-1, 1, -8, 6, 0, 1, 0, 14, -1, 12, 4, 8],\n [-1, -8, 5, -12, -12, 6, 2, -9, 0, -1, -10, 2],\n [-2, 6, -12, 10, 8, 2, 11, 8, 5, -1, 6, -4],\n [6, 0, -12, 8, 14, -2, -6, -2, -12, 7, 6, 0],\n [0, 1, 6, 2, -2, 12, 2, 1, 8, 2, -2, 10],\n [0, 0, 2, 11, -6, 2, 4, -3, -8, 12, 6, -7],\n [0, 14, -9, 8, -2, 1, -3, 11, -10, 2, -4, 12],\n [12, -1, 0, 5, -12, 8, -8, -10, -12, -8, 2, 12],\n [2, 12, -1, -1, 7, 2, 12, 2, -8, -6, -4, 4],\n [0, 4, -10, 6, 6, -2, 6, -4, 2, -4, -10, -8],\n [-5, 8, 2, -4, 0, 10, -7, 12, 12, 4, -8, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32895505317797", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[7, 1, -16, -7, -13, -3, 4, 9, -12, -2, 7, -7],\n [0, 15, -8, 14, -2, -14, -4, 5, -10, 3, 9, 2],\n [13, 11, -1, 15, 0, 7, -12, -5, 5, -5, 12, -11],\n [-9, -11, 13, 2, 13, 8, -7, -15, 7, 11, -14, 9],\n [5, 15, -3, -14, 11, 9, -7, 9, 6, -10, -5, 5],\n [-6, -8, -12, -11, -10, 1, -2, -16, -2, -8, -10, -8],\n [-6, -14, -4, -12, 15, 5, 9, -14, -9, 7, -4, -6],\n [-3, -12, -4, 7, -1, 12, 2, 0, 14, 12, 15, 0],\n [-10, -12, 7, 16, 6, -3, -13, -16, -15, 12, -8, 11],\n [16, 6, 3, 14, 9, 14, 15, -2, -2, 8, 3, 5],\n [3, -2, 13, -3, 4, 0, -12, -2, 10, 3, 0, -8],\n [-13, -1, -1, 12, 15, 15, -1, -2, 1, -13, -13, 0]], determine the value at position (2, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564243224623", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[0, -2, 4, -14, -4, 12, -8, -1, 5, 5, -4, 2],\n [-2, 7, -2, 3, 6, -6, -8, -3, -11, -6, -8, 6],\n [4, -2, 14, -2, -2, -4, -8, -2, 14, 11, 0, 12],\n [-14, 3, -2, 12, 6, 0, -11, -4, -10, 7, -16, 5],\n [-4, 6, -2, 6, 8, 2, 11, 0, 0, 7, -2, 10],\n [12, -6, -4, 0, 2, 14, -6, -7, 2, 4, -2, -2],\n [-8, -8, -8, -11, 11, -6, -2, 3, -6, 4, 10, -3],\n [-1, -3, -2, -4, 0, -7, 3, -8, -10, 4, -1, 1],\n [5, -11, 14, -10, 0, 2, -6, -10, 8, 0, 6, 10],\n [5, -6, 11, 7, 7, 4, 4, 4, 0, -2, -8, 6],\n [-4, -8, 0, -16, -2, -2, 10, -1, 6, -8, 15, 2],\n [2, 6, 12, 5, 10, -2, -3, 1, 10, 6, 2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9753220341743657", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-5, 6, -11, 15, -2, 9, 3, -5, 9, 13, 12, 13],\n [-4, 5, 0, 6, 8, -11, 9, 4, -11, 5, 0, -6],\n [-13, -7, 0, 1, 2, 5, -2, 2, 8, 1, -5, 15],\n [9, 9, 11, 8, 13, -3, -16, 16, -6, 4, 5, -12],\n [1, 12, 1, -5, 4, 13, -2, 11, -13, 11, 13, 10],\n [-1, 15, -5, -2, 2, 1, 9, -6, 13, 11, 6, -2],\n [-6, 4, 14, -2, 0, 8, 7, 16, -13, -16, -6, 4],\n [8, 11, -11, -11, 5, -2, 16, 0, -5, 14, 15, 6],\n [-12, -15, 14, -5, 3, -3, -6, 14, 16, 9, -15, 14],\n [10, -12, -6, 11, -1, 9, 7, -13, -5, 1, -3, 0],\n [-1, 3, 11, -16, -1, -13, 15, 12, -9, -15, 7, -3],\n [-16, 16, -6, 3, -2, 11, 4, 6, -8, 3, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1475627101750719", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 10) of the 7th power of the matrix:\n[[-12, 16, 13, -1, 7, 8, 10, -12, 4, -11, -8, 10],\n [-16, 13, -2, 15, 3, -13, 3, 11, 8, -6, -9, 10],\n [5, -9, 16, -8, 5, -8, 14, -13, -3, -9, 5, -11],\n [16, 1, -9, -10, 15, -10, -7, 14, 14, -7, 3, 12],\n [13, 14, 16, -13, 0, 15, 16, 14, 9, 14, 14, 11],\n [-7, -9, 2, 11, -12, 7, -10, 3, -15, -7, 1, -3],\n [-7, 15, -14, -9, -8, -6, -1, 7, 14, -12, 16, 13],\n [13, -2, -1, 9, -5, 2, 3, 4, -2, -1, -1, 6],\n [-13, 12, 7, -9, -12, 12, -7, -8, 5, -7, 3, 3],\n [10, -7, 2, 13, -1, -5, -12, -14, 7, 9, 14, -14],\n [-16, -6, -12, -10, 16, -4, 14, -4, -16, 16, -8, -11],\n [-8, 10, 12, -13, 8, -1, -6, -8, 10, 11, -12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10759609039", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 4) of the 7th power of the matrix:\n[[11, -15, -7, 2, 3, -7, -1, 9, 14, -16, 6, 10],\n [2, -1, -9, -1, -5, -8, -10, 6, -9, 6, 3, -6],\n [-16, -12, -3, -10, 7, -13, 10, -10, 7, -8, -16, 14],\n [6, -14, 3, 9, 15, 16, -12, -7, 13, -8, 15, 4],\n [9, 6, -8, -12, -9, -6, 1, 14, -9, 2, 5, -15],\n [-6, -14, 16, -7, -14, 11, -3, 11, 13, 13, 10, -15],\n [-4, 11, 3, 1, 0, 6, 14, -8, 8, 13, -12, 11],\n [-10, 2, 8, 1, 9, 3, -15, 13, 5, -12, -2, -2],\n [11, -5, -14, -7, -10, 0, 3, 11, -5, 1, -5, -9],\n [2, -11, 11, -16, 2, -14, 10, -11, 13, 10, -11, 0],\n [13, -2, 2, 13, -8, 9, -15, -4, -8, 4, -16, 3],\n [-12, -5, 4, 6, -9, 5, 9, 2, -2, 4, -4, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9178908800", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[8, 16, -14, 15, 6, -15, 15, -11, -10, 4, 16, -1],\n [-14, 9, 8, -2, 5, 3, 12, 2, 14, -3, -2, -16],\n [-5, -6, -8, 16, 10, -16, -7, -4, 12, -12, -6, 10],\n [10, 8, 7, 14, -10, 8, 5, -6, 8, 2, -13, 8],\n [11, -1, -15, 9, -9, 9, 4, 0, 13, -5, 14, -10],\n [-10, 10, 9, 2, 5, -16, 15, 12, 5, 3, 11, 11],\n [-9, 4, 1, -2, -7, 10, 1, 3, 16, 13, -14, -16],\n [-7, -16, 16, 12, 14, -10, 3, 5, -5, -7, 14, 4],\n [6, 14, 13, 5, 4, 3, 11, -1, 2, 7, 14, -12],\n [0, -16, 13, 15, 15, -15, 12, -12, 13, 1, -3, -6],\n [-13, 5, -14, 7, -9, 7, -1, -11, 4, 15, 5, -8],\n [1, -5, -11, 10, -16, -2, -3, -4, 4, -11, 3, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4275466146730", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 7th power of the matrix:\n[[2, -10, -12, -3, 8, 0, 0, 7, 3, 10, -6, 8],\n [-10, -14, -3, 4, 0, 5, -6, 13, -6, -8, 10, -13],\n [-12, -3, -7, 1, -1, -9, -5, -4, -14, 0, -14, -2],\n [-3, 4, 1, -5, 4, 0, 5, 3, -7, 10, -13, 12],\n [8, 0, -1, 4, 16, -8, 2, -12, 10, 1, 2, -8],\n [0, 5, -9, 0, -8, -11, -2, 7, 2, 8, 12, 2],\n [0, -6, -5, 5, 2, -2, 8, -3, 6, 12, -8, -4],\n [7, 13, -4, 3, -12, 7, -3, 16, 8, 4, -2, 10],\n [3, -6, -14, -7, 10, 2, 6, 8, 4, -6, 0, -5],\n [10, -8, 0, 10, 1, 8, 12, 4, -6, 5, -2, 0],\n [-6, 10, -14, -13, 2, 12, -8, -2, 0, -2, -6, -10],\n [8, -13, -2, 12, -8, 2, -4, 10, -5, 0, -10, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20493482118", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-12, 2, -4, 10, -14, 4, -2, 2, -3, 6, 7, 3],\n [2, 8, 6, 0, 6, 2, -10, -2, 13, 1, 10, 3],\n [-4, 6, -5, -5, -12, 2, 3, -6, -4, 0, 8, 0],\n [10, 0, -5, 4, -1, -8, -12, -4, -3, -1, 0, 12],\n [-14, 6, -12, -1, -2, -2, -7, -2, -1, 2, 0, 16],\n [4, 2, 2, -8, -2, 15, 2, -1, 4, 4, -12, 2],\n [-2, -10, 3, -12, -7, 2, 4, -13, 6, 2, -6, 2],\n [2, -2, -6, -4, -2, -1, -13, 14, -8, 13, -4, 12],\n [-3, 13, -4, -3, -1, 4, 6, -8, -6, 4, 1, 6],\n [6, 1, 0, -1, 2, 4, 2, 13, 4, 1, -10, 1],\n [7, 10, 8, 0, 0, -12, -6, -4, 1, -10, -2, -4],\n [3, 3, 0, 12, 16, 2, 2, 12, 6, 1, -4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3284809362506015", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-15, 15, 16, 15, 8, -14, -10, 8, 6, 11, -5, -9],\n [8, 13, 15, 15, 8, 9, -9, -12, -15, 2, -14, -5],\n [15, -11, -9, -12, -4, 14, -4, -16, -13, 3, 12, 15],\n [16, -3, 2, -14, -6, -8, 11, -15, -4, 14, -3, -2],\n [-12, -15, 16, 10, -14, -15, 11, 13, 6, 16, -3, -3],\n [-4, -13, 2, 7, -11, -5, -8, -4, 7, -2, 13, 15],\n [15, 1, 2, -2, 5, 8, 7, -11, -7, -5, -12, 3],\n [1, 16, -5, 16, -12, -8, 16, 13, 0, -1, 2, -15],\n [-11, -6, -8, 10, -3, 3, 15, -9, -6, -15, -12, 13],\n [-6, -1, 8, 8, -6, -16, 16, -16, -8, 10, 2, 0],\n [-5, -15, -9, 16, -4, 4, 2, 13, 3, 1, 4, -10],\n [-12, -8, 1, -16, -3, -9, 3, 14, -10, -2, 0, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84856975881282", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (10, 4) of the result:\nA =\n[[4, 9, -12, 16, -12, 11, 4, -9, -15, -3, 4, 10],\n [1, -12, 1, 9, 12, 11, -11, 9, 1, 13, 16, 15],\n [9, 5, -5, 5, 4, 7, 8, -15, -16, -7, -12, 0],\n [-16, -3, 4, -11, -6, 3, 3, 4, 7, 9, -14, 11],\n [-7, 7, -10, 6, 6, 7, 14, 5, 10, -12, 1, -9],\n [0, -5, 5, -11, 13, -15, -12, -15, -12, 14, 0, 10],\n [14, -7, -5, 1, -4, -9, -13, -10, 4, -2, 5, -16],\n [-11, -16, 2, 10, -7, -3, 15, -14, -1, 16, -12, 0],\n [6, 9, -10, -10, -2, 13, 3, -14, 5, -10, 14, -14],\n [0, 5, -14, 13, 7, 16, -7, -10, -1, 15, -15, -9],\n [-2, -14, 3, -13, 6, -9, -7, -12, -7, 9, -1, 6],\n [0, 11, 1, -6, -2, -16, 16, -8, 0, -2, -13, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20197809969", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-11, 2, 6, 13, -16, -8, 5, -16, 8, -1, 9, 11],\n [-12, 5, -3, -8, -3, -1, 13, 15, -11, 0, -16, 1],\n [-6, -6, 11, -5, -1, -7, -9, 9, -3, -8, 2, 12],\n [12, 11, 7, 11, -5, 2, -11, -15, 14, 12, -5, 16],\n [8, 1, 13, 1, -10, -2, 13, -12, -12, 16, -11, -13],\n [-4, 9, 3, 15, 15, -16, 8, 8, -16, -14, 4, 8],\n [4, -14, 12, 5, 6, -4, 6, 2, -2, -2, 9, -14],\n [0, 13, 11, -1, -6, 7, 6, 8, -4, 2, -15, -9],\n [-12, -6, -15, 15, 7, -5, -1, 7, 0, 15, 3, 13],\n [5, 14, 7, 7, -4, 8, 14, -3, 3, 11, 8, -6],\n [1, 2, -14, 10, 6, -4, 9, -3, -11, -9, -2, -9],\n [-1, 12, 12, -7, -16, -12, -14, -3, 10, 12, -16, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3833764657606", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[-14, 8, 4, 0, -2, 0, -2, -8, 9, 3, 7, 6],\n [8, 3, 4, 7, 6, 13, 12, 4, 15, -2, -3, -5],\n [4, 4, -1, -4, -8, 4, -13, 0, -7, -1, -3, -5],\n [0, 7, -4, 9, -4, 3, 4, -9, -2, 2, 0, -1],\n [-2, 6, -8, -4, 11, -10, -8, 8, 0, -14, 2, -4],\n [0, 13, 4, 3, -10, -1, -5, 8, 10, 3, -10, 6],\n [-2, 12, -13, 4, -8, -5, 1, 4, -8, -2, 4, -3],\n [-8, 4, 0, -9, 8, 8, 4, -13, -7, -3, -2, 13],\n [9, 15, -7, -2, 0, 10, -8, -7, -7, 0, -7, -13],\n [3, -2, -1, 2, -14, 3, -2, -3, 0, 4, -4, -6],\n [7, -3, -3, 0, 2, -10, 4, -2, -7, -4, 11, 6],\n [6, -5, -5, -1, -4, 6, -3, 13, -13, -6, 6, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11598114889904", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-16, -1, 3, 7, -2, -7, -5, 10, -4, 13, -14, -5],\n [12, 13, 5, 0, 10, 5, -10, -6, -1, 5, -14, 7],\n [-6, -2, -3, 0, 4, 11, 5, -16, 6, 15, -13, -11],\n [-1, -7, 7, -7, -5, 16, 10, 8, -7, 8, 15, 9],\n [-13, -8, 10, -8, 9, -6, 15, 13, -8, -6, 6, 0],\n [15, -6, 5, 15, -8, 0, 8, -1, 16, -15, -5, 8],\n [-3, -8, 13, -5, -7, 7, -5, 9, 15, -4, 2, -4],\n [5, 6, -16, -9, -4, -7, -14, 11, 10, 4, -6, 7],\n [-5, -10, 15, -7, 11, 9, 12, 10, -7, -13, 5, -7],\n [-13, -10, 6, -14, 7, 13, -5, 4, 0, -14, -2, 15],\n [-8, 5, 15, -12, -13, -12, -10, -6, -11, 12, 0, 11],\n [2, -5, 2, 16, -12, -16, 14, -5, 1, 11, -4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643182361265", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[0, -12, -3, -2, 12, -8, 9, -2, 5, 2, -4, 6],\n [-12, 16, 1, 8, 12, 0, 5, 2, 0, 0, -8, 0],\n [-3, 1, -3, 7, 2, 4, -13, -1, 11, 0, 5, 16],\n [-2, 8, 7, -3, 8, -11, 0, 13, 8, -8, -9, -2],\n [12, 12, 2, 8, -15, -4, 14, 9, -10, -8, -6, -6],\n [-8, 0, 4, -11, -4, 5, 5, -11, -9, -9, -8, 6],\n [9, 5, -13, 0, 14, 5, -2, 10, -12, 0, -4, 15],\n [-2, 2, -1, 13, 9, -11, 10, 2, -1, -8, -4, -4],\n [5, 0, 11, 8, -10, -9, -12, -1, -16, -2, 7, 1],\n [2, 0, 0, -8, -8, -9, 0, -8, -2, -12, 0, 0],\n [-4, -8, 5, -9, -6, -8, -4, -4, 7, 0, -5, -10],\n [6, 0, 16, -2, -6, 6, 15, -4, 1, 0, -10, -13]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229324848150966", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[13, 11, 4, -5, -4, -4, 10, 11, 1, -1, 4, -7],\n [-3, 11, 12, -6, 13, 10, -14, -16, 15, 4, -15, -7],\n [14, 1, -10, -12, 12, -13, -14, -4, -14, -9, -13, -5],\n [7, 2, 1, 8, -10, -6, 2, 3, 10, 14, 8, -15],\n [12, 14, -11, 4, 16, -8, -7, 5, 14, -6, 2, -5],\n [-1, -4, -4, -2, 1, -1, -12, 10, -15, 10, -16, -3],\n [6, 5, 10, 8, 10, 4, -14, 8, -13, -2, -14, -6],\n [11, -14, 1, -8, -2, -9, -3, -4, -7, 13, -12, 5],\n [-12, -5, 4, 9, -16, -7, 7, 14, 6, 4, -15, 14],\n [-15, 13, 8, 2, -16, 11, 3, -12, 13, 6, 10, -16],\n [-8, -10, 9, -1, -11, -5, 7, 0, -15, 14, 12, -16],\n [-3, -6, 15, 3, -15, 14, -12, 15, -8, -7, 9, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1137902061667859", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[6, 13, 6, 6, 8, 3, 16, 16, -16, 16, 7, -8],\n [14, 11, 6, 13, 1, 9, 16, -1, 12, -1, 16, 6],\n [9, 0, 7, 2, 10, -15, -9, -2, -4, 10, 5, -16],\n [-12, 12, -2, 13, -11, -11, 6, -12, 5, 3, 3, 13],\n [0, 6, -4, -7, -13, 2, 11, 10, 6, 2, -1, -12],\n [7, -12, 12, -11, 12, 16, 10, -11, -7, -10, -10, 12],\n [-1, -16, 12, -4, -5, 6, -1, -3, -1, -11, 7, 10],\n [8, 12, 14, -14, -4, -13, -6, -2, -15, -2, -11, -4],\n [-4, -5, -1, 3, -4, 2, 10, 12, 2, 10, -15, -16],\n [-3, -9, 10, 16, 14, 13, 8, -16, 14, 4, 0, -8],\n [12, -9, 2, -11, 7, -11, -14, 14, 14, -5, -9, 9],\n [9, -2, -4, 5, -4, -8, 7, -14, 6, -5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906307449256", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-8, -8, -10, 9, 1, 2, -7, 8, 2, 6, -12, -1],\n [-8, 1, -9, -2, 0, 0, -3, 4, 6, 1, 6, 6],\n [-10, -9, 1, -6, 0, 2, -5, 2, 4, 8, -6, -8],\n [9, -2, -6, 9, -6, 10, -4, -4, -3, -8, 1, 10],\n [1, 0, 0, -6, 1, -12, 5, 7, -6, 0, -2, 7],\n [2, 0, 2, 10, -12, -5, -6, 10, 0, 2, -9, -6],\n [-7, -3, -5, -4, 5, -6, -16, -4, -14, 2, 16, 0],\n [8, 4, 2, -4, 7, 10, -4, -7, -12, 8, -10, -2],\n [2, 6, 4, -3, -6, 0, -14, -12, 4, 2, -6, -2],\n [6, 1, 8, -8, 0, 2, 2, 8, 2, -10, 12, -4],\n [-12, 6, -6, 1, -2, -9, 16, -10, -6, 12, -12, -5],\n [-1, 6, -8, 10, 7, -6, 0, -2, -2, -4, -5, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2626054694019714", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[6, 10, -13, -4, -6, -6, 2, 16, -3, -4, -10, 16],\n [15, -9, 2, -11, -16, 13, -2, -8, 12, -15, 13, -13],\n [2, 3, -12, -8, 3, -1, 3, 3, 9, 16, -5, 4],\n [6, 3, 6, -11, -5, -9, 10, -1, 15, 12, -10, -1],\n [12, 8, -13, 10, 6, 6, 13, 7, -1, -10, 6, 14],\n [2, -13, -11, 2, 10, 12, -5, -4, 11, -12, 0, 10],\n [9, -13, -9, 9, 16, -5, -4, 4, 8, -14, 2, -10],\n [0, -4, 7, -9, -9, -15, 13, -14, 9, 0, -14, 16],\n [13, -2, -9, 13, 6, -5, -9, -8, -9, 16, 16, -6],\n [6, 8, -2, -7, 3, -1, 4, -16, 8, -3, 2, -9],\n [-2, 1, -16, 16, -16, -13, 0, -15, -7, 9, 10, 8],\n [12, 1, 5, 9, 9, 4, 4, -9, -15, -5, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2052555451931442", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-2, -14, 4, 2, 15, -6, 1, 12, -14, -13, 11, -8],\n [-10, -16, -8, 9, -9, 2, 9, -7, 13, 14, -9, -4],\n [13, -2, -14, 12, 7, 6, -8, -15, -2, 15, 1, 12],\n [-14, 16, -10, 13, 10, 12, 14, -16, 10, 10, 12, -12],\n [-14, 12, -4, 16, 3, -14, -11, 0, -13, 16, 16, -11],\n [-3, -10, -11, -14, 5, -9, 7, -4, -4, -16, 15, -12],\n [-10, 15, 11, 16, -3, -4, 12, -16, 10, 13, -16, -10],\n [-16, 1, 2, -4, 6, -15, -14, 5, -9, 6, -9, 8],\n [-6, -11, 0, 1, 16, 1, -10, 12, -12, -1, 14, -12],\n [-7, 12, 12, -1, -13, -16, -9, 11, -16, 11, -14, -15],\n [8, -6, 1, 3, 0, -10, 0, -13, 13, -16, -5, 0],\n [-1, 11, 15, 2, 12, 12, -1, -13, 4, -16, 2, 9]], determine the value at position (11, 7).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6799695215", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 2, -1, 0, 0, -9, 6, -5, -4, 0, 8, 8],\n [2, 9, 0, 3, 14, -4, -3, 1, 0, 4, 0, 4],\n [-1, 0, -7, 6, -4, 1, -8, 0, -6, -4, 4, 12],\n [0, 3, 6, 12, -2, -2, 6, 2, 4, -3, -3, -12],\n [0, 14, -4, -2, 16, -6, 14, 10, 2, -12, 0, 2],\n [-9, -4, 1, -2, -6, -6, -14, 4, -4, 4, -8, -8],\n [6, -3, -8, 6, 14, -14, -7, 13, 0, 10, -6, -2],\n [-5, 1, 0, 2, 10, 4, 13, -5, -12, 4, -4, 0],\n [-4, 0, -6, 4, 2, -4, 0, -12, 14, -5, 2, 10],\n [0, 4, -4, -3, -12, 4, 10, 4, -5, -12, 0, 2],\n [8, 0, 4, -3, 0, -8, -6, -4, 2, 0, -6, -2],\n [8, 4, 12, -12, 2, -8, -2, 0, 10, 2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1425385014876", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[10, -1, 3, 11, 4, 16, -8, 7, -4, 13, 16, 7],\n [3, -16, 6, 16, 0, -15, 14, 14, -1, -10, -16, 13],\n [1, 9, -6, -16, -12, 5, -4, 0, -10, -10, -5, 6],\n [-9, -2, 13, -8, 4, -3, -9, -8, 9, 3, -11, 6],\n [16, 4, 9, -12, -8, 16, 8, 0, 2, -6, -9, -11],\n [-11, -9, 7, 2, 10, 3, 7, -12, -1, 16, -7, -12],\n [2, 4, -14, 11, 2, -1, -15, -9, -5, 7, -16, 1],\n [6, 10, -11, 11, 6, 8, -6, -16, -7, -8, 9, -7],\n [1, -8, 9, -8, -2, 7, -15, -13, 14, 3, 9, -12],\n [-13, 5, -11, 14, -12, -10, -12, -13, 10, -8, -15, 2],\n [0, 0, 7, -4, 11, -3, 6, 6, -7, 0, 10, -6],\n [2, 10, -1, 6, 16, 5, -3, -4, 5, -10, -16, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3061012355830", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[5, 6, -2, -2, 14, 11, -14, 8, 16, 16, 6, 11],\n [-1, -12, -6, -5, 4, 1, -3, 16, 4, 9, 8, 8],\n [3, -15, -5, 15, 16, 14, 16, 3, -3, -5, 9, -11],\n [-4, 5, 2, 6, 15, -6, -13, -5, 13, -7, 7, 6],\n [-16, -13, 11, -14, -15, -11, 0, 6, 4, 14, -5, 12],\n [-4, 9, 16, 3, -7, -16, 12, 5, -16, -9, -8, 6],\n [3, -1, 5, 6, -16, -3, 6, -9, 15, -15, -4, 10],\n [-10, -14, 4, -9, -16, 0, 9, 12, -9, -9, -9, 8],\n [10, 5, -14, 7, 16, 12, -9, -6, -1, 16, -6, 12],\n [7, -15, -12, 7, -10, 14, 13, -11, -12, -2, 10, -8],\n [6, 0, 6, 12, -6, -4, -5, -15, -6, -3, 5, 4],\n [8, -14, -15, 10, 16, 1, -6, -10, 10, 5, 14, -11]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8070656125294", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[16, -10, -11, -16, 12, -6, 11, -2, 13, 6, -5, 11],\n [14, 13, -1, 13, -13, 16, 16, 11, 4, -2, 9, -3],\n [-2, -15, -1, -6, -6, 16, -15, 16, -14, 3, 16, 9],\n [-3, 12, -15, -9, 10, -9, -10, -6, 13, 4, 4, -10],\n [3, -3, 3, -12, 14, -5, -5, -15, 9, -13, 13, 3],\n [-15, -2, -3, 13, 10, -15, 4, -3, 10, 4, 6, -9],\n [-5, 11, 16, 16, -8, -2, -7, -15, -14, 6, -7, 2],\n [1, -8, 14, 13, -5, 0, 10, 4, 10, -3, -4, -14],\n [7, 15, -9, 6, -1, -8, 1, 14, -11, -3, 7, 16],\n [2, 12, -11, -14, 1, 4, 12, 14, -9, 15, -1, 5],\n [-15, -2, 0, -4, 8, -7, -6, 16, -3, 5, -13, 9],\n [-16, -7, -15, 12, 8, 6, 13, 8, -4, -2, 3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38379038513681", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 1) of the matrix A^9 where A is:\n[[8, -6, 4, 0, 2, -8, -1, -14, 2, -8, -10, 15],\n [-6, 12, 6, 4, -4, 10, 1, -12, -8, 0, -2, 0],\n [4, 6, 13, -8, 6, 6, -8, 2, 11, 2, 8, -2],\n [0, 4, -8, -1, -6, 0, 0, 5, -5, 12, 5, 8],\n [2, -4, 6, -6, -15, 12, -9, 11, -2, -8, -2, 5],\n [-8, 10, 6, 0, 12, 13, 2, 4, 3, -11, 4, 10],\n [-1, 1, -8, 0, -9, 2, -12, -4, -2, -12, -2, 0],\n [-14, -12, 2, 5, 11, 4, -4, -11, -4, 4, 5, -12],\n [2, -8, 11, -5, -2, 3, -2, -4, -8, 10, -3, 6],\n [-8, 0, 2, 12, -8, -11, -12, 4, 10, -3, 2, 11],\n [-10, -2, 8, 5, -2, 4, -2, 5, -3, 2, 0, -3],\n [15, 0, -2, 8, 5, 10, 0, -12, 6, 11, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4083053228370", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-10, -2, 8, 4, -10, -10, 10, 4, 0, 6, -4, 4],\n [-2, 10, -10, 2, -3, -6, -4, 1, 8, -4, 2, 2],\n [8, -10, -3, -4, -6, -12, 2, 8, -3, -2, -2, -2],\n [4, 2, -4, -5, -14, 10, -9, 2, -8, -1, 7, -8],\n [-10, -3, -6, -14, -7, 1, -1, 0, -2, 10, -9, -12],\n [-10, -6, -12, 10, 1, 7, 6, 0, -3, 12, -2, -14],\n [10, -4, 2, -9, -1, 6, 9, 7, -2, -4, -1, -3],\n [4, 1, 8, 2, 0, 0, 7, 8, 5, 2, -13, -4],\n [0, 8, -3, -8, -2, -3, -2, 5, -4, 15, -7, 8],\n [6, -4, -2, -1, 10, 12, -4, 2, 15, 16, 0, 3],\n [-4, 2, -2, 7, -9, -2, -1, -13, -7, 0, -16, -11],\n [4, 2, -2, -8, -12, -14, -3, -4, 8, 3, -11, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2743201553328963", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[11, -1, 5, -1, 16, -4, 11, -1, -15, 9, 11, -14],\n [4, 15, -11, -12, 7, -16, 6, -1, -9, 8, -6, -5],\n [-9, -7, 4, 1, 1, 9, 3, 8, 14, 1, -1, 1],\n [-3, -10, 12, 6, 0, 1, 2, -15, 12, -15, 1, 4],\n [16, -15, -7, -2, -5, -14, -13, -8, -7, 14, -6, 10],\n [-11, 13, 1, -11, -4, -5, -10, -3, -8, -10, 4, 2],\n [10, -15, -3, 16, -5, 4, 13, 5, -15, 12, 7, 15],\n [-5, -10, -15, 2, 1, -15, 2, -11, 0, 6, -8, 4],\n [4, 10, -6, 13, 11, 3, -13, 1, 12, 10, -16, -12],\n [-11, -12, 15, 14, -7, 14, -9, 10, 12, -3, 6, -13],\n [10, 2, 14, -14, 12, -4, 10, 15, -14, -11, -14, -4],\n [-6, 10, -15, -5, -5, 6, 14, -7, -11, 8, 14, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113454192180501", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (12, 5) of the result:\nA =\n[[-2, -10, -6, 6, 6, 4, -2, 2, 3, 11, -8, -2],\n [-10, -7, -6, -6, 11, -2, 0, -12, 2, -10, 2, 10],\n [-6, -6, -3, 1, -2, -9, -1, 1, -2, 1, 0, -6],\n [6, -6, 1, -10, -9, -5, 12, -9, 0, 2, 4, 2],\n [6, 11, -2, -9, -13, -6, 4, -4, 2, -4, -2, 10],\n [4, -2, -9, -5, -6, 8, 9, 4, -8, 8, -14, 3],\n [-2, 0, -1, 12, 4, 9, -13, 6, 4, 6, 8, 0],\n [2, -12, 1, -9, -4, 4, 6, -10, 8, -4, -4, -3],\n [3, 2, -2, 0, 2, -8, 4, 8, -1, 3, 4, 10],\n [11, -10, 1, 2, -4, 8, 6, -4, 3, -11, 6, -7],\n [-8, 2, 0, 4, -2, -14, 8, -4, 4, 6, 10, -2],\n [-2, 10, -6, 2, 10, 3, 0, -3, 10, -7, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22574858856660", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 8th power of the matrix:\n[[-5, 0, 0, 1, -10, 4, -8, 8, -1, -4, -10, -10],\n [0, 1, -10, -2, 12, -6, -7, -2, -4, 4, -3, -4],\n [0, -10, -4, -1, 3, -3, -4, 6, 9, -4, 2, -12],\n [1, -2, -1, 14, -3, -7, 4, -4, -2, -12, 8, -7],\n [-10, 12, 3, -3, -14, -10, 2, -10, 2, 2, -6, 10],\n [4, -6, -3, -7, -10, 10, -6, -3, 8, -2, -10, 1],\n [-8, -7, -4, 4, 2, -6, 13, 5, -5, 0, 3, 1],\n [8, -2, 6, -4, -10, -3, 5, 6, 8, -10, 0, -5],\n [-1, -4, 9, -2, 2, 8, -5, 8, 3, 9, 0, 6],\n [-4, 4, -4, -12, 2, -2, 0, -10, 9, -13, -2, -6],\n [-10, -3, 2, 8, -6, -10, 3, 0, 0, -2, -10, -6],\n [-10, -4, -12, -7, 10, 1, 1, -5, 6, -6, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "701758178716", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[9, 6, -5, -4, -5, 10, 8, 8, 4, 4, -6, -8],\n [6, 3, 0, 11, 6, 14, 11, 12, 8, -4, -11, 1],\n [-5, 0, 9, -8, 8, -3, -4, -4, -4, -8, 0, -2],\n [-4, 11, -8, 1, -6, -5, 0, 8, 1, -4, -14, -1],\n [-5, 6, 8, -6, 11, 0, -11, 6, 0, -2, 2, 6],\n [10, 14, -3, -5, 0, 0, 1, 10, -7, -12, 12, 8],\n [8, 11, -4, 0, -11, 1, 10, -12, 12, -1, 6, 4],\n [8, 12, -4, 8, 6, 10, -12, 1, -8, -8, -9, -10],\n [4, 8, -4, 1, 0, -7, 12, -8, -14, 0, -2, 14],\n [4, -4, -8, -4, -2, -12, -1, -8, 0, -3, 7, -2],\n [-6, -11, 0, -14, 2, 12, 6, -9, -2, 7, 8, -10],\n [-8, 1, -2, -1, 6, 8, 4, -10, 14, -2, -10, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3606863928714", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 9) of the 9th power of the matrix:\n[[-6, -6, -2, -9, 0, -2, 6, 7, -4, 6, 0, -2],\n [-6, 10, 6, 7, 8, 8, 10, 0, 16, 0, 6, 0],\n [-2, 6, -1, 10, -12, -4, 6, -4, -1, 4, 6, 2],\n [-9, 7, 10, -10, -1, 10, -8, 4, -10, -10, 8, -12],\n [0, 8, -12, -1, -4, -2, -8, -2, -10, -5, -6, 6],\n [-2, 8, -4, 10, -2, 8, 1, -9, 6, 4, 8, -8],\n [6, 10, 6, -8, -8, 1, 5, -13, 4, -2, -4, 3],\n [7, 0, -4, 4, -2, -9, -13, 16, -8, -6, 11, 14],\n [-4, 16, -1, -10, -10, 6, 4, -8, 12, 3, -4, 9],\n [6, 0, 4, -10, -5, 4, -2, -6, 3, 12, -2, -4],\n [0, 6, 6, 8, -6, 8, -4, 11, -4, -2, -3, 15],\n [-2, 0, 2, -12, 6, -8, 3, 14, 9, -4, 15, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-230369466798247", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[8, -8, 0, -3, 7, -14, -1, 1, -3, -7, -7, -11],\n [-14, 5, -15, -5, -16, -4, 15, 8, -12, 1, -7, 2],\n [13, 15, -6, 5, 13, -16, -11, -3, -14, -2, 14, 2],\n [5, -10, 10, -12, 6, -13, -15, -13, -13, -11, 0, -13],\n [5, 4, -5, -10, 11, -4, 16, -4, -13, 8, 3, -8],\n [13, 6, -6, -2, 5, 0, -5, -16, 15, -13, 7, -10],\n [-5, 5, 4, 12, 0, 11, 0, -13, -11, -2, 7, -9],\n [10, 14, -8, 1, -15, 5, 3, -13, -4, 3, -11, -2],\n [-9, 13, -14, 10, 13, 12, -1, 3, -1, 4, 1, 14],\n [-15, 7, -11, 0, 9, -15, 9, -16, -15, 16, -6, 13],\n [10, -10, -15, 13, -14, -15, 13, 12, 5, 1, 13, -15],\n [3, -1, -13, -4, -3, -8, -3, -6, -7, 13, -10, -11]], determine the value at position (2, 9).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5918613615017", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 1) of the 7th power of the matrix:\n[[0, 0, -7, 3, 0, 0, -10, 10, 9, -15, -12, 12],\n [0, 0, -5, 4, -13, 1, 15, -13, 8, 3, 2, -10],\n [-7, -5, -1, 2, 4, -7, 1, -6, 4, 0, 5, -2],\n [3, 4, 2, 10, -4, -4, 6, -3, 9, 2, 2, -2],\n [0, -13, 4, -4, 15, 7, -14, 10, -6, 3, -10, 3],\n [0, 1, -7, -4, 7, 4, 4, 4, 4, -10, 10, 3],\n [-10, 15, 1, 6, -14, 4, -4, 13, 4, -6, 2, -2],\n [10, -13, -6, -3, 10, 4, 13, -10, 2, -2, 16, 7],\n [9, 8, 4, 9, -6, 4, 4, 2, -10, 12, -4, -4],\n [-15, 3, 0, 2, 3, -10, -6, -2, 12, -1, 6, 4],\n [-12, 2, 5, 2, -10, 10, 2, 16, -4, 6, -9, -8],\n [12, -10, -2, -2, 3, 3, -2, 7, -4, 4, -8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15005477525", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-15, 5, 11, 15, 8, -16, 6, -12, -6, -2, -12, -13],\n [-7, -8, 16, -11, 10, 11, 12, 15, 5, -2, 10, -7],\n [8, -6, -9, 4, -9, 7, 6, 7, -4, -12, -2, 7],\n [-6, 0, -9, 7, 10, -10, 7, 10, -14, 5, 5, 12],\n [-7, 0, -10, -14, -4, -11, 0, -15, 16, 6, 16, 8],\n [-3, 13, -8, 13, -10, -9, -10, 10, 8, 7, 11, -7],\n [-2, -14, -5, 16, 9, -11, -14, 10, -3, -6, 0, -1],\n [-16, -11, -2, 16, -10, -9, 13, -10, -3, -14, 9, 13],\n [13, 12, 8, -13, -16, -9, -15, 0, 6, 4, 12, -12],\n [15, 4, -8, -10, 1, -2, 8, -1, 3, -12, 16, -16],\n [-10, -13, -13, -4, 1, -6, -4, 14, -11, -6, 4, 9],\n [-2, 7, 1, -9, 11, 12, -15, 1, -16, -15, -3, 11]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1581541528404", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[4, 3, -13, 11, -16, -9, -1, 14, -10, -12, -15, -13],\n [-7, -16, -14, 9, 0, -9, 13, -9, 12, 1, 7, -8],\n [3, -4, 2, -12, 7, -9, -13, -9, -8, 14, 14, -10],\n [8, -4, -12, 1, -10, -2, 16, 14, -8, 2, -11, 15],\n [11, -7, 7, -8, 10, -2, 10, 10, 15, 10, 9, 0],\n [-1, 9, 13, -3, 1, 11, -1, -15, 3, 13, -8, -16],\n [10, -8, 3, 10, 16, -4, -3, -16, -10, 16, 11, -10],\n [7, -2, 7, 10, -14, -7, -5, 12, -9, -7, 0, -8],\n [-2, -13, 4, -10, -9, 3, -10, -11, -8, -3, 12, -14],\n [14, 7, 7, 8, 4, -2, -8, -14, -7, -2, -1, -4],\n [-16, 16, -9, -1, -3, 10, -16, 13, -7, 14, -5, 15],\n [-5, 11, 2, 7, 3, 5, -6, 11, 3, -12, -10, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-51193215659076", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[12, -5, 12, 5, 1, 5, 2, -8, -7, 2, -8, 11],\n [13, 8, 1, 9, 2, 10, -13, 9, -14, -10, -7, -13],\n [-10, 5, 13, 5, 12, -6, -1, -11, -4, 16, -9, -6],\n [16, 16, 10, 1, 15, 7, 5, -14, -14, -3, 15, -8],\n [-1, 8, -12, -4, 14, 4, -8, 4, -8, -7, -5, -6],\n [3, 16, -10, -16, -3, 4, -9, 0, -2, -15, -4, 12],\n [11, -9, 7, -10, 11, 5, 9, 0, -11, -6, -15, 15],\n [9, 14, 15, -15, -14, 16, -10, 4, 8, -1, 6, 0],\n [16, 1, 6, -8, -14, 7, -11, 2, -3, -14, -11, 0],\n [5, -13, -7, 15, -13, -4, 2, 9, 13, 14, -5, 2],\n [6, -7, -2, 0, -4, 7, -1, 13, -2, -13, -7, 15],\n [4, 12, 13, -10, 12, -7, 5, 0, 1, -12, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1526550861082169", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (7, 8) of the result:\nA =\n[[-9, -2, 0, -7, -11, 10, 2, 10, 2, 0, 8, 7],\n [-2, 10, -7, 2, 14, 8, -4, -6, -5, 0, -16, -10],\n [0, -7, -4, -3, 4, -8, -3, 10, 2, 6, 6, -11],\n [-7, 2, -3, -8, 4, 2, -8, -6, -4, 0, 14, 6],\n [-11, 14, 4, 4, 3, -5, 2, -1, 8, -4, 4, 8],\n [10, 8, -8, 2, -5, 4, -8, 0, 12, -1, -12, 6],\n [2, -4, -3, -8, 2, -8, -9, 2, -2, 1, 2, 0],\n [10, -6, 10, -6, -1, 0, 2, 16, -6, -4, -7, -1],\n [2, -5, 2, -4, 8, 12, -2, -6, -1, -4, 2, -6],\n [0, 0, 6, 0, -4, -1, 1, -4, -4, 11, 5, -2],\n [8, -16, 6, 14, 4, -12, 2, -7, 2, 5, 8, 3],\n [7, -10, -11, 6, 8, 6, 0, -1, -6, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3088976449", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[9, 1, -4, -8, -2, 4, 2, 4, 0, -3, 2, -8],\n [1, 5, -1, 0, -2, -2, -6, -6, -13, -5, -2, 10],\n [-4, -1, 7, -8, -10, 6, -6, -6, 8, 0, -14, 11],\n [-8, 0, -8, 6, -3, -8, -4, -6, 1, 7, -3, 1],\n [-2, -2, -10, -3, 0, 10, 10, -8, 2, -9, 4, -7],\n [4, -2, 6, -8, 10, 8, 9, 5, 1, 2, 3, 8],\n [2, -6, -6, -4, 10, 9, 4, 10, 5, 3, 1, -6],\n [4, -6, -6, -6, -8, 5, 10, -10, -4, 2, -2, 0],\n [0, -13, 8, 1, 2, 1, 5, -4, 13, 4, 5, -10],\n [-3, -5, 0, 7, -9, 2, 3, 2, 4, -2, -15, 6],\n [2, -2, -14, -3, 4, 3, 1, -2, 5, -15, -4, -3],\n [-8, 10, 11, 1, -7, 8, -6, 0, -10, 6, -3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7767789830010151", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[2, -3, -9, 4, 0, 2, -4, 0, -1, -3, -8, 2],\n [-3, 12, 8, 2, 8, -10, -9, 13, -8, 4, -4, 1],\n [-9, 8, 0, 2, -12, -6, -13, -2, 4, -9, -10, 8],\n [4, 2, 2, 6, -6, -3, -4, 12, 1, 2, -4, -4],\n [0, 8, -12, -6, 14, -14, -8, 6, 0, 0, 6, -10],\n [2, -10, -6, -3, -14, 3, -2, -10, -9, -11, 4, 0],\n [-4, -9, -13, -4, -8, -2, -16, 5, -9, 0, 4, -1],\n [0, 13, -2, 12, 6, -10, 5, -7, -12, -2, -4, 9],\n [-1, -8, 4, 1, 0, -9, -9, -12, -2, -8, -4, 2],\n [-3, 4, -9, 2, 0, -11, 0, -2, -8, 13, 12, 3],\n [-8, -4, -10, -4, 6, 4, 4, -4, -4, 12, -8, -8],\n [2, 1, 8, -4, -10, 0, -1, 9, 2, 3, -8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29282528055879", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-4, -4, 16, 10, 2, 5, 0, -15, -5, 16, 11, 9],\n [8, 11, 14, 14, 10, -16, 16, -16, -8, 16, -2, -2],\n [12, 4, 1, -1, 12, 10, -2, -8, 11, -15, 4, -6],\n [15, 5, -1, 14, -7, 4, -9, 16, 5, 13, 6, -2],\n [9, -1, -7, 11, 9, 14, 1, 0, 15, -12, 12, -6],\n [16, -13, 16, -16, 4, 0, 12, -14, 7, -15, 14, -10],\n [12, -6, 8, 2, -6, 16, -12, -14, 14, -5, -13, 15],\n [7, -15, -12, -5, 8, 7, 8, 1, 3, 16, 12, 12],\n [5, -5, -13, -12, -7, 5, 8, -16, -7, -2, 14, 0],\n [-5, -12, -8, 0, 12, 0, -3, 3, 10, 3, 6, -8],\n [2, 15, -5, -15, 4, -6, 11, -5, -12, -2, 15, 0],\n [-3, -8, 0, -10, 15, -11, -1, -15, -7, -13, -12, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1455254613700", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[13, -15, 1, -10, 6, 3, -2, 11, -14, -14, -5, -9],\n [-8, 7, 7, -6, -11, 8, -16, -8, -5, -4, 12, 15],\n [14, 9, 7, -2, -11, 12, 14, -1, -7, -13, 12, -9],\n [-6, -16, 6, 13, -2, 12, 7, -8, -6, -2, 9, 7],\n [5, 1, -8, 12, 15, -5, 0, 8, -3, 8, 10, -4],\n [-7, -8, -4, -10, -3, -12, -4, 3, 11, -2, 4, 0],\n [-11, 8, -7, -3, 2, -6, 15, -7, 12, 12, 5, -3],\n [-15, -5, 5, -16, -5, -5, -13, 0, 2, -16, 0, -10],\n [16, -11, -11, 15, 11, 12, 13, 5, -12, 12, -15, -7],\n [3, 1, 1, -5, 8, 3, -6, 3, 16, -7, 8, -7],\n [7, 16, -2, 7, -2, -7, -12, 5, 14, 6, -6, -7],\n [5, 5, 10, -16, -12, -6, 16, -1, 13, 11, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22501086383281", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-16, -4, -12, -6, 7, -10, 5, -2, 0, 6, 4, 7],\n [-4, -2, 0, -8, -8, -12, -2, 7, 0, 16, 4, -13],\n [-12, 0, 0, 8, -16, 9, 0, -2, 4, 2, 8, -4],\n [-6, -8, 8, -12, 0, -6, -6, 11, 12, -6, 14, -8],\n [7, -8, -16, 0, 5, 1, 2, 1, 2, 1, -12, 10],\n [-10, -12, 9, -6, 1, -2, 2, 0, 0, 1, 8, 6],\n [5, -2, 0, -6, 2, 2, -4, 0, -3, 6, -9, 2],\n [-2, 7, -2, 11, 1, 0, 0, 9, 12, 8, -10, -6],\n [0, 0, 4, 12, 2, 0, -3, 12, -6, -1, -5, 2],\n [6, 16, 2, -6, 1, 1, 6, 8, -1, -16, -9, -6],\n [4, 4, 8, 14, -12, 8, -9, -10, -5, -9, 6, 1],\n [7, -13, -4, -8, 10, 6, 2, -6, 2, -6, 1, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3409720806109", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-11, -13, -1, -6, 7, -3, -9, 13, 14, -11, 7, -16],\n [4, -11, -2, 15, 1, 15, -5, -6, -15, 5, 4, -11],\n [-11, -5, -13, -10, -5, 13, -8, -10, 5, 10, 7, -3],\n [-4, -6, 15, -12, 0, -15, 15, 6, -12, -9, 10, -15],\n [-10, 5, -10, -8, 7, 1, 9, -2, 5, 8, 8, 8],\n [8, -10, 7, 2, 5, 6, 3, 3, -10, -6, -9, -6],\n [8, 14, 9, -7, 16, -10, 3, -2, -1, 4, -16, -8],\n [13, 4, 1, 5, 9, -5, 14, -15, -1, 6, -11, 5],\n [-6, 4, -4, 1, 13, 7, -16, 11, -13, -13, -3, -6],\n [6, -5, -13, -16, -7, -10, -15, 6, -5, -5, -1, -9],\n [-11, -2, -6, 13, -7, 6, 1, -8, -8, -11, -1, -5],\n [-15, 0, 9, -8, -12, 11, 13, 0, 2, -11, -13, -3]], determine the value at position (12, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5126703861", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-1, 11, 10, -8, -5, -6, 12, 0, 12, 3, -2, -4],\n [11, 3, 3, -2, 10, 7, -2, -9, -12, 2, 2, 0],\n [10, 3, 10, 13, 0, 4, 16, 8, -4, 12, 6, 5],\n [-8, -2, 13, 5, 5, -4, 0, 7, -6, 1, 2, -2],\n [-5, 10, 0, 5, -11, 10, -3, -12, 12, 3, 4, 8],\n [-6, 7, 4, -4, 10, -16, 2, 4, 1, 0, -6, -4],\n [12, -2, 16, 0, -3, 2, 5, -3, 7, 0, 5, 0],\n [0, -9, 8, 7, -12, 4, -3, 10, 12, 3, -11, 11],\n [12, -12, -4, -6, 12, 1, 7, 12, 15, -1, -6, 0],\n [3, 2, 12, 1, 3, 0, 0, 3, -1, 11, 0, 3],\n [-2, 2, 6, 2, 4, -6, 5, -11, -6, 0, -4, 7],\n [-4, 0, 5, -2, 8, -4, 0, 11, 0, 3, 7, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80331609437805", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 9) of the 7th power of the matrix:\n[[-2, 2, -8, -2, -1, 3, 3, -11, 10, -8, 11, 12],\n [2, -9, -4, 4, -12, -4, 9, 2, 11, 12, -7, 0],\n [-8, -4, 6, 11, 0, 7, -10, 12, -8, -2, 10, 2],\n [-2, 4, 11, -3, 5, -12, 8, 0, 6, 4, 10, -9],\n [-1, -12, 0, 5, 13, 0, 8, 10, 4, 7, 12, -2],\n [3, -4, 7, -12, 0, 8, -11, 10, -16, 2, -14, 13],\n [3, 9, -10, 8, 8, -11, 15, 12, -12, 10, -2, 2],\n [-11, 2, 12, 0, 10, 10, 12, 4, -10, 10, -6, 0],\n [10, 11, -8, 6, 4, -16, -12, -10, 12, 0, 1, 10],\n [-8, 12, -2, 4, 7, 2, 10, 10, 0, -9, 4, -10],\n [11, -7, 10, 10, 12, -14, -2, -6, 1, 4, 7, -6],\n [12, 0, 2, -9, -2, 13, 2, 0, 10, -10, -6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64368778141", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[6, 2, 8, 2, -10, 0, 4, -6, -4, -2, 3, 8],\n [2, 6, 2, 2, -3, 1, -9, -10, -6, 4, 6, 1],\n [8, 2, 7, 1, 1, -5, 0, -8, -6, 14, 1, 14],\n [2, 2, 1, 8, 3, -1, -2, 0, -9, -10, 9, -10],\n [-10, -3, 1, 3, -7, 2, -3, 4, -3, -2, 4, -14],\n [0, 1, -5, -1, 2, 4, 4, 0, -8, 0, 2, -3],\n [4, -9, 0, -2, -3, 4, 8, 2, -2, -10, 0, -4],\n [-6, -10, -8, 0, 4, 0, 2, -4, 12, -10, -2, -4],\n [-4, -6, -6, -9, -3, -8, -2, 12, -13, 8, 2, 2],\n [-2, 4, 14, -10, -2, 0, -10, -10, 8, -11, 6, 0],\n [3, 6, 1, 9, 4, 2, 0, -2, 2, 6, -16, 0],\n [8, 1, 14, -10, -14, -3, -4, -4, 2, 0, 0, 14]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154753548978", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[10, -4, -6, -8, -9, -7, -15, 7, -6, -16, -12, 10],\n [-10, -16, 15, 0, 1, -13, -4, -12, 5, 9, -13, 6],\n [-12, -8, -4, -8, -13, 9, -3, -15, 14, 9, -15, -15],\n [11, 6, -10, 5, -16, -13, 14, 16, -12, -6, 15, -16],\n [-11, 11, 0, -6, 10, -5, -4, 14, 8, 13, 4, 11],\n [10, -5, -7, 9, 12, -11, 8, -9, -6, 0, -4, -2],\n [2, 2, -7, 11, 8, -2, -1, 10, -12, 7, -15, 16],\n [15, 15, -1, 6, 9, -12, -10, -7, 5, 4, 2, 8],\n [-4, 2, -10, 14, -15, -13, -16, 6, 0, 5, -9, -10],\n [-16, 8, 7, 16, -6, 15, 12, -16, -9, 12, 14, -10],\n [14, 15, 13, -5, -7, 9, -12, 6, -8, 16, 13, 16],\n [-15, -13, 9, 13, -7, 14, -2, 4, -11, -16, -7, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33431533651546", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-8, 0, -1, -15, -1, 11, -4, -11, 8, 9, -2, -15],\n [5, 11, 0, 6, -2, 13, -16, -1, 8, 6, 16, -8],\n [-1, -12, -5, -12, 6, -9, -1, 3, 11, 13, -6, 0],\n [-7, 7, 14, -6, -9, 14, 16, -8, -14, -4, 11, 7],\n [-7, -2, 11, -16, -4, -13, 13, -14, 3, 10, -5, -1],\n [15, 16, -1, 12, 10, 14, 7, 14, -8, -11, 13, 9],\n [-10, -9, -6, -14, -13, 16, 3, -12, -3, -4, 7, 13],\n [-6, -8, -4, -4, 15, -10, -6, -16, 11, -9, -2, -12],\n [5, 3, -13, 8, -1, 10, 12, -5, -10, 7, -12, 16],\n [-11, -9, 5, -3, -8, -4, 15, -3, 8, 14, 3, -10],\n [-7, -11, 8, -11, 0, 5, 6, 12, -10, 3, 9, 12],\n [12, -10, -12, -4, -11, 15, 16, 16, 2, 1, -3, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19658782249532", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[14, -2, -12, 10, -8, -1, -4, 8, -1, 10, 6, -5],\n [-2, -1, 10, -6, -14, -2, 6, -6, -3, 10, -4, 0],\n [-12, 10, -15, -3, 10, 11, -2, -9, 2, 11, -2, 4],\n [10, -6, -3, -15, -4, -2, 12, -6, 12, -4, 4, 6],\n [-8, -14, 10, -4, -2, 2, -6, -9, 12, 6, 4, -8],\n [-1, -2, 11, -2, 2, 11, -8, -4, 10, -8, 2, 2],\n [-4, 6, -2, 12, -6, -8, -11, -4, -3, 6, 0, 4],\n [8, -6, -9, -6, -9, -4, -4, 0, 4, -6, 0, -5],\n [-1, -3, 2, 12, 12, 10, -3, 4, 8, 4, -4, -1],\n [10, 10, 11, -4, 6, -8, 6, -6, 4, 15, 0, -2],\n [6, -4, -2, 4, 4, 2, 0, 0, -4, 0, 0, -3],\n [-5, 0, 4, 6, -8, 2, 4, -5, -1, -2, -3, -7]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2974759441", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-8, 6, 0, -2, 0, 11, 8, -8, 4, -3, 7, 9],\n [6, 10, -1, 2, -1, -10, 1, 12, -6, 0, 2, -6],\n [0, -1, 2, 6, 6, -7, 2, -10, 0, 2, -10, 0],\n [-2, 2, 6, -7, 2, 6, -1, -2, 0, -10, -6, 2],\n [0, -1, 6, 2, -10, -8, 12, 5, 6, 6, -8, 4],\n [11, -10, -7, 6, -8, 11, 0, 12, 9, -2, 4, 12],\n [8, 1, 2, -1, 12, 0, -9, -5, 0, 0, -6, 13],\n [-8, 12, -10, -2, 5, 12, -5, -13, 0, -10, -4, 6],\n [4, -6, 0, 0, 6, 9, 0, 0, 2, 10, 0, -1],\n [-3, 0, 2, -10, 6, -2, 0, -10, 10, -12, -8, 10],\n [7, 2, -10, -6, -8, 4, -6, -4, 0, -8, 5, -6],\n [9, -6, 0, 2, 4, 12, 13, 6, -1, 10, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3083209980167", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (7, 10) of the result:\nA =\n[[3, 9, 0, 14, 1, -14, 1, 3, 4, 13, -13, -2],\n [-10, 15, 16, -4, 0, -11, -13, -2, -9, 13, 6, -8],\n [7, -9, -11, 8, -4, 8, 1, -8, 16, -11, -3, -11],\n [1, 9, -6, 1, -2, 13, 8, -1, -5, -3, -4, 13],\n [-1, -16, 12, 10, -4, 0, 11, 3, -12, 7, -8, 16],\n [10, 16, 12, 3, 2, -12, 8, 12, 9, -15, -2, -11],\n [-16, -8, -1, -3, -7, 2, -9, -5, -11, -11, -11, -6],\n [10, 9, 11, -9, 8, 2, -1, 9, -2, -5, 7, -4],\n [0, -4, 0, -16, -6, 3, 14, -11, 11, -16, -1, -5],\n [11, -2, -9, -13, 14, 13, -11, 4, 13, -1, -9, 10],\n [16, -5, 6, -16, -10, 8, 4, -5, 15, -1, -16, 9],\n [-3, -11, 3, -14, -5, 16, -16, 2, -15, 6, -9, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6602374830", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-9, 10, 9, 16, -14, -8, -7, 12, 4, 1, 0, 4],\n [-14, 10, 15, 12, 12, 9, -8, 10, -5, -1, -15, 10],\n [-8, -15, -10, -9, -11, 2, -2, 11, 13, 10, -7, 14],\n [-16, 15, -1, -11, -15, -15, -14, 2, -13, 1, 1, 4],\n [4, 13, 0, -12, -12, -8, -6, -3, -11, -3, -9, 13],\n [-16, 8, -4, 10, 8, -13, 14, 1, 0, -6, -5, -14],\n [-2, -11, -12, 14, -9, -7, -14, -5, 11, -5, 13, 2],\n [4, 0, -3, -6, 12, -10, -16, -10, -3, -1, -1, 4],\n [-4, 1, 12, 4, -8, 14, 0, 14, 7, -11, 15, 14],\n [1, -8, -14, -10, 9, -4, 12, 16, -12, -2, -7, -13],\n [15, 7, 3, -13, -6, -6, -1, -16, 16, -10, -14, -10],\n [-16, 16, -10, -13, 1, -3, -2, 8, 1, -13, -15, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-633808835577", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (11, 12) of the result:\nA =\n[[3, -2, -11, -4, -1, -15, -16, -12, 13, 14, 15, -14],\n [-14, -12, 5, 15, 6, -9, -13, -11, 10, 2, 12, -11],\n [-14, 15, -1, 16, -15, 9, 11, -6, 7, -1, 8, 6],\n [8, 16, 5, -7, -16, 5, 15, 6, 13, 6, -5, 2],\n [-10, 10, 9, 1, 11, -6, -15, 0, 12, 15, -2, 1],\n [11, 10, 16, -7, 7, 10, 3, 8, 9, 4, -4, 16],\n [-7, 11, 16, -6, -3, 3, 3, -9, -2, 16, 2, -5],\n [0, 16, 3, 14, 2, 2, -4, -16, -6, 10, -16, -2],\n [1, 8, -16, 2, -7, -5, -15, 15, 9, 3, -11, -10],\n [-15, 0, 9, 14, 1, -3, -12, 6, -16, 3, -15, -16],\n [-7, -12, -4, -13, 7, 10, -15, 15, 0, -5, -5, 4],\n [-9, 5, -7, 3, 11, 8, 11, -13, 9, -4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201815532693", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-13, 3, 9, 13, -11, -4, 0, 10, 16, 1, 3, 16],\n [14, 2, 16, 0, 16, -12, 10, -10, -3, -13, 1, -1],\n [10, 3, 2, -16, 6, -8, 11, 3, -1, -4, 16, -14],\n [-2, -1, 13, 8, -3, -16, 16, 12, -9, -16, 7, -16],\n [-7, 1, 4, -7, 5, -8, -8, 4, 14, -15, 7, 16],\n [-6, -16, -9, -8, 4, 5, 12, -14, 8, 1, -6, 13],\n [8, -6, 7, 15, -14, 8, 3, 3, 0, 3, 1, -3],\n [-1, 15, -9, -1, -13, 11, -3, -12, -15, 7, -14, 6],\n [-6, -16, -11, -11, 9, -4, 8, 5, 0, -3, -14, -13],\n [11, -15, -13, -5, 13, 4, 11, -12, 16, 15, 10, -14],\n [-13, -14, -16, 10, -14, 13, -16, -7, -14, -14, 3, -6],\n [2, 10, 7, -11, -16, 2, -7, 15, -15, -3, -4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-200520405287633", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 1) of the 7th power of the matrix:\n[[10, 2, 4, 4, 6, 10, -4, -2, -6, -10, 8, 0],\n [2, -9, -2, -4, 2, 10, -4, 6, 3, -1, -2, 1],\n [4, -2, -2, 2, -1, 9, 4, -8, 0, -4, 14, -4],\n [4, -4, 2, -4, -8, -4, -5, 4, -2, 4, -12, -4],\n [6, 2, -1, -8, -16, 11, 0, -12, 8, 10, 4, -1],\n [10, 10, 9, -4, 11, 16, -4, 7, -7, 10, 12, 0],\n [-4, -4, 4, -5, 0, -4, -9, 4, -4, 2, 3, 0],\n [-2, 6, -8, 4, -12, 7, 4, 9, 4, -10, -4, 2],\n [-6, 3, 0, -2, 8, -7, -4, 4, -8, -2, -1, 3],\n [-10, -1, -4, 4, 10, 10, 2, -10, -2, 11, -2, -10],\n [8, -2, 14, -12, 4, 12, 3, -4, -1, -2, 10, 7],\n [0, 1, -4, -4, -1, 0, 0, 2, 3, -10, 7, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21905858806", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 6) of the matrix A^7 where A is:\n[[-9, -6, 7, 10, 0, 0, 0, 10, 7, 0, 2, 2],\n [-6, -3, 8, -7, 8, 0, -8, 2, 2, 8, -2, 0],\n [7, 8, 9, 2, -2, 12, -4, 2, -3, 0, 6, -6],\n [10, -7, 2, -16, 8, 4, 2, 2, -8, 4, 4, -5],\n [0, 8, -2, 8, -14, -10, 0, 13, 6, -4, -6, -6],\n [0, 0, 12, 4, -10, -14, -1, 14, 1, 3, 4, 6],\n [0, -8, -4, 2, 0, -1, -1, -4, 12, 10, -10, -5],\n [10, 2, 2, 2, 13, 14, -4, -4, -10, -8, 7, -2],\n [7, 2, -3, -8, 6, 1, 12, -10, 12, 1, -4, 2],\n [0, 8, 0, 4, -4, 3, 10, -8, 1, -3, 14, 12],\n [2, -2, 6, 4, -6, 4, -10, 7, -4, 14, 12, 7],\n [2, 0, -6, -5, -6, 6, -5, -2, 2, 12, 7, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20705622800", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-1, -7, 0, 6, -16, 12, 8, -11, -7, -3, 6, 2],\n [14, 2, -16, -4, 0, 15, 16, 11, 12, 7, -1, -4],\n [9, -10, -3, 15, -6, 15, -6, 3, 5, 6, 12, -5],\n [14, 12, 14, -5, 10, -2, 13, -10, 7, 1, 7, 15],\n [-5, 11, -6, -14, -14, 12, 15, 14, -16, 4, 3, -6],\n [-7, -14, -3, 14, -8, -11, 12, 5, -14, -15, 11, -12],\n [-8, 15, 0, -6, 1, 2, 8, 14, 6, -3, 10, -4],\n [7, 16, -10, -8, 4, 15, -15, 8, -16, -6, -1, 6],\n [-2, 10, -1, 16, -9, -16, 2, 9, -14, 7, 5, -16],\n [-8, 16, 6, -7, 15, -15, -10, 7, -14, -5, 10, -16],\n [15, 10, 14, 16, 15, -13, 8, 12, -8, -3, -12, 0],\n [15, -11, -12, 12, 11, -7, 6, 2, -13, 15, 3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24862989993187", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[6, -7, 7, -4, -2, 12, -1, 5, 0, -8, -7, -3],\n [-7, -16, -8, -6, 10, -8, -2, -4, 3, 8, 8, -4],\n [7, -8, -8, 0, 14, 12, 12, 8, 7, 9, -6, -4],\n [-4, -6, 0, -1, -3, 4, 0, -2, -3, 2, -5, 6],\n [-2, 10, 14, -3, 8, 6, -2, 4, 8, 2, 2, -2],\n [12, -8, 12, 4, 6, 8, 4, 3, 0, -2, -6, 8],\n [-1, -2, 12, 0, -2, 4, -8, 0, 8, -6, -7, -4],\n [5, -4, 8, -2, 4, 3, 0, 2, 13, 11, 8, -4],\n [0, 3, 7, -3, 8, 0, 8, 13, -2, 8, 2, 8],\n [-8, 8, 9, 2, 2, -2, -6, 11, 8, -15, -2, 2],\n [-7, 8, -6, -5, 2, -6, -7, 8, 2, -2, -12, -1],\n [-3, -4, -4, 6, -2, 8, -4, -4, 8, 2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78594037514466", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-16, -7, 7, -2, 4, 5, 7, -7, 6, -1, -12, 16],\n [8, 9, -15, 14, 2, 1, -14, -10, 6, -16, -10, 5],\n [-14, 2, 13, -8, -4, 9, 11, 8, -14, -6, 13, 16],\n [-14, -12, 14, -13, -9, 0, 5, 7, 14, 8, 15, 9],\n [10, 6, 3, 10, 0, -3, -14, 10, -3, 11, 8, -6],\n [-5, 16, 3, 6, 2, -16, -7, -16, -12, 5, -15, -8],\n [-10, 4, -10, -8, -8, -5, -8, -7, -7, 0, -13, -1],\n [10, -11, -8, 15, 13, -3, 12, 11, 5, 14, 0, 0],\n [-2, 15, 11, -6, 0, -5, -8, 8, 9, -13, 2, -4],\n [12, -8, -10, -10, 4, -8, 10, 4, -12, -12, -9, -2],\n [-4, 16, 15, 6, 1, -5, 6, -15, 10, 14, 5, -12],\n [0, -10, 1, -15, 14, 11, -14, -8, 16, 11, 11, 1]], determine the value at position (7, 9).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5177267276314", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (11, 7) of the matrix A^8 where A is:\n[[-2, -6, 8, -12, 10, -5, -7, -8, -15, -8, -1, -16],\n [4, -16, -3, 15, 7, 16, 13, 9, -3, -5, -14, -10],\n [4, 10, -7, -7, 0, 1, 9, -15, -8, -12, 9, -2],\n [8, 9, 11, 6, 4, 5, 2, -7, 14, 14, -6, 0],\n [16, 5, 9, -15, 15, -14, 6, -16, -12, -16, 1, -12],\n [1, 15, 9, 16, 7, 10, 2, 1, -2, 10, -6, 7],\n [-14, -10, -5, 16, 5, -3, 9, 2, 4, 14, -12, 0],\n [15, -13, -7, 13, -8, 9, 5, 4, 6, -5, 14, 0],\n [4, 16, -2, 15, -2, 12, -6, 12, 5, 9, 1, 8],\n [4, 7, 11, -14, -4, -11, -6, 6, -8, 0, -8, 2],\n [15, 11, 11, -2, 2, 16, 6, 11, -13, 14, -12, 16],\n [15, -2, -8, 7, 1, 0, -16, -6, 16, -11, 12, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-678438466384", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[1, -2, 2, -2, 4, 4, 8, 0, -2, -8, 10, 2],\n [-2, 7, 0, 0, 7, -2, -6, 6, -8, 0, 0, -6],\n [2, 0, -6, -13, -1, 7, -12, 6, -2, 8, -6, -5],\n [-2, 0, -13, -16, -8, -8, -1, -12, -9, 10, 0, 2],\n [4, 7, -1, -8, 15, -8, 2, -10, 12, -6, -6, 2],\n [4, -2, 7, -8, -8, 0, 3, -9, -2, -6, 10, -10],\n [8, -6, -12, -1, 2, 3, -9, 5, 13, 10, -9, 2],\n [0, 6, 6, -12, -10, -9, 5, -3, 0, -10, 12, 4],\n [-2, -8, -2, -9, 12, -2, 13, 0, 4, 1, 4, 6],\n [-8, 0, 8, 10, -6, -6, 10, -10, 1, -11, -4, 8],\n [10, 0, -6, 0, -6, 10, -9, 12, 4, -4, -4, -10],\n [2, -6, -5, 2, 2, -10, 2, 4, 6, 8, -10, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6826674526951", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 4) of the 7th power of the matrix:\n[[3, -4, 5, -6, -5, -2, -6, 2, -10, -8, 0, 10],\n [-4, 13, -5, 10, 1, 9, -5, 11, 12, 7, 9, -4],\n [5, -5, -12, 0, -10, -2, 8, -5, 5, -2, -4, 0],\n [-6, 10, 0, 11, -2, -4, -5, 6, 3, -4, -3, 2],\n [-5, 1, -10, -2, 3, -12, -10, -7, 13, 2, -6, 0],\n [-2, 9, -2, -4, -12, 7, 7, -9, 2, 0, 0, -7],\n [-6, -5, 8, -5, -10, 7, -8, 15, 1, -4, -8, 0],\n [2, 11, -5, 6, -7, -9, 15, -4, 2, 0, -7, 4],\n [-10, 12, 5, 3, 13, 2, 1, 2, -13, 12, 14, 6],\n [-8, 7, -2, -4, 2, 0, -4, 0, 12, -4, -6, 1],\n [0, 9, -4, -3, -6, 0, -8, -7, 14, -6, -5, 4],\n [10, -4, 0, 2, 0, -7, 0, 4, 6, 1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3012749071", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-16, -1, 4, 8, 8, -4, 2, -14, 4, 8, 2, 0],\n [-1, -5, 4, 2, -4, -6, 9, -6, 6, 1, 6, -4],\n [4, 4, -14, -1, -6, -11, 0, -12, 10, -4, 14, 10],\n [8, 2, -1, -14, 13, -3, -4, -3, -3, 10, -8, -8],\n [8, -4, -6, 13, -6, 16, 7, -1, 2, -12, -6, -4],\n [-4, -6, -11, -3, 16, 15, 0, -8, 2, 4, 0, 6],\n [2, 9, 0, -4, 7, 0, 3, 2, -12, -4, 4, 2],\n [-14, -6, -12, -3, -1, -8, 2, -11, -10, -6, -2, 5],\n [4, 6, 10, -3, 2, 2, -12, -10, 0, -8, -6, 6],\n [8, 1, -4, 10, -12, 4, -4, -6, -8, 1, -15, 12],\n [2, 6, 14, -8, -6, 0, 4, -2, -6, -15, 15, 14],\n [0, -4, 10, -8, -4, 6, 2, 5, 6, 12, 14, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-314990856718299", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-1, -11, 15, 4, 12, -6, -12, 10, 11, 14, -6, -4],\n [-11, 10, 13, 2, -3, -8, 11, 11, 8, 9, -13, -14],\n [4, 0, -5, 8, 4, 1, -11, 3, 3, 15, 14, 3],\n [13, -14, 3, -9, 4, 6, -16, -15, -7, 13, 7, 15],\n [13, -3, -14, 8, -10, 0, 10, 6, 15, -15, -6, -10],\n [-7, 8, -15, 13, 0, 12, 1, 0, 5, 8, 3, -1],\n [8, -2, -2, -2, 1, -16, 16, -14, 5, 4, 10, -13],\n [-16, -13, 7, 12, 5, 6, 4, -3, -9, -1, 7, 9],\n [-10, 8, 9, 9, 13, -15, -8, -6, -2, -5, -1, 15],\n [1, 4, -1, -10, -12, 16, 14, 4, -14, -7, -6, 5],\n [0, 8, 11, 3, 13, 14, -4, -7, 16, 3, -3, -9],\n [-9, 11, -7, -3, -3, -11, 0, 4, 11, -2, -8, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "426719340044096", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[0, 1, -13, 3, -4, -6, 16, 11, -9, 3, 1, -10],\n [16, -6, 13, 3, -7, 13, 1, 8, 15, 14, 11, 9],\n [-13, 3, -9, -15, 10, 4, -9, 6, -9, -12, -16, 4],\n [-7, -15, 4, -4, 11, 13, 1, -15, 2, 4, 9, 8],\n [2, 8, 3, -11, 1, 1, 3, -7, 16, 2, -15, -14],\n [13, 2, 4, -3, 14, 4, 0, 7, 3, -1, -5, 7],\n [-4, 10, 4, -14, -3, 13, -7, -16, 11, 2, 13, 3],\n [3, 6, 14, 15, 9, -3, -11, 16, -9, -13, -4, 12],\n [8, -6, 12, 5, -6, 11, -9, 7, -7, -2, 4, 3],\n [-4, -15, 10, -10, 9, 13, 2, 4, 9, -7, 10, -9],\n [9, -16, 6, -8, 14, -10, -8, -10, 11, -1, -7, 7],\n [-7, 12, 8, 13, 2, 14, 13, 11, 2, -6, 11, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7763860291936", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 8) of the matrix A^8 where A is:\n[[0, 10, -16, -1, -13, 6, 15, -14, 4, 7, -2, -6],\n [-14, 2, -9, 9, -14, 15, -7, -7, -6, -3, 14, -8],\n [-11, 1, 6, 13, -14, -2, -14, -2, -14, 12, 14, -10],\n [-10, -6, 11, 8, 0, 4, 3, -7, -11, -5, 0, 16],\n [2, -12, 12, 13, -16, -5, -2, -12, -6, 3, 12, -3],\n [9, -7, 10, 8, -7, 15, 6, 16, 15, 5, 5, 6],\n [2, 6, 5, 13, 2, 5, -16, 9, -13, -5, 11, -14],\n [11, 12, 3, -15, -16, 1, -8, 8, 2, 8, -2, 9],\n [3, -14, 8, 4, 7, 8, -16, 12, 15, -16, -1, 15],\n [-2, -12, -7, 5, -9, -2, 3, 8, -5, 9, -13, 9],\n [-7, -2, -12, 15, 15, 5, 5, -5, -6, 7, -1, -1],\n [-16, 6, 11, 15, -14, -4, 11, 11, 7, -4, 7, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52217228666", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 1) of the matrix A^9 where A is:\n[[0, -5, 1, 16, 14, 13, 15, -7, 14, -2, 10, 10],\n [-16, -5, -13, 6, 6, 2, 3, 3, 12, -4, 11, 7],\n [5, 5, -6, -9, 15, 7, -5, 4, -14, 1, -11, -2],\n [-2, 7, -10, -8, -6, -1, -10, 8, -3, -16, 3, 11],\n [-8, 3, 14, 4, 5, -4, 8, 5, 3, 15, -1, 3],\n [5, -2, -5, -8, -2, 5, -5, 10, 2, 8, -7, -5],\n [-9, -6, 2, 6, 7, -2, 3, 8, -3, -7, 12, -5],\n [16, 6, -3, 6, 5, 12, -15, 3, -12, 10, -14, 1],\n [-4, 5, -4, -5, 15, -10, -11, -11, 8, 10, -12, 2],\n [-8, -16, -8, -7, -3, 8, 2, 0, 1, -8, -16, -11],\n [0, -8, -6, 1, -10, -10, -6, -7, 7, -5, -8, 5],\n [15, -9, 4, -1, 16, 8, -11, -13, 6, -8, -6, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2130423695727", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (10, 1) of the result:\nA =\n[[-10, 0, 5, -8, -4, 10, 7, -2, 14, -2, 10, 6],\n [0, 12, -10, 15, 12, -7, -4, 1, 1, -3, 2, 2],\n [5, -10, -2, 0, 10, -8, 9, -1, -8, 0, 2, -10],\n [-8, 15, 0, -10, 4, 12, -6, -3, -5, -8, 8, -2],\n [-4, 12, 10, 4, 14, -5, 7, 1, 4, -10, 2, 4],\n [10, -7, -8, 12, -5, 15, 8, 13, 13, -2, 12, -6],\n [7, -4, 9, -6, 7, 8, 5, -6, 2, -4, -13, 0],\n [-2, 1, -1, -3, 1, 13, -6, 10, 1, -6, 4, -6],\n [14, 1, -8, -5, 4, 13, 2, 1, 2, -4, 14, 6],\n [-2, -3, 0, -8, -10, -2, -4, -6, -4, 5, -13, -3],\n [10, 2, 2, 8, 2, 12, -13, 4, 14, -13, -2, 2],\n [6, 2, -10, -2, 4, -6, 0, -6, 6, -3, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-102008930990587", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 9) of the 9th power of the matrix:\n[[7, -8, 11, -6, -3, 9, -9, 11, 3, 8, -7, -6],\n [9, 6, 2, 1, 2, -2, -1, 3, 2, -6, -10, 2],\n [7, 14, -9, 7, -9, -4, -7, 2, 6, 16, 13, 13],\n [12, -8, -9, 8, -9, 9, -6, 6, 15, -16, -8, 11],\n [16, 15, -9, 1, -10, 1, -5, -13, -4, -6, -1, -3],\n [-1, 5, 1, 8, -10, 3, 10, 12, -7, -6, 3, 16],\n [-4, -1, -6, -12, -14, -15, -7, -11, 4, 14, 15, 12],\n [-16, 16, 0, -1, -10, -4, 3, -13, -12, -1, -8, -5],\n [-3, -2, -12, 1, -9, -9, 8, -13, 9, -6, -11, 16],\n [5, 12, -12, -16, 5, 14, -14, -14, -10, -16, 7, 13],\n [15, 15, 4, -1, -13, 0, -4, -6, 8, 13, -4, 7],\n [-9, 1, -10, 5, -10, -4, -15, -15, 12, 10, 1, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-443200507210", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-13, -2, 3, -6, 2, -8, 0, 12, -6, -16, 1, 6],\n [-2, 7, 0, -6, -2, 12, 7, -3, -2, -3, -10, 6],\n [3, 0, 9, -16, -4, 2, 8, 7, -12, -4, -16, -4],\n [-6, -6, -16, 2, -4, 2, 2, -5, -2, -4, 6, 0],\n [2, -2, -4, -4, 10, 6, -3, 2, -3, 6, 9, 8],\n [-8, 12, 2, 2, 6, 0, 15, 8, -10, 0, 10, 4],\n [0, 7, 8, 2, -3, 15, -13, 10, -12, 10, -6, -1],\n [12, -3, 7, -5, 2, 8, 10, 13, 2, -8, -6, 2],\n [-6, -2, -12, -2, -3, -10, -12, 2, -9, -6, -1, 14],\n [-16, -3, -4, -4, 6, 0, 10, -8, -6, -8, 2, -2],\n [1, -10, -16, 6, 9, 10, -6, -6, -1, 2, -9, 6],\n [6, 6, -4, 0, 8, 4, -1, 2, 14, -2, 6, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3605539393847", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-13, -9, 1, 15, 6, -2, -10, 14, 15, -3, 2, -1],\n [-8, -16, 8, -9, 15, -9, -4, -14, -15, 11, -13, 6],\n [-10, 13, -8, 2, -8, 6, -6, -4, 12, 14, -9, 2],\n [-12, 10, -3, 5, 5, -12, -1, 9, -1, -5, -1, -5],\n [15, -12, 11, -13, 12, 2, 8, 7, 2, 6, 14, 2],\n [15, -4, 1, -10, 7, 0, -2, -8, -9, -6, 7, 13],\n [4, -5, -8, -5, 11, 12, 12, -11, -1, 11, -16, 12],\n [-11, 10, 5, -10, -16, -4, -3, -2, -5, -13, 4, -15],\n [4, -3, -15, -6, -3, 3, 10, -11, -10, -16, -4, 0],\n [-16, -16, 2, 13, -4, -10, 3, -8, -4, 3, 8, -12],\n [8, -5, 9, 5, -16, -9, -14, 5, 4, 4, 14, -16],\n [10, -15, 12, -16, -9, -10, 6, 6, 2, -2, -9, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-160175345388", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 12) of the 7th power of the matrix:\n[[-4, 13, 3, 2, -4, -8, 14, -7, 4, -6, -8, 8],\n [13, 3, 2, 6, 5, -3, -2, 5, -2, -10, -9, 0],\n [3, 2, -14, 2, -4, 0, -1, 2, -11, -6, 5, 3],\n [2, 6, 2, -15, 4, 4, 4, -12, 10, 5, 5, -6],\n [-4, 5, -4, 4, 9, 11, -1, -2, 12, -10, 3, 14],\n [-8, -3, 0, 4, 11, 0, 4, 4, -2, -13, 3, 0],\n [14, -2, -1, 4, -1, 4, 3, 8, -10, -5, 4, -8],\n [-7, 5, 2, -12, -2, 4, 8, -16, -12, 10, 0, -4],\n [4, -2, -11, 10, 12, -2, -10, -12, 1, 2, 3, -2],\n [-6, -10, -6, 5, -10, -13, -5, 10, 2, 0, -2, 8],\n [-8, -9, 5, 5, 3, 3, 4, 0, 3, -2, -5, -1],\n [8, 0, 3, -6, 14, 0, -8, -4, -2, 8, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19504300849", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[10, 0, 6, 2, 1, 3, 3, -5, -11, 0, 1, 14],\n [0, 16, -2, -1, 1, 0, 12, -8, -8, 8, 10, 2],\n [6, -2, -12, -12, -15, 0, 4, 6, 8, 2, -4, 0],\n [2, -1, -12, -13, 4, -6, 6, 0, 8, 2, -9, 10],\n [1, 1, -15, 4, 16, -1, 1, -14, 1, 5, -3, -16],\n [3, 0, 0, -6, -1, 12, 10, -1, 0, -10, 2, 3],\n [3, 12, 4, 6, 1, 10, -15, -2, 7, 13, 6, 4],\n [-5, -8, 6, 0, -14, -1, -2, 4, -6, 6, 2, 4],\n [-11, -8, 8, 8, 1, 0, 7, -6, -8, -2, -6, 4],\n [0, 8, 2, 2, 5, -10, 13, 6, -2, 11, -3, 2],\n [1, 10, -4, -9, -3, 2, 6, 2, -6, -3, 13, 5],\n [14, 2, 0, 10, -16, 3, 4, 4, 4, 2, 5, -12]], determine the value at position (6, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11577476956", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 5) of the matrix A^9 where A is:\n[[-6, -7, 4, -8, 4, 10, -6, -6, 9, 2, -5, -2],\n [-7, -1, -1, -8, 6, -15, 8, -6, 0, 8, 6, 8],\n [4, -1, 4, 8, 9, -11, 5, 0, 6, 11, -10, 10],\n [-8, -8, 8, -2, 4, 0, -2, 2, -12, 7, 8, 5],\n [4, 6, 9, 4, 10, -8, -10, 2, 8, -2, -3, 8],\n [10, -15, -11, 0, -8, -12, 8, 8, -8, -12, 1, 2],\n [-6, 8, 5, -2, -10, 8, 14, -6, -10, 5, 8, 2],\n [-6, -6, 0, 2, 2, 8, -6, 2, 4, 15, -14, -3],\n [9, 0, 6, -12, 8, -8, -10, 4, -11, -4, 2, 10],\n [2, 8, 11, 7, -2, -12, 5, 15, -4, -9, -8, -12],\n [-5, 6, -10, 8, -3, 1, 8, -14, 2, -8, 13, 6],\n [-2, 8, 10, 5, 8, 2, 2, -3, 10, -12, 6, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-52455528720013", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[1, 12, -8, 13, -8, 4, -9, -2, -7, 0, -8, -10],\n [12, -16, 12, -2, -5, 0, 10, -5, 2, -4, 4, -8],\n [-8, 12, -9, 4, 6, 8, -1, -10, 2, 7, -2, 6],\n [13, -2, 4, -12, 8, -1, -2, -1, 1, 4, -11, 4],\n [-8, -5, 6, 8, 9, -10, -4, 9, -2, -4, 7, 3],\n [4, 0, 8, -1, -10, -3, -2, 3, 2, 4, 14, -9],\n [-9, 10, -1, -2, -4, -2, -12, -2, -7, 2, -12, 2],\n [-2, -5, -10, -1, 9, 3, -2, 5, -4, -2, 4, 5],\n [-7, 2, 2, 1, -2, 2, -7, -4, 5, 12, 10, 8],\n [0, -4, 7, 4, -4, 4, 2, -2, 12, -2, 2, 4],\n [-8, 4, -2, -11, 7, 14, -12, 4, 10, 2, -15, 8],\n [-10, -8, 6, 4, 3, -9, 2, 5, 8, 4, 8, -12]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16473289335282937", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[1, -2, 9, -15, 14, 8, 8, 15, 5, -7, -5, 4],\n [-2, -6, -10, 7, 13, -3, -11, -9, -5, -12, -4, 2],\n [5, -5, 15, 0, 9, -1, -5, -1, -12, -9, -10, 10],\n [9, -4, 0, -10, -8, -7, -3, -4, -9, -7, 16, 3],\n [-13, -16, 2, 7, -6, 5, -14, 0, 3, -2, -6, -4],\n [9, 6, -4, -1, -3, 12, 11, 10, -4, -14, -12, -1],\n [14, 5, -14, -12, -14, -2, -2, 10, -4, 1, -7, 15],\n [-13, -15, 13, 14, -14, -12, -3, -10, -2, 2, 2, 0],\n [-4, 4, -16, 1, 7, 13, -10, 10, 10, -14, -1, -13],\n [-16, 16, 9, -14, -13, 16, -12, 12, -6, -14, 1, 13],\n [0, 13, 13, 16, 0, -1, 16, -15, -15, 7, -12, -14],\n [15, -3, -12, 9, 0, 2, -6, -10, -4, 8, -5, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2547199066522860", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[11, -2, 16, -6, 15, -1, -8, -5, 2, -3, -5, 7],\n [-8, 4, -5, -12, -8, 3, -11, -4, -1, 3, -12, 0],\n [-7, 13, -10, -6, -9, 14, -16, 8, 11, 6, 12, 5],\n [-7, 0, -4, -1, -5, -2, 2, 4, 15, -12, -2, 15],\n [-16, -2, 3, 14, 3, 7, -7, -3, 12, -8, -7, -15],\n [6, 1, -16, -6, 16, 7, 8, 6, 5, 16, 2, 6],\n [9, 5, -14, -13, 16, -6, 3, 15, -2, 8, 0, 5],\n [16, 8, -3, 13, 5, 5, 2, -13, -9, -7, 11, 4],\n [-16, -6, -1, -3, -16, 14, -5, 10, 0, -1, -16, 13],\n [6, 10, -1, 7, 11, 13, 9, 7, 14, 8, -15, -10],\n [6, 12, 13, 12, 14, -15, -2, -1, -9, 11, 0, -3],\n [4, 10, 4, 15, -1, 11, 12, 7, 4, -9, 11, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59020526556157", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[2, 2, 9, -11, 9, 11, 15, 8, 5, 14, -11, 14],\n [-16, -8, -5, 4, -14, -12, -4, 12, 11, 8, -7, -2],\n [13, -4, -12, -3, -7, 14, -12, -11, -4, -4, 16, 6],\n [4, -9, 14, 14, 3, -15, 7, -6, -13, 9, -3, 3],\n [8, -7, -12, -13, 3, 6, -12, 12, 12, 15, 5, -10],\n [16, 5, 11, 4, -13, -11, 2, -6, 0, 1, -4, -6],\n [10, -1, -2, -3, -2, 1, -5, 9, 1, 9, 1, -16],\n [-1, 4, -9, -15, 2, 12, 13, -14, -9, 1, 9, 8],\n [-9, 1, 7, -12, 9, -7, -6, -13, -7, -5, -7, -5],\n [-12, 10, 16, 15, -12, 6, 7, -15, 13, -7, -16, -4],\n [-14, -1, -3, -12, 8, 12, 0, -8, 1, -5, 11, 15],\n [3, -16, -5, 5, -9, -5, 7, 11, -5, 14, 11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-486383754692827", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[5, -10, -13, 12, -7, 4, -13, 7, 4, 1, 9, -9],\n [6, -8, 8, 15, -10, 16, 14, 0, 5, 12, 1, -7],\n [-2, -10, -3, 9, 1, 1, -11, 8, -5, 13, 2, 4],\n [-1, -10, 2, 9, 1, -5, -12, 9, -12, 1, -11, -16],\n [-6, -1, 9, 1, 9, 16, -16, 10, 5, 2, -4, -14],\n [10, -8, 3, 9, 4, 15, 5, -3, 12, 14, 0, 6],\n [8, 1, -1, -15, 9, -5, -7, 12, -15, -1, 5, -11],\n [14, -15, 11, -10, 4, 8, 1, -4, -9, -3, 0, -4],\n [-6, -7, 0, 12, -15, -16, 10, 2, 1, -8, 8, 5],\n [-4, 12, 5, -1, 2, -9, -5, -15, -12, -3, -1, -7],\n [-9, 8, 10, -7, -10, -2, -4, 16, -15, -6, 4, -3],\n [8, 6, -16, -11, 1, -12, -16, 13, -16, -3, 11, 14]], determine the value at position (10, 10).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56572066940", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[6, 15, -9, 4, 8, 2, 0, -10, -2, -2, 6, -2],\n [15, -14, 0, -1, 2, -4, -12, -1, 8, -4, 2, -2],\n [-9, 0, -3, 2, 13, -13, 15, 0, 0, -4, -3, 2],\n [4, -1, 2, 2, -4, 3, -2, -4, -8, 14, 0, 0],\n [8, 2, 13, -4, -8, -5, 0, -12, -14, -2, 13, 4],\n [2, -4, -13, 3, -5, 10, -4, 0, 0, 8, 6, 0],\n [0, -12, 15, -2, 0, -4, -6, -4, -6, -2, -1, 10],\n [-10, -1, 0, -4, -12, 0, -4, 3, -6, 10, 2, -7],\n [-2, 8, 0, -8, -14, 0, -6, -6, 13, -4, 10, 1],\n [-2, -4, -4, 14, -2, 8, -2, 10, -4, 13, -6, 5],\n [6, 2, -3, 0, 13, 6, -1, 2, 10, -6, 2, -2],\n [-2, -2, 2, 0, 4, 0, 10, -7, 1, 5, -2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-73639755332", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 8) of the matrix A^8 where A is:\n[[11, -12, 2, -9, 11, -12, -9, 7, 3, -11, -12, -7],\n [11, -5, -2, -14, 6, -10, -16, -9, 10, 5, 14, -6],\n [4, -2, 11, 6, 10, 2, -1, -5, 6, -10, 13, -1],\n [15, 4, -13, -10, 10, -11, 3, -5, -3, 0, 3, -15],\n [4, -5, -4, -16, 1, -3, 14, 7, -5, 8, -3, 1],\n [7, 9, 13, -13, 12, 1, -13, 16, -15, -5, 5, 9],\n [-3, -8, -7, -10, 3, -2, 7, -15, 3, -4, 8, -14],\n [-5, 16, 11, -6, 0, -3, 14, -12, -15, -4, 3, -6],\n [-3, -13, -14, -6, 8, 6, 0, 14, -3, 1, -14, 2],\n [6, 14, 7, 0, 10, -8, 15, -3, 5, -3, -3, 11],\n [16, 5, 11, -14, 5, 6, -11, -3, 5, 3, 6, -4],\n [-8, -11, 11, -10, 2, 14, 12, 16, 5, -14, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176253868762", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-4, -4, -4, 1, -2, 2, -4, -9, -2, 10, -2, 2],\n [-4, -2, 7, -5, -4, -15, 0, 0, -1, -10, -12, 4],\n [-4, 7, 15, -8, 0, -3, -6, -2, -6, -5, 4, -1],\n [1, -5, -8, -4, 6, 2, 2, -2, -4, -14, 12, -2],\n [-2, -4, 0, 6, 9, 12, -9, -11, 0, 8, -6, 4],\n [2, -15, -3, 2, 12, -3, 8, -6, 4, -10, 10, 8],\n [-4, 0, -6, 2, -9, 8, -6, -1, 6, -2, 0, 0],\n [-9, 0, -2, -2, -11, -6, -1, 4, 12, 1, 10, -8],\n [-2, -1, -6, -4, 0, 4, 6, 12, 10, -10, -5, -8],\n [10, -10, -5, -14, 8, -10, -2, 1, -10, 2, 2, 6],\n [-2, -12, 4, 12, -6, 10, 0, 10, -5, 2, -5, -1],\n [2, 4, -1, -2, 4, 8, 0, -8, -8, 6, -1, -4]], determine the value at position (11, 12).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152133467379", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 3) of the 7th power of the matrix:\n[[12, 6, -2, -10, 0, 2, 4, -4, -12, -8, -12, 9],\n [6, 12, 2, -8, 6, 4, 11, 0, 0, 6, 0, -10],\n [-2, 2, -16, 0, -4, 4, 4, 2, 3, -3, -2, -2],\n [-10, -8, 0, 0, -8, 8, -2, -4, -4, -12, 8, -1],\n [0, 6, -4, -8, 15, -4, -4, -8, -3, -5, -10, -2],\n [2, 4, 4, 8, -4, -12, -14, 0, 2, 0, 0, -8],\n [4, 11, 4, -2, -4, -14, -13, 4, -12, 7, 12, -4],\n [-4, 0, 2, -4, -8, 0, 4, -14, -6, -4, 1, 3],\n [-12, 0, 3, -4, -3, 2, -12, -6, 8, 5, 9, 2],\n [-8, 6, -3, -12, -5, 0, 7, -4, 5, -11, 0, -2],\n [-12, 0, -2, 8, -10, 0, 12, 1, 9, 0, 13, 13],\n [9, -10, -2, -1, -2, -8, -4, 3, 2, -2, 13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19689119576", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (11, 1) of the result:\nA =\n[[1, 7, -8, 4, -6, -1, -7, 0, -12, -6, 0, 2],\n [7, -4, -12, 6, -14, -2, -8, -2, 2, 0, 2, 0],\n [-8, -12, 4, -2, 1, 0, -9, -13, -2, 8, -2, -10],\n [4, 6, -2, -2, 7, -14, -2, -4, 2, 6, -2, 2],\n [-6, -14, 1, 7, -11, 0, -6, 5, -3, 6, 1, 0],\n [-1, -2, 0, -14, 0, 1, 1, 4, 4, -2, -10, 5],\n [-7, -8, -9, -2, -6, 1, 12, -6, -1, -6, -4, -6],\n [0, -2, -13, -4, 5, 4, -6, 10, 2, 0, -10, 1],\n [-12, 2, -2, 2, -3, 4, -1, 2, -14, -4, 0, 7],\n [-6, 0, 8, 6, 6, -2, -6, 0, -4, -13, -4, 2],\n [0, 2, -2, -2, 1, -10, -4, -10, 0, -4, 8, 5],\n [2, 0, -10, 2, 0, 5, -6, 1, 7, 2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1763827046", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[4, -4, 15, -7, 15, 3, -1, -12, 0, 9, -13, 9],\n [3, -4, -10, 7, -14, -14, -1, 14, 16, -3, 8, -15],\n [-4, 1, 3, -15, -10, -4, -9, -14, -3, 6, -9, 16],\n [10, -6, 16, -6, 1, 11, 9, 13, -7, -14, 15, -7],\n [4, -10, 8, 8, -8, -9, 11, -7, -3, 12, -16, 2],\n [-3, 3, -9, 7, -10, -12, -3, -8, 3, 9, 8, 3],\n [-11, -10, 3, 1, -9, 10, -12, 14, 4, -14, 9, 0],\n [13, 6, 8, -13, -6, 1, 16, 1, -1, 5, 4, 14],\n [14, 10, -14, 14, 9, 7, -7, 12, -4, -11, -3, 13],\n [-13, 11, -7, 9, 12, -9, 1, -8, 5, 1, 16, -15],\n [9, 0, -13, -8, -7, -12, 5, 2, 16, -11, 6, -3],\n [14, 16, 0, -16, -5, -14, 7, -3, 11, 10, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-118176343460720", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 2) of the 7th power of the matrix:\n[[8, -4, 6, -1, 0, 9, 0, -4, -10, -2, 13, 5],\n [-4, 16, 4, 3, -2, -12, 16, 3, -2, -8, 6, 0],\n [6, 4, -3, 9, 0, -14, 2, 1, -6, 4, 2, 2],\n [-1, 3, 9, -5, -12, 8, 0, -6, 1, 8, 10, 2],\n [0, -2, 0, -12, 5, 0, -5, -10, -2, -2, 0, -14],\n [9, -12, -14, 8, 0, -12, -10, 1, -13, -8, -4, -1],\n [0, 16, 2, 0, -5, -10, 13, 8, -6, 6, -2, -3],\n [-4, 3, 1, -6, -10, 1, 8, -12, 0, 5, 4, -2],\n [-10, -2, -6, 1, -2, -13, -6, 0, -5, 0, -3, 2],\n [-2, -8, 4, 8, -2, -8, 6, 5, 0, -9, 12, -14],\n [13, 6, 2, 10, 0, -4, -2, 4, -3, 12, 4, 5],\n [5, 0, 2, 2, -14, -1, -3, -2, 2, -14, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25513169170", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (8, 6) of the result:\nA =\n[[-5, 0, 16, -6, -6, 11, 13, -3, 4, 15, 10, -9],\n [16, 4, 12, -1, -13, 8, -12, 2, -11, 13, 11, -4],\n [-14, -13, -7, -11, -16, -16, -10, -1, 7, -13, -1, -10],\n [8, -2, -8, -6, -10, 6, -14, -10, -14, -5, -14, -10],\n [6, -2, 6, -12, 12, 2, 7, 6, 11, 0, -8, 0],\n [-16, -8, -11, -2, -11, 1, 7, 13, 2, 11, 6, 7],\n [10, -4, -6, -2, 13, -11, 8, 14, -6, -13, -2, 7],\n [-3, 7, 6, -12, 9, 13, -14, 1, 5, 11, 13, -15],\n [-8, -16, 4, 11, 15, -11, 6, -11, 5, 14, 2, -9],\n [-9, 3, 7, -4, -10, -9, 10, -14, 0, -12, -8, -11],\n [-9, 9, 3, 9, -14, 8, -2, -6, 15, 15, -11, -15],\n [6, 12, -10, 13, -1, -16, -4, -16, 5, 12, -1, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21021280455", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[8, -2, -11, -12, -10, 6, 10, -10, -2, -2, 4, -4],\n [-2, -13, 8, -2, 2, -10, -2, 0, 2, 12, -3, -7],\n [-11, 8, 15, 6, -12, 14, 5, -1, -10, 2, 2, 0],\n [-12, -2, 6, 3, 12, 6, -1, -4, 8, -9, 8, 2],\n [-10, 2, -12, 12, -13, 3, -5, -6, 4, -6, -1, -5],\n [6, -10, 14, 6, 3, -16, -9, -3, 6, -2, 5, 1],\n [10, -2, 5, -1, -5, -9, 16, -2, 8, -11, -2, -5],\n [-10, 0, -1, -4, -6, -3, -2, 3, 6, 2, 14, -3],\n [-2, 2, -10, 8, 4, 6, 8, 6, 15, -2, -2, -12],\n [-2, 12, 2, -9, -6, -2, -11, 2, -2, 12, -6, 9],\n [4, -3, 2, 8, -1, 5, -2, 14, -2, -6, -1, 6],\n [-4, -7, 0, 2, -5, 1, -5, -3, -12, 9, 6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3318007986770475", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (7, 1) of the result:\nA =\n[[0, -16, -4, -5, 15, 7, 7, -8, -13, 8, 7, 6],\n [-2, 8, -7, -7, -11, -12, 12, 3, -16, 5, 6, 9],\n [-3, -5, -2, -1, -2, -9, -3, -15, -5, 7, -15, 1],\n [-13, 11, 8, -10, -5, 2, -13, -15, 7, -6, 7, -8],\n [-10, 12, 7, -14, -16, 16, -7, -2, -6, 16, 15, 3],\n [15, -9, 0, -15, -6, -3, 1, -7, 6, 7, -6, 11],\n [10, -9, -15, -16, -13, -14, 9, -10, 5, -7, -7, -16],\n [-6, -7, -3, -15, -7, 15, 12, -16, -13, 16, 7, 5],\n [-7, 9, -3, -5, 3, 5, 0, 11, 6, -1, 6, 6],\n [14, -2, -4, -3, 5, -8, -9, -3, -10, -14, 6, 0],\n [8, 6, -6, 15, -16, 10, 11, 9, -8, 13, -14, 14],\n [-7, 15, -16, -9, -7, 7, 2, -10, -8, 15, 2, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22033076875658", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -4, -11, 2, 6, 2, 4, -10, 4, 2, 4, 0],\n [-4, 13, 6, -9, -6, 10, -1, 4, 0, -4, 4, -6],\n [-11, 6, 16, -4, 7, 4, 0, 2, -6, -2, -1, -4],\n [2, -9, -4, -1, 6, 6, 7, -14, 8, 7, 5, 2],\n [6, -6, 7, 6, 14, -8, -6, 0, -10, -6, 0, 6],\n [2, 10, 4, 6, -8, -2, 6, 9, 4, -7, 2, 14],\n [4, -1, 0, 7, -6, 6, 3, 1, 1, -3, 1, -4],\n [-10, 4, 2, -14, 0, 9, 1, -4, 2, 9, 10, 4],\n [4, 0, -6, 8, -10, 4, 1, 2, -4, 1, 12, -14],\n [2, -4, -2, 7, -6, -7, -3, 9, 1, 11, -8, 4],\n [4, 4, -1, 5, 0, 2, 1, 10, 12, -8, 8, 6],\n [0, -6, -4, 2, 6, 14, -4, 4, -14, 4, 6, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1723115004764992", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[7, 6, 7, 8, 4, 0, -6, -8, 0, -12, -6, 5],\n [6, 7, 6, -4, -7, -4, 2, 0, 7, 6, -4, -2],\n [7, 6, -3, 2, -9, 2, -8, 7, -1, 10, 1, 4],\n [8, -4, 2, 13, -2, 10, -4, 2, -3, -2, -2, -6],\n [4, -7, -9, -2, -15, -4, 4, 0, 4, -4, 10, 0],\n [0, -4, 2, 10, -4, -16, -6, 6, 6, -2, -2, 5],\n [-6, 2, -8, -4, 4, -6, 13, -14, 12, 3, -5, -4],\n [-8, 0, 7, 2, 0, 6, -14, 15, -5, 4, 0, 9],\n [0, 7, -1, -3, 4, 6, 12, -5, 9, 4, -10, 4],\n [-12, 6, 10, -2, -4, -2, 3, 4, 4, -11, 0, 4],\n [-6, -4, 1, -2, 10, -2, -5, 0, -10, 0, 12, -13],\n [5, -2, 4, -6, 0, 5, -4, 9, 4, 4, -13, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87294155758", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-4, 8, -3, -6, 13, -10, -15, -14, 16, 15, 0, 11],\n [4, 2, 16, -6, 16, 6, -10, -9, 13, -10, 5, 10],\n [2, 10, -11, -1, 7, 7, 13, 3, -6, 2, 8, 5],\n [-16, 3, 6, 7, 6, -10, -8, 12, -7, -2, -9, 5],\n [3, 1, 6, 11, -7, 6, -7, -16, 12, -12, 12, 3],\n [-9, 8, -16, -1, -12, -4, -16, -9, -16, 3, 8, 12],\n [-14, 12, 1, 1, 7, -11, 11, -3, 9, -10, -6, 4],\n [-12, 14, 10, 16, -12, 9, 3, -3, -12, -5, -4, 10],\n [10, -1, -13, -4, 1, -5, 2, 0, -10, 4, -16, -3],\n [-14, 15, -8, -6, 6, 13, -12, 13, 9, -13, 10, 12],\n [-10, -1, -9, 8, 7, 4, -1, -6, -9, -11, -6, 11],\n [-6, -11, 13, -3, -4, -11, 16, -6, -16, 10, 13, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47437465173", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[11, 14, 0, -4, -4, 6, -4, -2, 0, -5, 11, 2],\n [14, 2, 13, 0, 2, 2, -4, 0, 10, 0, -14, -10],\n [0, 13, -3, 0, -2, -2, 0, 4, 2, 4, -1, 6],\n [-4, 0, 0, 9, 11, 10, 12, 4, -16, -2, -16, -10],\n [-4, 2, -2, 11, -15, 6, -2, 7, -4, -10, -6, 0],\n [6, 2, -2, 10, 6, -12, -2, -4, -10, 8, 4, 10],\n [-4, -4, 0, 12, -2, -2, 5, 2, -1, 2, -5, 7],\n [-2, 0, 4, 4, 7, -4, 2, -1, -2, -8, 0, 0],\n [0, 10, 2, -16, -4, -10, -1, -2, -1, 8, 7, 10],\n [-5, 0, 4, -2, -10, 8, 2, -8, 8, 5, -4, -8],\n [11, -14, -1, -16, -6, 4, -5, 0, 7, -4, 8, -2],\n [2, -10, 6, -10, 0, 10, 7, 0, 10, -8, -2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171773839934535", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-11, 0, -8, 10, 7, 0, 0, -2, -12, -2, -1, 9],\n [0, 15, -14, 10, -12, 0, 6, -3, 10, 2, 9, -4],\n [-8, -14, -8, 14, -5, -2, -9, -3, 10, -3, 0, -6],\n [10, 10, 14, 14, -4, -2, 0, -2, 12, -9, -4, 7],\n [7, -12, -5, -4, -16, -3, -2, -1, 6, -7, 8, -16],\n [0, 0, -2, -2, -3, -11, -10, -1, 6, -2, 2, 5],\n [0, 6, -9, 0, -2, -10, -10, -4, 9, 8, -9, 5],\n [-2, -3, -3, -2, -1, -1, -4, 1, 14, -15, -6, -6],\n [-12, 10, 10, 12, 6, 6, 9, 14, -7, 3, 0, -2],\n [-2, 2, -3, -9, -7, -2, 8, -15, 3, -4, 10, -2],\n [-1, 9, 0, -4, 8, 2, -9, -6, 0, 10, 14, 2],\n [9, -4, -6, 7, -16, 5, 5, -6, -2, -2, 2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340133622543210", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (2, 11) of the result:\nA =\n[[6, -13, 4, 10, -6, 7, 10, 10, 11, -15, 9, -2],\n [7, 2, -10, 0, -13, 13, -3, 3, 12, 9, 2, -9],\n [3, -16, -1, -16, -9, -9, -15, 11, 14, -1, -6, -3],\n [16, -9, -4, -1, 4, 0, 1, -12, 11, -12, -13, -14],\n [16, -14, -9, 6, -11, 10, 5, -16, 10, -8, 8, -3],\n [1, 1, 10, -8, -5, 1, -3, -7, 3, 5, -12, 13],\n [-16, 9, -10, -10, -12, 3, 11, 6, -9, -1, -11, -6],\n [-4, -15, -15, -4, 2, 16, 8, 1, 12, -6, 6, 6],\n [-14, 1, -8, 3, 7, 0, -5, 16, -11, 13, -11, 6],\n [-10, 9, -14, 8, -14, -2, -13, 4, 13, -10, -4, -10],\n [6, -10, -7, -3, -12, 2, 16, -3, -14, -10, 13, 10],\n [-6, -1, 0, 2, -15, 10, -16, -15, -2, -16, -11, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-308271885162", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[10, 0, 7, 5, -2, 4, 10, -1, -3, -13, 7, -4],\n [-12, 16, -9, 2, -7, 2, 14, -3, 8, -9, -13, -12],\n [-11, 13, 2, 1, 4, 0, 14, 4, -6, -1, -8, 6],\n [6, -14, -11, 3, -2, 13, 15, -11, 14, -1, 12, 5],\n [11, -2, 4, -9, -16, 13, -15, 7, -12, -5, -12, -3],\n [-5, 10, -15, -14, -9, -15, 12, 8, -13, -7, 0, -16],\n [-14, 13, -12, -6, -8, -3, 2, -4, 4, -15, 13, 6],\n [10, -16, -10, -15, 6, 14, 12, -3, -12, -6, 16, 12],\n [-11, -10, -7, 3, -8, 0, -11, -16, -6, 0, -8, -1],\n [10, -12, -9, -8, -4, -14, 10, 3, 16, -4, 7, 7],\n [3, 10, 1, 11, 16, 15, -10, -2, -3, 14, 14, 9],\n [8, -11, 10, 15, -5, 13, 7, 7, 5, -13, 2, 8]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33472777396050", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 12) of the 7th power of the matrix:\n[[-12, -14, 6, 1, -2, -4, 14, 3, -2, 4, -7, 6],\n [-14, -11, 10, 10, -6, 0, 12, 10, 4, -8, -2, -6],\n [6, 10, 8, 7, -7, 11, -12, -2, -4, 13, 2, 0],\n [1, 10, 7, -4, 2, -2, -2, -8, -10, 0, 8, -6],\n [-2, -6, -7, 2, 13, -15, 1, 2, -6, -10, 3, -1],\n [-4, 0, 11, -2, -15, -12, -2, -10, 1, -9, 8, 0],\n [14, 12, -12, -2, 1, -2, -11, -9, 0, 0, -4, -12],\n [3, 10, -2, -8, 2, -10, -9, 5, 0, -8, 6, 10],\n [-2, 4, -4, -10, -6, 1, 0, 0, 10, 12, 2, 6],\n [4, -8, 13, 0, -10, -9, 0, -8, 12, -5, 14, 9],\n [-7, -2, 2, 8, 3, 8, -4, 6, 2, 14, 15, -7],\n [6, -6, 0, -6, -1, 0, -12, 10, 6, 9, -7, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35388718430", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[9, 12, -11, 2, 8, -7, -7, -1, -2, -2, -16, -11],\n [2, -11, -13, -7, -8, -16, 0, 11, -5, -1, -3, -11],\n [13, 9, 3, -12, -2, 14, 1, -4, -6, -5, 2, 2],\n [-16, -3, 0, -15, 4, 3, 6, 13, -16, -11, -2, 0],\n [9, -15, -6, -7, -13, 2, 9, 1, 5, 12, -2, 16],\n [-6, 3, 10, -2, -14, -1, 11, -2, 9, 10, -3, -14],\n [-14, 6, -12, -15, -15, -2, -15, 11, -3, -5, 13, -9],\n [15, 3, -2, -3, 9, 8, 2, 3, 9, 15, 6, -3],\n [5, 13, 11, 13, -14, -13, -6, -4, -15, 13, -1, 15],\n [-2, 6, 0, 1, 15, -1, -16, -3, -15, -11, 9, -9],\n [7, 14, 4, 3, -15, 3, 5, -4, 3, 14, 6, 9],\n [13, -8, 15, -5, -5, 10, 9, -3, -3, -6, -9, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27729287391005", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-13, -16, -11, -15, 2, 14, 2, 6, -8, 2, -4, -9],\n [11, 10, -8, -2, 8, -16, -6, -2, 9, 16, 10, -5],\n [3, -5, -11, 3, 6, -2, 11, -9, 3, -11, 9, 1],\n [-3, 3, -16, 6, -1, 2, -9, 7, -1, -4, 13, -4],\n [4, 2, 10, 6, -1, 7, -1, -1, -6, 9, -1, -2],\n [1, 1, -12, -15, 13, 14, 8, 14, 2, 1, 16, -14],\n [1, 9, 11, 15, -10, 11, 15, 5, -8, 0, -7, 10],\n [0, 15, -6, 8, 0, 10, -2, -12, -4, -11, 3, -14],\n [11, -14, 16, -15, 12, -3, -10, -13, 4, 8, -8, -5],\n [-5, -12, 12, 10, 3, 12, 2, 16, -9, 13, 14, -16],\n [2, 1, 0, 14, 3, 12, 4, -8, 13, 16, 1, -7],\n [-16, 11, 16, 1, -8, 11, 6, 9, 16, 3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75623351499880", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (8, 5) of the result:\nA =\n[[15, -6, 9, -16, -5, -8, -9, 14, 3, 2, 15, -12],\n [14, 5, 3, -5, 2, -15, -13, 13, 6, 4, -12, -10],\n [-5, -6, -3, -14, 6, -14, 7, 16, 15, 13, -14, -11],\n [15, -11, -13, -13, -4, -14, -1, 7, 7, 7, -12, 2],\n [-10, 13, 8, -16, -15, -9, -13, 15, -11, 16, -7, 7],\n [-14, 10, 7, -1, 15, -1, -8, -1, -1, -13, -6, 7],\n [14, 7, 7, 7, 15, -2, 5, -5, 0, -15, -11, 14],\n [8, 11, 9, -13, 12, -2, 16, -1, -12, 5, -7, 14],\n [-3, 2, 4, 7, 15, 13, 0, 14, 0, -3, -11, 13],\n [2, 10, 14, -1, -4, -2, 9, 12, -16, 16, 4, -10],\n [-16, -16, 1, 15, 14, 1, -1, -16, -6, 13, 11, 9],\n [6, -7, -6, -11, 12, 5, -3, -11, 3, -6, -15, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1563790869051", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -12, -2, 9, -6, 16, -6, -8, -6, 16, 16, 10],\n [1, -6, 13, -1, 7, -16, -6, -11, -5, 9, 2, -16],\n [3, -5, 7, 15, 16, -7, 5, -3, -13, 12, -11, 8],\n [-9, -6, -16, -11, 11, 15, -8, -15, 5, 6, -14, -1],\n [13, 2, 9, -1, 5, -11, -12, -3, 7, -3, -8, -6],\n [-7, 14, 8, 3, 14, -1, -11, -6, 2, -16, 10, 4],\n [-3, 3, 14, -15, 1, 4, 8, -4, 0, -5, 5, 7],\n [-2, -10, -14, 3, 9, 11, -8, -10, -3, 1, -7, -2],\n [-13, 2, 11, 6, 5, 5, -6, 14, 10, -12, 12, -12],\n [1, 12, -15, -3, 6, 12, -9, -13, 15, 12, 12, -16],\n [-14, 2, -3, 15, 6, 9, 1, -2, 8, 5, 1, -5],\n [10, 3, -1, -2, -7, -12, 0, 13, -13, 5, 14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3054761322772510", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-1, 8, 0, 1, 12, 10, 14, 6, 8, 5, -4, 0],\n [-14, -16, 0, 12, 1, -8, 9, 7, 16, -5, -2, -3],\n [-8, 14, -15, -16, 6, -16, 16, -6, -8, -10, 7, -9],\n [-15, -11, -5, 2, 12, 2, 14, 12, 4, 16, 4, -7],\n [-13, -5, -7, -14, -9, -12, 5, 6, -13, -1, 5, 4],\n [10, -9, -10, 13, 8, -2, 11, -8, -12, 5, -2, 10],\n [0, 2, 1, -7, -15, -15, 10, -1, 15, 9, 15, -9],\n [13, -12, 15, -9, 5, -16, -6, -11, 3, 3, 1, 1],\n [-10, 15, 9, 7, -5, 9, 13, 1, -13, 6, 12, -8],\n [-5, -5, -1, 2, -5, -16, -16, 2, -15, -4, -13, 2],\n [16, 0, 0, -13, -9, 13, 15, -15, 8, 9, -4, 2],\n [7, -8, 15, -16, 14, 1, -2, 7, -16, -2, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4444389512184", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[13, -4, -12, -6, -11, 8, 12, 16, -10, 1, -7, 6],\n [-3, 2, 13, -8, -12, 15, 11, -7, -13, 11, 7, 10],\n [-16, 4, -10, -2, -3, 13, -16, -14, 16, -6, 6, 8],\n [-13, 15, 3, -1, 3, 7, -9, -13, 13, -16, 10, 14],\n [-4, 5, -10, -1, 10, -14, 1, -3, -16, 2, -14, 5],\n [-16, -10, 12, -10, -8, 15, 15, -1, -12, 15, 2, 16],\n [12, 4, -10, -1, -4, 1, -7, 6, 6, 16, -5, 3],\n [-11, -7, -7, -14, 11, -2, -8, -13, 13, 16, -5, -5],\n [0, 16, 2, 3, 9, 14, -7, -9, -10, 16, 5, -8],\n [2, 15, -4, 5, -2, -2, 15, -3, 13, -3, 11, -12],\n [7, -8, -6, 3, -12, 16, 11, 13, 10, -6, 0, 15],\n [6, 1, 5, 11, -2, 3, 15, 6, -9, 1, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2260690076065627", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[3, -5, -4, 5, 3, 12, -3, 6, 10, 6, 1, 4],\n [-5, -3, 0, 2, -3, 10, -1, -10, 1, -8, 2, 15],\n [-4, 0, -12, -8, 8, -1, -9, -4, 0, -4, -7, -1],\n [5, 2, -8, 10, 9, -8, 3, -2, -6, 4, 0, 0],\n [3, -3, 8, 9, 3, -4, -10, 5, 2, -2, -1, -5],\n [12, 10, -1, -8, -4, 4, -8, -2, -6, 6, 6, -6],\n [-3, -1, -9, 3, -10, -8, 16, -2, -10, -4, 3, -15],\n [6, -10, -4, -2, 5, -2, -2, 5, -10, -5, 5, 14],\n [10, 1, 0, -6, 2, -6, -10, -10, -6, -2, 4, 4],\n [6, -8, -4, 4, -2, 6, -4, -5, -2, 1, 8, 1],\n [1, 2, -7, 0, -1, 6, 3, 5, 4, 8, -14, 2],\n [4, 15, -1, 0, -5, -6, -15, 14, 4, 1, 2, -13]], determine the value at position (4, 10).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-796843381", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (3, 12) of the result:\nA =\n[[11, 1, 6, 3, 0, -8, 5, -4, -11, 3, 0, -8],\n [1, -15, -2, 2, 10, -2, 4, 3, -1, 4, -4, -6],\n [6, -2, -1, 4, -14, 14, 2, -4, 4, -1, 10, -12],\n [3, 2, 4, 16, -4, 3, -4, -11, -2, 6, -12, -14],\n [0, 10, -14, -4, 8, -10, 1, -5, 0, 12, -6, 0],\n [-8, -2, 14, 3, -10, -14, 8, -5, -10, -2, -8, 2],\n [5, 4, 2, -4, 1, 8, -1, -10, -2, -9, 10, 8],\n [-4, 3, -4, -11, -5, -5, -10, -11, -4, -4, -6, 2],\n [-11, -1, 4, -2, 0, -10, -2, -4, 15, -3, 1, -8],\n [3, 4, -1, 6, 12, -2, -9, -4, -3, -10, -8, 6],\n [0, -4, 10, -12, -6, -8, 10, -6, 1, -8, -10, -10],\n [-8, -6, -12, -14, 0, 2, 8, 2, -8, 6, -10, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-584061391066", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[9, 8, 6, 4, 12, 4, 6, 12, 4, 10, -9, -4],\n [8, -1, 14, -8, -6, 2, 1, -5, -10, 10, -3, 12],\n [6, 14, 12, 6, 5, 8, -6, 0, -4, 8, -2, 11],\n [4, -8, 6, -6, 2, 11, -1, 2, 7, -2, -8, -4],\n [12, -6, 5, 2, 12, 4, 4, -3, 0, 2, 7, 8],\n [4, 2, 8, 11, 4, 2, 0, 3, -2, -6, -1, -4],\n [6, 1, -6, -1, 4, 0, 11, 2, -9, 2, -2, -14],\n [12, -5, 0, 2, -3, 3, 2, 14, -4, -12, 1, 14],\n [4, -10, -4, 7, 0, -2, -9, -4, -8, 4, -4, 8],\n [10, 10, 8, -2, 2, -6, 2, -12, 4, -3, 2, -10],\n [-9, -3, -2, -8, 7, -1, -2, 1, -4, 2, -7, 14],\n [-4, 12, 11, -4, 8, -4, -14, 14, 8, -10, 14, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1166929247910", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[12, 1, 13, -4, -6, 8, 9, 3, 8, -7, -4, 15],\n [8, 7, 12, 4, -5, -10, -10, 4, 0, -13, 16, -9],\n [1, -1, 14, 0, 12, 0, 9, -7, -2, 14, -9, -15],\n [-2, 7, 11, -11, -14, -1, -15, -7, -14, -6, 8, -15],\n [-8, 2, 13, -16, 6, -16, -6, -1, 12, -10, -13, -7],\n [7, 13, -7, -10, 16, 3, -11, 5, -1, -1, 6, -14],\n [5, 11, 2, 4, 16, -14, 16, -9, -6, 11, 11, 12],\n [3, 14, 0, -3, 16, 4, 1, -8, 1, -12, -5, -15],\n [-15, 4, -1, 3, 3, -5, 6, 16, -10, -13, -2, -6],\n [-12, -3, -8, 15, 4, 8, 1, -6, 14, 14, 1, 5],\n [0, 6, 11, -10, -15, -15, 5, -16, -6, 10, -3, -9],\n [0, -4, -10, -2, -2, -3, 13, -3, -13, -8, 16, -9]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1372743059958", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-2, 2, -15, 2, -8, -7, -12, 2, -7, 0, 0, -10],\n [2, 5, -6, 12, 3, -2, 10, -2, -12, -2, -6, 2],\n [-15, -6, 16, -4, 0, -8, -2, -2, 11, 0, 8, 6],\n [2, 12, -4, -9, -12, -13, 2, -2, -8, 8, 1, -2],\n [-8, 3, 0, -12, 11, 2, -2, -2, 8, -2, 2, 4],\n [-7, -2, -8, -13, 2, -16, -9, 8, 2, 0, -6, -5],\n [-12, 10, -2, 2, -2, -9, -12, 5, 6, -10, 9, -14],\n [2, -2, -2, -2, -2, 8, 5, 10, -6, 9, 8, 0],\n [-7, -12, 11, -8, 8, 2, 6, -6, 16, 3, -10, -6],\n [0, -2, 0, 8, -2, 0, -10, 9, 3, -7, 10, -6],\n [0, -6, 8, 1, 2, -6, 9, 8, -10, 10, -7, -4],\n [-10, 2, 6, -2, 4, -5, -14, 0, -6, -6, -4, 1]], determine the value at position (5, 8).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11832996824", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (7, 7) of the 8th power of the matrix:\n[[16, 13, -8, -6, -13, -15, 10, 1, -6, -15, 14, 8],\n [2, 15, -10, -3, -16, 16, -1, 14, -15, -5, 2, -2],\n [-1, -1, 11, -6, -11, 10, 0, -6, -4, -4, -9, 8],\n [-3, 4, 3, 3, 10, 16, 14, -1, -10, -1, -13, -14],\n [13, 2, 10, 12, 0, -16, 4, 16, 8, -6, 11, 3],\n [8, -9, 15, 3, 3, -8, -4, 5, 13, 6, -6, -3],\n [-1, 11, 10, -7, 3, 10, 5, 15, 15, -12, -8, -10],\n [1, -16, -11, -3, 7, 0, 0, 4, -4, -3, -13, 7],\n [-11, 3, 15, 6, -3, 5, 0, -15, -10, -3, 3, 11],\n [-4, -10, -14, -12, 16, -8, 10, -2, 1, -13, 4, 1],\n [-10, -15, -1, 11, 13, 14, -9, -10, 1, 4, -13, 15],\n [-1, 1, 5, 10, -5, 15, -10, -7, -7, -10, -14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118847532912", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (5, 4) of the result:\nA =\n[[15, 6, 2, -6, 2, -4, 4, 14, 4, 3, 6, -5],\n [6, -5, 8, -6, -7, 2, -3, 2, -2, 4, 6, -7],\n [2, 8, -4, 8, 6, 10, 0, 11, 6, 3, 9, -9],\n [-6, -6, 8, 5, 0, 1, -10, -4, -4, -4, -1, -2],\n [2, -7, 6, 0, -2, 0, 10, 9, 6, 4, 0, 4],\n [-4, 2, 10, 1, 0, -15, 2, 2, -3, 9, 2, 1],\n [4, -3, 0, -10, 10, 2, -13, 2, 10, 0, -5, 2],\n [14, 2, 11, -4, 9, 2, 2, -2, -4, -8, -12, -14],\n [4, -2, 6, -4, 6, -3, 10, -4, -12, 10, 6, -2],\n [3, 4, 3, -4, 4, 9, 0, -8, 10, -4, 1, -7],\n [6, 6, 9, -1, 0, 2, -5, -12, 6, 1, 15, 4],\n [-5, -7, -9, -2, 4, 1, 2, -14, -2, -7, 4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-748442601", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[10, 11, 7, -13, 11, 3, 12, 16, 13, -14, 2, 4],\n [4, 3, 16, -8, 14, 15, 6, 6, -1, 4, -5, -11],\n [-3, 5, 14, 11, -12, 9, 10, 12, -1, 9, -9, -6],\n [-14, -15, -16, -16, 3, 14, -1, -14, -11, -5, -7, -15],\n [14, -2, 16, -15, 10, 7, 10, 14, -10, 9, 5, -15],\n [-1, 8, -1, 6, -3, -8, 14, -10, -16, 4, 12, -9],\n [-8, 2, 10, 4, 6, -3, -5, -12, -10, -12, 8, 13],\n [-6, -9, 11, -5, 14, 4, -1, 7, 5, -4, -8, -9],\n [6, -7, 0, 12, -15, -6, -9, 4, 16, -10, 8, -8],\n [10, -7, 9, 10, 5, 3, 9, 12, -4, -10, -6, -14],\n [-16, -16, 16, 9, -14, 7, -1, -3, 16, -8, 2, 13],\n [-7, -6, 9, 9, -3, -1, 13, -8, -4, -16, -15, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10069215107858", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-16, -12, 15, -7, 5, 7, 14, 4, -7, 10, 16, -1],\n [-12, 7, 10, -3, -7, -1, 12, -2, 5, -11, 10, 12],\n [11, 2, 16, -7, -6, 13, -3, -1, -10, -13, -1, -8],\n [-8, 15, 9, 2, -13, 14, -4, -7, 3, -11, -9, -2],\n [12, -9, -8, 12, 6, -5, 11, -2, 12, 1, 1, -7],\n [-10, -15, 1, -7, 3, -7, -4, 7, -6, 3, -1, -4],\n [-8, 14, -3, -5, 6, 15, -16, -1, -6, 12, -15, -1],\n [-1, 10, 16, 9, -6, -10, 8, -9, 11, -11, 12, -14],\n [-11, -16, -2, 12, -2, -5, -11, -10, -13, -7, -4, -10],\n [-12, 1, -10, -9, 9, -11, 1, -7, -8, -5, 12, 4],\n [4, 10, -5, 12, 9, 9, 11, -3, 8, -9, -2, 10],\n [-12, -13, 4, 3, -11, 12, -14, 0, 8, 4, -15, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "933587247507714", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[0, 13, 3, 3, -2, 8, -3, 10, -1, 4, -10, -14],\n [13, -6, 6, -12, -5, 2, 10, -1, -8, -10, -2, -2],\n [3, 6, -7, -1, -1, 12, 6, -12, 8, 3, 4, 1],\n [3, -12, -1, 14, 6, -10, -8, -6, -10, -4, 0, 14],\n [-2, -5, -1, 6, -14, -12, 2, 0, -5, 6, 8, -8],\n [8, 2, 12, -10, -12, 14, 10, -4, 6, 8, -8, 0],\n [-3, 10, 6, -8, 2, 10, -2, -5, 6, 10, -2, 6],\n [10, -1, -12, -6, 0, -4, -5, 10, -14, 7, 0, 11],\n [-1, -8, 8, -10, -5, 6, 6, -14, -8, -4, 0, 1],\n [4, -10, 3, -4, 6, 8, 10, 7, -4, 3, 6, -4],\n [-10, -2, 4, 0, 8, -8, -2, 0, 0, 6, 13, 8],\n [-14, -2, 1, 14, -8, 0, 6, 11, 1, -4, 8, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95078846221", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-14, -4, -11, 8, -3, 0, 8, 2, 6, -2, 0, 12],\n [-4, -15, -9, -6, -13, -8, -6, -10, 12, 2, 12, -2],\n [-11, -9, -9, 2, -1, 6, 0, -2, -10, 6, -10, 2],\n [8, -6, 2, -11, 10, 6, -10, -4, 2, -2, 0, -6],\n [-3, -13, -1, 10, -4, -10, 4, -8, -4, 14, -9, 1],\n [0, -8, 6, 6, -10, 5, -13, -6, 6, 2, 12, -5],\n [8, -6, 0, -10, 4, -13, 3, 14, 1, -4, -8, -4],\n [2, -10, -2, -4, -8, -6, 14, -13, 1, 15, -4, 4],\n [6, 12, -10, 2, -4, 6, 1, 1, 0, 2, 4, 11],\n [-2, 2, 6, -2, 14, 2, -4, 15, 2, 8, -6, -6],\n [0, 12, -10, 0, -9, 12, -8, -4, 4, -6, -6, -12],\n [12, -2, 2, -6, 1, -5, -4, 4, 11, -6, -12, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246991730360543", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[15, -5, 8, 8, -9, -11, -13, 9, 14, 4, 7, -7],\n [-10, 9, 11, -15, -3, -10, 0, -2, 5, 15, 9, 6],\n [9, 7, 5, 10, 4, -9, -3, -15, -10, 10, -9, -13],\n [-7, -7, -1, -14, 6, -15, -16, -6, 3, 4, 13, 8],\n [0, 6, 2, 4, -10, -11, -15, -14, -6, 5, -8, 3],\n [-15, -1, 9, 6, -3, 4, 6, -5, -13, 0, 14, 11],\n [-3, 14, 16, -8, 5, 13, -8, -8, -5, 11, -1, -11],\n [-8, 14, -10, 15, 7, 13, 9, 16, 9, 2, -16, 3],\n [-5, 5, -10, 5, 10, -3, -4, 3, -9, 1, -13, 6],\n [6, -13, -15, 5, -16, -7, 14, -3, 2, 12, 13, -6],\n [13, 5, -15, 8, -9, 15, -10, 5, 12, -15, -2, 3],\n [9, -6, 6, -13, -13, -16, 6, 7, 10, -10, -13, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35397489390", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[6, 4, -6, 10, 11, 0, 10, -10, -6, -6, 0, 6],\n [4, 5, -10, 4, -10, -12, -4, 7, -8, 10, 8, -2],\n [-6, -10, -4, 2, 0, 1, 2, -5, -1, 0, 9, -3],\n [10, 4, 2, 5, -10, 0, 9, -10, 0, -2, -8, 8],\n [11, -10, 0, -10, -10, 4, 12, 3, -1, 2, -1, -6],\n [0, -12, 1, 0, 4, -13, 6, -11, 0, 6, 4, -6],\n [10, -4, 2, 9, 12, 6, -8, -4, 10, -3, -14, 9],\n [-10, 7, -5, -10, 3, -11, -4, -6, -2, -14, 4, 6],\n [-6, -8, -1, 0, -1, 0, 10, -2, 15, 14, -13, 2],\n [-6, 10, 0, -2, 2, 6, -3, -14, 14, 5, -8, -4],\n [0, 8, 9, -8, -1, 4, -14, 4, -13, -8, -4, -10],\n [6, -2, -3, 8, -6, -6, 9, 6, 2, -4, -10, -7]], determine the value at position (9, 9).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4062006057086", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[2, 5, 10, -15, 4, 8, 5, -8, 14, -16, -2, 13],\n [-4, -3, 8, 16, 4, 15, -1, -12, 10, 9, 2, 5],\n [-7, -2, 13, -3, 6, -10, 9, 12, -7, 13, 6, -7],\n [9, 1, -16, -14, -7, 12, -12, -12, -2, 9, 9, -13],\n [9, 12, 5, -16, 11, 2, -5, -11, -6, -16, -16, -10],\n [12, -10, 14, -16, 9, 12, -7, -12, 13, -13, -10, 3],\n [11, -10, -6, -3, -9, 7, 14, -15, -9, 10, 7, -11],\n [-6, -1, 12, 13, -10, -1, 14, -6, 2, -3, -2, -9],\n [-5, 7, -4, 1, 12, 3, -14, 14, -10, -8, 0, -10],\n [-12, 7, -2, -15, -2, 4, -3, -15, 8, 10, 2, 13],\n [-7, 14, -4, -4, 10, 2, 2, -2, 11, 11, 16, 5],\n [-8, -11, -15, 9, -12, 6, -11, -16, 16, 9, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52713609392", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (6, 7) of the result:\nA =\n[[0, -1, 13, -15, -13, -4, 0, 6, 12, -8, -2, -15],\n [12, 0, -3, -2, 9, -14, 1, -10, 6, 9, -2, 7],\n [3, 7, -3, 15, 6, 16, -15, -4, 13, -6, -5, 1],\n [3, -4, -11, -7, 16, -13, -13, -5, -12, 8, 8, 16],\n [-2, 3, -5, -3, 5, 7, -5, 3, 11, -6, 5, 16],\n [-3, -4, 8, -1, 13, -16, 11, 14, -15, -15, 16, 13],\n [1, 7, -16, 7, 4, 12, -4, -7, -4, -6, -11, -7],\n [-4, 5, 0, -14, 13, 10, -13, 16, 14, 2, -6, -2],\n [3, -9, -15, 10, -3, 7, 11, 0, 16, 6, -9, 16],\n [2, -5, -13, 14, 4, -5, -10, 1, -6, 16, 5, -9],\n [14, 10, 11, 6, 10, -7, 6, 16, 9, -4, 14, 10],\n [-4, -10, -5, -12, -11, 9, 2, -2, -8, -4, 12, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50672432269938", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -3, -6, -4, 9, 1, 7, 1, 0, -8, 6, -4],\n [-3, -8, -4, 13, 1, 2, 1, -2, 2, 10, 8, 9],\n [-6, -4, -8, 2, -1, 10, 7, 5, -2, -2, 2, 2],\n [-4, 13, 2, -11, 6, -2, -3, 0, 0, 13, 6, 10],\n [9, 1, -1, 6, 13, -3, -11, 10, 0, 12, -6, -6],\n [1, 2, 10, -2, -3, 11, -3, 5, 2, -1, 13, 1],\n [7, 1, 7, -3, -11, -3, 1, -2, -3, 2, 4, 5],\n [1, -2, 5, 0, 10, 5, -2, -12, -3, 0, -2, -6],\n [0, 2, -2, 0, 0, 2, -3, -3, -12, -4, 4, -3],\n [-8, 10, -2, 13, 12, -1, 2, 0, -4, -9, -6, 8],\n [6, 8, 2, 6, -6, 13, 4, -2, 4, -6, -4, -5],\n [-4, 9, 2, 10, -6, 1, 5, -6, -3, 8, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12956152574631", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[0, -7, 9, 11, 11, 6, 3, 0, -9, -2, 6, -3],\n [10, -4, 8, 9, -6, -8, 16, -1, 3, -10, 16, -4],\n [-13, 14, 13, -14, 10, 15, -11, -9, 7, -2, 8, 10],\n [-4, 3, -12, -10, -12, 11, 12, -10, 9, 2, -7, 3],\n [14, -11, -2, 7, 13, -8, -16, -2, -11, -2, -10, 10],\n [-7, 15, 4, -3, -3, -15, 7, -7, -11, -14, 9, -7],\n [4, 8, -15, -16, 7, -7, 5, 15, -1, 13, 14, 13],\n [-12, 7, 10, -3, -4, 3, 11, -11, -8, 5, 6, -9],\n [-16, -10, -5, 0, -1, -13, -8, -8, 10, -5, 6, -8],\n [-4, -15, -15, 12, 5, 4, -11, 11, -1, -16, 6, -9],\n [-9, -16, -6, -9, 14, -9, 7, 10, 12, 1, -8, -3],\n [-4, 7, -3, -9, -5, 14, 4, -13, -6, -10, -5, -12]], determine the value at position (3, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1409439894319", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-14, 15, -5, 13, 16, -14, 9, -14, -3, -3, 0, -2],\n [-5, 13, -10, 14, -3, 11, -5, -11, -13, 16, -12, -8],\n [1, 15, 14, 10, -4, -13, -8, -9, -11, 16, -11, 0],\n [-4, 5, 2, 11, 8, -9, 15, -6, 1, 10, -2, -4],\n [10, 2, -4, -10, -16, 4, -1, 12, 7, 2, 10, -16],\n [10, -3, -6, 6, 3, 9, 1, 13, -13, 2, -12, -15],\n [-7, -6, 5, -9, -14, 1, 5, -6, -15, 5, -2, -9],\n [2, -8, -12, -9, 16, -2, -2, -10, 4, 9, -16, 9],\n [9, 11, -8, 9, -4, -12, 1, 6, 11, -12, 10, 3],\n [-3, -11, 10, -15, -8, -6, -12, -6, -14, 9, -3, -8],\n [2, 0, 7, -3, -7, -10, -4, 14, 12, -11, -9, 8],\n [-12, -7, 6, -16, -4, 9, 2, 9, -15, 2, -5, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884208963012", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-4, -2, 4, 1, -6, 3, -8, 4, -7, 2, -8, -2],\n [-2, -6, 5, -8, -1, 6, 6, 6, 4, -6, -4, 2],\n [4, 5, -13, 2, -8, -2, -4, -6, -4, 0, 6, -7],\n [1, -8, 2, -15, -6, 4, -6, 4, 4, 12, 8, 6],\n [-6, -1, -8, -6, 5, -1, 2, 12, 8, -6, 6, 16],\n [3, 6, -2, 4, -1, -15, 2, -1, 8, -2, -10, 12],\n [-8, 6, -4, -6, 2, 2, 4, -9, 0, -8, -7, 4],\n [4, 6, -6, 4, 12, -1, -9, -16, 4, 6, -4, -8],\n [-7, 4, -4, 4, 8, 8, 0, 4, 16, 4, -4, -3],\n [2, -6, 0, 12, -6, -2, -8, 6, 4, -11, -16, 2],\n [-8, -4, 6, 8, 6, -10, -7, -4, -4, -16, -2, 2],\n [-2, 2, -7, 6, 16, 12, 4, -8, -3, 2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7982628173906", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[16, 1, 12, -9, -15, -13, -2, -9, 13, 7, -5, -3],\n [15, -3, 11, 3, -4, 0, 13, 0, 15, 2, -8, 9],\n [-16, 2, -5, 11, 14, -4, -6, -5, 6, 12, -8, -3],\n [15, -14, -10, -11, 10, 11, 6, -7, 0, -2, -3, -6],\n [12, 1, 9, 8, -16, -14, 2, -6, 11, 1, -3, -4],\n [2, 15, 16, -11, 13, -7, 13, -8, -11, -11, 3, 0],\n [-15, -15, -7, -16, 3, 15, 0, 5, -12, -16, 14, 1],\n [-12, 8, -10, -3, -10, 13, 0, -4, 7, -5, 1, 6],\n [5, 8, 8, 4, 12, -9, -12, -15, 6, -15, 5, 4],\n [0, 14, 8, -10, 8, 1, 15, -9, -3, -11, 6, -2],\n [5, -14, -8, -12, -5, 12, -16, 16, 4, 4, 10, -15],\n [-9, -5, 5, -8, 12, -14, 5, -13, 12, -4, 7, -15]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25503918403594", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[-14, -3, 6, 0, -5, -6, -12, 6, 9, -1, -5, -2],\n [-3, -2, 12, 2, -6, -10, -5, 2, -4, 0, 7, 1],\n [6, 12, 13, 0, 10, 4, 9, 12, 8, 4, 15, -2],\n [0, 2, 0, -1, 0, -7, 0, -8, 9, -3, -2, 6],\n [-5, -6, 10, 0, -15, -6, 2, 8, 0, -6, 8, -14],\n [-6, -10, 4, -7, -6, 7, 2, 2, 10, -6, 0, 5],\n [-12, -5, 9, 0, 2, 2, -8, 10, -11, 6, 8, 0],\n [6, 2, 12, -8, 8, 2, 10, 0, -10, -13, -11, 2],\n [9, -4, 8, 9, 0, 10, -11, -10, -4, 2, -6, -12],\n [-1, 0, 4, -3, -6, -6, 6, -13, 2, -5, -6, -8],\n [-5, 7, 15, -2, 8, 0, 8, -11, -6, -6, -13, 2],\n [-2, 1, -2, 6, -14, 5, 0, 2, -12, -8, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23687187703193", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 8) of the 7th power of the matrix:\n[[11, 3, 14, 4, 0, 2, -6, -3, -15, -4, 2, 2],\n [3, 12, 4, 8, 3, -6, -2, 0, 6, 2, -5, -12],\n [14, 4, 10, -2, -2, 10, -10, 6, 8, -14, 2, 7],\n [4, 8, -2, -6, -5, 8, 6, 6, -2, -10, 5, -1],\n [0, 3, -2, -5, -14, -1, -4, 8, -14, -8, -12, 12],\n [2, -6, 10, 8, -1, 14, 4, -13, -11, 0, 2, 3],\n [-6, -2, -10, 6, -4, 4, -9, 0, -2, 6, -10, 4],\n [-3, 0, 6, 6, 8, -13, 0, 1, -8, 3, -7, 8],\n [-15, 6, 8, -2, -14, -11, -2, -8, -14, 2, 4, 5],\n [-4, 2, -14, -10, -8, 0, 6, 3, 2, 7, 12, 8],\n [2, -5, 2, 5, -12, 2, -10, -7, 4, 12, -4, -2],\n [2, -12, 7, -1, 12, 3, 4, 8, 5, 8, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13946293778", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[-13, 6, 11, 6, 12, 0, 2, 6, 14, -11, 4, 5],\n [6, -2, 6, 14, 0, -2, 4, -7, -3, 8, -6, 1],\n [11, 6, 8, 6, -3, 8, -2, -10, 4, -2, -8, 2],\n [6, 14, 6, -1, -11, -16, 3, -5, -2, -14, 5, 7],\n [12, 0, -3, -11, 7, -9, -4, 5, -4, 10, 0, 6],\n [0, -2, 8, -16, -9, -9, -3, 6, -4, 1, 3, 1],\n [2, 4, -2, 3, -4, -3, 13, -2, 3, 4, -12, 5],\n [6, -7, -10, -5, 5, 6, -2, 8, 0, 0, 0, 0],\n [14, -3, 4, -2, -4, -4, 3, 0, 16, -2, 8, -9],\n [-11, 8, -2, -14, 10, 1, 4, 0, -2, -12, 7, 6],\n [4, -6, -8, 5, 0, 3, -12, 0, 8, 7, 2, -2],\n [5, 1, 2, 7, 6, 1, 5, 0, -9, 6, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5988434619", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[7, 10, -8, 6, -3, 9, -9, 14, -9, 13, -1, 14],\n [14, -3, 8, -16, 12, 11, 12, -7, -9, 13, 13, -11],\n [-2, 7, -4, -8, 3, -4, 10, 1, -9, -9, 7, 10],\n [3, -9, 7, -5, 16, -3, 4, 16, -16, -11, -3, 11],\n [8, 6, 0, 14, 11, -10, 1, -1, -11, -15, 3, 6],\n [-15, 8, -11, 12, -8, -8, -3, -2, -1, -8, 11, -13],\n [-5, 5, -16, -13, 16, 3, -15, -7, -9, -3, 10, -4],\n [-4, 12, -9, 7, -12, 11, -15, 4, 10, -9, -5, -7],\n [-10, -7, 12, 8, 9, 9, -11, 5, -5, -10, 9, -4],\n [1, -12, 14, 0, -2, 5, -12, -1, 16, -13, 16, 11],\n [-6, -12, -10, 7, -13, -5, -13, 8, -14, 0, 9, -8],\n [-4, -12, -12, -5, 11, -7, -16, 11, -15, 6, -12, 16]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34485441689772", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[14, 5, -10, 4, 9, -6, 5, -6, -7, -3, 8, 6],\n [5, -6, 4, -12, -4, 4, 4, 7, 0, -4, -4, 6],\n [-10, 4, -4, 6, -16, -8, 6, 8, 2, 6, -6, 4],\n [4, -12, 6, 12, 6, 2, 6, -2, 6, 1, -4, -8],\n [9, -4, -16, 6, 9, 8, -9, 0, -12, 6, 4, -2],\n [-6, 4, -8, 2, 8, -13, -12, 6, -10, 4, 14, -8],\n [5, 4, 6, 6, -9, -12, -9, 0, -8, -7, -4, 10],\n [-6, 7, 8, -2, 0, 6, 0, -6, 6, 0, 0, 0],\n [-7, 0, 2, 6, -12, -10, -8, 6, -8, 15, -2, 13],\n [-3, -4, 6, 1, 6, 4, -7, 0, 15, 13, -3, 0],\n [8, -4, -6, -4, 4, 14, -4, 0, -2, -3, -6, -6],\n [6, 6, 4, -8, -2, -8, 10, 0, 13, 0, -6, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192366135399235", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[5, 0, -8, -8, -2, -3, -8, -8, 16, 14, -7, -7],\n [-12, 1, 16, 1, -5, 8, 10, -8, -4, 5, -15, -2],\n [6, -4, 3, -4, 10, 0, 14, 9, 5, 15, 5, 11],\n [-16, -13, -1, 6, -3, -14, -16, -1, -9, -16, 4, -15],\n [-5, -3, 5, 3, 0, -10, 4, 5, 5, 4, -4, -11],\n [8, 14, 8, 15, 12, -5, -1, -8, -4, -5, 9, -2],\n [-13, -7, -5, 5, 13, -2, -12, -13, 9, 2, -3, 10],\n [9, 6, -15, -4, -5, -14, -13, 14, 11, -6, -1, 12],\n [-2, 4, -3, -1, 10, 11, -3, -7, -8, 11, -3, 2],\n [-4, -14, -10, 11, -3, 5, 14, -16, -5, 7, 13, 10],\n [-1, 4, -13, -15, 4, -10, -10, -15, -5, -16, -14, -16],\n [-1, -9, 4, -12, 14, 9, -16, 6, -4, 15, -12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54418679175075", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[11, -10, -6, 10, -4, -8, 14, -2, 4, 8, -14, 5],\n [-10, 5, 5, 2, -3, 2, 14, -12, 2, -6, -2, 0],\n [-6, 5, -14, 11, 4, -9, 16, -10, 4, -2, -4, 6],\n [10, 2, 11, 0, -2, -9, 8, 10, 6, 5, 6, -2],\n [-4, -3, 4, -2, -10, 2, 8, -4, 2, 4, 5, -4],\n [-8, 2, -9, -9, 2, 3, 7, 4, -7, 4, -6, -4],\n [14, 14, 16, 8, 8, 7, 9, -3, 6, -2, 2, 14],\n [-2, -12, -10, 10, -4, 4, -3, 10, -4, -8, -8, -6],\n [4, 2, 4, 6, 2, -7, 6, -4, 14, -4, -4, 6],\n [8, -6, -2, 5, 4, 4, -2, -8, -4, 10, -2, -16],\n [-14, -2, -4, 6, 5, -6, 2, -8, -4, -2, 6, 6],\n [5, 0, 6, -2, -4, -4, 14, -6, 6, -16, 6, -9]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96183752923143", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-5, 8, -2, 8, -4, 3, 1, 2, -13, 4, -4, -2],\n [8, 12, -6, -1, 16, -9, -10, 12, -7, 10, 4, -2],\n [-2, -6, 14, -1, 11, 9, 0, -2, -2, 2, -4, 4],\n [8, -1, -1, 5, -3, 4, -8, -2, 6, 5, 0, -2],\n [-4, 16, 11, -3, -4, 8, -4, -12, 6, 4, 12, 0],\n [3, -9, 9, 4, 8, 14, -2, 4, 10, 4, -7, 8],\n [1, -10, 0, -8, -4, -2, 0, -2, 2, -4, -2, -10],\n [2, 12, -2, -2, -12, 4, -2, 10, -3, 6, 10, 0],\n [-13, -7, -2, 6, 6, 10, 2, -3, -1, 4, -8, 4],\n [4, 10, 2, 5, 4, 4, -4, 6, 4, -15, 4, 2],\n [-4, 4, -4, 0, 12, -7, -2, 10, -8, 4, -5, 4],\n [-2, -2, 4, -2, 0, 8, -10, 0, 4, 2, 4, -4]], determine the value at position (12, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-437823650800", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-2, -15, 16, 14, -16, -2, -2, 3, -10, -5, -4, -12],\n [-11, -12, -11, -11, -6, 10, -1, -14, 5, 15, 8, 1],\n [2, 13, 10, 1, -4, 14, -14, 14, 7, 5, 16, -2],\n [-3, -2, 12, 9, 5, -13, 16, -12, 11, 15, 12, 7],\n [13, -8, 1, -6, 5, 6, 12, -4, 15, -7, -11, 4],\n [-14, 4, 3, -14, -12, -6, 0, -13, -9, 5, 15, 10],\n [-11, 14, -13, 13, 16, 14, 11, 8, 0, 14, 0, -7],\n [5, 14, 13, 3, -3, -2, 2, 14, 6, -3, 5, 13],\n [-9, 14, -1, 7, 4, -9, 1, -11, -3, 13, -3, -10],\n [-13, 2, 8, 8, 2, 13, 13, -2, 12, 16, 6, 6],\n [13, -1, 16, 10, -7, 3, -13, 3, -2, -2, 0, 3],\n [0, -5, -6, 13, 9, 8, 0, -16, 9, -14, -6, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157838678809648", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[11, 14, -13, 11, 10, 14, -2, 12, -4, 6, -1, 0],\n [14, -15, 2, 2, -6, -1, 2, 1, -4, -16, -5, 10],\n [-13, 2, -13, 7, -6, -14, 10, 4, -6, 3, 4, 6],\n [11, 2, 7, 7, -6, 1, 0, -2, 11, 10, 6, 12],\n [10, -6, -6, -6, 10, 8, -5, -7, 4, 7, 6, 0],\n [14, -1, -14, 1, 8, 5, 2, 4, 4, -3, -5, -2],\n [-2, 2, 10, 0, -5, 2, 11, 12, 3, -6, 5, 4],\n [12, 1, 4, -2, -7, 4, 12, 10, -3, 6, 12, 11],\n [-4, -4, -6, 11, 4, 4, 3, -3, 5, -2, -2, 4],\n [6, -16, 3, 10, 7, -3, -6, 6, -2, 3, -3, 2],\n [-1, -5, 4, 6, 6, -5, 5, 12, -2, -3, 14, 9],\n [0, 10, 6, 12, 0, -2, 4, 11, 4, 2, 9, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138005323909096", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-6, -9, -13, -5, 15, -5, 8, 7, 3, -10, 15, -11],\n [2, 1, -5, -7, 6, 1, 4, -4, -15, -15, 1, -7],\n [15, 8, 7, 4, 9, -12, -11, 15, 15, -9, 1, -16],\n [7, 0, 1, 3, 9, 13, 10, 6, 9, -12, -3, 15],\n [-13, 5, 16, -4, -9, -8, 11, -16, -2, -10, 0, -5],\n [12, -3, -4, 15, 8, 10, 7, -4, 12, 13, 10, -10],\n [-4, -10, -11, 5, -3, 4, 1, 12, 9, 11, -6, 0],\n [-5, 11, 7, 14, 12, -12, -4, -8, 14, 6, -1, 3],\n [-9, 0, 2, 10, -2, 7, -12, -8, 8, -2, 10, -11],\n [-1, 12, 16, 1, -16, -4, -11, 3, 1, -10, -1, -3],\n [-3, -13, -3, -16, 16, -9, 10, 16, 13, 3, -11, -16],\n [-8, 15, 16, 1, 2, 16, -12, -5, -16, -11, 0, -9]], determine the value at position (1, 12).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21759290949682", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-12, 11, -2, 11, 7, 9, -9, -1, -10, 0, 14, -10],\n [-14, 1, 10, 0, 15, -6, -5, -5, -5, 3, -14, 14],\n [-12, 3, -16, -6, 14, 7, -2, -15, 12, 5, -6, 14],\n [3, -2, 0, -13, 14, 12, 13, -12, 12, 3, -8, -3],\n [1, 0, 0, -11, 4, -7, 11, 4, -16, -13, -11, 8],\n [-16, -14, 7, 6, 9, -12, -3, 7, 16, 0, 16, -2],\n [-3, -16, -3, -5, 15, -15, 16, 1, -1, 8, 9, -12],\n [-1, -1, -6, -9, -14, -1, -10, 11, -15, 14, -6, -6],\n [-16, 13, 13, 16, -5, -7, -13, 16, 14, 14, -12, 4],\n [1, 1, -13, 3, 3, 11, -4, 1, 16, -8, 9, -16],\n [8, 7, 13, -5, -2, 3, 10, 12, -15, -2, -7, 9],\n [-9, -16, -2, -13, -14, -15, 2, 2, 2, 3, -15, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104761941805843", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[5, 2, 6, 2, 8, 0, -4, 3, 1, -4, -3, 4],\n [2, -9, -10, -2, 4, -10, 4, -1, 6, 12, 6, -6],\n [6, -10, 13, -8, -6, 6, -8, 0, -2, 5, -14, -4],\n [2, -2, -8, 15, -4, -8, -10, 2, 1, 8, -2, 3],\n [8, 4, -6, -4, -1, -2, -4, -5, -9, 4, 2, 1],\n [0, -10, 6, -8, -2, -9, 2, 10, -10, -5, 10, -9],\n [-4, 4, -8, -10, -4, 2, 2, 13, -8, 0, 4, 3],\n [3, -1, 0, 2, -5, 10, 13, -12, -3, 8, -1, -12],\n [1, 6, -2, 1, -9, -10, -8, -3, -16, -9, -2, -1],\n [-4, 12, 5, 8, 4, -5, 0, 8, -9, -10, -6, -10],\n [-3, 6, -14, -2, 2, 10, 4, -1, -2, -6, 4, 0],\n [4, -6, -4, 3, 1, -9, 3, -12, -1, -10, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1110471176813948", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[9, 2, 0, -4, 11, 6, -10, 0, 8, 1, -2, 10],\n [2, 15, 0, 8, 6, -2, -5, -4, 0, 3, -3, -16],\n [0, 0, -3, -10, -2, -5, 0, -10, 6, 7, -7, -8],\n [-4, 8, -10, -7, 4, 12, -4, 5, 8, 2, -2, 7],\n [11, 6, -2, 4, -6, 4, -2, 6, 4, -8, -5, 0],\n [6, -2, -5, 12, 4, 7, 2, 0, 2, -8, -2, 4],\n [-10, -5, 0, -4, -2, 2, 3, 6, -7, 2, 6, 0],\n [0, -4, -10, 5, 6, 0, 6, 7, -6, -10, 15, 0],\n [8, 0, 6, 8, 4, 2, -7, -6, -1, 2, 7, 4],\n [1, 3, 7, 2, -8, -8, 2, -10, 2, -11, -2, 2],\n [-2, -3, -7, -2, -5, -2, 6, 15, 7, -2, -6, -6],\n [10, -16, -8, 7, 0, 4, 0, 0, 4, 2, -6, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "835414395153", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-6, -6, 2, -4, 4, -9, -8, -4, 4, -14, -2, -3],\n [-6, -9, -5, -10, 4, 5, -3, 10, -4, -8, -4, 2],\n [2, -5, 1, 0, 6, 0, 4, -6, 0, 2, -2, 3],\n [-4, -10, 0, 2, 4, -6, -2, 5, -2, 1, -1, 12],\n [4, 4, 6, 4, -12, 3, -11, -2, 9, 10, -14, -4],\n [-9, 5, 0, -6, 3, -12, -8, -8, -8, -4, 2, 2],\n [-8, -3, 4, -2, -11, -8, -14, -8, 4, 4, 6, 2],\n [-4, 10, -6, 5, -2, -8, -8, 6, 4, 2, -9, -2],\n [4, -4, 0, -2, 9, -8, 4, 4, 6, -1, -2, 1],\n [-14, -8, 2, 1, 10, -4, 4, 2, -1, -7, 3, 6],\n [-2, -4, -2, -1, -14, 2, 6, -9, -2, 3, 5, -6],\n [-3, 2, 3, 12, -4, 2, 2, -2, 1, 6, -6, -13]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8903122116027", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-14, -4, -2, 14, 12, -2, -6, 0, -2, -8, -6, 8],\n [-4, -7, -10, -8, 6, 8, 3, -6, 6, -2, -3, 8],\n [-2, -10, 16, 2, -6, 5, 0, -10, 15, 4, -3, 4],\n [14, -8, 2, -3, -5, 10, -4, -13, -8, -4, -3, 12],\n [12, 6, -6, -5, -12, -8, 0, -6, -12, -1, 3, -2],\n [-2, 8, 5, 10, -8, 8, 1, 11, 7, 6, -6, -2],\n [-6, 3, 0, -4, 0, 1, -12, 3, 2, -1, 8, 4],\n [0, -6, -10, -13, -6, 11, 3, 8, 0, -4, 4, 6],\n [-2, 6, 15, -8, -12, 7, 2, 0, -10, 1, 10, -6],\n [-8, -2, 4, -4, -1, 6, -1, -4, 1, -7, -5, -2],\n [-6, -3, -3, -3, 3, -6, 8, 4, 10, -5, -9, -5],\n [8, 8, 4, 12, -2, -2, 4, 6, -6, -2, -5, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3785013707837221", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (9, 10) of the result:\nA =\n[[-13, -5, 10, -3, -1, 12, -5, -2, -16, 11, -9, 15],\n [8, -5, -11, 14, -8, 8, 3, -2, 9, -6, 10, 4],\n [-11, -6, 14, -6, -9, 2, 15, 9, -1, 16, -7, 6],\n [-13, 2, 2, -3, 16, 1, -9, -7, 14, 8, 8, -14],\n [-2, 15, 4, 16, 10, -3, -7, 7, -7, 14, 11, -13],\n [2, -1, 15, -11, -7, -1, -15, -9, -12, 13, -9, 12],\n [-14, -4, 10, -5, -11, -2, -9, 7, 15, 14, -14, -4],\n [-2, 9, -5, 8, 11, 2, -8, 15, -14, -12, 1, -2],\n [8, 1, -10, 5, 7, 5, 10, -15, -6, 9, -10, 2],\n [2, -7, 14, -16, 0, -7, 4, 0, -14, 5, 13, -12],\n [-14, -16, 0, 5, 10, 16, 4, -16, -13, -11, 11, -5],\n [6, -5, 16, 4, 10, 15, -16, 15, -14, 16, -16, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-140490519652", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 6) of the 7th power of the matrix:\n[[2, 1, 15, -11, 0, -5, -15, 3, 3, 15, -14, 9],\n [-5, -14, 11, -8, 9, -11, -12, -8, 11, 9, -16, -13],\n [-4, 4, 1, 3, -13, 15, 10, 8, -10, 13, 6, 12],\n [4, 16, 1, 10, -3, 14, -9, -14, -6, 6, -12, 13],\n [-1, -3, -10, 16, -15, -12, -2, -15, 7, 12, 12, 4],\n [8, 5, 2, -4, 16, 16, -5, 6, 12, 12, -16, 7],\n [-12, -12, -4, 15, 10, 7, -14, -16, 12, 5, -12, 4],\n [-5, 11, -6, -2, -1, -2, 15, -1, 16, 3, 15, -7],\n [-1, -12, 3, 10, 3, -4, 2, -2, 10, 0, -7, -12],\n [10, 11, -13, -10, -9, -2, 12, -8, 3, -16, -10, -7],\n [-11, 8, -5, -3, -6, -5, 2, 11, 2, 12, 6, -1],\n [4, -16, 8, -1, 16, 8, 5, -14, -14, -6, -12, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6912057411", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-1, 15, 12, -11, 5, -8, -7, -3, 3, -12, -10, -3],\n [-2, 0, 3, -1, 4, -6, -13, 8, -15, -15, 10, 14],\n [-9, -9, -12, 5, -12, -11, -10, 1, 8, -14, 8, 4],\n [14, -1, 5, 12, -5, -16, 9, -7, 8, 8, -13, 1],\n [-9, -10, 0, -11, 4, -15, -4, 15, -4, 12, -12, 9],\n [15, 1, 0, 3, -2, -2, -13, -8, 16, -7, -16, -8],\n [5, 9, 16, -7, 2, -13, 2, -10, -5, 10, 15, 10],\n [4, -12, 2, -10, -3, -8, -8, -12, -8, 13, -3, -14],\n [7, 11, -6, 0, 1, 0, 8, -3, 4, -6, 10, -13],\n [-10, 1, 2, 1, -2, -6, -5, -5, -1, 11, 13, -1],\n [-1, 3, -8, -12, 14, 1, 5, -15, -14, 11, -6, -7],\n [3, 14, 5, 1, -5, -2, 11, -2, 0, -6, 9, 12]], determine the value at position (11, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5704791770287", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[8, -11, 2, -6, 8, -7, 2, 0, -6, 14, -8, -2],\n [-11, -5, 14, 12, -2, 0, -6, -7, -2, -12, 11, -12],\n [2, 14, -15, 0, -2, -8, -3, 7, 7, 0, 0, 12],\n [-6, 12, 0, -2, -5, -8, 10, 6, 6, -3, 6, 2],\n [8, -2, -2, -5, -13, -6, 10, 0, 0, 8, 0, -12],\n [-7, 0, -8, -8, -6, -1, -4, -4, -4, 2, 8, 2],\n [2, -6, -3, 10, 10, -4, 14, 8, 2, -3, 2, 12],\n [0, -7, 7, 6, 0, -4, 8, 7, 6, -4, 12, 4],\n [-6, -2, 7, 6, 0, -4, 2, 6, -1, 2, -6, -5],\n [14, -12, 0, -3, 8, 2, -3, -4, 2, 3, -2, 6],\n [-8, 11, 0, 6, 0, 8, 2, 12, -6, -2, 14, -2],\n [-2, -12, 12, 2, -12, 2, 12, 4, -5, 6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12921802271895", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[7, -13, 0, 7, -16, -15, -11, -3, 4, 8, -9, 10],\n [-3, -13, -9, 10, 2, 13, 11, 10, -14, 11, 2, 10],\n [6, 2, -4, 13, -9, 12, -11, 0, 12, -15, 16, 14],\n [-5, 14, 9, 15, -14, 3, -15, -4, 12, -11, -9, 9],\n [-7, -16, -15, -16, -13, -14, 7, 0, 10, 8, 3, 13],\n [-11, -10, 10, -12, 9, -6, 6, -14, -2, 8, -1, 15],\n [9, -12, -7, -6, 16, 11, -1, -15, 12, -15, 5, -6],\n [15, -12, 10, -5, -9, -14, 15, 5, 11, 9, 4, -6],\n [10, -10, -8, 9, -11, -5, -16, -13, -9, -15, -5, -9],\n [14, 4, 14, 15, 3, 2, 13, -8, 3, 1, -4, 13],\n [12, 13, -12, -13, 14, 16, -16, 2, -2, -15, -13, -14],\n [6, -11, 13, 6, -2, 0, -8, -15, 12, 14, 15, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38480808393844", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[13, 12, 3, 6, -4, -4, 5, 0, 4, -6, 6, 3],\n [12, -7, 6, -14, 4, 2, -6, 2, 6, -4, -10, 2],\n [3, 6, 2, 9, 0, -5, 5, 3, -4, -11, -6, 7],\n [6, -14, 9, 10, 8, -5, -2, 7, 4, -6, 14, 12],\n [-4, 4, 0, 8, 1, -10, 4, -2, -15, -10, 0, 10],\n [-4, 2, -5, -5, -10, 13, 6, 4, 0, -4, -8, -1],\n [5, -6, 5, -2, 4, 6, 5, -9, 8, -8, -8, 10],\n [0, 2, 3, 7, -2, 4, -9, -1, 8, 0, 12, 10],\n [4, 6, -4, 4, -15, 0, 8, 8, 15, -8, 0, 10],\n [-6, -4, -11, -6, -10, -4, -8, 0, -8, -11, -8, -4],\n [6, -10, -6, 14, 0, -8, -8, 12, 0, -8, 1, 8],\n [3, 2, 7, 12, 10, -1, 10, 10, 10, -4, 8, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "292115867174821", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[16, -13, -9, -6, -15, 5, -13, 8, -2, -5, 16, 15],\n [-11, -16, 3, -12, -15, -3, 0, 1, 0, 14, 14, 2],\n [15, 0, 7, -13, -12, -16, 9, -14, 6, -4, 5, 14],\n [-9, 13, -5, 5, -2, 13, 7, 8, -15, -16, 3, 9],\n [-9, 2, 14, -2, -15, -15, 12, 16, -7, 4, 4, -4],\n [-1, 2, 7, 6, -13, 14, -9, 8, 6, -6, 11, 6],\n [-6, -9, -9, 0, 5, -9, -16, -3, -12, 10, 6, -5],\n [13, -9, -15, -12, -4, 0, -2, -5, -14, -7, -15, -2],\n [-10, 3, -9, 9, -9, 13, 3, 14, 12, 13, 14, -13],\n [12, 13, 5, 15, -5, 13, -12, -15, -11, -7, -1, 5],\n [-3, -1, -16, -1, 3, 15, -15, 5, -12, -15, 15, -6],\n [9, 14, -2, -5, 9, -6, 5, 11, 5, 4, -7, 8]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1149905726863", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, -8, -13, -2, 12, -7, 16, -10, 0, -13, -7, -16],\n [3, -10, -8, 15, 11, 11, -15, -13, 0, -11, -9, -5],\n [2, 12, 15, 11, -12, -5, -12, 16, 14, 8, -10, 8],\n [12, -6, 4, 6, -11, 6, -7, -12, 1, 4, -2, -5],\n [-10, 11, -10, 1, 3, 9, -3, -2, -1, 6, 3, 2],\n [-7, -9, 4, -16, 1, 6, -1, 8, -12, -6, -11, -3],\n [9, 10, -3, 12, 1, 1, -3, -10, 11, -12, -2, -12],\n [-13, 0, -16, -7, 16, 10, 7, 11, 2, -15, -16, 8],\n [-14, -10, 8, -2, -13, -15, -11, 4, 5, 12, -3, -10],\n [-12, -2, -3, 11, 9, -11, -9, -7, 5, -7, 2, 15],\n [-3, 7, 1, 10, 1, -13, 12, 14, -14, 0, -14, -10],\n [14, 10, -14, -4, 1, 5, -5, 2, 13, 14, 0, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44091802490103", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[-13, -12, -10, -1, 9, 3, -13, 15, -8, -14, 15, -15],\n [11, -12, -3, -7, 15, 11, -16, -14, 8, 13, 13, -2],\n [14, 8, 6, 9, 5, -1, 0, 10, 0, 0, 3, -15],\n [6, 11, 9, -5, 0, 11, -6, -6, -2, 9, 12, 9],\n [6, -6, -13, -7, 16, -13, -9, 5, 4, 13, 13, -1],\n [-15, 6, 13, 11, -12, -8, 2, -10, 9, -3, 15, 13],\n [-7, -15, -12, -11, 11, -2, 12, 13, 14, 14, 9, -8],\n [-10, -4, 3, 11, 13, 10, 13, 7, 13, -16, 7, 3],\n [-9, 0, 14, -13, 16, 12, 2, -3, 8, -16, 5, -13],\n [16, -1, -5, -10, -13, -5, -10, -2, -11, 0, 0, -13],\n [-10, -10, 16, 6, 11, 11, 16, 5, 5, -13, 7, -1],\n [-4, -2, 16, 13, 6, -12, -12, -13, -1, -6, 10, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640967660173127", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[16, -1, -9, -14, 2, -10, -2, 1, 1, -12, -9, 4],\n [-1, -12, -2, -6, -6, -4, -1, 0, -12, 11, 4, 10],\n [-9, -2, -10, -8, 0, 9, 3, 1, -3, 9, 2, -10],\n [-14, -6, -8, 2, 0, -12, 3, 0, 2, -1, -2, 2],\n [2, -6, 0, 0, 8, 4, -4, -2, 11, 6, -3, 0],\n [-10, -4, 9, -12, 4, 2, -12, 10, -6, -6, 1, -2],\n [-2, -1, 3, 3, -4, -12, -8, 12, 0, 14, 0, -1],\n [1, 0, 1, 0, -2, 10, 12, -7, -10, -8, -14, -6],\n [1, -12, -3, 2, 11, -6, 0, -10, 13, -6, -1, -4],\n [-12, 11, 9, -1, 6, -6, 14, -8, -6, 12, 6, 6],\n [-9, 4, 2, -2, -3, 1, 0, -14, -1, 6, 10, 0],\n [4, 10, -10, 2, 0, -2, -1, -6, -4, 6, 0, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83805417012942", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-16, -2, 4, -2, 2, -6, 3, 6, 13, -13, -2, -10],\n [-2, 6, -12, 5, 4, -1, -4, 7, -6, 2, 14, -1],\n [4, -12, 0, -10, -10, 4, 1, 9, -5, -11, -4, -1],\n [-2, 5, -10, -6, -4, -1, -12, -2, -14, -6, -4, 6],\n [2, 4, -10, -4, -5, -2, 4, 2, 8, 14, 2, 2],\n [-6, -1, 4, -1, -2, -14, 0, 5, -4, 2, 6, -9],\n [3, -4, 1, -12, 4, 0, 7, 2, -8, 8, -13, 0],\n [6, 7, 9, -2, 2, 5, 2, -11, 12, 2, -4, -8],\n [13, -6, -5, -14, 8, -4, -8, 12, 11, 9, 5, 4],\n [-13, 2, -11, -6, 14, 2, 8, 2, 9, 10, 6, 0],\n [-2, 14, -4, -4, 2, 6, -13, -4, 5, 6, -14, -5],\n [-10, -1, -1, 6, 2, -9, 0, -8, 4, 0, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65168892462886", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (8, 6) of the result:\nA =\n[[4, -1, -2, -8, -11, -13, -3, -11, -6, -11, -10, 4],\n [-1, 9, -2, 3, 4, -5, -13, 4, 3, -2, -2, -2],\n [-2, -2, -15, 2, 14, 9, -5, -2, 12, -13, 3, -10],\n [-8, 3, 2, 13, 2, 6, -6, -8, -12, 2, -4, -4],\n [-11, 4, 14, 2, 6, -10, -12, -4, 2, -2, 0, -8],\n [-13, -5, 9, 6, -10, -16, -2, -10, 0, -4, 12, -4],\n [-3, -13, -5, -6, -12, -2, -7, 0, -1, -13, 10, 2],\n [-11, 4, -2, -8, -4, -10, 0, -11, -4, 6, 5, -8],\n [-6, 3, 12, -12, 2, 0, -1, -4, 15, -10, -8, 0],\n [-11, -2, -13, 2, -2, -4, -13, 6, -10, -2, -4, -13],\n [-10, -2, 3, -4, 0, 12, 10, 5, -8, -4, 3, 10],\n [4, -2, -10, -4, -8, -4, 2, -8, 0, -13, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-188959982203738", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 1) of the matrix A^7 where A is:\n[[12, -5, 3, 0, 2, 14, 10, 6, 0, -2, 8, -5],\n [-5, 6, 14, 4, 10, -1, -6, -2, -4, 7, -2, 0],\n [3, 14, 10, -8, -6, 7, -12, 4, -2, -4, 10, -1],\n [0, 4, -8, 11, -11, -3, -6, -5, -10, -2, 4, -10],\n [2, 10, -6, -11, -1, -3, -4, -5, -4, -3, 2, 0],\n [14, -1, 7, -3, -3, -2, -2, 14, 6, 6, -12, 8],\n [10, -6, -12, -6, -4, -2, -10, -4, 10, 6, -8, -8],\n [6, -2, 4, -5, -5, 14, -4, -2, -8, -1, -6, 1],\n [0, -4, -2, -10, -4, 6, 10, -8, 13, -4, -6, -9],\n [-2, 7, -4, -2, -3, 6, 6, -1, -4, 6, 14, -6],\n [8, -2, 10, 4, 2, -12, -8, -6, -6, 14, -4, 2],\n [-5, 0, -1, -10, 0, 8, -8, 1, -9, -6, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2658351939", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-11, -16, 3, 1, -8, 15, 0, 2, -4, -16, -7, 9],\n [16, -9, 3, -15, 11, 12, 8, 9, -9, 13, -16, 11],\n [13, -4, 4, 4, -6, 10, -12, -4, -5, 16, 13, -14],\n [6, 14, -11, -6, -11, 1, -16, 1, -6, -11, -12, 7],\n [-15, -15, -5, -15, 12, 16, -12, 16, -4, 14, 2, 8],\n [16, -14, 7, -14, -10, -4, 7, 13, -12, 6, 10, 1],\n [3, -11, 13, -11, 0, -2, 0, 8, 13, 0, -12, -6],\n [11, 3, -15, 16, -7, 2, 8, 10, 6, -9, -15, 8],\n [-8, 8, 12, 5, -3, -6, -4, 16, -14, 15, -12, -5],\n [2, 10, -7, 11, 16, 0, -6, 1, 14, 11, -16, 14],\n [10, -5, -5, 10, 10, 0, 8, 13, -7, -2, 2, -13],\n [-2, -2, 16, -4, 0, 2, -4, -11, 13, 14, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75986791523601", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[12, -15, -1, -5, 11, 9, 15, -13, -12, 0, 3, 12],\n [8, 1, 5, -9, -7, 0, 3, 10, -15, 12, -11, 3],\n [2, -6, 1, 5, -3, -11, 4, -9, 1, 5, -11, -8],\n [-1, -6, 4, 6, 3, 0, 14, 1, 12, 15, -9, -8],\n [-11, -12, -4, 8, 14, 0, 9, 3, -11, 15, 16, 3],\n [-6, -7, 2, 10, 3, -12, -7, 15, 11, 12, 5, -8],\n [-15, -4, 10, 13, 12, 9, -13, -7, 3, -7, 13, -6],\n [-1, -10, 6, -16, -10, -13, -15, 0, -8, -6, 2, -3],\n [-2, -9, 16, -15, -15, 3, 6, 1, 13, 4, -14, 0],\n [7, -13, -8, 16, 15, -9, -2, 14, -12, 12, -3, -4],\n [9, 3, 14, 10, 16, 12, 10, -13, -6, 8, -12, -15],\n [-4, 10, 0, 14, -6, -8, -6, -10, -11, 13, 12, 14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-636244215115724", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[6, 1, -4, 3, -4, 0, -2, -11, 0, 6, 8, 0],\n [1, -12, 4, -12, 4, -3, -8, 4, -15, -14, 0, 6],\n [-4, 4, -6, 2, 12, 10, 6, 0, -12, 0, 4, 0],\n [3, -12, 2, 4, -7, 14, 0, -14, -6, -7, 6, 3],\n [-4, 4, 12, -7, 8, 1, -10, -1, 10, -8, 10, -8],\n [0, -3, 10, 14, 1, -7, 0, 12, -6, -4, 12, -2],\n [-2, -8, 6, 0, -10, 0, 2, 0, 4, 12, 10, -6],\n [-11, 4, 0, -14, -1, 12, 0, -10, -4, -8, -4, 12],\n [0, -15, -12, -6, 10, -6, 4, -4, -5, 8, -5, -16],\n [6, -14, 0, -7, -8, -4, 12, -8, 8, 7, -8, -1],\n [8, 0, 4, 6, 10, 12, 10, -4, -5, -8, -15, 4],\n [0, 6, 0, 3, -8, -2, -6, 12, -16, -1, 4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11659631888659", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[10, -2, -7, 10, 0, 5, -3, 11, -9, -9, 12, -16],\n [-8, -9, -13, 4, -12, 6, 6, -15, -14, -6, 11, -14],\n [-8, 15, -7, -5, 3, -5, -8, 8, -6, -8, -4, -4],\n [-10, -5, 6, 10, 11, 14, -5, -13, 3, -14, 12, -11],\n [-12, -5, 3, 8, 15, -14, -16, -16, -15, -4, 1, 4],\n [-15, 7, -11, -14, -3, 14, 13, -8, -16, 12, 8, 3],\n [-5, 5, -3, 11, -10, -11, 15, 9, -11, 12, -11, -16],\n [-9, -9, 9, 5, -1, -7, 0, -9, 3, -16, 14, 5],\n [8, -5, 12, -15, -3, 7, 8, 7, -5, -14, -2, -7],\n [-7, 10, -11, 13, -8, 16, 6, 4, -16, -5, 6, 10],\n [15, 2, 1, -9, 11, -12, -4, -2, -13, 14, 13, -15],\n [-10, -8, 12, 13, 2, 5, -14, 13, -1, -15, -6, 11]], determine the value at position (11, 7).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13210785144", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[12, 10, -11, 1, -12, -7, 5, 7, -10, 16, -5, 0],\n [3, -2, -8, -1, -9, 6, -10, 11, 14, -7, -2, -10],\n [5, 5, 4, 4, 9, -7, 8, -11, -2, 7, -1, -13],\n [1, -6, -4, -11, 16, 4, 14, 1, 0, -8, -2, 12],\n [-13, 7, -6, 7, -5, 14, -13, 3, -11, -12, -3, -2],\n [0, -2, 8, -3, 11, 14, 10, -1, -4, 4, 3, -9],\n [3, 15, -11, -3, -5, -1, -4, 10, 13, 16, 15, -3],\n [3, 10, 16, 15, 12, -10, 5, 8, -6, -14, -12, 16],\n [-8, -6, -14, -9, -8, 16, 6, -14, -1, -9, -16, 7],\n [12, -4, -15, 16, -3, -7, -13, -1, 16, -4, -12, -9],\n [-9, 14, 4, -7, 4, -6, 7, 11, 14, -5, 7, 11],\n [1, 16, -2, 11, 11, -5, 6, 13, 7, -8, -4, 3]], determine the value at position (4, 8).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1989563488718", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 4) of the matrix A^7 where A is:\n[[2, -11, 4, -6, 4, 0, 8, 1, -6, -2, -6, 4],\n [-11, 7, -5, 4, -2, 6, 9, 2, 0, 12, -2, -10],\n [4, -5, -6, -10, -2, -2, 0, 13, 0, -6, 4, -5],\n [-6, 4, -10, -11, -3, -4, 16, -1, 4, 6, 8, 2],\n [4, -2, -2, -3, 14, -12, -4, 4, 2, -9, -3, -8],\n [0, 6, -2, -4, -12, 11, -1, 6, 2, 4, -8, -15],\n [8, 9, 0, 16, -4, -1, -11, 2, 2, 6, -4, 0],\n [1, 2, 13, -1, 4, 6, 2, 6, 7, 2, -5, -4],\n [-6, 0, 0, 4, 2, 2, 2, 7, 16, -6, -6, 0],\n [-2, 12, -6, 6, -9, 4, 6, 2, -6, -4, -1, 5],\n [-6, -2, 4, 8, -3, -8, -4, -5, -6, -1, 2, -12],\n [4, -10, -5, 2, -8, -15, 0, -4, 0, 5, -12, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19134632743", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-2, -9, 12, 13, 8, -14, -16, 10, 7, 7, -14, -16],\n [-10, 5, -6, -13, 1, -6, 16, -15, 6, 8, -8, 3],\n [-8, -2, -2, 16, 5, -4, -3, -2, 16, -14, -10, -12],\n [9, -15, -16, -13, 11, -7, -2, 1, -5, -9, -16, -11],\n [-1, 4, -4, -11, 12, -15, -13, 3, -9, -15, -13, 1],\n [16, -7, 1, 2, 14, -2, 3, 15, 11, 9, 1, -6],\n [-7, -15, 16, -3, -8, -10, 6, -10, -16, 3, -9, 14],\n [2, -12, -1, -10, 4, 8, -15, -9, 2, 2, -16, 11],\n [-3, 6, -9, 14, 6, -10, -15, 2, 11, 16, 1, -7],\n [9, -2, 15, 0, -16, -2, 9, -13, 10, -10, 12, 4],\n [-2, -10, 11, -8, 13, 15, -4, 16, -15, 3, 5, 9],\n [-14, 4, 12, -16, 4, -12, -14, 9, 11, 4, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51290416106389", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-12, -12, 4, -6, 2, 0, 2, -3, -1, -1, 9, 4],\n [-12, 14, -6, 8, -5, -14, -4, -1, 8, -6, 0, -7],\n [4, -6, 4, 4, 2, 11, 6, -12, -3, -3, -8, -4],\n [-6, 8, 4, 15, 3, 4, 4, 12, -2, -9, -2, 4],\n [2, -5, 2, 3, -14, 4, -4, 1, 1, -2, -4, 0],\n [0, -14, 11, 4, 4, 14, -4, 9, -8, -4, 8, -4],\n [2, -4, 6, 4, -4, -4, 2, -4, -6, 6, 11, -11],\n [-3, -1, -12, 12, 1, 9, -4, 16, 14, 7, 12, 9],\n [-1, 8, -3, -2, 1, -8, -6, 14, 0, -4, 4, -15],\n [-1, -6, -3, -9, -2, -4, 6, 7, -4, 2, 2, 8],\n [9, 0, -8, -2, -4, 8, 11, 12, 4, 2, 15, -12],\n [4, -7, -4, 4, 0, -4, -11, 9, -15, 8, -12, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27846844830325", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (8, 9) of the matrix A^8 where A is:\n[[-6, 0, 0, -1, 6, -5, 6, 2, 15, -16, -2, 7],\n [9, 7, -7, -11, -15, 1, 7, -5, 7, -9, -16, 8],\n [-7, -10, 12, 9, 15, 15, 16, 1, 5, -2, 6, -4],\n [5, 5, 12, -14, 2, -11, -3, 11, 14, 9, -11, -14],\n [-8, -14, 0, 10, -3, -13, -9, -6, 5, 16, 15, 7],\n [-15, 14, -10, 4, -5, -14, -1, 5, -6, -3, -4, -1],\n [11, -10, 1, -2, 1, -6, -6, 0, -11, -12, 16, 4],\n [-8, 16, -12, 3, 6, -1, 10, -13, -2, 3, -12, -1],\n [-3, 10, -15, 12, -12, 11, -15, -14, 5, 9, -12, -13],\n [16, 0, -9, -4, 9, 10, 13, 10, 8, 12, 7, 0],\n [-15, -1, -14, 6, -10, 7, -9, 4, 0, 10, -5, 8],\n [14, 13, 5, -2, 6, 3, 12, 11, -8, 15, -9, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184309544303", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[8, 0, 10, -9, -12, 12, -11, -8, 1, 6, -9, 0],\n [0, -8, 3, 4, -7, -4, -10, -2, 11, 8, -2, -10],\n [10, 3, 4, -2, -4, -2, 6, 10, -2, 4, -1, -2],\n [-9, 4, -2, -6, -11, 14, 0, 6, -2, -8, 1, 0],\n [-12, -7, -4, -11, 9, 2, 5, -2, -2, 4, -7, 6],\n [12, -4, -2, 14, 2, 9, 3, -9, 0, -11, 12, 4],\n [-11, -10, 6, 0, 5, 3, 0, 4, -10, 0, 3, 2],\n [-8, -2, 10, 6, -2, -9, 4, 1, 8, 5, -6, -4],\n [1, 11, -2, -2, -2, 0, -10, 8, -2, -6, -3, -6],\n [6, 8, 4, -8, 4, -11, 0, 5, -6, -6, -9, -2],\n [-9, -2, -1, 1, -7, 12, 3, -6, -3, -9, -5, 6],\n [0, -10, -2, 0, 6, 4, 2, -4, -6, -2, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1731919932280668", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[10, 7, 5, 8, -10, 8, -4, 3, -8, -4, 8, 2],\n [7, -10, 2, -8, 10, 0, 8, -5, -2, -10, 7, 1],\n [5, 2, -15, -2, -4, -10, -2, -2, -10, -4, -8, 7],\n [8, -8, -2, -8, -3, -7, 4, 7, 2, -7, -2, -3],\n [-10, 10, -4, -3, 15, 0, 4, 0, 5, 5, -4, -12],\n [8, 0, -10, -7, 0, 16, 6, 9, 5, 3, 14, 1],\n [-4, 8, -2, 4, 4, 6, 11, -2, 4, 6, 0, 6],\n [3, -5, -2, 7, 0, 9, -2, -14, 8, -2, 4, 2],\n [-8, -2, -10, 2, 5, 5, 4, 8, -14, 3, 12, -4],\n [-4, -10, -4, -7, 5, 3, 6, -2, 3, -15, -12, 15],\n [8, 7, -8, -2, -4, 14, 0, 4, 12, -12, 16, 6],\n [2, 1, 7, -3, -12, 1, 6, 2, -4, 15, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126982449405835", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 11) of the 9th power of the matrix:\n[[-1, 0, -8, 5, -1, -6, -12, 2, -4, -3, -2, -10],\n [0, 7, -4, 10, 8, 14, 6, -1, -8, 0, -6, 4],\n [-8, -4, 6, -6, 15, 3, 4, 1, 6, -1, 7, 2],\n [5, 10, -6, -2, 8, -4, -1, -1, 6, 6, -8, 4],\n [-1, 8, 15, 8, 10, 8, -10, -2, -11, -6, -4, 11],\n [-6, 14, 3, -4, 8, -15, 11, -10, 2, 12, 4, 11],\n [-12, 6, 4, -1, -10, 11, -10, 1, -10, 0, -14, 4],\n [2, -1, 1, -1, -2, -10, 1, -6, -5, 4, -4, 4],\n [-4, -8, 6, 6, -11, 2, -10, -5, -3, -6, -6, 0],\n [-3, 0, -1, 6, -6, 12, 0, 4, -6, -11, -3, 0],\n [-2, -6, 7, -8, -4, 4, -14, -4, -6, -3, -6, -1],\n [-10, 4, 2, 4, 11, 11, 4, 4, 0, 0, -1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66190357082425", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[11, -10, -1, 10, -3, -1, -2, 14, -2, -1, 4, 4],\n [-10, -3, 10, -10, 2, 4, 3, -5, 14, -7, -12, -7],\n [-1, 10, 14, 0, -10, -8, 4, 10, 6, 0, 1, -9],\n [10, -10, 0, -14, 4, 1, 0, -1, 1, 3, 8, -3],\n [-3, 2, -10, 4, -13, -2, 2, 9, -10, -2, 0, -5],\n [-1, 4, -8, 1, -2, -14, -8, -1, -2, 7, -2, 4],\n [-2, 3, 4, 0, 2, -8, 1, 4, -5, -10, 10, 9],\n [14, -5, 10, -1, 9, -1, 4, 8, 3, 6, 6, 2],\n [-2, 14, 6, 1, -10, -2, -5, 3, 16, 0, -3, 8],\n [-1, -7, 0, 3, -2, 7, -10, 6, 0, 13, -8, 2],\n [4, -12, 1, 8, 0, -2, 10, 6, -3, -8, 7, -7],\n [4, -7, -9, -3, -5, 4, 9, 2, 8, 2, -7, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145161785774", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[10, 10, -6, -6, -16, -13, -16, -10, -8, -10, 2, -1],\n [1, -10, 8, 14, 6, 6, 16, -8, 2, 16, 15, -5],\n [-3, -4, -7, 16, 11, 4, 4, 12, 15, -2, 5, 8],\n [1, -2, -1, -4, 9, -7, -14, -7, 9, 0, -12, -1],\n [5, -14, -10, 4, 8, -6, -10, 5, -5, -7, 2, -1],\n [-13, -11, -11, 1, 10, -14, -11, 12, 11, 11, 9, 3],\n [-1, 7, -4, 15, -9, -6, -4, 12, 12, 2, -1, 14],\n [10, -3, 12, 6, 11, -7, 9, 6, 1, -13, -6, -4],\n [8, -10, 13, -11, 15, 4, 12, 8, -7, 2, -13, 12],\n [0, -12, -11, -13, 10, -16, -1, 8, -13, -6, 1, 6],\n [-12, 0, -4, -13, 13, -2, -9, -11, -13, 9, 8, 4],\n [12, -7, 3, 3, 8, -10, -12, -10, 13, 11, 0, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1165505064005", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[1, 2, -14, 10, 6, 2, -4, 11, -1, -4, 2, -4],\n [2, -3, 12, -2, 1, -12, -1, -4, 16, -10, -1, 3],\n [-14, 12, -3, -5, 2, 6, 0, 8, -6, 1, -2, 6],\n [10, -2, -5, 9, 2, 10, -13, -2, 2, -10, -4, 3],\n [6, 1, 2, 2, -2, 3, 1, 0, -4, -1, -8, -6],\n [2, -12, 6, 10, 3, 16, 2, 9, 10, 3, 8, 0],\n [-4, -1, 0, -13, 1, 2, -12, 11, -7, 7, 10, -8],\n [11, -4, 8, -2, 0, 9, 11, 10, 0, 4, 10, 4],\n [-1, 16, -6, 2, -4, 10, -7, 0, -3, 6, 5, -6],\n [-4, -10, 1, -10, -1, 3, 7, 4, 6, 12, 0, 2],\n [2, -1, -2, -4, -8, 8, 10, 10, 5, 0, 0, -1],\n [-4, 3, 6, 3, -6, 0, -8, 4, -6, 2, -1, -13]], determine the value at position (3, 10).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-120847180000", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-16, 0, 1, 1, 6, 10, 14, -6, -6, -6, 11, 4],\n [0, -1, 2, 8, 0, -6, -4, 9, 0, 3, 14, -10],\n [1, 2, -5, -7, 6, -4, 0, -4, 4, 6, -4, 14],\n [1, 8, -7, 11, -10, -10, -10, 9, 10, -11, 6, -3],\n [6, 0, 6, -10, -12, 4, 8, 6, -4, 2, 13, -7],\n [10, -6, -4, -10, 4, -7, 1, 7, 2, -6, 3, -4],\n [14, -4, 0, -10, 8, 1, -8, 2, 14, -4, 6, -2],\n [-6, 9, -4, 9, 6, 7, 2, 9, -8, 4, -12, 7],\n [-6, 0, 4, 10, -4, 2, 14, -8, -3, 0, -6, 0],\n [-6, 3, 6, -11, 2, -6, -4, 4, 0, -3, -2, -2],\n [11, 14, -4, 6, 13, 3, 6, -12, -6, -2, -9, 8],\n [4, -10, 14, -3, -7, -4, -2, 7, 0, -2, 8, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10854119200466", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-3, 6, 10, -4, 5, -6, -2, 12, -2, 8, 4, -8],\n [8, 11, 6, 12, 13, 8, 3, -16, 7, 12, 8, 2],\n [2, 16, 6, 11, -14, -5, -9, -11, -15, 4, -6, 16],\n [-4, -2, -5, 6, 1, 8, 12, 3, 2, -3, 13, -7],\n [-9, -15, 5, 7, -11, -12, 13, 13, 15, -14, -5, 9],\n [-5, -8, -9, 5, -8, 7, -5, -5, 1, 0, 14, -8],\n [15, 2, -14, 7, 9, 3, -3, 15, -9, -6, -11, 15],\n [16, 0, 5, -15, 15, 6, -4, 11, -1, -4, 7, -13],\n [15, 9, -2, -1, -16, 11, 0, -1, 14, -1, -13, 7],\n [10, 4, -4, -8, -10, 12, 6, 1, 7, -12, 7, 4],\n [12, 16, -7, 4, 1, 13, 16, -4, -12, -11, 3, -5],\n [-5, -4, -12, 3, 13, 0, 4, -13, 5, -10, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59412795426581", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 2, 1, 16, -8, -1, 3, 6, -11, -5, 5, -1],\n [7, 7, -7, 13, -4, -7, 9, -12, 2, 0, -16, 15],\n [-16, -6, 0, 5, -3, 6, 1, 2, 10, 1, 0, 9],\n [13, -1, 0, -7, 13, 13, 9, -10, -12, 4, -9, 12],\n [15, 7, -14, 16, -13, -6, 11, -9, -15, -11, 15, 2],\n [1, 8, 0, -15, 5, 16, 3, -5, -15, 11, 2, -6],\n [-3, 7, -15, -10, -8, 16, 10, -13, 16, -9, -8, -5],\n [-6, -1, -15, -14, -8, -10, 9, -5, -1, 14, 7, -16],\n [9, 10, -12, 10, 4, -2, -5, -6, 8, -13, 5, 10],\n [8, 7, -8, 5, 10, 7, -16, -16, -3, 12, 3, 16],\n [3, 0, 13, -4, 5, -8, 11, 6, 6, 15, 0, 11],\n [4, 13, 2, 6, -11, 2, -13, 6, -12, 16, -5, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54346943760372", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-3, 0, 4, -8, 8, -12, 4, -8, 4, -4, -4, 2],\n [0, -12, -10, 2, 1, -11, 2, -12, -11, -10, -1, -5],\n [4, -10, 13, -2, 9, 2, 0, 10, 6, 4, -2, 6],\n [-8, 2, -2, 12, -6, 1, 16, 2, -11, -10, 6, -2],\n [8, 1, 9, -6, 4, 6, 0, -9, 2, 5, -8, -5],\n [-12, -11, 2, 1, 6, 2, 0, 2, 6, 14, -12, 7],\n [4, 2, 0, 16, 0, 0, -16, -4, 6, -4, -11, -6],\n [-8, -12, 10, 2, -9, 2, -4, 10, -3, 4, 8, -4],\n [4, -11, 6, -11, 2, 6, 6, -3, 2, 1, -2, -6],\n [-4, -10, 4, -10, 5, 14, -4, 4, 1, -4, -4, 4],\n [-4, -1, -2, 6, -8, -12, -11, 8, -2, -4, -16, 0],\n [2, -5, 6, -2, -5, 7, -6, -4, -6, 4, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2945497269754", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-4, -10, -3, 2, -11, -3, 9, -5, 7, 5, 4, 13],\n [-13, 12, -6, -1, 8, -13, -7, -1, -13, 1, 2, 15],\n [-4, 2, -8, 15, 7, 9, -13, 13, 16, 16, 14, -2],\n [-5, -6, 6, -4, 10, -7, 5, 6, -8, -15, 3, -9],\n [11, 3, -10, -8, 15, 15, 12, 10, 10, -2, 15, -15],\n [-2, -6, -8, -14, 15, -13, 12, -2, -6, -7, -2, -6],\n [-7, -1, 6, -6, -12, -3, 6, 4, 14, -4, 7, 2],\n [-13, -10, 1, 8, -5, 0, -9, -14, 14, 15, 0, -7],\n [6, -14, -4, 6, 11, 14, 9, -9, 4, -6, -14, -10],\n [-13, 12, -8, -8, -14, 0, -7, 6, 1, -12, 9, 0],\n [1, -1, -13, 2, -1, 4, -15, 12, -6, 8, 6, -3],\n [-5, -6, -13, -7, -4, 12, 4, -9, -9, 12, 3, 0]], determine the value at position (9, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-486590797951", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[11, -4, 10, -6, 6, 10, -16, -6, 10, -4, 4, -2],\n [-4, -6, -9, -6, -4, 2, 2, -6, 4, 12, -5, -14],\n [10, -9, 9, -6, 10, -12, 3, 6, -2, -7, 9, 7],\n [-6, -6, -6, -8, 3, -1, -8, -3, -6, 4, 12, 0],\n [6, -4, 10, 3, 12, -4, 2, 2, -2, 4, -12, 12],\n [10, 2, -12, -1, -4, 11, -11, -1, -8, 0, -1, 2],\n [-16, 2, 3, -8, 2, -11, 12, 8, -4, 0, -5, 0],\n [-6, -6, 6, -3, 2, -1, 8, 0, -9, 6, 6, 10],\n [10, 4, -2, -6, -2, -8, -4, -9, -7, -4, -1, -6],\n [-4, 12, -7, 4, 4, 0, 0, 6, -4, 8, -1, -2],\n [4, -5, 9, 12, -12, -1, -5, 6, -1, -1, 12, 6],\n [-2, -14, 7, 0, 12, 2, 0, 10, -6, -2, 6, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6227517342568541", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-6, 2, 6, -8, -4, 0, -9, 0, -1, -8, -1, -2],\n [2, 3, 2, -6, -7, -9, 3, 1, 1, 6, 14, -7],\n [6, 2, 0, -12, -10, 7, 5, 6, 2, -2, 6, 2],\n [-8, -6, -12, 2, 3, 6, -12, -5, 2, -12, 10, 0],\n [-4, -7, -10, 3, -14, -7, -6, 0, 1, -10, 6, 9],\n [0, -9, 7, 6, -7, 1, 9, -8, 7, -4, 1, 8],\n [-9, 3, 5, -12, -6, 9, 5, -1, 2, -14, -4, 6],\n [0, 1, 6, -5, 0, -8, -1, -7, -6, -4, 10, -4],\n [-1, 1, 2, 2, 1, 7, 2, -6, 14, 10, 0, 4],\n [-8, 6, -2, -12, -10, -4, -14, -4, 10, 2, -15, -12],\n [-1, 14, 6, 10, 6, 1, -4, 10, 0, -15, -8, -4],\n [-2, -7, 2, 0, 9, 8, 6, -4, 4, -12, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20027958171889", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[14, -11, -16, -6, 4, 1, 7, -11, -9, 0, 14, 13],\n [13, -15, 12, -1, -12, -11, 1, -4, -13, -9, 16, -6],\n [-10, 8, 2, -14, -16, -6, 11, -10, -3, 4, -11, 16],\n [-10, 14, 10, 6, -16, 9, -14, 3, 4, 13, 13, 9],\n [-11, 6, -10, 12, 3, -6, -11, 3, 10, 13, -1, 16],\n [-2, 15, 4, -16, 9, 10, 0, -2, 5, 9, -8, 16],\n [-6, 2, 4, -15, -6, -13, -9, -8, -16, 8, -12, -3],\n [-8, 0, 9, -11, -12, -5, -3, -7, 13, -6, -5, 10],\n [-16, 11, 3, 7, 10, -7, 10, 6, -1, 7, 10, -5],\n [16, -6, 16, 11, -6, 14, 13, 5, -9, -14, 2, 5],\n [-14, 5, -4, 16, -2, -12, -6, 13, -14, -16, 12, 5],\n [13, 15, -6, -9, -2, -3, 12, -8, 3, -2, -6, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2639564755679", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[12, -4, -2, -5, -4, -8, -10, 1, 14, 13, 4, 8],\n [-4, 9, -6, 4, -6, -10, 6, -3, 2, 0, 0, 0],\n [-2, -6, 12, -11, -5, -6, 2, 2, -4, 0, 10, 4],\n [-5, 4, -11, -8, -7, -10, -4, 6, -6, -3, -6, 0],\n [-4, -6, -5, -7, -3, 0, -2, 6, -10, -3, 0, 6],\n [-8, -10, -6, -10, 0, 0, 2, -1, 14, -10, -10, -5],\n [-10, 6, 2, -4, -2, 2, -8, 0, 0, 8, 14, 6],\n [1, -3, 2, 6, 6, -1, 0, -11, -6, 10, -4, -8],\n [14, 2, -4, -6, -10, 14, 0, -6, -8, -4, 8, 3],\n [13, 0, 0, -3, -3, -10, 8, 10, -4, -13, -2, -2],\n [4, 0, 10, -6, 0, -10, 14, -4, 8, -2, 5, -2],\n [8, 0, 4, 0, 6, -5, 6, -8, 3, -2, -2, 16]], determine the value at position (5, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6196034753", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (2, 10) of the result:\nA =\n[[0, -4, -14, -15, -8, -6, 0, 10, -4, -4, 2, 4],\n [-4, -6, 2, -6, 2, -9, 6, 12, 0, 1, -6, 7],\n [-14, 2, 13, -6, 1, -8, 14, -9, 10, 13, -10, 4],\n [-15, -6, -6, -8, 6, -4, 5, 6, -2, 0, 4, 4],\n [-8, 2, 1, 6, -12, -12, -4, -6, 4, -2, -2, 1],\n [-6, -9, -8, -4, -12, 0, 2, -8, -2, 2, 0, 8],\n [0, 6, 14, 5, -4, 2, 15, -7, 6, 12, 6, -4],\n [10, 12, -9, 6, -6, -8, -7, 14, 3, -12, 9, -11],\n [-4, 0, 10, -2, 4, -2, 6, 3, 14, -2, -1, 3],\n [-4, 1, 13, 0, -2, 2, 12, -12, -2, 15, -3, 8],\n [2, -6, -10, 4, -2, 0, 6, 9, -1, -3, 16, 2],\n [4, 7, 4, 4, 1, 8, -4, -11, 3, 8, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63762420925149", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 2, 10, 10, 3, -8, -10, 0, -6, -2, -6, 2],\n [2, 14, 12, 2, -8, 8, -2, -9, 4, 2, 8, -4],\n [10, 12, 12, 2, -2, 2, 0, 8, -3, 6, 4, 4],\n [10, 2, 2, 8, -3, -4, -1, 8, -14, 8, -1, -11],\n [3, -8, -2, -3, 4, 0, -1, 11, 5, -6, -6, 0],\n [-8, 8, 2, -4, 0, -7, 10, -4, 8, 0, -3, 0],\n [-10, -2, 0, -1, -1, 10, 1, -8, 2, -2, 8, 14],\n [0, -9, 8, 8, 11, -4, -8, -13, 3, -3, 10, 9],\n [-6, 4, -3, -14, 5, 8, 2, 3, 7, -1, 3, 0],\n [-2, 2, 6, 8, -6, 0, -2, -3, -1, -11, 8, 2],\n [-6, 8, 4, -1, -6, -3, 8, 10, 3, 8, 1, 7],\n [2, -4, 4, -11, 0, 0, 14, 9, 0, 2, 7, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2888096799425074", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-10, 2, 4, -9, 4, 0, 8, 2, -3, 2, 14, 6],\n [2, 1, -2, -2, 8, 2, 6, 2, 8, -13, -12, 2],\n [4, -2, -15, 4, -2, -4, -1, 8, 2, 0, -10, 5],\n [-9, -2, 4, -4, -6, 4, 1, -2, 6, 0, -5, 6],\n [4, 8, -2, -6, 7, 6, -1, -12, -1, -16, 4, -6],\n [0, 2, -4, 4, 6, 2, -6, 3, -4, 11, -4, 4],\n [8, 6, -1, 1, -1, -6, -10, 9, -16, 10, 10, 5],\n [2, 2, 8, -2, -12, 3, 9, -1, 2, 3, 4, -7],\n [-3, 8, 2, 6, -1, -4, -16, 2, 10, -9, 1, 0],\n [2, -13, 0, 0, -16, 11, 10, 3, -9, 10, 0, 10],\n [14, -12, -10, -5, 4, -4, 10, 4, 1, 0, -2, 7],\n [6, 2, 5, 6, -6, 4, 5, -7, 0, 10, 7, -16]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163710768759763", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (4, 5) of the result:\nA =\n[[-3, 0, -2, 10, 0, -15, 8, -9, -7, 11, -1, 0],\n [-16, 5, -13, 10, 4, -6, 14, -13, 6, 7, -6, -5],\n [-7, 13, -2, -10, 15, -10, -11, 13, -2, -11, 10, -13],\n [-2, -1, -2, 4, 6, 8, -8, 15, -12, 12, 4, -16],\n [-10, -11, 2, -3, -11, -8, 15, -9, 5, -9, -8, -7],\n [5, -4, -9, -4, 12, -7, 13, -11, 12, -12, -10, -6],\n [3, 10, -2, 12, -5, 16, 16, -2, 14, 8, -15, 1],\n [9, -3, -10, 9, -2, -6, 13, -15, 9, -4, 15, 4],\n [-3, -2, 5, -8, -9, -7, -1, -8, 13, -16, -6, -9],\n [-11, 16, -6, -7, 10, 0, 8, -11, 1, -14, 0, -2],\n [-1, 3, -15, -14, 13, -8, 3, -5, -4, -14, 10, 1],\n [-6, -5, 3, -10, -1, 2, -3, 11, -10, -8, 7, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6890195550131", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[14, 1, 10, -5, -2, -4, -4, -4, 10, 2, -4, 2],\n [1, -16, 2, 1, 13, 0, -10, -8, -8, 0, 2, 10],\n [10, 2, 3, -5, -4, 9, 11, -10, 2, 3, 6, -2],\n [-5, 1, -5, 14, 10, -4, 11, 0, 1, -4, 6, -14],\n [-2, 13, -4, 10, 11, -8, -5, -10, 0, 10, 4, 2],\n [-4, 0, 9, -4, -8, 11, 0, -10, -4, -14, 6, -6],\n [-4, -10, 11, 11, -5, 0, -5, 16, -4, -8, 0, -6],\n [-4, -8, -10, 0, -10, -10, 16, -9, -2, -4, -9, -9],\n [10, -8, 2, 1, 0, -4, -4, -2, 5, -4, -10, -4],\n [2, 0, 3, -4, 10, -14, -8, -4, -4, -1, 14, -12],\n [-4, 2, 6, 6, 4, 6, 0, -9, -10, 14, 0, -2],\n [2, 10, -2, -14, 2, -6, -6, -9, -4, -12, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68439215809098", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[8, 10, -7, 7, -5, -4, 12, -15, 1, 11, 6, 5],\n [10, 5, 12, -4, 2, 0, -7, 8, 10, 8, 6, 2],\n [-7, 12, 1, -11, 3, -6, 4, -4, 4, 0, -12, 2],\n [7, -4, -11, -9, -4, 6, 3, -8, 12, 5, -3, 6],\n [-5, 2, 3, -4, -16, 4, 3, 4, 11, 10, 2, -2],\n [-4, 0, -6, 6, 4, 5, -10, -2, 10, -8, 2, 2],\n [12, -7, 4, 3, 3, -10, 1, 2, -8, 7, -2, 8],\n [-15, 8, -4, -8, 4, -2, 2, 13, 6, -2, -6, -5],\n [1, 10, 4, 12, 11, 10, -8, 6, 12, -6, -3, -6],\n [11, 8, 0, 5, 10, -8, 7, -2, -6, 10, -3, 3],\n [6, 6, -12, -3, 2, 2, -2, -6, -3, -3, -12, 4],\n [5, 2, 2, 6, -2, 2, 8, -5, -6, 3, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "173196998478", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 7) of the 9th power of the matrix:\n[[15, 6, -4, 1, -9, 0, -9, 10, 8, 0, 6, 2],\n [6, 9, -5, 10, -8, -12, -8, 2, -6, 12, -2, 6],\n [-4, -5, -5, -8, 0, 8, -12, 9, 12, -8, 9, 1],\n [1, 10, -8, 16, -7, 4, -11, -4, 0, 0, -5, 0],\n [-9, -8, 0, -7, 4, -14, 6, 8, -8, 0, 1, 12],\n [0, -12, 8, 4, -14, 15, -6, 1, 3, -4, 5, -12],\n [-9, -8, -12, -11, 6, -6, 10, 12, -2, 5, -10, -3],\n [10, 2, 9, -4, 8, 1, 12, 14, -2, -2, 0, 6],\n [8, -6, 12, 0, -8, 3, -2, -2, 11, -10, -12, 0],\n [0, 12, -8, 0, 0, -4, 5, -2, -10, 3, -1, -12],\n [6, -2, 9, -5, 1, 5, -10, 0, -12, -1, -4, -4],\n [2, 6, 1, 0, 12, -12, -3, 6, 0, -12, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61808170022166", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[5, 7, 5, 6, 11, -15, -13, 4, 9, -2, -2, 5],\n [-16, 9, -7, 3, -16, -5, 7, 9, -15, 3, 2, 8],\n [-16, 14, -13, -14, -6, 2, -8, 3, -8, 1, 15, -13],\n [13, -6, 2, 1, -12, 2, 3, -15, 2, -6, -4, 3],\n [-15, -8, -10, -13, -15, 6, -16, -12, 15, 2, 14, -13],\n [-10, 15, 16, -11, -2, 11, -1, 4, 5, 16, 8, 9],\n [2, 3, 13, 3, 5, 10, 15, 5, -9, -5, 8, 1],\n [-16, 15, -15, 5, -1, 11, -1, 16, 8, -5, -1, 16],\n [11, -1, 12, 12, 7, 6, 0, -13, 6, 5, 10, 13],\n [5, -11, 10, 5, -4, 7, 16, 13, 5, -10, -8, 15],\n [0, 5, 9, 15, 12, -7, 6, -12, -6, -5, 3, -7],\n [9, -5, 8, -9, 3, -7, 8, 13, -5, -9, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220521547654", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-13, -5, -12, 8, 0, 8, 4, -3, -8, -8, 4, -7],\n [-5, 14, 6, -2, -8, 6, 2, 0, 8, -8, 2, 8],\n [-12, 6, -4, 5, 1, 8, 10, 6, -3, -4, -8, 6],\n [8, -2, 5, -4, 3, 0, -6, 2, -7, -4, -1, 2],\n [0, -8, 1, 3, -9, 8, 12, -8, -10, 6, 7, 0],\n [8, 6, 8, 0, 8, -13, 1, 2, 4, 14, 0, -7],\n [4, 2, 10, -6, 12, 1, -4, 1, -8, -12, 10, -8],\n [-3, 0, 6, 2, -8, 2, 1, 15, 2, 4, -4, 3],\n [-8, 8, -3, -7, -10, 4, -8, 2, 16, -14, -2, -2],\n [-8, -8, -4, -4, 6, 14, -12, 4, -14, -8, 2, -4],\n [4, 2, -8, -1, 7, 0, 10, -4, -2, 2, 10, -6],\n [-7, 8, 6, 2, 0, -7, -8, 3, -2, -4, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4850501897003658", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-13, -3, 0, -3, 4, 4, -10, 0, 2, -1, -4, 3],\n [-3, -13, 10, 1, 4, -2, 6, 2, -7, 1, 3, -1],\n [0, 10, -7, 6, 4, 1, -11, 12, 0, 0, -4, 0],\n [-3, 1, 6, -11, -10, 4, 10, 1, 2, -4, -6, 14],\n [4, 4, 4, -10, -7, 6, 2, 8, -4, -2, -3, 9],\n [4, -2, 1, 4, 6, 15, 8, -4, -8, -5, 12, -16],\n [-10, 6, -11, 10, 2, 8, 11, -8, 6, -4, -8, 1],\n [0, 2, 12, 1, 8, -4, -8, -3, -8, -4, -2, 1],\n [2, -7, 0, 2, -4, -8, 6, -8, -12, -12, -6, -2],\n [-1, 1, 0, -4, -2, -5, -4, -4, -12, 7, -3, 3],\n [-4, 3, -4, -6, -3, 12, -8, -2, -6, -3, 10, 12],\n [3, -1, 0, 14, 9, -16, 1, 1, -2, 3, 12, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2339993226810520", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[16, -10, -8, -10, 3, 10, -4, -6, 6, 1, -5, 0],\n [-10, 5, 0, 2, -12, -11, -1, -10, -4, 14, -3, 12],\n [-8, 0, 7, 4, -8, -10, -2, -6, 0, -2, -8, 13],\n [-10, 2, 4, 16, 0, -8, 4, -10, -8, 2, -14, -11],\n [3, -12, -8, 0, 5, -7, 2, -8, 8, 4, -1, -6],\n [10, -11, -10, -8, -7, 6, 6, 6, -8, -9, -6, -8],\n [-4, -1, -2, 4, 2, 6, 15, 6, 2, 8, -2, 0],\n [-6, -10, -6, -10, -8, 6, 6, 0, 8, -4, 1, 0],\n [6, -4, 0, -8, 8, -8, 2, 8, -8, -5, 0, -6],\n [1, 14, -2, 2, 4, -9, 8, -4, -5, -2, 11, -4],\n [-5, -3, -8, -14, -1, -6, -2, 1, 0, 11, -8, -9],\n [0, 12, 13, -11, -6, -8, 0, 0, -6, -4, -9, -6]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "243034006024409", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 12) of the 8th power of the matrix:\n[[-6, 10, -13, 9, 9, -2, -4, 5, 4, -6, -15, -6],\n [9, -2, -4, -2, 2, -6, -5, 6, -16, 13, 6, 8],\n [4, 11, -6, 7, -5, -14, 16, -4, -15, -1, 3, 15],\n [6, -7, 6, 0, -9, -13, -9, 6, 16, -3, 4, -13],\n [9, 1, -16, -14, 10, -1, 6, 15, -3, -6, -14, -2],\n [-9, 9, 3, -15, 16, 0, 2, -5, -6, 4, 10, 6],\n [-2, 5, -4, -6, 0, -2, -2, -4, 12, -14, -7, -1],\n [12, 1, -15, 8, 8, 11, 2, 0, 5, 1, 9, -2],\n [12, -10, 1, -6, -9, 8, -3, -7, -1, 12, -11, -9],\n [5, 6, -14, 9, -15, 3, 1, -3, 11, 13, -1, 1],\n [-10, -6, -2, -5, 8, -15, -6, 16, -5, -13, 3, 9],\n [-14, -15, -9, 8, 7, 2, 15, -16, -15, -5, 9, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7707462693", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-3, -9, -12, 3, -10, -12, 6, 6, 6, 0, 2, 12],\n [-13, -12, -7, -3, -13, -11, -6, 6, 3, 1, -3, -16],\n [6, 14, -3, -10, -11, 6, -4, 5, 1, 16, -6, -10],\n [12, -16, 8, 9, -2, 12, 8, -11, 10, -13, -13, 11],\n [4, -14, 0, 14, 8, 7, 6, -5, 7, 0, -12, -7],\n [-2, -3, -1, 6, 6, -1, 16, -1, -15, 13, 10, 13],\n [16, -16, 16, -15, -5, -2, -10, -14, -10, -10, -1, 15],\n [11, -14, 7, 5, -11, -8, -5, -2, -11, -2, -5, -3],\n [-15, 1, 10, 0, 8, -11, 8, -1, -9, 11, -10, 11],\n [14, 13, -14, -12, -13, 8, -8, 16, -12, -11, -9, 10],\n [7, 10, 15, -2, -9, 14, -9, 13, 7, -15, 15, -10],\n [16, 6, 12, 15, 12, -5, -15, -10, -9, 2, -8, -2]], determine the value at position (6, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35810116826", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[8, 3, 0, -3, 2, -3, -3, 0, 12, -5, 8, 8],\n [3, 5, 5, 4, -7, -7, 0, -2, 10, 9, -4, 6],\n [0, 5, 3, 11, 2, 6, -1, -2, 4, 10, -4, -4],\n [-3, 4, 11, -4, 8, 10, -6, -2, -4, 0, -2, 0],\n [2, -7, 2, 8, -1, 2, 4, 10, -10, -6, 4, -14],\n [-3, -7, 6, 10, 2, -14, 3, 4, -7, -5, -2, 10],\n [-3, 0, -1, -6, 4, 3, -15, 2, 4, 10, -6, 6],\n [0, -2, -2, -2, 10, 4, 2, -6, -2, 0, 10, 4],\n [12, 10, 4, -4, -10, -7, 4, -2, 7, 8, 3, -6],\n [-5, 9, 10, 0, -6, -5, 10, 0, 8, -4, 4, 2],\n [8, -4, -4, -2, 4, -2, -6, 10, 3, 4, 16, 2],\n [8, 6, -4, 0, -14, 10, 6, 4, -6, 2, 2, 16]], determine the value at position (11, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1447961062", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[4, -1, -4, 9, 3, -11, 7, -3, 0, 2, 2, -1],\n [-1, -15, -9, 4, -5, 6, -14, -4, -2, 6, 4, 11],\n [-4, -9, 14, -4, 4, -4, 3, 2, 2, 4, 6, -1],\n [9, 4, -4, 12, 12, 6, 4, 8, 0, -5, 12, 4],\n [3, -5, 4, 12, -15, -3, 9, -5, 16, -6, 4, 10],\n [-11, 6, -4, 6, -3, 2, 2, -9, -4, -5, 10, -6],\n [7, -14, 3, 4, 9, 2, -14, 5, 2, 1, -10, -6],\n [-3, -4, 2, 8, -5, -9, 5, -2, 0, -7, -6, -5],\n [0, -2, 2, 0, 16, -4, 2, 0, 1, -2, 8, 2],\n [2, 6, 4, -5, -6, -5, 1, -7, -2, -2, 5, 1],\n [2, 4, 6, 12, 4, 10, -10, -6, 8, 5, -2, 1],\n [-1, 11, -1, 4, 10, -6, -6, -5, 2, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6681237706292", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 12) of the matrix A^9 where A is:\n[[-15, -2, -12, -6, -8, 7, 9, -2, 14, 4, -6, 2],\n [-2, 2, 1, -10, -2, -8, -4, 0, 10, 0, -3, 0],\n [-12, 1, -9, -2, -3, 0, -2, -4, -8, -2, 2, 8],\n [-6, -10, -2, 8, -3, 5, -2, -8, 2, -8, -9, 0],\n [-8, -2, -3, -3, -13, 6, 4, -4, -1, 8, 5, 8],\n [7, -8, 0, 5, 6, 16, 0, 4, -1, 1, -10, -10],\n [9, -4, -2, -2, 4, 0, -16, 4, 6, 2, 10, -1],\n [-2, 0, -4, -8, -4, 4, 4, 7, 8, 0, -9, -8],\n [14, 10, -8, 2, -1, -1, 6, 8, 3, 2, -3, -1],\n [4, 0, -2, -8, 8, 1, 2, 0, 2, 9, -2, 2],\n [-6, -3, 2, -9, 5, -10, 10, -9, -3, -2, -14, -14],\n [2, 0, 8, 0, 8, -10, -1, -8, -1, 2, -14, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58155639981142", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 2, -6, 1, -2, 13, -10, 6, 2, -8, -5, -13],\n [2, 13, -2, -11, 0, 4, 0, -6, -4, 10, -3, 6],\n [-6, -2, 0, 2, 13, 4, -5, 8, 3, 6, 9, 4],\n [1, -11, 2, -7, -4, 8, 0, -2, 4, -11, 6, 3],\n [-2, 0, 13, -4, -2, 2, 0, -8, -6, 6, 0, 0],\n [13, 4, 4, 8, 2, -1, 12, -9, 8, 6, -2, -10],\n [-10, 0, -5, 0, 0, 12, 5, 8, -9, -8, 4, 14],\n [6, -6, 8, -2, -8, -9, 8, 7, 4, 4, 2, -8],\n [2, -4, 3, 4, -6, 8, -9, 4, -12, 7, -4, -9],\n [-8, 10, 6, -11, 6, 6, -8, 4, 7, 2, -9, -2],\n [-5, -3, 9, 6, 0, -2, 4, 2, -4, -9, 5, -6],\n [-13, 6, 4, 3, 0, -10, 14, -8, -9, -2, -6, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72422889145851", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-10, -2, 1, 10, 6, 12, 7, 8, 3, 4, -15, 3],\n [-6, -15, -2, 9, -14, 1, 3, 7, -1, 6, -7, 5],\n [3, -7, 9, 5, -5, -10, 16, 1, -6, -5, 15, -7],\n [14, -14, -5, -1, 12, -16, 11, -9, -1, 9, 5, 8],\n [7, -10, 4, -16, -15, 0, 11, 2, 13, -3, 12, -15],\n [-6, 15, -8, -8, -8, -14, 10, 4, 11, 16, -12, 14],\n [16, 8, 5, -9, -8, -6, 14, 12, 6, 3, 6, -8],\n [1, 13, 9, -1, 3, -1, 7, -1, 15, 0, 7, 8],\n [-2, 4, -1, 2, 3, -12, -2, -7, -6, -9, 7, 4],\n [-15, 2, -3, -5, 3, 3, 14, 12, -6, -6, 1, -7],\n [1, -8, -11, -5, -16, -7, -15, -9, 8, 13, 10, -4],\n [15, -11, 3, -3, 6, -4, 7, -7, -7, -9, 1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "310863165522780", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[4, 9, -6, -6, 13, -16, -2, 11, -12, -9, 5, 13],\n [-13, -15, 4, 16, -3, -1, 11, -8, -6, 2, 12, -8],\n [-10, 14, -14, -9, -8, -2, -9, 0, 15, 6, -16, -10],\n [-3, -7, 4, 16, -5, -4, 14, -2, -8, -11, -14, -3],\n [-3, 6, -16, 16, 7, 9, -7, 1, -7, -11, -12, -8],\n [-14, -9, -7, 8, -14, 10, 6, 14, -13, -5, 2, 0],\n [9, 6, 8, -11, 3, -12, 12, -5, 9, 6, -13, -9],\n [10, 11, -9, -3, -11, 5, 8, -9, 14, -13, 1, 0],\n [3, 13, -7, 15, 1, 16, -2, 7, 14, 15, 16, -6],\n [15, -14, -9, 16, 2, -9, 9, 2, -8, -10, -13, -11],\n [-1, -7, -3, -10, -15, 14, 12, 0, -1, -10, -2, 11],\n [-11, -11, 10, -3, 0, -7, -15, -3, 4, 11, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2748062375389252", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[5, -2, 8, 4, 8, 4, -2, -4, -6, 4, -6, 4],\n [-2, 7, -10, -11, 6, 4, 0, -6, -2, 6, 7, -4],\n [8, -10, -2, -8, 2, -14, 0, 2, 1, 9, 2, 10],\n [4, -11, -8, 8, 0, 1, 8, 4, 8, -2, -4, 0],\n [8, 6, 2, 0, -14, -6, -14, 7, -2, 0, 0, -9],\n [4, 4, -14, 1, -6, -9, 2, 6, 2, -6, 0, 4],\n [-2, 0, 0, 8, -14, 2, 11, 6, -6, -2, 7, -2],\n [-4, -6, 2, 4, 7, 6, 6, 7, 8, 4, 0, -6],\n [-6, -2, 1, 8, -2, 2, -6, 8, -6, 6, 12, 2],\n [4, 6, 9, -2, 0, -6, -2, 4, 6, -3, 11, 8],\n [-6, 7, 2, -4, 0, 0, 7, 0, 12, 11, -15, -4],\n [4, -4, 10, 0, -9, 4, -2, -6, 2, 8, -4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "661834445727", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-3, 0, 2, -10, -6, 0, -8, 4, -10, 0, -12, 0],\n [0, -16, 7, -7, 12, 0, 2, 8, 6, 0, -7, -2],\n [2, 7, -13, -2, -2, -13, -3, 7, -6, -11, -6, 0],\n [-10, -7, -2, 8, -2, 12, -4, 4, 2, 2, -10, 6],\n [-6, 12, -2, -2, 8, -16, 3, -6, 10, 4, 1, -5],\n [0, 0, -13, 12, -16, 6, -2, 0, -6, -12, 0, -6],\n [-8, 2, -3, -4, 3, -2, -1, -6, 8, -7, -3, -4],\n [4, 8, 7, 4, -6, 0, -6, -7, -2, -6, 6, -6],\n [-10, 6, -6, 2, 10, -6, 8, -2, -10, 2, 0, 0],\n [0, 0, -11, 2, 4, -12, -7, -6, 2, -13, 8, 15],\n [-12, -7, -6, -10, 1, 0, -3, 6, 0, 8, -7, -10],\n [0, -2, 0, 6, -5, -6, -4, -6, 0, 15, -10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95435005843225", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (1, 1) of the result:\nA =\n[[9, 0, 4, -3, -10, -1, 10, 12, 11, -10, 0, 0],\n [0, -2, 12, 0, 1, 8, -8, -11, -9, -1, 5, 4],\n [4, 12, 12, -7, -2, 0, 8, 2, -2, -10, 3, -6],\n [-3, 0, -7, -11, -2, -13, 8, -1, -2, 7, 6, -6],\n [-10, 1, -2, -2, 3, -2, -10, -4, 3, 12, 2, 0],\n [-1, 8, 0, -13, -2, 8, -14, -2, 8, 10, 0, -8],\n [10, -8, 8, 8, -10, -14, 6, -8, 10, -10, -14, -8],\n [12, -11, 2, -1, -4, -2, -8, 14, -6, 5, 2, -11],\n [11, -9, -2, -2, 3, 8, 10, -6, -3, -6, -10, 2],\n [-10, -1, -10, 7, 12, 10, -10, 5, -6, 5, 12, -4],\n [0, 5, 3, 6, 2, 0, -14, 2, -10, 12, -6, -10],\n [0, 4, -6, -6, 0, -8, -8, -11, 2, -4, -10, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7857361884572", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[3, 13, 6, -4, 4, -6, -2, -2, -3, 0, 2, 12],\n [13, 6, -5, -10, -15, -8, 5, 3, 2, 4, 8, 11],\n [6, -5, 9, -3, 8, -2, -8, -10, -2, -1, -6, -2],\n [-4, -10, -3, 1, 8, 2, 0, -2, 8, 6, 8, -12],\n [4, -15, 8, 8, -16, 0, 2, 3, 2, 4, -2, 8],\n [-6, -8, -2, 2, 0, -6, 5, -8, -12, 1, 12, -10],\n [-2, 5, -8, 0, 2, 5, -14, -9, -16, -5, 4, 12],\n [-2, 3, -10, -2, 3, -8, -9, 7, -4, 4, -3, 2],\n [-3, 2, -2, 8, 2, -12, -16, -4, -1, -6, 1, 0],\n [0, 4, -1, 6, 4, 1, -5, 4, -6, -3, 10, -14],\n [2, 8, -6, 8, -2, 12, 4, -3, 1, 10, -5, -10],\n [12, 11, -2, -12, 8, -10, 12, 2, 0, -14, -10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-157860760793", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[0, 4, 12, -12, -2, -6, 0, -2, -8, -2, 0, 10],\n [4, 10, 0, -2, -7, -12, -6, -9, 0, -5, 3, 0],\n [12, 0, -9, 4, -2, -6, 2, 6, -4, -6, 8, 2],\n [-12, -2, 4, -13, -6, 2, -14, -8, -2, -3, 10, -6],\n [-2, -7, -2, -6, -15, -6, -1, 6, -7, -10, 6, 2],\n [-6, -12, -6, 2, -6, 12, -4, -4, 2, -2, 2, 2],\n [0, -6, 2, -14, -1, -4, 7, -13, 0, 0, 12, -8],\n [-2, -9, 6, -8, 6, -4, -13, 15, -11, -10, -13, -5],\n [-8, 0, -4, -2, -7, 2, 0, -11, 6, -10, -14, 4],\n [-2, -5, -6, -3, -10, -2, 0, -10, -10, -1, 1, -4],\n [0, 3, 8, 10, 6, 2, 12, -13, -14, 1, -16, -1],\n [10, 0, 2, -6, 2, 2, -8, -5, 4, -4, -1, 9]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46409592116463", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[3, -7, -11, 13, -14, 3, -14, -1, -13, 0, 12, -13],\n [-7, -8, -6, -16, 14, 0, 1, -10, 9, 7, 16, 9],\n [12, 7, -5, 11, 9, 8, -2, 14, -9, 10, -13, -5],\n [14, 4, 3, 0, 14, -2, 15, -15, 11, 4, -4, 16],\n [10, 9, 1, -7, 2, -5, 7, -16, -8, 12, 11, 1],\n [2, 5, 1, -5, -8, -2, -8, -8, 14, -11, -2, -7],\n [-16, -9, 7, 4, 13, -14, -11, 8, 16, -6, -5, -16],\n [-13, -12, -6, 13, 16, 4, 5, 8, -13, -5, -13, 6],\n [-11, 16, 16, -11, -10, 4, -2, -15, 6, -14, -5, -2],\n [16, -4, -4, 11, -4, 7, 13, -13, -4, -5, -16, 0],\n [7, -10, 6, 4, 7, -14, 12, 11, -15, -13, 0, 3],\n [9, 5, 2, 14, 8, 13, -8, 13, 15, -2, -16, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-132293087661122", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[-14, -2, 7, -1, -10, -1, 11, -5, 8, 13, -9, -6],\n [13, -11, 13, -3, 11, -12, 4, -11, 7, -1, -10, 9],\n [4, 1, 0, 4, -11, 2, -15, 2, 5, -1, 8, -6],\n [-5, 11, -15, -5, 8, -15, 16, -4, 7, 3, 3, -5],\n [-9, 16, 14, 12, 1, 3, -9, 7, -16, -14, -6, -14],\n [4, -12, -16, -3, -13, 2, 3, -10, -8, -4, -13, 2],\n [0, 8, -3, -12, -10, -3, 16, -5, -13, -11, -16, 3],\n [9, 6, -5, -4, 1, 14, 11, -12, 3, 3, -3, -2],\n [13, 1, 9, 2, -13, 10, -14, -5, -15, 14, -12, 3],\n [-6, 14, 8, -13, 4, -16, 11, -16, -1, -15, -15, 0],\n [5, -1, -4, -10, 0, 4, 14, -2, 6, 9, 13, -6],\n [9, -11, -14, 8, -2, 4, -11, 6, -5, 10, -2, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1148384761904", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[8, 6, -4, -6, 12, 6, -3, 0, 4, 6, -15, -1],\n [6, 0, 0, 5, -4, 8, -6, -3, 10, 3, -6, 8],\n [-4, 0, -16, -2, -8, -7, -10, 4, -2, 1, 8, 4],\n [-6, 5, -2, -7, -6, -6, 1, 4, 0, 12, 1, -2],\n [12, -4, -8, -6, 8, 8, 2, -11, -12, -4, 6, 5],\n [6, 8, -7, -6, 8, -14, 2, -12, 6, -4, 2, -3],\n [-3, -6, -10, 1, 2, 2, -16, 0, -4, -4, 7, 2],\n [0, -3, 4, 4, -11, -12, 0, 10, 2, -8, 12, -6],\n [4, 10, -2, 0, -12, 6, -4, 2, 4, 2, 0, -8],\n [6, 3, 1, 12, -4, -4, -4, -8, 2, -6, 14, -8],\n [-15, -6, 8, 1, 6, 2, 7, 12, 0, 14, -12, -4],\n [-1, 8, 4, -2, 5, -3, 2, -6, -8, -8, -4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3005425056584", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 12) of the 8th power of the matrix:\n[[-14, -4, 13, -3, 9, -10, 11, -9, -2, -12, 16, -14],\n [5, 5, 15, 6, 4, -13, -2, 4, 3, 3, 8, 14],\n [-13, 12, 13, -8, -12, 1, 16, -4, 16, -15, -5, 12],\n [12, 6, -12, 14, 6, -1, -9, -8, -15, 1, 2, -9],\n [0, -12, -9, -7, -14, -14, 14, 10, 11, 10, -1, -2],\n [-9, 11, -2, 7, -12, -11, -12, 8, -10, 14, -14, 1],\n [12, -16, 12, 16, 7, -10, 16, -13, -7, -7, 3, 0],\n [-4, -10, 13, 5, -6, -4, 6, -7, 11, 0, 13, 5],\n [3, -11, 1, 14, 9, -15, 14, -4, 8, 15, 12, 11],\n [2, 2, -10, 2, -9, -3, -9, -15, 12, 7, -2, -9],\n [-14, -6, -10, -12, 4, 5, 15, -10, 9, 10, -13, 1],\n [-15, 16, -16, 13, 8, 9, 14, -1, -13, -4, 10, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "704013657625", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-1, -5, 4, 4, 6, -12, 1, 0, -4, 1, 13, 8],\n [-5, 16, 4, 6, 12, -1, 10, -6, 4, 12, -5, -8],\n [4, 4, 6, -10, 4, -8, 8, -9, -7, -8, 2, 4],\n [4, 6, -10, 11, -8, 0, -4, -4, 0, 0, 7, -2],\n [6, 12, 4, -8, 3, -3, -2, -4, -12, 0, 0, -4],\n [-12, -1, -8, 0, -3, -8, 5, -8, -10, -8, -2, 2],\n [1, 10, 8, -4, -2, 5, 16, 4, -6, 1, -9, 0],\n [0, -6, -9, -4, -4, -8, 4, 9, -1, -4, -4, 1],\n [-4, 4, -7, 0, -12, -10, -6, -1, 3, -5, -10, 5],\n [1, 12, -8, 0, 0, -8, 1, -4, -5, 7, 10, -6],\n [13, -5, 2, 7, 0, -2, -9, -4, -10, 10, -8, -5],\n [8, -8, 4, -2, -4, 2, 0, 1, 5, -6, -5, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144354129089417", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, 10, -10, -15, 6, 4, 6, -16, 12, 1, 16, -11],\n [-7, 11, -5, -13, 8, -10, 3, 6, -9, 0, 12, 9],\n [-7, -6, -2, 1, -13, 10, -12, -11, -7, 2, -5, 7],\n [-1, -8, -4, 1, 15, 2, 4, 4, -11, -15, -11, 0],\n [13, -6, 8, -8, 8, -9, -14, 9, 5, 7, 4, -1],\n [-7, -15, 16, 10, 0, -6, -8, -7, -6, -2, -15, 0],\n [-6, 15, -12, 1, -15, 10, -9, 11, 11, -12, 13, 10],\n [10, 8, 10, -5, -13, 7, 0, 15, -5, -11, 15, -15],\n [-1, 10, -13, 11, -1, 6, -7, 1, -13, 4, 9, -1],\n [2, 4, 4, 4, -4, -16, 16, -8, 14, 5, -11, 10],\n [6, 13, -14, 3, 5, 4, -2, -2, -2, -12, 3, 5],\n [11, 10, -4, -3, -7, -7, 2, 10, 7, -16, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1346003809638", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[0, 11, 10, 16, 7, -16, -9, -15, 1, -2, -13, -2],\n [9, -4, -7, 10, 10, 7, 14, -7, -4, 2, -14, -2],\n [-8, -14, -13, 12, 12, 14, 5, 1, -15, -5, 5, 9],\n [8, 15, -8, -7, 15, -14, 13, -12, 13, -16, -8, -13],\n [3, 7, -4, -4, 2, 0, 3, -2, 16, 12, -9, 4],\n [-7, -16, 15, 7, -3, 11, 10, -2, 8, -16, -13, 10],\n [14, 3, 7, 0, 13, -10, 16, -13, -9, -15, 12, 0],\n [3, 12, -11, 3, 10, -11, -11, -10, -11, -16, 13, 5],\n [0, 3, 15, 15, -11, -11, -9, -6, 12, 16, -16, 10],\n [-9, -4, 12, 9, 9, 15, 7, -14, -4, -6, -12, -16],\n [15, -4, 0, -15, 4, 4, -11, 13, -2, -2, -8, -5],\n [-10, 7, 4, -8, 15, -15, -10, -15, -5, -2, -11, -10]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22138116934441", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-6, -14, 14, 4, 12, 2, -10, -6, -14, 16, 11, 15],\n [-13, 0, 9, 0, -9, -8, -10, -16, -1, -15, -9, 5],\n [10, 1, -1, 9, 5, -16, 15, 5, 10, 16, 13, 2],\n [16, 8, -11, 12, -2, -5, -2, 14, -16, 3, 12, -6],\n [-8, -1, -1, 16, 2, 8, 7, 15, -14, -4, 13, 6],\n [13, -5, 7, 7, 13, 0, -2, 7, 15, 7, -14, -16],\n [3, 4, -5, 4, 2, 2, -15, 16, -7, 15, 13, 0],\n [13, -3, -12, -4, -1, -4, 12, 7, 1, -9, -12, -3],\n [-14, -11, 0, 12, 5, -11, 10, -3, 3, 10, -14, 0],\n [-13, -4, -16, 4, -14, 8, -16, -3, -14, -8, -12, 8],\n [16, -12, -5, -6, 16, -1, -14, -12, 2, -6, 4, -8],\n [1, -5, 6, -4, 11, 6, -2, -9, -2, -16, -5, -8]], determine the value at position (6, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9386963144", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[16, 4, 14, 13, 2, 0, -16, 8, -7, 16, -3, -11],\n [3, -5, 10, -6, -2, 11, -15, -3, -12, -7, -3, 1],\n [0, 11, 14, 16, -13, 6, 4, 8, -2, -3, -4, 16],\n [4, 7, 8, 6, -13, 4, 7, 9, 8, -9, -11, -14],\n [-1, -11, 4, -14, -16, -10, 7, 3, -9, 8, 11, 8],\n [-5, 3, 1, 16, 16, -5, -3, 3, 1, -7, 0, -12],\n [11, 16, 4, 11, -16, -14, -4, 9, -11, 8, 2, 5],\n [-6, 8, 9, -7, 11, 2, 2, 1, 9, -9, -12, -9],\n [13, -9, -7, 10, -2, 3, 1, -5, 1, 10, -9, 15],\n [-8, -9, -9, -16, 8, -10, 15, -7, 5, 0, -6, -1],\n [8, 13, -5, 9, 9, -5, 14, 9, 11, -11, -16, -15],\n [10, -9, -7, -8, -6, -13, 13, 10, 0, -8, -11, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5555183614182", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 2) of the matrix A^7 where A is:\n[[-12, -10, 6, -2, -6, -2, -8, -10, -5, -4, -6, -5],\n [-10, -15, -2, 5, -10, 9, -7, 4, -9, -10, -10, 2],\n [6, -2, 7, 0, 0, 4, -4, 6, -8, -5, -12, 8],\n [-2, 5, 0, 12, 8, 9, -2, -2, 4, -8, 4, -8],\n [-6, -10, 0, 8, 14, -12, -8, 14, -8, -2, 5, 0],\n [-2, 9, 4, 9, -12, -9, 6, -10, -12, -4, 3, 7],\n [-8, -7, -4, -2, -8, 6, -2, 4, -10, -2, 6, 3],\n [-10, 4, 6, -2, 14, -10, 4, 2, 6, -12, 3, -2],\n [-5, -9, -8, 4, -8, -12, -10, 6, -1, 10, 4, 0],\n [-4, -10, -5, -8, -2, -4, -2, -12, 10, -14, -10, 5],\n [-6, -10, -12, 4, 5, 3, 6, 3, 4, -10, 8, -10],\n [-5, 2, 8, -8, 0, 7, 3, -2, 0, 5, -10, -14]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-92621258642", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-3, -6, 4, 2, -3, 10, -6, 6, -4, 0, 4, 4],\n [-6, -12, 8, -6, 4, 12, -6, 0, 2, -2, -4, 9],\n [4, 8, -13, -4, -10, 8, -1, -8, 10, -7, 2, 0],\n [2, -6, -4, 9, 12, 4, -10, -3, 0, -15, 2, -1],\n [-3, 4, -10, 12, 10, 0, -4, 0, -10, -8, 2, -2],\n [10, 12, 8, 4, 0, -1, 0, 4, 0, 0, 10, -4],\n [-6, -6, -1, -10, -4, 0, 6, -2, 0, 8, 8, 11],\n [6, 0, -8, -3, 0, 4, -2, 1, -14, -10, -4, -4],\n [-4, 2, 10, 0, -10, 0, 0, -14, 16, 6, 4, 2],\n [0, -2, -7, -15, -8, 0, 8, -10, 6, 11, 4, 1],\n [4, -4, 2, 2, 2, 10, 8, -4, 4, 4, -14, 8],\n [4, 9, 0, -1, -2, -4, 11, -4, 2, 1, 8, 15]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10091719677771", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (3, 2) of the result:\nA =\n[[4, 9, -8, -11, 16, -2, 1, 6, -10, -3, -3, 3],\n [13, 12, -10, 13, 13, 9, -12, 8, 13, 2, 13, -9],\n [5, 13, 1, 6, 7, -1, -9, -4, -3, 3, 15, -9],\n [-15, 6, -15, 11, -12, 8, -16, 5, -10, 6, 7, 9],\n [-3, 14, 10, 5, 0, 13, 4, -9, -15, -11, -4, 12],\n [13, 3, -2, -7, 7, 1, -14, 11, -5, 16, -1, -14],\n [16, 7, -16, -3, -8, -1, -8, -5, 14, -11, 13, 8],\n [12, 12, 5, -13, -8, 4, -6, -4, 3, -7, 6, 15],\n [7, -6, 16, 10, 6, -13, -2, -14, -14, 8, 5, -6],\n [-6, -9, 11, 3, 5, -6, 6, 7, -14, 13, 6, -16],\n [1, -14, 7, 8, -15, 5, -8, -1, -1, -2, -10, 10],\n [1, -10, 5, -4, 2, 9, 0, 0, -1, -4, -12, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553668169314", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[12, 12, 10, -5, -12, 13, 12, 6, -16, -12, -13, -6],\n [-3, 15, -4, 15, -8, 14, 0, -4, 13, 9, -6, -14],\n [2, 5, 5, 15, -10, 7, -8, 8, 5, 7, -10, 6],\n [-16, -12, 6, 4, -2, -15, 4, 1, 1, 1, -2, -6],\n [-5, -16, 15, -7, -5, 6, 10, -16, 16, 2, 6, -6],\n [-13, -14, -6, -8, 7, -8, -2, -16, -6, 6, -8, -11],\n [-5, -2, -14, -16, -4, 16, -6, -1, -14, -1, 15, 9],\n [11, 10, 0, 10, -5, 2, 16, 0, -8, -5, 16, -2],\n [12, -4, -14, 4, 14, -4, 15, 1, 1, -7, -1, 6],\n [14, 12, -1, 13, 8, 2, 15, -5, -2, -2, 3, -11],\n [2, 12, 10, 16, 2, -12, 3, -10, 11, 5, 13, 4],\n [-8, -4, 16, 9, -16, -15, 13, -1, -8, -2, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19468658217737", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 8) of the 8th power of the matrix:\n[[-13, -1, -6, 15, 5, -16, 9, -14, 15, 16, 16, -15],\n [5, -5, -15, -9, 0, -13, -16, -11, 5, -6, -15, 1],\n [-8, -11, -5, 4, 9, -7, -1, -2, 6, 4, -1, -6],\n [3, 4, -1, -6, 16, 5, 8, 16, -2, -16, -13, 0],\n [11, 15, -9, 2, 7, -14, -3, 15, -5, 14, 14, 15],\n [15, -1, -16, -4, -6, -6, 8, -12, 4, -5, -4, -14],\n [-5, 3, -13, -10, -14, -4, 12, 4, 8, -14, 13, 5],\n [-15, -8, -13, -9, 2, 4, -3, -16, 3, 2, -1, -7],\n [-15, -16, -9, -8, 1, -2, -1, 4, 8, 7, -1, -8],\n [-2, -4, 7, 16, -5, -7, 14, -13, -7, -14, 5, 4],\n [-14, 12, -12, -14, 13, -9, -4, 3, -4, -11, -7, 9],\n [-11, 9, 11, -5, -13, 7, -2, 7, -4, -14, 10, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-573732966409", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[9, 6, 16, 4, -3, -4, 15, -5, -7, 5, 8, 12],\n [-10, 12, -1, -9, -8, 3, 2, -1, 12, 11, 0, -13],\n [13, 13, 14, 15, 1, -11, -14, -3, 0, 10, 9, -3],\n [7, 4, -16, 15, -6, 0, -14, 12, 2, 16, -12, -15],\n [-8, 8, 3, -6, -5, -16, 7, 0, -1, -9, 7, -11],\n [-8, -14, 6, 14, 0, 4, -14, -3, -1, -13, -8, -2],\n [-16, -7, -6, 14, 0, -13, 1, -10, -5, 2, -9, -7],\n [-10, 11, 1, -16, 12, 5, 5, 7, 8, 3, 13, -10],\n [-14, -11, -1, -4, -10, 12, -6, -15, 7, 9, -8, -11],\n [13, -3, -3, -3, 7, 1, -15, 15, 9, 14, 4, 12],\n [-3, -16, 15, -5, -14, -3, 5, 9, 6, -13, 9, 9],\n [9, 13, 12, 15, -3, 12, -12, 13, 5, 15, 0, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470554464122", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-11, -10, 2, -4, -10, 8, 4, -4, -8, -1, -4, 0],\n [-10, -10, 5, 6, -8, -1, 9, 6, 2, -10, -8, -6],\n [2, 5, -15, 2, -6, 7, 10, -6, 6, -8, 2, -2],\n [-4, 6, 2, 9, 0, -10, -4, -12, -8, 5, 8, 14],\n [-10, -8, -6, 0, 4, 7, 10, 1, -10, -2, 4, 4],\n [8, -1, 7, -10, 7, -13, 2, 0, 2, -2, 4, -6],\n [4, 9, 10, -4, 10, 2, -1, 6, 8, -2, -2, -5],\n [-4, 6, -6, -12, 1, 0, 6, 1, -8, -8, 3, 0],\n [-8, 2, 6, -8, -10, 2, 8, -8, 1, -8, 1, -1],\n [-1, -10, -8, 5, -2, -2, -2, -8, -8, 10, 2, 2],\n [-4, -8, 2, 8, 4, 4, -2, 3, 1, 2, 15, 8],\n [0, -6, -2, 14, 4, -6, -5, 0, -1, 2, 8, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96154710895434", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-10, 0, 13, -13, -13, -2, 5, -6, 15, 2, -1, -7],\n [0, -11, 16, 3, -3, 11, -11, 2, -11, -12, -15, -11],\n [-3, -3, 13, 7, 13, -6, -3, 5, -14, 12, -9, -10],\n [7, -12, 3, -12, -11, 11, -2, 9, 4, 4, -8, -7],\n [8, 4, 14, -15, -1, 14, -5, 6, 0, -3, 16, -11],\n [6, 14, -12, -14, 11, 14, 0, 5, -4, 4, 4, -11],\n [-7, -3, 6, -10, 7, -2, 6, -12, 3, -7, 6, 10],\n [14, -11, -4, 11, -1, 0, 14, -7, 14, -11, 3, 4],\n [-1, 8, -9, -3, 6, -5, 3, 7, -4, 16, 15, 12],\n [10, -4, 5, -10, -10, 12, -3, -15, -10, 0, 16, 5],\n [-3, -16, -9, -9, 12, 0, 10, -9, -11, 13, 6, -2],\n [-3, 10, -14, -5, -14, -16, 0, 1, -7, -5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1553799651917", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 12) of the matrix A^9 where A is:\n[[-3, -9, 0, -2, -11, -10, 15, -8, 3, -15, 1, -15],\n [-2, -6, -14, -8, 6, -7, 7, 15, -13, -10, 12, 12],\n [-8, -15, -14, 11, 3, -13, 13, 14, 5, -8, -8, 14],\n [-1, 5, 14, -4, 11, -10, 8, -16, -6, 1, 14, -1],\n [13, 8, 11, 7, 4, -6, 10, -8, -1, -6, -3, -2],\n [5, 5, 8, 5, -14, 13, -16, -14, 0, 16, -4, -9],\n [15, 9, -11, -5, -9, 12, 3, -4, -9, 1, 9, 3],\n [16, -9, -5, -15, -1, -6, 0, 13, -9, 6, -7, -11],\n [-16, -6, 6, -14, -3, -4, 3, -2, -12, 4, -6, -10],\n [-5, -13, 6, 9, -15, -1, -6, 6, 6, 13, 3, -1],\n [-6, 14, 7, 9, -15, -2, 5, 9, -13, -11, 5, 6],\n [8, -14, 3, 16, 3, -11, -5, 2, 8, 1, -2, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1803932115473", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[7, 4, -2, 9, -7, -14, 12, -12, 7, -12, 15, 9],\n [10, -5, 15, -11, -4, 14, 1, 12, -7, -14, 1, 12],\n [9, 15, 10, -6, -11, 14, -9, 7, 1, -8, 5, -7],\n [-16, -14, 9, -10, 10, -2, 6, 4, -4, 15, 3, -12],\n [15, 11, 11, -5, -11, 9, 0, -7, 9, -1, 15, -1],\n [-3, 8, -16, -1, 16, 5, 11, 6, -15, -2, -12, 15],\n [6, 6, 16, -11, 16, 3, -15, 3, 6, 9, 9, -15],\n [-15, 16, -7, 11, -2, 1, 10, -5, -3, 14, -8, 9],\n [10, -1, -15, 0, 12, 15, 8, -14, -14, 10, -3, 16],\n [4, -7, 0, -10, 10, 14, 7, -7, 11, 16, -4, 12],\n [10, -6, -7, 12, -3, 4, 8, -10, -2, -9, 5, -4],\n [8, 11, -1, -10, -11, -2, -15, -5, -3, -15, 11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2635915010150257", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-1, -12, -4, -16, 12, -15, 0, 7, 1, -9, 11, -13],\n [1, -9, 3, 0, -6, 1, 3, -13, 9, -4, 4, 7],\n [14, 2, 16, 6, -11, 9, -16, -5, -7, 9, 10, 10],\n [-16, -3, -3, 15, 15, 2, -9, -3, -12, 14, 15, 7],\n [5, 4, 16, -2, -2, -14, 13, 1, -9, 2, 10, -12],\n [9, -3, -16, 15, 10, 1, 1, -6, -11, 12, -12, -2],\n [-8, 16, 0, -6, 13, -4, -6, -10, 4, -10, 5, 15],\n [-13, -2, 4, 11, -11, -15, 14, 10, -8, -16, -2, 6],\n [0, -10, -14, 2, 13, -7, 1, 6, 6, -13, -8, -6],\n [-16, -7, 14, -3, 11, 7, 11, -13, -3, -12, 15, 0],\n [9, 14, 11, 11, 12, 9, 5, 11, 5, 1, -12, 12],\n [-6, 7, 8, -1, 3, -4, -5, -13, 13, 12, 1, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1788324263334112", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-8, -7, -7, -9, 2, -14, 6, -15, -2, -10, -12, 2],\n [14, -15, -4, -3, 9, -10, 4, -2, -4, 3, 9, -13],\n [3, 2, 14, 2, -15, 9, 5, 0, 7, -5, 5, 3],\n [-14, -2, -3, -7, 3, 6, -8, -7, -14, -5, 3, 8],\n [8, 11, -1, 4, -10, -5, 1, 1, -6, 15, 16, 16],\n [-2, 1, 5, -11, 5, -11, -2, 13, 13, 15, 3, 0],\n [12, -6, 3, 3, -9, 0, -5, 15, 5, 10, 9, 14],\n [12, 14, 7, -13, -3, -4, 6, -9, -4, -16, 10, 0],\n [-8, 10, 9, 4, -13, -3, -6, -13, -12, 15, -1, 11],\n [-15, -9, 8, 6, 8, 0, 9, 4, -12, 7, -7, -15],\n [9, -8, 13, 15, -9, -14, -13, 8, 10, -1, 6, 9],\n [-2, 9, 8, -6, -4, -16, 14, 5, -12, 2, 14, 6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "430211975659", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 14, 4, -14, -6, -5, 8, 4, -10, 14, -6, -16],\n [-3, 6, -12, -12, -15, -11, 0, -12, -3, 11, -5, 16],\n [7, 1, -6, 8, 2, -13, -10, 1, -2, -2, -15, -10],\n [12, 8, 4, -5, -9, 4, 7, -15, 12, -4, 8, -10],\n [-6, 12, 0, -4, -8, 13, -8, 4, -3, 10, 10, 8],\n [-5, -9, 12, -12, 2, 8, 1, 6, 13, -16, 9, 3],\n [4, 3, -14, 0, 10, 1, -7, 3, 6, -9, -16, -10],\n [-13, 11, 2, -11, 9, 2, 0, 12, 4, -12, 0, -10],\n [10, 14, 9, -11, 14, -5, -2, -16, 9, -11, 7, 2],\n [1, -1, 0, -6, -13, -1, -8, 6, -7, 9, -14, 3],\n [0, 11, -16, 8, 16, 4, 13, -4, 6, -11, 2, -7],\n [-1, -4, 5, -15, 9, -12, 13, 5, 1, 12, 2, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "628780013967", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-9, 10, 12, 16, -10, -13, 9, -4, -6, 8, 4, -15],\n [8, 15, -16, 16, -11, -4, 0, -1, 5, -10, -15, -16],\n [2, -1, 12, -9, 9, -6, -7, -13, 6, -15, 16, 15],\n [3, -4, -14, 12, 1, -11, -3, -13, 9, -5, 11, -11],\n [-13, -9, 14, 15, -13, 11, -10, -8, -14, 16, 3, 2],\n [-1, -14, -11, 12, -3, 9, -8, 16, 2, -8, -11, 6],\n [-8, 9, -7, -11, -3, 0, -13, -3, 7, -4, -16, 16],\n [0, -3, 0, -1, -10, -5, 6, -11, 13, 5, -16, -14],\n [-16, 16, -6, 15, 2, 4, -6, 5, 2, 11, 15, 9],\n [2, -2, -12, -5, 6, 0, -6, 14, -9, 5, 15, -7],\n [-11, -6, 1, 16, -4, -12, 8, -13, 12, 7, 4, -6],\n [10, -7, -6, -8, -14, -11, 8, -10, 10, 5, 2, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140055257104199", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[5, 9, -8, -8, 10, 8, 2, 2, 4, 1, 2, 4],\n [9, -4, -4, -10, 3, 4, 12, -14, 0, 2, 2, -8],\n [-8, -4, -15, 0, -6, 4, -6, -3, -10, 2, -6, 6],\n [-8, -10, 0, -14, 4, -8, -8, 5, -8, 8, 8, 4],\n [10, 3, -6, 4, -10, -4, 4, -4, 0, -10, 4, 9],\n [8, 4, 4, -8, -4, -3, 3, 5, 1, 2, -4, -6],\n [2, 12, -6, -8, 4, 3, -2, 2, 15, 2, 14, -11],\n [2, -14, -3, 5, -4, 5, 2, -13, 2, -8, 4, 1],\n [4, 0, -10, -8, 0, 1, 15, 2, 5, -2, 3, 0],\n [1, 2, 2, 8, -10, 2, 2, -8, -2, 2, -4, 4],\n [2, 2, -6, 8, 4, -4, 14, 4, 3, -4, 5, 3],\n [4, -8, 6, 4, 9, -6, -11, 1, 0, 4, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3191391873943160", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[16, 7, -6, 8, 15, -16, 12, -6, 5, -5, -16, -1],\n [-1, -14, 13, -14, 14, -5, 13, 8, 6, 0, -16, 0],\n [1, -7, 16, -11, 4, 13, 9, -10, 4, 16, -14, -5],\n [16, 7, -10, -9, -10, -13, 5, 16, -6, -8, -2, 11],\n [13, 6, -13, -3, 2, 7, -10, 1, -2, -12, 3, -10],\n [-7, -16, 6, 13, 2, 16, -1, 13, 7, 15, -1, 2],\n [-14, 0, 14, -14, -5, 13, -11, -4, -12, 5, -8, 16],\n [10, -5, 1, -8, 8, 13, -1, 10, 6, -11, 14, -3],\n [10, 0, -11, -3, 2, -7, 14, 10, -14, 11, 7, -6],\n [-6, 14, -3, -6, -11, -16, -5, -15, -8, -1, -16, 16],\n [-15, 12, -8, -9, 11, -14, -6, -16, -11, -4, 10, 6],\n [15, 12, -11, -3, -3, 16, 7, -6, -3, 9, 9, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2324198426925", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[11, 14, -15, 5, 1, 15, -11, -13, 13, -5, -9, 4],\n [14, 5, -3, -8, 16, -1, 1, -1, 13, -5, -3, 13],\n [4, -11, 7, -4, 11, 0, -7, -4, 16, -10, -12, 16],\n [-3, 4, 1, -3, 10, 9, 11, -16, -4, 5, -14, 4],\n [-16, -7, 7, -9, -13, 15, 8, 14, -7, -4, -3, -13],\n [-14, -14, -14, -9, 10, -8, -11, 3, -7, 11, -13, -15],\n [-16, -14, -12, -9, -1, -5, 3, -3, 11, 16, 7, -15],\n [-11, 16, -12, 7, 11, 16, 1, 8, 12, -4, -1, -4],\n [3, -14, -3, -5, 16, 0, 1, -5, 9, 11, -4, -5],\n [-13, 3, -7, -7, 11, -5, 5, 4, -2, -1, -15, -2],\n [-2, 6, 1, 12, 16, 12, 0, 9, -8, 4, -16, -8],\n [10, -3, 14, 13, 1, 0, 0, 11, 7, 11, -3, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "890138499475", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[4, 11, -8, -4, -1, 6, 15, 16, 4, -13, -6, 5],\n [-4, 2, 7, -13, 8, 14, 4, 13, -12, -13, 15, -12],\n [-1, 10, -5, -16, -15, -9, 8, -16, -3, 15, 12, 2],\n [13, 6, -12, 6, -10, 14, -3, 10, 6, 9, -10, 4],\n [7, 0, -8, -2, -13, 7, 14, -5, -9, 0, -8, 0],\n [-1, -4, -5, 13, -14, -12, -4, -4, 11, -12, 3, 11],\n [1, 6, 10, -15, 14, 1, 6, -1, 9, 8, 5, -8],\n [6, 10, -7, -1, -13, 14, -13, -3, -1, 2, -14, -14],\n [3, -15, 3, 9, 2, 16, 11, -3, -3, 12, 9, 16],\n [-12, -15, -8, 2, 10, 10, 9, -3, -14, 4, -9, -11],\n [-15, -11, -6, -12, -7, -10, 1, -7, -10, 14, -9, -7],\n [11, 9, 3, -15, 6, 6, 0, 4, 9, 14, -9, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1621119561147", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (7, 2) of the 8th power of the matrix:\n[[4, 0, 4, 10, -2, 6, 8, 4, -9, 8, 0, -2],\n [0, -7, 0, -12, 2, 4, 0, 3, 2, -12, -3, 0],\n [4, 0, -9, 4, 4, 3, 8, 0, -2, 4, 2, -10],\n [10, -12, 4, 3, 8, 6, 4, -2, -7, 6, 2, 14],\n [-2, 2, 4, 8, 3, -4, 12, -2, 10, -1, -1, -4],\n [6, 4, 3, 6, -4, -2, 8, -4, -3, 0, 6, -2],\n [8, 0, 8, 4, 12, 8, 9, 7, -4, 1, -10, -6],\n [4, 3, 0, -2, -2, -4, 7, 13, 5, -12, -4, -10],\n [-9, 2, -2, -7, 10, -3, -4, 5, -5, 4, -2, 10],\n [8, -12, 4, 6, -1, 0, 1, -12, 4, 9, -3, -2],\n [0, -3, 2, 2, -1, 6, -10, -4, -2, -3, 4, 2],\n [-2, 0, -10, 14, -4, -2, -6, -10, 10, -2, 2, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34861942796", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[14, -2, 4, 8, -8, 1, -10, 4, -6, -4, 6, 4],\n [-2, -3, -6, -4, -10, -2, -10, -8, 13, 8, 13, -6],\n [4, -6, -5, 0, -10, 15, 3, 3, -5, 1, 7, -2],\n [8, -4, 0, -7, 11, 7, -4, 6, -3, 12, -2, -2],\n [-8, -10, -10, 11, -8, 14, -7, 3, 8, -16, 5, 2],\n [1, -2, 15, 7, 14, 10, -10, -4, 8, 9, 14, 0],\n [-10, -10, 3, -4, -7, -10, 13, 12, -4, 5, -3, 6],\n [4, -8, 3, 6, 3, -4, 12, -11, 1, 0, 1, -2],\n [-6, 13, -5, -3, 8, 8, -4, 1, 1, 0, -2, 11],\n [-4, 8, 1, 12, -16, 9, 5, 0, 0, 0, -6, -10],\n [6, 13, 7, -2, 5, 14, -3, 1, -2, -6, 3, -10],\n [4, -6, -2, -2, 2, 0, 6, -2, 11, -10, -10, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2708650229158", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (6, 7) of the result:\nA =\n[[1, 6, 3, 14, 8, -14, 3, 8, 13, 4, 13, -1],\n [6, -6, -5, -12, 5, 0, 4, 10, -4, 13, -2, 1],\n [-6, -10, 15, -4, -1, 9, 4, 1, 3, -5, 4, 15],\n [-8, -6, -6, 11, 0, 16, 7, 4, -6, 15, 9, 1],\n [-5, 3, 10, -16, -2, -3, 10, -14, -15, -5, 12, 6],\n [-8, -2, -16, -7, 4, -6, -13, -7, -7, 14, -6, -13],\n [6, -6, -12, 5, -6, -6, -9, 11, -15, -4, -3, -12],\n [-8, -10, -3, -7, 0, -7, 15, 7, 3, -2, -3, -2],\n [-5, 1, -2, -11, -9, 1, 14, -14, 7, 14, 10, 7],\n [7, -5, 10, 12, -16, -16, -5, -13, -10, -2, 9, 8],\n [14, 8, 8, 8, 0, -6, 4, -1, 16, -10, -6, -12],\n [-2, 8, -9, -16, 16, -3, -12, 9, 5, -15, -14, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12702753101", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-6, -2, 12, 0, -8, 4, 14, 2, 0, 0, -7, 1],\n [-2, 3, 6, -10, -7, -16, 8, 7, -12, -1, 0, -5],\n [12, 6, -16, -4, 11, 6, 8, 2, 1, -1, 4, -10],\n [0, -10, -4, 12, 2, -2, -8, 2, 0, 12, 0, -12],\n [-8, -7, 11, 2, 1, -2, 6, 4, -9, -6, -4, -4],\n [4, -16, 6, -2, -2, 5, 3, 6, -8, -10, 1, -6],\n [14, 8, 8, -8, 6, 3, -6, -4, 7, 0, 0, -10],\n [2, 7, 2, 2, 4, 6, -4, 0, 6, 2, 1, -11],\n [0, -12, 1, 0, -9, -8, 7, 6, -13, 2, -8, 2],\n [0, -1, -1, 12, -6, -10, 0, 2, 2, -10, 6, -6],\n [-7, 0, 4, 0, -4, 1, 0, 1, -8, 6, -4, 6],\n [1, -5, -10, -12, -4, -6, -10, -11, 2, -6, 6, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12508207140590525", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-5, 16, 16, -9, -5, 10, 10, -6, -7, 3, 16, 1],\n [-1, -16, -2, -12, -2, 5, 8, 16, 7, -7, -13, -11],\n [-8, -3, 11, 1, 14, 2, 16, 14, 8, -10, -13, -15],\n [8, 8, 8, 5, -16, 15, -2, -3, -10, -14, -15, 12],\n [-7, -4, 2, 1, -13, 13, -8, -7, -16, -15, -12, 15],\n [14, 11, -10, -15, -6, 2, 10, 6, 14, -11, -8, 16],\n [6, 12, 13, -11, 0, -15, -3, -1, 7, -13, 12, 9],\n [2, 1, 11, 11, 14, -5, 4, 15, -13, 6, -4, 0],\n [14, 5, -8, -11, -8, -15, -9, -8, 4, -5, -14, 7],\n [11, -8, -13, 10, -14, -6, -8, 13, 16, -2, 13, -6],\n [14, -15, -10, -8, 9, -7, 14, -2, 0, 10, -3, 11],\n [-9, 11, 13, 12, -5, 2, -12, -5, -11, -12, 7, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-135188932716", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 1) of the matrix A^8 where A is:\n[[8, 11, 7, 6, -16, -3, 2, 16, -11, 6, 10, -3],\n [5, -3, 5, -8, -6, -5, 8, -15, -8, 15, -3, 12],\n [2, -12, 0, 5, -6, 13, 12, -2, 0, 10, -15, -11],\n [-13, 6, 14, -16, -4, -11, -1, 15, -2, -13, -5, -7],\n [-15, 7, -1, 0, -9, 12, 14, 0, -13, 6, -6, 6],\n [-12, 15, -12, 0, 6, 13, 10, 16, -1, 14, -13, 3],\n [15, -1, 12, 12, -14, -10, 4, 12, 14, 0, 4, 11],\n [6, 14, 11, -6, -16, 7, -4, 10, -16, -8, 4, -7],\n [-8, -14, 12, 5, 13, 7, -14, -9, 9, 14, 16, -1],\n [-6, -2, 8, -3, -8, -7, 6, -11, 11, -4, -4, 13],\n [-12, -10, 9, 6, 11, 7, 16, -4, -4, 14, 12, 14],\n [14, 7, 13, -10, 3, -15, 1, -5, 4, 2, -11, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-220704065913", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-13, 3, -14, -8, 10, -12, -13, 2, -1, 5, -1, 4],\n [-12, -1, -15, -4, 15, -3, 4, -13, -7, -1, -6, 16],\n [5, -6, 11, -6, -10, -2, 3, -1, 12, -12, 4, -2],\n [-11, 6, 12, -16, -12, -8, -2, 16, 7, -11, -6, 8],\n [1, 5, -3, -7, 0, 12, -11, -10, -12, 10, 0, -10],\n [-16, -2, -6, 9, -3, -4, -13, 16, -3, -4, 0, -11],\n [5, 6, 15, -16, -13, -13, 16, 13, -2, 15, 9, -9],\n [9, 0, 13, -5, -11, 12, -3, -16, 10, -11, 16, 14],\n [15, 16, 3, -12, 0, 16, 6, -11, 12, -13, -10, -2],\n [4, -1, -11, -4, -9, 16, -14, 6, -9, 3, 13, -6],\n [3, -15, 0, -2, -16, -12, -12, -9, -13, -5, 13, 2],\n [5, 11, 13, -11, 3, -2, -9, 11, -6, -11, 10, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-245643579460", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[2, -5, 0, -9, 14, 2, 3, -15, -11, 10, 1, 3],\n [-8, -14, 1, -5, 2, 9, 16, 16, -11, -8, -7, 10],\n [0, 3, -4, 14, 0, -6, 10, -4, -2, 5, 8, 2],\n [12, 6, 2, -14, 2, -4, 16, 7, 16, -15, 2, 16],\n [10, -15, 16, -10, -7, 11, 8, 14, -4, 14, 12, -8],\n [14, 12, -13, 0, 0, 2, -14, 16, 1, 4, 7, -1],\n [14, -14, 0, 16, -10, 5, -10, 16, -12, -4, 13, -7],\n [-3, -10, 14, -13, -13, -3, -2, -3, -4, 7, 6, -1],\n [10, 4, -9, 16, 11, 10, 0, -3, 13, 0, -14, -11],\n [8, -11, -14, 2, -6, -2, 15, 14, 5, -10, -16, 15],\n [4, -9, 10, 6, -1, -3, 8, -12, -14, -13, -6, -9],\n [16, 5, -2, -5, 7, -10, 7, -3, -4, -7, -16, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1129945392606", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-9, -7, 0, 3, -10, 3, 1, 8, 2, -8, 0, -4],\n [-7, -12, 4, -4, -4, 10, 6, -1, 10, -10, 0, 4],\n [0, 4, 4, -5, 10, 0, 4, 7, 8, -12, 0, -13],\n [3, -4, -5, 13, 1, 4, -1, -4, 8, -12, 10, 8],\n [-10, -4, 10, 1, 3, 14, 6, -10, -6, -4, 4, 3],\n [3, 10, 0, 4, 14, -1, 0, 2, 12, -2, -5, -3],\n [1, 6, 4, -1, 6, 0, 8, 6, -7, 3, -3, -2],\n [8, -1, 7, -4, -10, 2, 6, 7, 0, 0, 11, -8],\n [2, 10, 8, 8, -6, 12, -7, 0, 4, -6, -2, -6],\n [-8, -10, -12, -12, -4, -2, 3, 0, -6, -2, 0, 10],\n [0, 0, 0, 10, 4, -5, -3, 11, -2, 0, 12, 2],\n [-4, 4, -13, 8, 3, -3, -2, -8, -6, 10, 2, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1881884893178", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-1, -2, -2, 8, -2, 9, 5, 4, -2, 10, 6, 2],\n [-2, 13, 12, 2, 4, -3, -4, -4, 0, -2, 0, 5],\n [-2, 12, -12, -10, 8, -1, -5, -6, -6, 6, 1, 6],\n [8, 2, -10, 7, 3, -2, -5, 4, -6, 8, -4, 6],\n [-2, 4, 8, 3, -14, -2, 4, -2, -2, -10, -4, -14],\n [9, -3, -1, -2, -2, 5, -12, 2, -2, 4, 5, -6],\n [5, -4, -5, -5, 4, -12, 3, 0, 6, 4, 14, 5],\n [4, -4, -6, 4, -2, 2, 0, 3, 5, 14, 9, 10],\n [-2, 0, -6, -6, -2, -2, 6, 5, 10, 3, 4, -4],\n [10, -2, 6, 8, -10, 4, 4, 14, 3, -6, 4, 10],\n [6, 0, 1, -4, -4, 5, 14, 9, 4, 4, 1, 0],\n [2, 5, 6, 6, -14, -6, 5, 10, -4, 10, 0, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664449972663134", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[9, -4, 11, 9, 6, -6, -4, 2, -2, 0, -2, 4],\n [-4, -16, 6, -4, -16, -11, 4, -12, 2, 6, -2, -4],\n [11, 6, 10, -10, -8, 2, 2, 4, -12, 7, -2, -6],\n [9, -4, -10, -8, 2, 7, 2, -9, -2, 6, 4, -6],\n [6, -16, -8, 2, 7, -8, 2, -4, 0, 8, -6, -1],\n [-6, -11, 2, 7, -8, -16, -6, -10, 0, -10, 0, -2],\n [-4, 4, 2, 2, 2, -6, 12, 2, 6, 8, -2, 14],\n [2, -12, 4, -9, -4, -10, 2, -16, 0, -6, 8, 2],\n [-2, 2, -12, -2, 0, 0, 6, 0, 6, 9, 2, 8],\n [0, 6, 7, 6, 8, -10, 8, -6, 9, -6, 7, -6],\n [-2, -2, -2, 4, -6, 0, -2, 8, 2, 7, -10, 2],\n [4, -4, -6, -6, -1, -2, 14, 2, 8, -6, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114114702285355", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-12, -2, 15, -14, 6, 10, -4, -8, 12, -5, 6, -3],\n [-2, -8, 8, -4, -11, 2, 5, 2, 11, 1, -4, -4],\n [15, 8, 9, -15, 2, -2, 0, 5, 8, 4, 6, 8],\n [-14, -4, -15, -15, 4, 0, -1, 4, 8, -7, -4, -7],\n [6, -11, 2, 4, 12, 10, 6, 6, 2, 13, 4, 6],\n [10, 2, -2, 0, 10, -12, 2, 0, 8, -16, -5, 4],\n [-4, 5, 0, -1, 6, 2, -4, 10, -2, 4, -4, -10],\n [-8, 2, 5, 4, 6, 0, 10, 5, 0, 4, 4, 6],\n [12, 11, 8, 8, 2, 8, -2, 0, 7, 7, -9, -5],\n [-5, 1, 4, -7, 13, -16, 4, 4, 7, 7, 0, -6],\n [6, -4, 6, -4, 4, -5, -4, 4, -9, 0, -12, 1],\n [-3, -4, 8, -7, 6, 4, -10, 6, -5, -6, 1, 12]], determine the value at position (11, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6429945402881", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-15, -8, -3, -6, 2, 0, -8, -4, -4, -7, 1, -5],\n [-8, -3, -4, 6, 9, 2, -4, -5, -3, 0, 2, 10],\n [-3, -4, 2, -7, 1, 8, -10, -4, 0, 0, 1, -1],\n [-6, 6, -7, 4, 4, -11, -2, -9, 8, -4, -3, -3],\n [2, 9, 1, 4, -6, -2, 2, -10, -2, -9, -12, -8],\n [0, 2, 8, -11, -2, -1, -16, -7, 6, 6, 3, -3],\n [-8, -4, -10, -2, 2, -16, -13, 1, 2, 2, 9, -6],\n [-4, -5, -4, -9, -10, -7, 1, -6, 0, -12, -5, 10],\n [-4, -3, 0, 8, -2, 6, 2, 0, -2, 8, -4, -8],\n [-7, 0, 0, -4, -9, 6, 2, -12, 8, 10, -9, 13],\n [1, 2, 1, -3, -12, 3, 9, -5, -4, -9, -11, 0],\n [-5, 10, -1, -3, -8, -3, -6, 10, -8, 13, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2164458937596589", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[-1, 12, -6, -4, 2, 1, 8, 2, 6, 4, 6, 2],\n [12, -1, -10, 5, -3, -1, 10, -6, 0, 9, 6, 1],\n [-6, -10, 13, 4, 0, 4, 0, 0, -4, 8, -3, -1],\n [-4, 5, 4, -2, 1, 4, -2, -6, 0, 0, -14, 1],\n [2, -3, 0, 1, -3, -6, 7, -12, -3, 14, 12, 3],\n [1, -1, 4, 4, -6, -1, 4, -4, 10, 6, 2, 3],\n [8, 10, 0, -2, 7, 4, 12, 9, 8, 5, 10, -6],\n [2, -6, 0, -6, -12, -4, 9, 5, 0, 5, 6, 2],\n [6, 0, -4, 0, -3, 10, 8, 0, -16, -4, -6, 1],\n [4, 9, 8, 0, 14, 6, 5, 5, -4, -15, 2, -7],\n [6, 6, -3, -14, 12, 2, 10, 6, -6, 2, 8, 8],\n [2, 1, -1, 1, 3, 3, -6, 2, 1, -7, 8, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1448739761558668", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[5, 10, -5, 16, -8, -3, 1, 1, -8, -10, 16, 16],\n [-6, -16, -6, 9, -10, -9, 12, -9, 2, 10, 3, -2],\n [0, -13, -15, -10, 2, -5, -3, -12, 9, 8, -7, 3],\n [-5, -10, 7, -16, 6, -8, -5, -13, -13, -11, -16, -2],\n [-9, -4, 1, 6, 8, 12, -6, 9, -8, -2, 0, 16],\n [2, 7, 10, 12, 4, 11, 14, 16, 7, 2, 12, -7],\n [0, 16, 3, -12, -16, 4, 4, -2, -11, 11, 0, -13],\n [-1, -6, 7, 12, 13, -3, 5, 7, -16, 2, 15, -3],\n [-12, -10, 3, 0, -13, -12, -14, 12, 13, 5, -7, 7],\n [-6, 4, -10, 16, 5, 5, 14, -14, 8, 11, 0, -9],\n [-13, 3, -9, 7, 9, 11, -9, -13, 1, 11, -12, 12],\n [-11, 13, 14, -3, 9, 9, -7, -10, -1, -3, 9, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3931437855084", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (1, 1) of the result:\nA =\n[[13, 6, -15, -13, 9, -3, -3, -16, 11, 3, 2, -14],\n [16, -3, -9, 3, 5, 9, -3, 6, -12, -16, 9, -2],\n [-5, 4, 0, -8, -16, 14, 0, 3, -13, 8, -10, 10],\n [-15, -12, -13, -14, 8, 9, 10, 16, -8, -9, -4, -13],\n [-12, -3, -5, 3, -12, 8, -4, 6, 14, 10, -7, -15],\n [3, 11, -2, -16, 7, 12, 9, 2, 3, -16, -1, -4],\n [7, 7, 8, 14, 0, -3, 11, 5, -9, -16, -6, 12],\n [-2, -8, 0, 10, 2, -14, 2, 6, -10, -9, -12, 12],\n [12, 12, 6, -5, 0, -2, 2, 6, 2, 12, 0, -12],\n [-6, 5, -15, -4, 9, 16, 5, -10, 11, -12, 16, -15],\n [-12, 6, 6, -13, -11, -11, 11, -4, -10, 15, 5, 2],\n [7, 16, -16, 3, -10, -15, 15, -12, -15, -14, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24888346069778", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-10, 16, -2, 1, 16, -9, -2, 14, 11, -11, -8, -13],\n [0, 0, 2, -1, 4, 15, 10, 4, -4, 0, 5, 3],\n [4, -6, 1, -13, -15, -12, -10, 14, 13, -4, 16, 12],\n [-6, -5, 12, 10, 10, -4, 3, -13, -6, 0, -3, -3],\n [12, 10, 7, -14, -12, -4, -12, -10, -8, 11, -15, 11],\n [-13, 7, -15, 16, 7, 16, 0, 3, 3, 6, -12, 13],\n [4, 0, -2, 2, 10, 1, 6, -8, 2, -15, 14, 15],\n [0, 9, 4, 2, -2, -13, -8, 16, 10, -14, -15, -16],\n [-13, 2, -16, -2, -16, 5, -4, -5, 1, -15, -10, 2],\n [-16, 1, -12, -3, 12, 7, -6, 10, 5, -6, 4, -13],\n [0, -15, 3, -6, -15, 8, -4, 0, 15, -3, 4, 16],\n [-1, 5, -6, 12, 9, 4, 2, -2, 14, 14, 10, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1633916290899", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-8, -10, 4, -3, 8, -8, -6, 0, 6, 8, 10, 0],\n [-10, -5, 15, 2, 6, -2, -5, -6, -5, 3, -12, -4],\n [4, 15, -14, 3, 2, 12, -3, 8, -4, -3, 4, 6],\n [-3, 2, 3, 5, 10, -6, -2, 2, -4, 4, -2, -8],\n [8, 6, 2, 10, 7, 8, 2, 8, 8, 0, -3, 2],\n [-8, -2, 12, -6, 8, 1, 0, 6, 2, -15, -2, -2],\n [-6, -5, -3, -2, 2, 0, -5, -7, -8, 6, -8, 7],\n [0, -6, 8, 2, 8, 6, -7, 2, 2, 0, -8, 5],\n [6, -5, -4, -4, 8, 2, -8, 2, -10, -2, 15, -5],\n [8, 3, -3, 4, 0, -15, 6, 0, -2, -5, -4, 4],\n [10, -12, 4, -2, -3, -2, -8, -8, 15, -4, -10, -6],\n [0, -4, 6, -8, 2, -2, 7, 5, -5, 4, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-288999514244", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[1, -4, -4, -5, 4, 2, 0, -4, 6, 8, 0, 10],\n [-4, 8, -10, -2, 7, 6, 2, -4, -7, 0, -6, 0],\n [-4, -10, 8, -5, 2, 12, 10, 2, 11, -9, -2, -10],\n [-5, -2, -5, -15, -4, 12, -4, -5, 6, -6, -9, 6],\n [4, 7, 2, -4, 15, 6, 0, 12, -2, 2, -2, 1],\n [2, 6, 12, 12, 6, 0, 3, 10, 0, 0, -12, 2],\n [0, 2, 10, -4, 0, 3, 11, 9, 9, -1, 10, 2],\n [-4, -4, 2, -5, 12, 10, 9, 3, 5, 0, -2, 6],\n [6, -7, 11, 6, -2, 0, 9, 5, -16, 4, 4, -10],\n [8, 0, -9, -6, 2, 0, -1, 0, 4, -1, 11, -2],\n [0, -6, -2, -9, -2, -12, 10, -2, 4, 11, 10, 6],\n [10, 0, -10, 6, 1, 2, 2, 6, -10, -2, 6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1969096831274", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-2, 10, 4, 6, -12, -3, -4, 0, 0, -4, -4, 4],\n [10, -8, 6, 0, 4, 9, 0, -2, 8, -14, -2, -14],\n [4, 6, -1, -8, 14, 7, 9, -8, -4, 14, -2, 3],\n [6, 0, -8, 14, 2, -6, -14, 9, -6, -8, -7, 0],\n [-12, 4, 14, 2, -1, 2, -6, -5, -4, -4, -2, -12],\n [-3, 9, 7, -6, 2, 5, -16, 8, -8, 6, 6, 4],\n [-4, 0, 9, -14, -6, -16, 12, -2, 0, 0, 4, -3],\n [0, -2, -8, 9, -5, 8, -2, 0, 0, 2, 11, 12],\n [0, 8, -4, -6, -4, -8, 0, 0, -15, -5, -2, -3],\n [-4, -14, 14, -8, -4, 6, 0, 2, -5, -9, -10, 7],\n [-4, -2, -2, -7, -2, 6, 4, 11, -2, -10, -14, -4],\n [4, -14, 3, 0, -12, 4, -3, 12, -3, 7, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3106230478406075", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, 8, -10, -13, -11, -4, 3, -4, -11, -8, 13, 10],\n [-8, -7, -16, -14, 16, -14, 14, -11, -1, -4, 16, -16],\n [-8, 5, -16, 6, 1, -5, -12, 3, 2, -15, -13, 10],\n [-9, -10, 12, 1, -6, -9, -15, -8, -11, 12, -3, -2],\n [-12, -6, 6, 1, -7, 4, -11, -5, -11, -5, -15, 10],\n [-4, -5, -14, 8, 7, 16, -10, -6, -11, 15, 8, -12],\n [-5, 4, -9, -2, 0, -11, 5, 6, -11, 3, 16, 9],\n [2, -13, -9, 11, 11, 3, 9, 15, 13, 5, 15, 3],\n [-3, -5, -16, 6, 11, 5, -7, 8, 15, 6, 2, 0],\n [7, -11, 2, 2, -5, 15, 8, 15, -13, -15, 6, -10],\n [3, 0, 5, -10, 6, -3, -7, -16, 0, -3, 0, -7],\n [1, -7, 3, -1, 0, 11, -8, 3, -11, -4, -8, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364045210801147", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[5, 6, 8, -10, -2, 12, -9, -7, -7, -4, 2, 6],\n [-2, 0, -7, 16, 1, -13, -13, -2, 14, -15, -5, 16],\n [3, -15, -16, 3, 7, -3, 12, 4, 15, 6, 12, -3],\n [-10, 6, 0, 15, -12, 3, -9, -9, 7, 8, 10, 15],\n [-10, -5, -10, -9, -13, 11, -1, 10, 9, -6, -16, 4],\n [15, -6, 6, -13, -15, 3, 11, -8, -12, -7, -8, -14],\n [14, -13, -10, -1, -1, 11, -4, 3, -13, 7, 15, 5],\n [-12, 15, 7, -9, 1, -8, -15, -16, -10, 3, -6, 3],\n [-15, 16, 5, 11, 14, -7, 5, 0, -10, -4, 12, 9],\n [-14, -7, 6, 3, -13, 15, 1, -16, 6, -4, -13, -8],\n [14, -15, -1, 4, 4, -15, -10, -2, -8, -16, -1, 6],\n [7, 7, -7, -6, 13, 16, -10, -11, -9, -1, 4, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-113071195761", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[10, -10, 2, 8, 0, -2, 9, 4, -6, -2, -4, -12],\n [-10, -6, -15, 2, -8, 0, 0, 6, 4, 5, 12, 2],\n [2, -15, -7, -4, -2, 4, -1, -6, 6, 12, -5, -4],\n [8, 2, -4, 11, 8, -2, -4, -2, -6, -6, 3, 4],\n [0, -8, -2, 8, 2, -13, -1, 4, -10, -3, 9, -10],\n [-2, 0, 4, -2, -13, 9, 6, -10, -12, 1, -4, -14],\n [9, 0, -1, -4, -1, 6, -13, -14, 0, -4, -1, 7],\n [4, 6, -6, -2, 4, -10, -14, 8, 1, -1, 5, -2],\n [-6, 4, 6, -6, -10, -12, 0, 1, 14, -10, -7, -14],\n [-2, 5, 12, -6, -3, 1, -4, -1, -10, 2, -9, 4],\n [-4, 12, -5, 3, 9, -4, -1, 5, -7, -9, 10, -7],\n [-12, 2, -4, 4, -10, -14, 7, -2, -14, 4, -7, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2700019957965", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-6, 2, -4, 10, -10, 6, -3, 9, -6, -7, 9, -4],\n [2, -9, 15, -9, 4, 0, 12, -4, -7, 0, -2, 3],\n [-4, 15, 2, 0, 2, -2, 7, 1, -4, -14, 4, 7],\n [10, -9, 0, 4, -12, 0, -2, -13, -6, -4, -8, 2],\n [-10, 4, 2, -12, 9, 5, 1, 4, 2, -2, -6, 2],\n [6, 0, -2, 0, 5, 2, 6, 6, 4, 5, -5, -2],\n [-3, 12, 7, -2, 1, 6, 10, -9, 7, 10, -2, 2],\n [9, -4, 1, -13, 4, 6, -9, -11, -8, 11, -6, -8],\n [-6, -7, -4, -6, 2, 4, 7, -8, 16, 7, 8, -4],\n [-7, 0, -14, -4, -2, 5, 10, 11, 7, 5, 4, -6],\n [9, -2, 4, -8, -6, -5, -2, -6, 8, 4, 3, -2],\n [-4, 3, 7, 2, 2, -2, 2, -8, -4, -6, -2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9998967835376", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[-7, 9, 3, -14, 8, 7, -11, -15, 13, -13, 3, 1],\n [-12, -2, 2, 4, -13, 4, 14, 9, -7, -9, 1, 1],\n [-4, -15, -7, -3, -14, -16, -2, -7, -4, 14, 8, 4],\n [-9, -9, 1, 0, -7, -5, -12, 3, 15, 10, -10, -1],\n [-2, -16, 1, 2, 8, -16, 15, 15, -7, 14, 4, -16],\n [7, 16, 9, 6, 2, 1, 16, -6, -6, 15, 12, -14],\n [2, -13, -6, 2, 8, 3, 4, -6, -1, 9, -7, -10],\n [-12, -16, 13, 7, 3, 10, -2, 8, -10, 16, -6, -4],\n [-13, 13, 4, -14, -11, -14, -1, -6, -9, 9, -7, 16],\n [12, 2, 8, 5, 10, -2, 10, 0, -16, -10, 2, 0],\n [-10, 15, 8, 8, 0, -6, 3, -11, -14, 10, -14, -7],\n [-7, 14, -11, 7, -2, -2, -14, 2, 13, 4, -14, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-629442498783", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 8) of the matrix A^9 where A is:\n[[0, 4, -12, -10, 10, 10, -10, 0, 8, 6, -6, -2],\n [4, 13, 7, -2, 0, -7, 12, -16, -9, 1, -11, 8],\n [-12, 7, -2, -10, 2, 12, 6, 15, -6, -14, 4, 7],\n [-10, -2, -10, 11, -4, 0, -4, 1, -10, -14, 0, 14],\n [10, 0, 2, -4, 14, -7, 0, -2, 3, -2, 14, 4],\n [10, -7, 12, 0, -7, 12, 8, -2, -14, 10, -15, -2],\n [-10, 12, 6, -4, 0, 8, 12, 5, -3, 10, -2, -8],\n [0, -16, 15, 1, -2, -2, 5, 2, 4, -6, -6, 14],\n [8, -9, -6, -10, 3, -14, -3, 4, 9, -9, -3, 2],\n [6, 1, -14, -14, -2, 10, 10, -6, -9, -12, 1, -8],\n [-6, -11, 4, 0, 14, -15, -2, -6, -3, 1, 10, 5],\n [-2, 8, 7, 14, 4, -2, -8, 14, 2, -8, 5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99165083703930", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 4) of the 7th power of the matrix:\n[[0, 0, 9, 3, 2, -12, 6, -2, 12, -15, -6, -14],\n [0, -12, 13, -4, 7, -1, 6, -3, -1, 5, -6, 7],\n [9, 13, 14, 6, 9, 7, -2, 7, 2, -14, -4, 0],\n [3, -4, 6, -11, -4, 7, 2, 6, 2, 6, 2, -6],\n [2, 7, 9, -4, -15, 10, 6, -8, -8, -9, 0, -2],\n [-12, -1, 7, 7, 10, 7, 4, -8, 1, 11, -4, 1],\n [6, 6, -2, 2, 6, 4, -2, 6, -6, 4, 8, 10],\n [-2, -3, 7, 6, -8, -8, 6, -4, 3, -7, 0, 1],\n [12, -1, 2, 2, -8, 1, -6, 3, 10, 0, -4, 10],\n [-15, 5, -14, 6, -9, 11, 4, -7, 0, 12, -4, 2],\n [-6, -6, -4, 2, 0, -4, 8, 0, -4, -4, -11, -9],\n [-14, 7, 0, -6, -2, 1, 10, 1, 10, 2, -9, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1277674675", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-16, 9, 10, 8, 2, -8, 13, -6, 12, 0, 11, -15],\n [-4, 4, 6, -14, -5, 2, -12, 16, 16, -8, 11, -14],\n [13, 4, 2, 15, 9, -14, -6, 8, -7, -16, -10, 0],\n [16, 13, 14, 10, 14, 9, 1, -8, 11, 6, -10, 9],\n [4, 15, 12, 10, -13, 14, -6, -4, -16, 3, 14, 10],\n [10, 9, -2, 10, -16, 10, -8, 13, -5, -8, -13, 14],\n [-14, 0, 15, -15, -6, -9, 10, 12, -8, -8, 0, -15],\n [5, 0, -15, 7, 9, 0, -14, 5, 16, -11, -5, 0],\n [16, 8, 15, -3, 15, 15, -11, 13, -5, 4, -8, -4],\n [-4, 2, -10, 16, -6, -7, -3, -6, 4, -6, 10, 7],\n [-16, -3, 10, -7, 15, -6, 13, -2, -16, 5, -7, 13],\n [7, -10, 16, -5, -3, 0, -8, 7, -7, 9, -13, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37405042095173", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (1, 6) of the result:\nA =\n[[10, -6, -2, 0, 13, -4, -6, 3, 0, 4, -8, -12],\n [-6, -14, 6, -4, -1, 0, 0, -6, 9, -10, 2, -4],\n [-2, 6, 3, 6, 0, -1, -5, 0, 0, 12, -5, -4],\n [0, -4, 6, 16, -3, -8, 4, 4, -11, -12, 0, 4],\n [13, -1, 0, -3, 2, 2, -14, 0, -10, -5, -4, -2],\n [-4, 0, -1, -8, 2, 5, 4, -2, -4, 2, -7, -12],\n [-6, 0, -5, 4, -14, 4, 2, 1, 0, 1, 0, 0],\n [3, -6, 0, 4, 0, -2, 1, -4, -4, 2, 6, -2],\n [0, 9, 0, -11, -10, -4, 0, -4, -12, -14, -3, -2],\n [4, -10, 12, -12, -5, 2, 1, 2, -14, 1, -2, 0],\n [-8, 2, -5, 0, -4, -7, 0, 6, -3, -2, 6, -6],\n [-12, -4, -4, 4, -2, -12, 0, -2, -2, 0, -6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3576005594400", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 9th power of the matrix:\n[[-6, 3, 10, -12, 6, -1, -1, -6, 6, 8, 0, -4],\n [3, 12, 15, 4, -4, -10, -4, -6, 4, -2, 13, 6],\n [10, 15, -13, 6, 2, -13, -10, -3, -12, 12, -6, -14],\n [-12, 4, 6, -12, -12, 6, 3, 6, 4, 2, 6, 1],\n [6, -4, 2, -12, -1, 6, -12, 1, 4, 0, 2, 0],\n [-1, -10, -13, 6, 6, -4, -8, -9, 1, -2, 0, 8],\n [-1, -4, -10, 3, -12, -8, -16, -4, 8, -2, -2, 8],\n [-6, -6, -3, 6, 1, -9, -4, 2, 4, 5, 4, -14],\n [6, 4, -12, 4, 4, 1, 8, 4, -2, -2, 0, 8],\n [8, -2, 12, 2, 0, -2, -2, 5, -2, 9, 0, 0],\n [0, 13, -6, 6, 2, 0, -2, 4, 0, 0, 5, 2],\n [-4, 6, -14, 1, 0, 8, 8, -14, 8, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14262263737144", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 11, 0, 13, -5, -10, 16, 5, 14, 8, 7, 15],\n [6, 13, -2, 9, -10, 13, 8, 6, 10, 14, 12, 0],\n [-10, -13, 1, -12, 16, -10, 5, 9, 10, -16, -4, -7],\n [6, -5, -2, -5, 7, 15, 9, -1, -1, 1, 1, -1],\n [-2, 6, -10, -9, -12, 12, 11, 13, 9, -4, 0, 12],\n [-10, -3, -1, -2, -10, 16, -11, -16, 6, -11, -7, -2],\n [-12, -5, 15, -12, -15, 16, -11, 9, 9, -9, 8, 6],\n [0, -1, 10, 8, 15, 8, 15, 2, 5, 2, -6, 5],\n [3, -1, -6, -11, -14, 2, -7, 15, 4, 14, -11, -13],\n [-4, -5, 6, -14, 0, 5, 12, 10, -10, -13, -6, 16],\n [11, 1, -11, 6, -1, 6, -11, 7, -2, -8, -9, 16],\n [9, 0, 14, -6, 9, -13, -9, 7, 6, -3, 2, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20175046254177", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-13, -6, 15, 2, 8, 16, -4, -14, -2, 13, -6, -13],\n [11, 13, -15, -3, 2, 14, 16, -7, -13, 12, -4, -1],\n [14, 16, -6, 9, -13, -9, 13, 3, -1, -2, -13, 10],\n [2, 4, 4, 8, 0, 1, 10, -13, 14, 2, 0, 0],\n [3, -1, -12, -10, -8, -3, -1, 7, -9, 9, 0, 9],\n [-14, -10, -12, 3, -12, 8, -8, -3, -6, 1, 4, -11],\n [-14, -7, 4, -8, 1, -3, -14, 11, -3, 6, -5, 0],\n [-7, -3, 8, 2, 4, 13, -5, -7, -4, -14, -16, -14],\n [9, 13, -13, -9, 14, 13, 9, -1, 5, 15, -4, 8],\n [-3, -16, 0, -1, 4, 10, -10, 11, 14, 16, 12, 7],\n [0, -11, 16, 9, -10, -1, -15, 6, 15, 12, -9, -2],\n [-3, -11, -4, -5, 10, -6, 11, -10, 3, -6, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3275513359555329", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (7, 12) of the matrix A^7 where A is:\n[[4, 10, 5, 8, 14, -1, 4, 12, -16, -14, 9, -8],\n [11, -8, -4, 6, -14, 4, 14, -2, 0, -3, -1, 0],\n [9, -3, 5, -14, -14, -2, -13, 15, -1, 13, 16, -9],\n [14, 13, -14, 3, -12, -12, -15, 9, -1, 15, -15, 10],\n [-2, 6, 5, 3, -16, 12, 5, 12, 5, -6, 4, -6],\n [5, -8, -10, -13, -5, 10, 12, -1, -4, -10, 13, -7],\n [13, -5, 16, -16, 6, 8, -1, -4, -8, 12, -5, -13],\n [-12, 8, 11, -1, 3, -10, 0, 0, 10, 4, 3, 15],\n [5, -2, 11, -15, 16, 5, 11, -7, -1, -3, 10, -6],\n [-10, -12, 7, 9, 5, -13, 3, -14, -13, -11, -5, -16],\n [7, 2, -13, 14, -13, 3, -14, 11, 12, 1, -7, -5],\n [-4, 6, 16, -15, 13, 13, 3, 9, 7, 0, 3, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16819908144", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-9, 8, -10, -5, 1, 10, 2, 4, 10, 4, 14, -12],\n [8, -14, 0, -2, -4, 10, -8, 6, -2, 8, 2, 5],\n [-10, 0, 10, 6, 8, -2, -2, 0, -16, -4, 2, 0],\n [-5, -2, 6, -13, 10, -5, -4, 10, -4, -11, 2, -6],\n [1, -4, 8, 10, 1, 10, 4, -2, 4, -5, 11, 0],\n [10, 10, -2, -5, 10, -11, 6, 3, 14, 0, -10, 2],\n [2, -8, -2, -4, 4, 6, -1, -1, 5, 4, -4, 2],\n [4, 6, 0, 10, -2, 3, -1, -13, 2, -14, -10, -4],\n [10, -2, -16, -4, 4, 14, 5, 2, -2, 4, 4, 0],\n [4, 8, -4, -11, -5, 0, 4, -14, 4, -9, 0, 6],\n [14, 2, 2, 2, 11, -10, -4, -10, 4, 0, -14, -4],\n [-12, 5, 0, -6, 0, 2, 2, -4, 0, 6, -4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20425454581349", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[8, -5, 6, 4, -12, 1, -1, 16, -10, -7, -13, 3],\n [-5, -1, 1, -14, 11, -10, 9, 12, -9, 7, -8, -15],\n [9, -5, 3, 3, 8, 11, 3, -15, -12, 6, -1, -16],\n [-1, 2, 2, 13, -8, -2, -7, -14, -1, -2, -8, -14],\n [-11, 10, -10, -2, 16, 7, 7, 2, 6, 11, -13, 8],\n [-2, -12, -15, 4, -5, -5, -8, -12, 1, -16, 12, 3],\n [3, 14, 5, -5, -11, -14, 14, 3, -15, 13, -1, 8],\n [3, -14, 0, 0, 5, 13, 8, -14, 2, -9, 1, -7],\n [4, 1, 14, -1, 3, 9, -14, -8, 5, -14, -4, -5],\n [-2, -8, -3, 9, 10, 15, -1, 14, -2, 12, 5, -13],\n [13, 15, -13, -16, -10, 7, 16, -2, 8, 8, -3, -5],\n [-5, -1, 8, -6, -12, -3, 12, -15, -15, -5, -12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "487182758533212", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 4) of the matrix A^8 where A is:\n[[16, -7, -4, -7, -2, -8, 9, -15, 5, -5, 0, 1],\n [4, 5, 4, 8, -4, 2, -2, -7, -10, 7, -4, 10],\n [-10, -11, -1, -12, -4, 9, 0, -6, -3, 5, 14, 12],\n [12, 11, 3, -12, 11, 14, 5, 11, 10, 9, 9, 10],\n [11, 2, -10, 12, 7, 5, -9, 3, 6, -5, 11, 6],\n [4, 8, 16, -13, -8, 4, -16, 8, 15, 0, -3, 4],\n [-14, -16, 0, 5, 14, -6, -13, 2, 14, 10, 1, -3],\n [-12, 6, 9, -6, 10, 3, -3, 11, -12, 16, 14, 9],\n [-10, -14, 7, -10, 11, 15, -10, -8, -2, -8, -13, -3],\n [1, -13, -14, 2, 10, 13, -4, 16, -13, 2, 15, -12],\n [0, 0, 0, 8, -9, 11, 2, -9, -8, 1, -14, 10],\n [-1, 13, -7, 6, 12, 14, 14, 0, -12, 8, 7, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114089145494", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-6, 7, 4, -10, 8, -4, -8, -9, -12, -14, 8, -5],\n [7, 16, -4, 14, 10, -9, -16, -6, -2, -1, 8, 2],\n [4, -4, -1, 14, -1, 8, 6, -5, -7, -4, 4, -8],\n [-10, 14, 14, 16, -2, 4, -2, -10, 2, 6, 12, 6],\n [8, 10, -1, -2, -3, -13, 7, 14, -2, -4, 3, 2],\n [-4, -9, 8, 4, -13, -15, -4, -2, -4, -10, 2, 4],\n [-8, -16, 6, -2, 7, -4, -7, -3, 2, -10, 10, 0],\n [-9, -6, -5, -10, 14, -2, -3, 11, -8, 10, 6, -2],\n [-12, -2, -7, 2, -2, -4, 2, -8, 9, 2, -12, -2],\n [-14, -1, -4, 6, -4, -10, -10, 10, 2, -2, -5, -8],\n [8, 8, 4, 12, 3, 2, 10, 6, -12, -5, 10, -8],\n [-5, 2, -8, 6, 2, 4, 0, -2, -2, -8, -8, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129818584684901", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-13, -2, 3, 6, 3, 1, 0, 8, 8, 2, -12, -14],\n [-2, -11, 6, -2, 16, 0, 8, -2, 7, -12, 4, -12],\n [3, 6, 15, -4, 1, 6, 6, 2, 0, -2, 0, 8],\n [6, -2, -4, 5, 6, -14, 0, 0, -3, -1, 11, -1],\n [3, 16, 1, 6, -5, -2, 12, -4, -6, -3, 12, -4],\n [1, 0, 6, -14, -2, 13, -10, 11, -4, 2, -6, 6],\n [0, 8, 6, 0, 12, -10, 9, -6, 0, -8, 0, -12],\n [8, -2, 2, 0, -4, 11, -6, -9, -12, 2, -6, 0],\n [8, 7, 0, -3, -6, -4, 0, -12, 3, 9, 8, -7],\n [2, -12, -2, -1, -3, 2, -8, 2, 9, 7, -3, 6],\n [-12, 4, 0, 11, 12, -6, 0, -6, 8, -3, -6, -14],\n [-14, -12, 8, -1, -4, 6, -12, 0, -7, 6, -14, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "445093545789936", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[1, 11, 0, -1, 0, 10, 10, -16, 10, -16, 10, 7],\n [4, 1, -12, 1, -10, 1, 8, 15, -16, -7, 15, -8],\n [3, 8, 11, -1, 11, 3, 10, 9, 9, 9, 5, -10],\n [-13, 7, 13, -8, 6, 12, -12, 16, -4, 6, 9, 10],\n [-8, 0, 5, -3, -5, 0, -4, 9, 9, 16, 6, 6],\n [10, -2, -3, -14, 11, 10, -12, -15, -6, 7, 14, 0],\n [4, -11, -1, 15, -11, 5, -6, -9, -9, 1, 6, -10],\n [8, 12, -2, -14, 2, -2, -7, -3, 12, -12, 2, 14],\n [11, -5, 2, 13, -9, 14, 16, -15, -8, -15, 9, 14],\n [5, -4, 1, 10, -9, -16, -3, -10, -15, -10, -10, -12],\n [-9, 6, 14, 2, 11, 8, 16, 14, -10, 13, 1, -5],\n [-13, 8, 8, -3, -16, -2, -3, -7, -6, -1, -15, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9417828061", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-13, 3, 1, -8, 1, 13, 9, 13, 0, -3, 11, 8],\n [15, -5, -2, -11, -15, 14, -11, -11, -15, -7, 9, -11],\n [3, 4, -7, 7, -2, -5, 13, -4, 11, 0, -11, -15],\n [-3, 7, -16, -10, -7, -1, 2, 9, 11, -1, 6, 6],\n [-9, -8, 9, -8, -8, 3, -12, -3, 8, 1, 15, 6],\n [-2, -5, 0, 6, 1, 15, 9, -1, -5, 15, 5, 5],\n [7, 12, 3, -4, -12, 1, -5, 13, -16, 14, -2, 2],\n [-12, -1, -11, -7, -1, -12, -16, -12, -5, 3, -9, -9],\n [-10, 13, 2, 8, -2, -16, 8, 11, 4, 6, 12, 16],\n [9, -4, -13, 16, -7, 3, 14, -4, -6, 10, -10, -2],\n [-6, -15, -6, 8, -2, -15, 5, -7, -11, 15, -4, 15],\n [-15, -4, -10, 15, 12, -6, -5, 10, 10, 13, -16, 9]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-159720295912", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-9, -2, -14, 9, -10, 0, 6, 4, 2, 6, 0, 2],\n [-2, -12, 2, -4, 10, 14, -10, 7, -9, 15, -4, 12],\n [-14, 2, -16, 0, -8, -3, -4, 6, 6, -8, 12, 8],\n [9, -4, 0, 6, 6, -6, 7, 0, 2, 3, 10, 6],\n [-10, 10, -8, 6, 2, -7, 2, -13, -6, -12, 6, 11],\n [0, 14, -3, -6, -7, -10, -9, -2, -2, -2, -4, 2],\n [6, -10, -4, 7, 2, -9, -11, 3, -11, -2, -7, 2],\n [4, 7, 6, 0, -13, -2, 3, 4, 5, -4, -4, 6],\n [2, -9, 6, 2, -6, -2, -11, 5, -8, 10, 1, 7],\n [6, 15, -8, 3, -12, -2, -2, -4, 10, 14, -6, -4],\n [0, -4, 12, 10, 6, -4, -7, -4, 1, -6, -9, 4],\n [2, 12, 8, 6, 11, 2, 2, 6, 7, -4, 4, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199951804277327", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[13, -4, 4, 0, 6, 8, 10, 6, -1, 2, -1, 10],\n [-4, -16, -10, 8, -6, 2, -2, 4, 4, 12, -2, 4],\n [4, -10, 12, 0, -1, 0, -6, 11, -4, -2, -8, -1],\n [0, 8, 0, -16, 0, 2, -2, 0, -1, 6, -9, 6],\n [6, -6, -1, 0, -12, -6, -4, -5, -12, 0, 11, -4],\n [8, 2, 0, 2, -6, -9, -6, 1, -9, -6, 2, -4],\n [10, -2, -6, -2, -4, -6, 13, 12, 2, -14, 0, 0],\n [6, 4, 11, 0, -5, 1, 12, -11, -14, 10, -2, -4],\n [-1, 4, -4, -1, -12, -9, 2, -14, -10, -1, 10, -8],\n [2, 12, -2, 6, 0, -6, -14, 10, -1, -9, 6, 0],\n [-1, -2, -8, -9, 11, 2, 0, -2, 10, 6, 16, -4],\n [10, 4, -1, 6, -4, -4, 0, -4, -8, 0, -4, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2980501493203", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[13, -2, 0, 9, 7, 2, -7, -2, 1, 10, -6, -10],\n [-2, -12, -2, 6, 10, -2, -10, -8, 8, 2, -6, 12],\n [0, -2, 5, -1, -8, 10, 5, 0, -8, 2, -12, 2],\n [9, 6, -1, 11, -2, -8, 0, -4, 6, 2, 2, 4],\n [7, 10, -8, -2, 6, -2, -2, -5, -3, -2, -4, 2],\n [2, -2, 10, -8, -2, 8, 2, 6, -2, 2, 7, 4],\n [-7, -10, 5, 0, -2, 2, 2, -14, 1, -1, 8, -10],\n [-2, -8, 0, -4, -5, 6, -14, 15, 12, -2, 12, 4],\n [1, 8, -8, 6, -3, -2, 1, 12, 9, -15, -4, -1],\n [10, 2, 2, 2, -2, 2, -1, -2, -15, -8, 2, 0],\n [-6, -6, -12, 2, -4, 7, 8, 12, -4, 2, 1, 10],\n [-10, 12, 2, 4, 2, 4, -10, 4, -1, 0, 10, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1503536953556", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, 2, -1, -8, 10, -6, 2, -9, 3, -6, -4, 0],\n [6, -5, -8, 10, 8, 6, -8, 8, 8, -7, -2, -14],\n [7, 7, -8, 16, -3, -14, -11, -1, 0, -12, 5, -1],\n [-4, -5, -7, -7, -3, 16, 11, 5, 1, -2, 0, -15],\n [-8, -4, 4, -3, -2, -15, 10, 4, -4, -10, 7, -16],\n [4, 3, 2, 4, 1, 8, 3, 14, 4, -1, -10, 15],\n [-10, -5, 1, -4, -16, -16, 8, -8, 4, -10, 2, 14],\n [16, 11, 4, -14, 4, -6, 10, 4, 14, -9, 15, 6],\n [-14, -7, 6, -12, -14, -13, -6, -6, 2, -13, 15, 14],\n [1, 16, -14, -11, -7, 2, -16, -4, 16, 3, -8, -7],\n [2, -2, 7, 4, 16, 14, 5, 10, 2, -6, -4, -10],\n [10, 7, 8, 6, 5, 5, -14, -6, 7, 8, 1, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479240568334573", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-7, 9, 7, 3, 16, 6, 8, -9, -11, 15, -9, 16],\n [-15, -14, -15, -7, -12, 16, 5, -13, 2, -7, -14, -9],\n [1, -15, -7, 3, 13, -10, 8, -3, -7, -3, 16, -8],\n [2, 4, 14, -14, -13, 15, -4, 1, -7, 0, 7, 2],\n [16, -11, 2, -16, -4, 8, -5, 12, 10, 9, -9, 7],\n [3, 3, -16, 7, 7, 6, -8, 15, -14, 16, -4, -8],\n [-16, -4, 4, -6, -4, -16, -12, 2, 4, 15, -12, -13],\n [-15, -13, 6, -2, -15, 12, -3, 5, 6, 7, 3, 13],\n [2, -14, -5, -12, -10, -2, 8, 1, 7, 7, 14, -7],\n [-13, -10, 9, -12, 13, -14, -9, 3, 15, 0, 7, 8],\n [-6, 9, -8, -13, 7, -5, 15, -10, 6, -1, -13, -15],\n [16, -2, 2, 11, 10, 7, 5, 12, 14, 5, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13984611295626", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[6, 3, 2, -13, 6, -6, -16, -14, 2, -10, 0, -7],\n [-10, -8, 12, 5, 13, 16, 5, -1, -14, -7, 0, -6],\n [11, 0, 16, 13, 6, -11, 0, -4, 2, 1, 16, -15],\n [8, 6, -6, -12, -1, -6, -13, 12, -8, 1, 1, 10],\n [-11, 10, -6, -8, -4, 1, 1, -16, 12, 6, 15, 10],\n [1, -1, 8, -16, -16, 16, -7, -11, 7, -11, -8, 16],\n [-2, -9, 9, -10, -7, 1, 9, -13, -9, 8, 1, -12],\n [-13, -9, -15, -14, 13, -10, 7, -10, -16, 13, -11, -16],\n [9, 14, -15, -6, 13, 6, -1, 10, 6, 16, 5, -1],\n [-13, -2, 0, 14, 14, 5, 5, -14, 1, 9, 7, 9],\n [4, -10, -12, 14, -2, -15, 1, -7, -15, -7, -5, 5],\n [4, 11, -14, 11, -12, -12, -8, 7, 14, -3, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13880665286420", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[6, -11, 0, -6, 2, 12, -2, 4, -4, 2, 0, 4],\n [-11, 11, 3, 0, 6, -12, 7, 7, -6, -5, 0, 0],\n [0, 3, 4, 12, -7, -2, -2, 9, 0, -4, 6, -4],\n [-6, 0, 12, -14, 5, -6, -4, 3, -4, -4, -4, -4],\n [2, 6, -7, 5, 4, 2, 0, 2, 4, 0, 11, -5],\n [12, -12, -2, -6, 2, 3, -5, 6, -2, 0, -4, -5],\n [-2, 7, -2, -4, 0, -5, 12, 8, -2, 6, 10, 8],\n [4, 7, 9, 3, 2, 6, 8, 9, 6, 0, -5, 2],\n [-4, -6, 0, -4, 4, -2, -2, 6, 1, 0, -11, 12],\n [2, -5, -4, -4, 0, 0, 6, 0, 0, -11, 3, 2],\n [0, 0, 6, -4, 11, -4, 10, -5, -11, 3, 5, -9],\n [4, 0, -4, -4, -5, -5, 8, 2, 12, 2, -9, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3388586686109", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (12, 9) of the 8th power of the matrix:\n[[6, -2, 2, 7, 2, 4, 12, -9, 2, 7, 11, 2],\n [-2, 11, 0, 8, -8, 0, -4, -3, -3, 0, 7, 0],\n [2, 0, -7, 0, 0, 0, -8, 12, 8, 5, 6, -10],\n [7, 8, 0, 10, 4, 5, -12, 2, 2, -7, 4, 6],\n [2, -8, 0, 4, -15, 4, -2, -12, -10, 2, -12, 0],\n [4, 0, 0, 5, 4, -5, -4, -12, 1, -4, -14, -6],\n [12, -4, -8, -12, -2, -4, 7, 2, 9, 0, 6, -2],\n [-9, -3, 12, 2, -12, -12, 2, -9, 2, -9, 2, 2],\n [2, -3, 8, 2, -10, 1, 9, 2, 6, -4, -3, 9],\n [7, 0, 5, -7, 2, -4, 0, -9, -4, 13, -12, -4],\n [11, 7, 6, 4, -12, -14, 6, 2, -3, -12, -7, 5],\n [2, 0, -10, 6, 0, -6, -2, 2, 9, -4, 5, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-744164093818", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-3, -3, -16, 6, -16, 11, 15, 6, 11, -12, -1, 3],\n [3, 0, -12, 3, -12, -14, 15, 8, -16, -15, -7, 1],\n [-4, 5, -10, 14, 15, -15, -13, 14, -9, -4, -15, -13],\n [13, 13, 0, -1, 15, -14, 11, -16, 8, 14, 10, -4],\n [10, 6, -13, -9, 2, 1, -6, -5, -1, -5, -9, -16],\n [-11, -10, -16, -3, 11, -16, 9, 8, 7, -10, 8, 14],\n [-4, 3, 12, 14, 7, -14, -11, -4, -6, -4, 11, -13],\n [5, 1, -15, 16, -12, -5, -1, 13, 1, 10, 10, -6],\n [-4, -15, 8, 16, 7, -16, 8, -4, -2, -11, 1, 11],\n [5, -9, 7, -5, 7, -16, 11, -9, -14, 0, -8, -6],\n [3, 2, -8, 2, 8, 11, 16, -3, 9, 8, 14, 14],\n [10, 9, -3, -15, -11, 9, 3, -14, 10, -9, 12, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1896909082598", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[3, -7, 1, 16, -14, 9, 2, -15, 5, 9, 6, 16],\n [11, 14, -14, -14, -15, 12, 14, -2, -7, 5, -8, -3],\n [3, -16, 9, -1, -1, -3, 8, 4, -2, -15, -12, 2],\n [-6, 11, -15, 16, 4, 11, 0, -5, 14, 8, 3, 6],\n [-11, -1, -14, 10, -6, -14, 6, -9, 0, -7, 9, 14],\n [4, 9, 15, -2, 10, 5, 10, 2, -9, 10, 12, 7],\n [-15, -1, -16, -12, -6, 8, -9, -2, -14, 11, 11, -4],\n [-11, -13, -12, 13, -6, 14, -6, -5, 7, 2, -16, -11],\n [-15, 3, -5, -7, -9, -14, 2, 3, -14, -11, 1, 5],\n [14, -6, -15, 7, -10, -10, 7, 15, 4, 0, 15, 8],\n [16, 0, 16, 7, -1, 8, -11, 10, -6, 12, 13, 10],\n [-10, -15, -8, 7, 11, 2, -2, -15, -3, 1, -7, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "711388561103", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[14, 4, 6, 0, -10, -11, -16, 1, -14, -16, -14, 1],\n [-2, -3, 0, 11, -1, 12, 2, 7, 3, 11, 4, 6],\n [-11, -9, -6, -7, 0, -5, 0, 9, 7, -15, 15, 7],\n [13, -3, 5, 12, 3, -1, -1, -9, -15, 7, -1, -1],\n [-15, -13, -7, 6, -3, 7, -7, 14, 9, -2, 10, 11],\n [4, -3, -10, -11, -1, 9, -13, -7, 9, -4, -9, 10],\n [-5, 15, -1, 5, -10, 15, 10, 1, -6, -10, 12, -13],\n [0, 8, -7, -1, -5, 0, -8, 15, 1, 7, -9, 16],\n [-5, -14, -16, 12, -12, 4, 13, 3, 14, 7, -15, -7],\n [13, -15, -14, -5, -16, -16, 12, -8, -5, -5, -7, 5],\n [2, -4, 3, 9, 7, -2, 3, 6, 4, -1, -13, -9],\n [1, 6, 1, -1, 9, 9, 1, 3, 3, 15, -6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1577534424234", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (5, 2) of the result:\nA =\n[[-4, 11, -10, 16, 5, 10, 14, -11, 12, 13, 6, 15],\n [-12, -14, -2, -15, 14, 16, 16, -3, 13, 12, -9, -4],\n [-1, 8, 16, -14, -4, -4, 9, -6, 16, 4, 6, 4],\n [1, -6, 0, -16, -14, -12, 7, 15, 1, 3, -15, -9],\n [-15, 1, -7, -14, -15, -11, 4, -1, -1, -15, -1, 15],\n [-1, -9, 10, -13, 15, 4, -3, -12, 7, 13, 4, 13],\n [7, 6, 15, 9, 3, -15, -8, -2, -15, -16, 4, -8],\n [10, 3, 5, 0, -15, -2, -8, 16, 16, -13, -16, -8],\n [-9, -1, 12, -7, 6, -7, 13, -16, -1, -11, 2, 0],\n [-6, 12, 11, -4, -13, -1, 4, -1, 3, 0, 6, -11],\n [-16, -16, -14, -2, -8, 8, 0, -9, -15, -11, 6, -4],\n [16, -7, 5, -4, -12, -11, -5, 6, 12, 14, -15, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2664921292812", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (8, 3) of the result:\nA =\n[[1, 7, -3, -13, -7, -9, 10, 13, -14, 12, 15, 7],\n [11, 14, 2, 12, -1, 16, 6, 1, -4, 0, -9, 0],\n [-6, 2, -4, 5, 3, 14, 14, 1, 11, 3, 5, -9],\n [12, 5, -14, -15, -8, -8, 9, -16, -1, 1, 14, -16],\n [-16, 7, -3, 6, -9, -15, -12, 16, -13, -9, 12, 12],\n [13, -5, -9, 2, -14, 6, -1, 11, 9, -5, 7, -3],\n [1, 6, -2, -14, -7, 15, -8, -8, 5, -15, 16, 15],\n [-6, 9, 13, -1, 0, 8, 7, -7, -12, 12, -1, 5],\n [-8, -16, 1, 2, 0, 4, -1, 3, -14, -7, 15, -8],\n [-3, 9, -13, -15, -16, -15, -13, 13, -13, 3, -8, 6],\n [11, 15, 4, 16, 10, -10, 2, -12, -9, 15, 13, 15],\n [-13, -11, -14, -15, 4, 13, 10, -3, 12, -1, -13, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2179040904", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-1, 1, 12, 0, -9, 2, 2, 8, -5, 2, -5, 3],\n [1, -8, -4, -15, -12, 4, -10, -9, -6, 12, -5, 3],\n [12, -4, 9, 0, -10, 9, 2, -2, 14, 0, 3, -7],\n [0, -15, 0, -14, -14, -2, 2, 0, 1, -8, 0, 0],\n [-9, -12, -10, -14, -12, 0, -9, 6, -4, -11, -6, 6],\n [2, 4, 9, -2, 0, -10, 12, -3, 10, 2, -6, -7],\n [2, -10, 2, 2, -9, 12, -1, 4, 4, 3, -4, -15],\n [8, -9, -2, 0, 6, -3, 4, -13, -7, -8, -4, -4],\n [-5, -6, 14, 1, -4, 10, 4, -7, -6, 8, 10, 1],\n [2, 12, 0, -8, -11, 2, 3, -8, 8, -15, -2, 3],\n [-5, -5, 3, 0, -6, -6, -4, -4, 10, -2, 10, 14],\n [3, 3, -7, 0, 6, -7, -15, -4, 1, 3, 14, 13]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1565349448807", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[0, -4, -2, -10, -1, -16, -1, -16, -16, 5, 11, 1],\n [-6, 0, 14, 15, 16, -1, -3, -2, 0, -8, -3, 7],\n [-6, 12, 8, -13, 15, 15, -14, -11, 2, 0, -12, -7],\n [10, 15, 4, 15, -2, -8, -15, -11, 10, 4, 5, -9],\n [3, -8, 2, 15, -6, 11, 4, -15, -10, 8, 4, -4],\n [9, 6, -4, 12, -8, 3, 4, -9, 9, 10, 6, 14],\n [-3, 0, -9, -7, -2, 14, 6, 6, 4, -7, 5, 12],\n [0, 11, 6, -16, -15, 0, -4, -10, 9, 11, -10, -8],\n [8, -9, -10, -11, -7, 10, 3, -14, 13, 13, 15, 14],\n [4, 3, -5, 1, 6, 11, -3, -9, -1, -16, -12, -12],\n [6, 1, -13, 12, -1, 3, 6, -12, 12, -16, -16, 14],\n [-9, 16, 15, 1, -9, 8, -4, 5, -10, 15, 13, -13]], determine the value at position (7, 12).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5318315994", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[2, 4, -1, 4, -10, 3, -14, -5, 6, 1, 2, -2],\n [4, -6, 9, -3, -10, 4, -11, -8, -8, 12, 5, 9],\n [-1, 9, -3, -4, 0, -12, -4, -2, 2, -14, 2, 8],\n [4, -3, -4, -7, -10, -2, -4, 12, -2, -2, 6, 12],\n [-10, -10, 0, -10, -5, -7, -7, -8, -10, 0, -15, 0],\n [3, 4, -12, -2, -7, -2, -2, -3, 10, 3, -2, -4],\n [-14, -11, -4, -4, -7, -2, 14, 1, 0, -2, -4, 11],\n [-5, -8, -2, 12, -8, -3, 1, -15, -4, -4, 3, -13],\n [6, -8, 2, -2, -10, 10, 0, -4, 0, -6, -4, 0],\n [1, 12, -14, -2, 0, 3, -2, -4, -6, 15, -6, -4],\n [2, 5, 2, 6, -15, -2, -4, 3, -4, -6, 0, 8],\n [-2, 9, 8, 12, 0, -4, 11, -13, 0, -4, 8, 7]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1243259030061", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-4, -9, 6, 2, 2, -7, -7, -9, -5, 7, -10, 5],\n [-15, 3, -2, 2, -6, -15, -11, 4, -16, -2, 2, 0],\n [15, 1, 9, -7, 1, 3, 0, 1, 3, -14, 16, 11],\n [5, 0, 6, 15, 8, 1, -4, 1, -7, 14, 2, -9],\n [-9, 0, -11, -2, -16, 8, -11, 6, 5, 16, 7, 13],\n [9, -16, -1, 2, 11, -12, 10, 1, -5, -11, -16, -16],\n [11, -8, 5, -12, -3, -1, -5, 3, 6, 1, -10, -12],\n [-15, -16, 0, -4, -8, -5, -9, 8, -5, -5, 16, 1],\n [15, -13, 10, 12, -15, -5, 2, 2, 9, 4, 5, -5],\n [3, -16, -10, -5, 15, 8, -9, -2, -1, -10, 8, 16],\n [-12, 13, -15, -3, -7, 4, 8, 14, -3, -12, 8, -15],\n [3, -7, -11, 16, -3, 9, 5, -3, 6, -1, 8, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "378628042546", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-6, 9, 2, 10, 3, 5, -6, 1, -2, 2, 4, -7],\n [9, 15, -1, 12, -2, 13, -5, 7, 0, 3, 0, 10],\n [2, -1, -10, 0, 7, 0, -5, 10, -10, 10, -7, -6],\n [10, 12, 0, -12, -6, -6, -6, -14, -9, 14, -3, -13],\n [3, -2, 7, -6, 10, 4, -10, 4, 11, -4, 4, 6],\n [5, 13, 0, -6, 4, 14, -2, -6, 12, 6, -2, -6],\n [-6, -5, -5, -6, -10, -2, 14, -7, 8, 6, -9, 2],\n [1, 7, 10, -14, 4, -6, -7, 9, 5, 3, -9, 0],\n [-2, 0, -10, -9, 11, 12, 8, 5, -2, -4, 3, -8],\n [2, 3, 10, 14, -4, 6, 6, 3, -4, -13, -6, -5],\n [4, 0, -7, -3, 4, -2, -9, -9, 3, -6, -9, 0],\n [-7, 10, -6, -13, 6, -6, 2, 0, -8, -5, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78992309499603", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 4) of the matrix A^9 where A is:\n[[3, 15, -4, 3, -9, -11, 16, 8, -3, 16, -1, -14],\n [-7, 16, -1, 14, 8, -3, -9, -8, -4, -3, -2, -12],\n [-4, -14, 16, 2, 14, 15, -15, -1, -12, 13, 1, 11],\n [16, -15, -15, 15, -5, -11, -2, 15, -2, -7, -2, 16],\n [-5, -13, -7, 3, 14, 14, 14, 3, -8, -4, 7, 8],\n [13, 7, -8, 12, -7, -3, 5, -5, -9, -14, 9, 3],\n [0, 14, -4, 15, -11, 15, 15, 15, -16, -6, -5, 4],\n [4, -7, -8, -5, 15, 4, 1, -12, -12, -10, -3, 5],\n [16, 12, -2, 14, 11, 1, -9, 16, -2, -10, -4, -6],\n [6, 6, -13, -10, 3, 12, 16, -10, 15, -12, -2, -15],\n [-16, -1, -11, -9, -1, -5, -11, -15, -6, -6, -7, -6],\n [-6, -9, -7, 15, 14, -13, -14, 13, -6, -14, 4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16692925535555", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (8, 1) of the result:\nA =\n[[-6, -4, 2, -4, -9, -7, -1, 0, -4, 3, 10, -4],\n [-4, -6, 0, 4, 0, 1, -4, -8, 8, -4, 11, 2],\n [2, 0, -2, -9, -14, 10, -8, -1, -6, -10, 3, 3],\n [-4, 4, -9, 15, 8, 7, 2, -8, 0, -2, 11, 0],\n [-9, 0, -14, 8, 16, 13, 2, -4, -5, 4, 2, 10],\n [-7, 1, 10, 7, 13, -1, 13, 10, 0, -2, -9, 8],\n [-1, -4, -8, 2, 2, 13, -5, 3, -2, 8, -1, -2],\n [0, -8, -1, -8, -4, 10, 3, 14, -7, -4, -4, 2],\n [-4, 8, -6, 0, -5, 0, -2, -7, 15, -8, 9, 6],\n [3, -4, -10, -2, 4, -2, 8, -4, -8, -4, -13, -7],\n [10, 11, 3, 11, 2, -9, -1, -4, 9, -13, -1, -6],\n [-4, 2, 3, 0, 10, 8, -2, 2, 6, -7, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143061151396", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[3, 0, -6, -5, 4, 6, 0, 11, -1, 3, 2, -4],\n [0, 6, 7, -12, 2, 0, 14, 0, 4, -3, 3, 0],\n [-6, 7, -15, -1, 12, 0, 12, -10, 7, -4, -2, -10],\n [-5, -12, -1, -2, 0, -14, -3, 2, 0, 6, -6, 0],\n [4, 2, 12, 0, -3, -1, 14, -2, 6, 6, 0, -10],\n [6, 0, 0, -14, -1, -13, 0, 6, -2, 7, 4, 3],\n [0, 14, 12, -3, 14, 0, -11, 1, 0, -8, 2, -1],\n [11, 0, -10, 2, -2, 6, 1, 5, -3, -4, -10, 4],\n [-1, 4, 7, 0, 6, -2, 0, -3, 10, 6, -15, -4],\n [3, -3, -4, 6, 6, 7, -8, -4, 6, 12, 6, 0],\n [2, 3, -2, -6, 0, 4, 2, -10, -15, 6, 5, 13],\n [-4, 0, -10, 0, -10, 3, -1, 4, -4, 0, 13, -14]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2951212128979", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (4, 11) of the result:\nA =\n[[9, -7, -12, -3, -7, -8, -14, -6, -14, -3, -14, -11],\n [-3, -1, 8, 10, 5, -6, 2, 2, -1, 13, -9, 13],\n [-9, 12, -3, -5, -4, -5, -3, -7, -9, 7, 8, -9],\n [-4, -14, -8, -7, 2, 11, 1, 1, -9, -9, 15, 4],\n [-14, 7, -1, 2, 5, 5, -4, -5, 11, -9, -8, 3],\n [-2, -13, 7, -11, 6, -2, 13, 3, 10, 10, 16, -7],\n [-8, -9, -3, -16, -7, -13, 1, 13, 9, -3, 12, -8],\n [5, 7, 14, -2, -10, 10, 8, -11, -13, -15, -3, -13],\n [-4, 12, 9, 9, -13, -3, -6, -14, 6, -9, 9, -3],\n [-12, 5, -3, -5, -14, 13, 3, -14, 16, -4, 1, -6],\n [9, -10, 9, -14, -16, 0, -5, -8, 0, 1, 6, 10],\n [-15, 10, -2, -12, 14, 2, 11, -15, 3, -14, -9, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18505371697065", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-5, 2, -4, 0, 4, 2, 0, 3, 14, 2, -9, -8],\n [2, 12, -2, -12, 5, -4, -6, -6, 2, 4, -2, -12],\n [-4, -2, -16, 2, 1, 0, 7, 10, 6, -14, 0, 2],\n [0, -12, 2, 12, 2, 7, -14, 4, -8, -4, -2, 10],\n [4, 5, 1, 2, 7, -6, 12, -4, -13, 2, 2, 2],\n [2, -4, 0, 7, -6, -2, -1, 1, 10, 1, -10, 2],\n [0, -6, 7, -14, 12, -1, -10, 0, 0, 8, 0, -6],\n [3, -6, 10, 4, -4, 1, 0, -11, -3, -2, 5, -2],\n [14, 2, 6, -8, -13, 10, 0, -3, 6, 2, 0, 12],\n [2, 4, -14, -4, 2, 1, 8, -2, 2, 16, 1, 14],\n [-9, -2, 0, -2, 2, -10, 0, 5, 0, 1, 9, 4],\n [-8, -12, 2, 10, 2, 2, -6, -2, 12, 14, 4, 14]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2547289943813843", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[11, -3, 3, 2, -8, 12, 10, -7, 0, -2, -1, -6],\n [-3, 5, -2, -9, -12, 11, 6, -8, -5, -1, 2, 2],\n [3, -2, 7, 6, 1, -13, -3, 14, 6, 0, 2, -1],\n [2, -9, 6, -16, -4, 3, 2, -4, 7, 5, -7, -6],\n [-8, -12, 1, -4, -8, 6, 10, -14, -8, -7, -9, 14],\n [12, 11, -13, 3, 6, -16, -2, 3, -4, 12, 10, 6],\n [10, 6, -3, 2, 10, -2, -13, 2, 2, -8, 2, 8],\n [-7, -8, 14, -4, -14, 3, 2, -2, 6, 3, 0, -11],\n [0, -5, 6, 7, -8, -4, 2, 6, 1, -2, -10, -2],\n [-2, -1, 0, 5, -7, 12, -8, 3, -2, -1, 4, 0],\n [-1, 2, 2, -7, -9, 10, 2, 0, -10, 4, -5, 0],\n [-6, 2, -1, -6, 14, 6, 8, -11, -2, 0, 0, 11]], determine the value at position (9, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2813233968923", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[16, -2, 2, 1, -3, 2, 8, 0, -8, -4, 1, -2],\n [-2, -15, 0, 0, 0, 6, -6, -4, -8, 4, -5, -14],\n [2, 0, 14, 1, -4, 2, 3, 10, -6, 7, -12, 9],\n [1, 0, 1, -10, 4, 0, -5, -9, -8, 5, -6, -6],\n [-3, 0, -4, 4, 1, -6, -1, -4, 6, -4, -2, -2],\n [2, 6, 2, 0, -6, 16, 10, -5, -4, 10, 11, 8],\n [8, -6, 3, -5, -1, 10, -4, 6, -8, 12, -4, -11],\n [0, -4, 10, -9, -4, -5, 6, 5, 0, -8, 8, 1],\n [-8, -8, -6, -8, 6, -4, -8, 0, 9, 2, 6, 0],\n [-4, 4, 7, 5, -4, 10, 12, -8, 2, 9, -10, 10],\n [1, -5, -12, -6, -2, 11, -4, 8, 6, -10, 10, -6],\n [-2, -14, 9, -6, -2, 8, -11, 1, 0, 10, -6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43993285439", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 14, -15, -12, -15, -15, 9, -7, 10, -9, -7, 7],\n [7, 14, -13, -3, 9, -5, 10, -11, 10, -3, 5, 3],\n [-14, -8, -1, -8, 15, 8, 10, 10, -15, 5, -15, -16],\n [-7, -5, 0, -14, 4, -5, 10, -2, -14, -12, 4, -4],\n [8, -3, 1, -14, -14, 15, 1, 15, 15, 12, 10, 7],\n [-11, -10, -3, 0, 10, -11, -14, -15, 2, 6, 0, -8],\n [-8, -8, -5, -14, 4, 11, 16, 5, 13, 14, -1, -16],\n [-8, -16, 6, 1, -13, -7, 10, -15, -13, 16, -9, -2],\n [-10, 13, 7, 3, -12, -10, -15, -7, -4, 4, -14, -3],\n [-1, -9, 7, -3, -11, 7, 12, 9, -12, -4, -14, -12],\n [5, 4, 10, 7, -9, -13, -11, 14, -12, -11, -15, -16],\n [12, 6, 1, -14, -1, 14, 5, -9, 5, -4, 12, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5175019868164", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-7, 4, -6, 1, 6, -4, 8, 11, 0, 9, 7, 2],\n [4, 10, 6, 1, 6, -6, 0, -4, -4, -2, -7, 7],\n [-6, 6, -4, 3, -9, -2, -13, -10, -8, 6, 8, -8],\n [1, 1, 3, 2, 10, 5, 0, -8, 10, 2, 6, 3],\n [6, 6, -9, 10, 9, -2, -8, 6, 2, -11, -14, -6],\n [-4, -6, -2, 5, -2, 9, -8, 1, -12, -6, 0, 11],\n [8, 0, -13, 0, -8, -8, 13, 4, 2, 0, -2, -6],\n [11, -4, -10, -8, 6, 1, 4, -13, 4, -5, 12, -10],\n [0, -4, -8, 10, 2, -12, 2, 4, -6, 6, 9, 2],\n [9, -2, 6, 2, -11, -6, 0, -5, 6, 5, -6, 0],\n [7, -7, 8, 6, -14, 0, -2, 12, 9, -6, -1, -6],\n [2, 7, -8, 3, -6, 11, -6, -10, 2, 0, -6, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1465558149967775", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-6, -8, -10, 0, 9, 10, 16, -12, -8, 6, 13, -16],\n [-9, -16, -7, -10, -14, -10, -9, 15, 15, -12, 10, -4],\n [-5, -7, -16, 4, -10, -7, 0, -16, -4, 6, 11, 2],\n [15, -7, 1, -9, -1, 0, 6, 9, 6, 6, -10, -5],\n [5, 0, -4, -3, -10, 2, -10, 10, 0, -6, -8, -14],\n [6, -13, -1, 4, 8, -12, -16, 15, 3, -6, 16, 15],\n [2, 1, 7, 15, -8, 7, -2, 5, -7, -15, -10, -16],\n [-8, 9, -2, 5, 6, -14, -6, 5, -3, -1, -12, -9],\n [-15, -6, 6, -16, -7, -11, -14, 2, 12, -2, 6, -9],\n [8, 7, -5, -16, -13, 13, 16, 13, -4, 13, 2, 3],\n [-13, 6, 8, -6, 14, -5, 13, -1, 15, 1, -9, 14],\n [-4, 1, 10, -11, -7, -10, -1, -15, 8, 9, 9, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114789024589", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[3, 3, -8, -8, -10, 12, 2, -6, 3, 2, -9, -4],\n [3, -5, 0, 10, 6, 1, -1, 14, 12, -6, -4, -9],\n [-8, 0, 16, 4, -2, 12, -4, -16, 6, 5, -3, -5],\n [-8, 10, 4, -1, 2, 11, -1, 2, 6, -10, 6, 2],\n [-10, 6, -2, 2, -1, -3, 9, 4, 9, 4, 0, -2],\n [12, 1, 12, 11, -3, 7, 7, 5, 12, -6, 16, 7],\n [2, -1, -4, -1, 9, 7, 8, 14, 12, 4, 4, -2],\n [-6, 14, -16, 2, 4, 5, 14, -1, 2, 4, -4, -4],\n [3, 12, 6, 6, 9, 12, 12, 2, 2, 0, -2, -6],\n [2, -6, 5, -10, 4, -6, 4, 4, 0, 6, -2, -2],\n [-9, -4, -3, 6, 0, 16, 4, -4, -2, -2, -5, 2],\n [-4, -9, -5, 2, -2, 7, -2, -4, -6, -2, 2, 10]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5536880032849", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[11, -10, -8, 4, -3, 6, -4, 6, 12, -5, 8, -6],\n [-10, 0, -2, 2, -2, 0, -2, -12, -10, 14, -8, 5],\n [-8, -2, 8, -3, -9, -12, -3, 2, 3, -4, 8, 4],\n [4, 2, -3, 14, 1, 3, -1, -6, 4, -13, -2, -4],\n [-3, -2, -9, 1, -6, 4, -6, 6, 10, -4, -4, 0],\n [6, 0, -12, 3, 4, 5, 1, 6, -12, 0, -3, -2],\n [-4, -2, -3, -1, -6, 1, -5, -6, -9, 8, -2, 0],\n [6, -12, 2, -6, 6, 6, -6, 5, -6, -10, 7, 0],\n [12, -10, 3, 4, 10, -12, -9, -6, -8, 10, 4, 4],\n [-5, 14, -4, -13, -4, 0, 8, -10, 10, -5, 8, 6],\n [8, -8, 8, -2, -4, -3, -2, 7, 4, 8, 13, 13],\n [-6, 5, 4, -4, 0, -2, 0, 0, 4, 6, 13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166935381452", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (6, 10) of the result:\nA =\n[[6, -5, 7, -1, 0, -2, -6, -8, -3, 9, 11, -6],\n [-5, 3, -4, -2, -12, -8, 16, -5, 1, 0, -6, 3],\n [7, -4, -12, 2, 14, 1, -1, 1, 3, -8, 8, -6],\n [-1, -2, 2, 9, 4, 2, -3, 5, 3, -8, 4, 0],\n [0, -12, 14, 4, 1, 10, -2, 1, 8, 0, 8, 8],\n [-2, -8, 1, 2, 10, -4, 4, -3, 2, 1, 4, -3],\n [-6, 16, -1, -3, -2, 4, -15, -9, 5, 5, -2, 2],\n [-8, -5, 1, 5, 1, -3, -9, 14, 12, 10, -4, 2],\n [-3, 1, 3, 3, 8, 2, 5, 12, -11, 2, -8, 10],\n [9, 0, -8, -8, 0, 1, 5, 10, 2, -9, 4, 4],\n [11, -6, 8, 4, 8, 4, -2, -4, -8, 4, -13, -3],\n [-6, 3, -6, 0, 8, -3, 2, 2, 10, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2954856164975", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 10) of the 9th power of the matrix:\n[[-1, -2, -4, 4, 0, 4, 5, 2, -10, -4, 3, -1],\n [-2, -15, 1, 6, 1, -5, -4, 2, 0, -5, -12, -4],\n [-4, 1, -11, 0, 2, 4, -2, 0, 2, 6, 2, 4],\n [4, 6, 0, -1, 2, 2, -6, -4, 1, -6, 2, 1],\n [0, 1, 2, 2, 6, -6, -6, 8, 3, -12, 2, 8],\n [4, -5, 4, 2, -6, 4, 10, 0, 0, 5, 6, 6],\n [5, -4, -2, -6, -6, 10, 7, -8, 2, 0, -1, 7],\n [2, 2, 0, -4, 8, 0, -8, -3, 0, 1, 4, -6],\n [-10, 0, 2, 1, 3, 0, 2, 0, 5, 10, 6, -8],\n [-4, -5, 6, -6, -12, 5, 0, 1, 10, -5, -2, 12],\n [3, -12, 2, 2, 2, 6, -1, 4, 6, -2, 1, -2],\n [-1, -4, 4, 1, 8, 6, 7, -6, -8, 12, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2966995211162", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[16, -4, -3, -1, 10, -12, 2, 0, 5, 12, 3, -3],\n [-4, -13, 6, 0, -8, -2, 0, -2, 1, -5, 0, 6],\n [-3, 6, -10, 14, 6, 0, -3, 1, 4, 7, 12, 5],\n [-1, 0, 14, 2, 5, 6, -8, 9, 12, -6, -12, 5],\n [10, -8, 6, 5, -1, -4, -5, 6, 2, 0, 1, -6],\n [-12, -2, 0, 6, -4, 13, -2, 13, -6, 2, 7, -5],\n [2, 0, -3, -8, -5, -2, 8, -6, 1, 8, -10, 12],\n [0, -2, 1, 9, 6, 13, -6, -12, 4, 1, 0, 2],\n [5, 1, 4, 12, 2, -6, 1, 4, 6, 0, -4, -4],\n [12, -5, 7, -6, 0, 2, 8, 1, 0, -1, -8, 0],\n [3, 0, 12, -12, 1, 7, -10, 0, -4, -8, -7, 3],\n [-3, 6, 5, 5, -6, -5, 12, 2, -4, 0, 3, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2501721474892290", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[9, 2, -6, 1, 0, 4, -4, 7, -4, -2, 5, 9],\n [2, -10, 4, -1, 10, 5, 12, -6, 0, 0, 0, -6],\n [-6, 4, 3, 3, 15, 4, -10, -1, 4, 4, 2, -5],\n [1, -1, 3, -9, 0, -6, 8, -6, -16, 8, 2, 0],\n [0, 10, 15, 0, 12, 8, 2, -4, 0, 5, 9, 14],\n [4, 5, 4, -6, 8, 0, 6, -10, -10, -10, -7, -7],\n [-4, 12, -10, 8, 2, 6, 0, 2, 0, -2, -14, 1],\n [7, -6, -1, -6, -4, -10, 2, -11, 5, -2, -10, 1],\n [-4, 0, 4, -16, 0, -10, 0, 5, -8, -10, 0, -3],\n [-2, 0, 4, 8, 5, -10, -2, -2, -10, 8, 0, 4],\n [5, 0, 2, 2, 9, -7, -14, -10, 0, 0, -14, 1],\n [9, -6, -5, 0, 14, -7, 1, 1, -3, 4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-129375628269", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[15, 13, 11, 2, 1, 3, -7, -6, 0, 6, -10, -11],\n [7, -9, -13, 0, -15, 5, -1, 4, -9, -10, -10, -13],\n [8, -11, 1, -2, 4, -1, 7, -6, -10, -14, 5, 9],\n [-13, -1, 0, 2, -2, -10, -15, 6, -9, -16, 0, -9],\n [4, 9, 14, 16, 13, 13, 4, 4, 12, -9, -12, -3],\n [4, -2, 13, -10, 10, -9, 14, 13, 10, -16, 16, -3],\n [-10, 5, -12, 4, 14, 10, -2, 6, 0, 13, -15, -15],\n [16, 3, -7, -12, 0, 1, -8, -7, 15, 1, 7, -15],\n [-1, -2, 3, -10, 1, 8, -4, -6, -9, 10, 3, -13],\n [-2, -4, 5, 9, -8, -12, 13, -13, 14, -3, 8, 11],\n [-2, -14, 14, -4, -8, -15, 6, 16, 11, -9, -15, 7],\n [5, -2, 7, -12, 10, 16, 4, 0, 9, 8, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105501415442994", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[7, 2, 2, -6, 0, -5, 0, 8, -10, -9, 4, 14],\n [2, 11, -8, 5, 0, 0, 0, 10, 4, 10, -6, 8],\n [2, -8, -11, 8, 5, 4, -5, -6, 2, -4, 6, 0],\n [-6, 5, 8, 14, 0, 2, 6, 0, -8, -2, 0, 4],\n [0, 0, 5, 0, 1, 12, 14, 2, 4, -5, -6, 9],\n [-5, 0, 4, 2, 12, 15, -3, -2, 6, 0, 4, -6],\n [0, 0, -5, 6, 14, -3, -9, 2, -4, 6, -10, -2],\n [8, 10, -6, 0, 2, -2, 2, -15, 5, -2, -8, -6],\n [-10, 4, 2, -8, 4, 6, -4, 5, 3, 12, -5, 5],\n [-9, 10, -4, -2, -5, 0, 6, -2, 12, 11, -14, 8],\n [4, -6, 6, 0, -6, 4, -10, -8, -5, -14, 4, -2],\n [14, 8, 0, 4, 9, -6, -2, -6, 5, 8, -2, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2763930255142", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (3, 6) of the result:\nA =\n[[-8, 3, 2, -6, -3, 8, -5, -10, -14, -1, -16, -2],\n [-6, -16, -14, 5, -11, 5, 11, -3, 15, 12, -12, -6],\n [-16, -10, -14, 5, 14, -14, 0, 1, -2, -1, 13, 0],\n [-2, 10, -16, 13, 13, -12, -16, -13, -6, -4, -7, 7],\n [3, 1, 6, 10, -2, 7, 13, -16, -14, 7, 15, -13],\n [-16, 4, -9, -5, -16, 5, -3, 8, 11, -9, 8, 6],\n [-1, -13, 16, 13, -6, -4, -13, 7, 16, 16, -5, 4],\n [16, 16, -8, 14, 13, -1, -5, -8, -11, 8, 11, 6],\n [12, 5, 7, 3, 10, 16, 2, 9, -14, 6, 10, 10],\n [-7, 7, -15, 5, -15, 11, 7, 5, -14, -15, 6, -4],\n [-2, 16, -4, 3, -10, -4, -13, 10, 15, -15, -2, -12],\n [-14, -1, 9, -11, 3, 5, 4, 15, -16, 6, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82470310135", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (12, 3) of the result:\nA =\n[[14, 12, -4, -15, -8, 15, 5, 1, 1, 2, 14, 12],\n [7, 16, 2, -1, 15, 4, 13, -10, -5, 11, -3, -10],\n [0, 6, -4, 3, -12, -11, -4, -14, 14, -14, -9, -10],\n [-10, -6, 7, 4, 3, 12, -7, -1, -7, 16, -12, -5],\n [-9, -11, 6, -14, 12, -13, -10, 4, -7, 15, 8, -4],\n [4, 2, -9, 3, -9, -1, 11, -7, 4, -2, -11, 4],\n [0, 9, -7, -10, 15, -13, -7, -2, 16, 8, -6, 0],\n [-5, -1, 16, 9, -7, -4, 1, 4, 6, 6, -12, -2],\n [7, -5, 2, 16, 8, -4, 7, -14, -5, -15, 3, 5],\n [-2, 16, -15, 10, 14, -4, 13, 9, 7, -16, 5, -7],\n [10, -15, 2, -6, -3, 16, 1, 12, 13, -14, 15, -2],\n [6, -1, -11, -1, 3, 11, 9, -11, -1, 16, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7439398709", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-15, -4, -6, -11, -1, -8, -8, 11, 6, 2, 14, 9],\n [-4, -13, 0, -10, 5, 4, -10, 2, 4, -9, -9, -4],\n [-6, 0, 5, 1, 5, -10, 8, 0, 12, 3, 1, 0],\n [-11, -10, 1, -1, 9, 10, 12, 0, 10, 0, 6, -8],\n [-1, 5, 5, 9, 14, 4, 2, -4, -2, -7, 2, -13],\n [-8, 4, -10, 10, 4, 10, -12, -2, -13, 0, -2, 6],\n [-8, -10, 8, 12, 2, -12, -14, -8, -4, -4, -2, -2],\n [11, 2, 0, 0, -4, -2, -8, -15, -6, -12, -11, 6],\n [6, 4, 12, 10, -2, -13, -4, -6, -14, -11, -6, -6],\n [2, -9, 3, 0, -7, 0, -4, -12, -11, 10, -2, 7],\n [14, -9, 1, 6, 2, -2, -2, -11, -6, -2, 1, -13],\n [9, -4, 0, -8, -13, 6, -2, 6, -6, 7, -13, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9518007808126", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[14, -3, 13, 14, 15, 0, 11, 0, -11, 12, -8, 14],\n [13, -8, -7, 16, -14, 12, -3, -2, -7, -1, 16, 11],\n [7, -2, -4, 2, -6, -4, 15, 9, -1, 0, -4, -4],\n [-2, -6, -16, 1, -16, 5, -15, 13, 1, -16, -14, -7],\n [-2, -14, -4, 7, 13, 15, -2, 1, 6, 15, 2, 12],\n [-5, -13, 5, -2, 4, 2, -9, -2, -13, 8, 9, -8],\n [14, -11, 8, -11, 2, -12, -12, -12, 3, -4, -8, -3],\n [-4, 16, 6, 13, 1, 1, -3, -5, 10, 12, -10, -2],\n [2, -8, 3, 5, 15, -14, 1, -1, -14, -5, 7, -6],\n [6, 16, -13, -3, -8, 16, 2, -14, 10, -11, 15, 1],\n [15, 3, -2, 6, -3, 4, -14, -10, 0, -13, -11, 15],\n [5, -9, 10, 11, -15, -15, 10, -10, -5, -9, -8, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51446838868410", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[1, 11, -11, 14, -2, -13, -12, 6, -4, 10, 14, 2],\n [13, 13, -12, -6, -7, -16, -2, 4, 5, 15, 9, -4],\n [-12, -3, -13, -9, -8, 14, -14, 10, -8, 12, 12, -7],\n [-4, -16, -3, 15, -1, 9, 16, 14, -9, 8, 16, 13],\n [-16, -16, 10, -13, 7, 7, -11, -16, 12, 7, -4, 11],\n [-2, 14, 5, -5, 0, 9, -4, 0, 9, 11, 15, 4],\n [-8, -1, -12, -8, -11, -2, 1, -12, -7, -1, 10, 6],\n [11, -6, -13, -13, -1, 11, 12, 0, -11, 1, -4, 8],\n [-6, -5, 15, -3, 8, 16, -11, -13, -10, 2, 14, 3],\n [4, 8, -5, 0, 15, -16, -2, -16, 8, -10, -11, -16],\n [-2, -4, 4, -4, 0, 0, -5, -6, -3, -2, 6, -13],\n [16, 8, 5, 15, -16, 7, -10, -11, -2, -16, -9, -5]], determine the value at position (7, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31633089192", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (9, 12) of the matrix A^7 where A is:\n[[7, -15, -1, -3, -8, 0, -6, 3, 4, -9, 8, -1],\n [-15, -10, -7, -8, 4, -6, 5, -6, 3, 4, -4, 12],\n [-1, -7, 8, 2, -1, 4, -2, -6, 6, -3, -6, -6],\n [-3, -8, 2, -12, -3, -8, 0, -8, 4, -2, -6, 10],\n [-8, 4, -1, -3, -7, 14, 15, -13, 6, -8, 0, 0],\n [0, -6, 4, -8, 14, 16, 0, 10, 8, 10, 5, 1],\n [-6, 5, -2, 0, 15, 0, -8, -10, 6, 2, -10, 4],\n [3, -6, -6, -8, -13, 10, -10, 0, -2, -2, -2, 0],\n [4, 3, 6, 4, 6, 8, 6, -2, 0, -8, 3, 4],\n [-9, 4, -3, -2, -8, 10, 2, -2, -8, 14, 2, 2],\n [8, -4, -6, -6, 0, 5, -10, -2, 3, 2, 14, -2],\n [-1, 12, -6, 10, 0, 1, 4, 0, 4, 2, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2054761158", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 7) of the matrix A^9 where A is:\n[[7, 11, -12, -8, -9, 1, -4, -11, -1, 1, 0, -15],\n [1, -6, -15, -15, 1, 5, -1, 10, 0, 0, -11, 16],\n [-4, -11, 9, 2, 2, 9, 5, -6, 5, 15, -10, 5],\n [-11, -2, 1, 12, -12, 7, 15, 13, -12, 1, 4, 5],\n [4, -12, 16, -10, 7, -9, -2, -11, -12, 6, 3, -5],\n [4, 5, 8, -5, -15, 13, -10, 1, 1, 11, -9, 2],\n [-11, -10, 3, 7, 12, 11, -12, 0, 16, -11, -14, -7],\n [-6, 6, -13, -10, 9, 16, 11, -1, -7, -10, -10, 8],\n [-12, 9, 13, -6, -10, 9, 5, -5, 5, -15, -5, -16],\n [-2, -10, 5, 16, 16, 12, 2, -12, -3, -8, -12, 4],\n [11, -15, -11, 14, 15, -6, -3, -7, -16, 14, -9, -15],\n [14, -5, 14, 15, 0, -9, 2, -6, -12, 11, -15, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7650802881659", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[1, 0, -3, -8, 2, -2, 8, 9, 5, 14, -10, 4],\n [0, 1, -4, -13, -14, -2, 1, -3, -2, 10, 6, -4],\n [-3, -4, -5, -2, -10, 12, -16, 11, 0, -6, -10, 4],\n [-8, -13, -2, -15, 0, 2, 6, -2, 14, 2, -10, 0],\n [2, -14, -10, 0, -9, -4, 12, 8, 6, 0, -8, -14],\n [-2, -2, 12, 2, -4, 2, 2, 15, 2, 8, -5, 0],\n [8, 1, -16, 6, 12, 2, -4, 2, -4, -3, -10, -10],\n [9, -3, 11, -2, 8, 15, 2, -12, -4, 0, 1, 0],\n [5, -2, 0, 14, 6, 2, -4, -4, -9, 8, 9, 13],\n [14, 10, -6, 2, 0, 8, -3, 0, 8, -6, 3, 6],\n [-10, 6, -10, -10, -8, -5, -10, 1, 9, 3, -5, 10],\n [4, -4, 4, 0, -14, 0, -10, 0, 13, 6, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-954966985682", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[3, 3, -9, -4, -2, -8, 11, -2, -2, 9, -7, -6],\n [3, 16, 5, -4, -4, 15, 5, 0, -10, 7, -6, 4],\n [-9, 5, -7, 12, -5, 6, -6, 12, -8, -4, 10, 14],\n [-4, -4, 12, 6, 2, -8, -14, 10, 6, 8, 2, -8],\n [-2, -4, -5, 2, 11, -2, 2, -3, -12, 10, -2, 0],\n [-8, 15, 6, -8, -2, 7, 7, 0, 0, -4, 7, -6],\n [11, 5, -6, -14, 2, 7, 0, 10, -5, 0, 5, -5],\n [-2, 0, 12, 10, -3, 0, 10, 6, -2, 10, 7, -8],\n [-2, -10, -8, 6, -12, 0, -5, -2, 0, -2, 0, 10],\n [9, 7, -4, 8, 10, -4, 0, 10, -2, 13, 4, -3],\n [-7, -6, 10, 2, -2, 7, 5, 7, 0, 4, 0, 2],\n [-6, 4, 14, -8, 0, -6, -5, -8, 10, -3, 2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "536766445710885", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[3, -2, 8, 4, -4, 0, 6, 4, -4, -10, 9, 4],\n [-2, 3, -8, 2, -14, -5, 6, -2, 2, 1, 6, 10],\n [8, -8, -12, 2, -12, 1, -2, -2, -2, -6, 8, 2],\n [4, 2, 2, -12, -6, 5, -10, 2, 6, -8, 0, 2],\n [-4, -14, -12, -6, 14, 8, 2, -5, -8, -2, -4, -1],\n [0, -5, 1, 5, 8, 15, 0, 2, -4, 2, -4, 14],\n [6, 6, -2, -10, 2, 0, -13, 5, -8, 2, 11, 13],\n [4, -2, -2, 2, -5, 2, 5, 8, -1, 0, 4, -1],\n [-4, 2, -2, 6, -8, -4, -8, -1, -1, -11, 0, 2],\n [-10, 1, -6, -8, -2, 2, 2, 0, -11, -6, 12, 0],\n [9, 6, 8, 0, -4, -4, 11, 4, 0, 12, -11, -5],\n [4, 10, 2, 2, -1, 14, 13, -1, 2, 0, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-369639506701167", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of absolute values of all entries of the result:\nA =\n[[-13, -1, 0, 2, -2, 5, 8, 8, -2, 2, 8, -3],\n [-1, -3, 0, 4, -3, 2, 2, -6, -12, 6, 8, -8],\n [0, 0, 16, -1, 4, 14, 1, 13, -2, -6, -4, -1],\n [2, 4, -1, -1, 2, 6, -4, 8, 11, -1, 12, -2],\n [-2, -3, 4, 2, 13, 4, -4, -2, -4, 11, -14, 12],\n [5, 2, 14, 6, 4, 9, -8, -10, 2, 8, -8, 0],\n [8, 2, 1, -4, -4, -8, -4, 1, 8, 14, 3, -11],\n [8, -6, 13, 8, -2, -10, 1, 11, 7, 0, -2, 4],\n [-2, -12, -2, 11, -4, 2, 8, 7, -3, 0, 8, -5],\n [2, 6, -6, -1, 11, 8, 14, 0, 0, -7, 7, -6],\n [8, 8, -4, 12, -14, -8, 3, -2, 8, 7, 10, -12],\n [-3, -8, -1, -2, 12, 0, -11, 4, -5, -6, -12, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6660223241630", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[3, 8, 14, -8, 7, -13, 7, -3, -9, 10, 13, -3],\n [1, -4, 12, 11, -13, 10, 7, 7, -14, 2, -8, 5],\n [5, -1, -9, 0, 10, -3, 5, 5, -6, 15, 10, 3],\n [2, -7, -4, 11, -9, 5, 11, -1, 0, 2, 1, 12],\n [-2, 4, -10, 5, -11, -3, 0, -16, -15, 4, -12, 3],\n [5, 6, -16, -4, 7, 8, 11, -13, 6, -13, 3, 0],\n [13, 11, 7, 14, 15, 12, -10, -2, -11, 0, 16, -16],\n [-14, -4, -6, -5, 1, -1, 16, -13, 7, -10, -8, 2],\n [12, -11, 5, 5, -14, 8, -3, -12, 1, 11, 13, -11],\n [14, 1, 8, -9, 11, -10, 8, -16, -15, 15, -5, 9],\n [5, 14, 16, 5, -9, -1, 11, -3, -13, 7, 2, 8],\n [0, -15, 10, -9, -12, -13, -11, 12, -9, -7, -7, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80843239584056", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (11, 12) of the matrix A^9 where A is:\n[[-5, 8, -2, -3, -11, -14, 10, 0, 8, -12, 13, 1],\n [3, 10, 0, -9, -5, -14, -3, -2, -14, 7, -15, -12],\n [-13, -15, -6, 0, -5, 2, -4, 2, 3, 4, 14, 14],\n [-12, -15, -6, 7, 14, -15, 9, 0, -6, -4, 9, 13],\n [3, -9, 3, -6, 11, -6, -8, 10, -11, 11, -4, 6],\n [-6, 4, 7, -6, 9, 3, 12, -13, 1, -5, 15, 14],\n [-9, 8, -6, 9, 2, 0, -7, 12, 11, 1, 15, -12],\n [1, -1, -14, -11, 16, -1, -15, -15, -12, 11, -16, -12],\n [-13, 12, -15, -2, -12, 14, 9, -3, -6, 2, -7, 0],\n [1, 8, -2, 16, 14, -11, -9, -6, 9, 12, -15, 7],\n [1, 16, 4, 5, 16, 15, 16, -3, 9, 10, -7, -10],\n [0, -13, 16, -1, 7, 4, 12, -2, 11, 1, -9, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-81449994994218", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[-11, -13, 8, -6, -6, -5, -9, 10, -7, -5, -8, -6],\n [-13, 1, 12, 0, 2, -8, -6, 8, -1, -10, 14, 6],\n [8, 12, -4, -7, 1, -4, -3, -1, 10, -3, 8, 6],\n [-6, 0, -7, -16, -6, -2, 6, -3, 2, -2, 2, -13],\n [-6, 2, 1, -6, 4, 14, 6, -1, -10, 14, -2, 4],\n [-5, -8, -4, -2, 14, -8, -11, 7, 2, 6, -14, 8],\n [-9, -6, -3, 6, 6, -11, -3, 5, 0, -3, 12, 14],\n [10, 8, -1, -3, -1, 7, 5, -2, -2, -12, -2, 0],\n [-7, -1, 10, 2, -10, 2, 0, -2, -15, -2, 6, 4],\n [-5, -10, -3, -2, 14, 6, -3, -12, -2, 4, -6, 4],\n [-8, 14, 8, 2, -2, -14, 12, -2, 6, -6, 12, -10],\n [-6, 6, 6, -13, 4, 8, 14, 0, 4, 4, -10, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5631198278920", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[10, -11, -6, 12, 15, -13, -12, 1, -9, 6, -5, 4],\n [5, 15, 11, 1, -14, 13, -4, -16, 9, 0, 15, 5],\n [8, 15, 7, -9, 13, -4, 6, -4, 13, -11, 13, 0],\n [7, -8, 2, 14, 8, 16, 15, 5, -14, -6, 7, 13],\n [-2, -6, 3, 7, -7, 14, 10, -12, -5, -6, 12, 10],\n [-1, -2, -4, 16, -12, 13, 9, -8, -12, -16, -14, -8],\n [9, -15, 11, 3, 9, -3, -15, 4, 2, -2, 15, -3],\n [-8, 14, 8, -7, -2, -15, 9, 15, 15, 11, 10, -2],\n [7, 4, -16, 4, 6, 5, 14, 12, -16, -16, 1, -6],\n [-11, -5, -9, -16, -15, -1, -9, -11, -13, 6, -3, 8],\n [-5, 4, -2, 0, 7, 11, 14, 14, 4, 16, -7, -15],\n [-6, -2, 8, 6, 11, -13, -14, -3, 12, 4, 0, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149931554183753", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-12, -12, 2, -5, 12, 2, -2, -12, -2, 3, 7, 10],\n [-12, 11, -4, -4, -13, 4, 6, -1, 8, 0, -8, -4],\n [2, -4, 13, 0, 9, 1, -3, -2, -6, -2, -3, -10],\n [-5, -4, 0, 3, 8, -1, -10, -10, -2, -6, -12, 7],\n [12, -13, 9, 8, 1, -8, 0, -10, -14, 8, 6, -2],\n [2, 4, 1, -1, -8, 4, 6, 2, -12, -2, 0, -4],\n [-2, 6, -3, -10, 0, 6, 2, -12, -11, -6, 0, 1],\n [-12, -1, -2, -10, -10, 2, -12, -8, 6, 4, 5, 4],\n [-2, 8, -6, -2, -14, -12, -11, 6, -15, 6, -12, 12],\n [3, 0, -2, -6, 8, -2, -6, 4, 6, 6, -6, -6],\n [7, -8, -3, -12, 6, 0, 0, 5, -12, -6, -15, 3],\n [10, -4, -10, 7, -2, -4, 1, 4, 12, -6, 3, -4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12149051220", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-12, 3, -16, 7, -5, -13, -8, 1, 0, -1, -12, -11],\n [3, -13, -4, 2, 5, -6, 4, 3, 15, 4, 8, -4],\n [-16, -4, -10, 16, -3, -8, -2, 2, -1, -2, 6, -5],\n [7, 2, 16, 1, -6, 4, 0, -2, -10, -4, 12, -2],\n [-5, 5, -3, -6, -11, -7, 10, 10, 0, 0, 3, 6],\n [-13, -6, -8, 4, -7, 1, -2, 12, -4, 2, -7, -6],\n [-8, 4, -2, 0, 10, -2, -6, 2, 10, 0, -2, -6],\n [1, 3, 2, -2, 10, 12, 2, -1, -7, -6, 4, -2],\n [0, 15, -1, -10, 0, -4, 10, -7, -11, 4, -1, -2],\n [-1, 4, -2, -4, 0, 2, 0, -6, 4, -11, -7, -5],\n [-12, 8, 6, 12, 3, -7, -2, 4, -1, -7, -10, -2],\n [-11, -4, -5, -2, 6, -6, -6, -2, -2, -5, -2, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16375217235730055", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-2, 4, 2, 2, 8, -6, 0, 11, 2, 4, -14, 4],\n [4, -12, -2, 0, -4, 0, 5, 0, 5, -6, -14, 9],\n [2, -2, -11, 10, 5, -4, 0, -1, -1, -9, -8, -14],\n [2, 0, 10, 16, 4, -4, -2, -6, 0, 12, -5, -1],\n [8, -4, 5, 4, -12, -13, 10, 8, -12, -4, 0, 13],\n [-6, 0, -4, -4, -13, -8, 4, 4, -3, -1, -2, -10],\n [0, 5, 0, -2, 10, 4, 15, -4, -10, 10, 2, 9],\n [11, 0, -1, -6, 8, 4, -4, -2, 0, 2, -1, 2],\n [2, 5, -1, 0, -12, -3, -10, 0, 8, -8, -3, 1],\n [4, -6, -9, 12, -4, -1, 10, 2, -8, -7, -10, 2],\n [-14, -14, -8, -5, 0, -2, 2, -1, -3, -10, -7, 8],\n [4, 9, -14, -1, 13, -10, 9, 2, 1, 2, 8, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102121934527554", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[5, -4, 4, 1, 0, -2, 8, 4, 6, 0, 4, 6],\n [-4, 9, -8, 0, 16, -1, -10, -3, 6, 6, 0, 4],\n [4, -8, 16, 8, 4, -4, 12, -13, 6, 8, -11, 5],\n [1, 0, 8, 3, -4, 6, -4, 3, -12, 4, 6, 6],\n [0, 16, 4, -4, 6, -6, 8, -1, -11, 4, 6, -3],\n [-2, -1, -4, 6, -6, 11, 3, 8, 8, 8, -11, 5],\n [8, -10, 12, -4, 8, 3, 1, 4, -4, 8, -9, -2],\n [4, -3, -13, 3, -1, 8, 4, 3, 13, -5, 12, 7],\n [6, 6, 6, -12, -11, 8, -4, 13, 5, 4, -6, 12],\n [0, 6, 8, 4, 4, 8, 8, -5, 4, 8, -4, 2],\n [4, 0, -11, 6, 6, -11, -9, 12, -6, -4, -14, 3],\n [6, 4, 5, 6, -3, 5, -2, 7, 12, 2, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1928876084592", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[3, 16, 12, -11, -4, -5, 4, -11, -9, 10, 1, 16],\n [5, -11, 0, -10, -15, -2, 14, -7, -14, -16, 1, -11],\n [7, -7, -9, 8, -14, 6, 8, -8, -10, 15, 5, -9],\n [-1, 8, 5, 10, -3, -2, -4, 7, -13, 4, 10, 14],\n [2, 1, -11, -7, -9, 3, -13, -13, -6, -9, 2, 16],\n [4, 0, 4, -6, 8, -16, 6, -14, 1, -5, -11, 2],\n [-9, -5, 6, -9, -13, -11, 10, 5, 4, -8, -13, 12],\n [-2, 12, 16, -8, -3, 6, 12, 10, -11, -14, -10, 9],\n [-6, 2, 2, -3, -12, 3, -8, -6, 16, -4, -13, 11],\n [7, -16, 2, 5, -1, 5, 7, 6, 11, -13, -14, 15],\n [0, 1, -7, 14, -11, -11, 8, -1, -3, -14, 6, -15],\n [-16, -2, -4, -2, -15, 4, 8, -12, 10, 1, 11, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8145367201107", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[14, 6, 4, 0, -2, -13, -7, 0, 2, -2, 4, -8],\n [6, 14, -4, 0, 1, -2, 0, -10, 6, 0, -9, -1],\n [4, -4, -7, 0, 2, 14, -4, -10, 8, -2, 2, -1],\n [0, 0, 0, 16, -6, -7, 2, -2, -2, 5, -3, -4],\n [-2, 1, 2, -6, -4, -1, 0, 0, -1, 0, -10, 0],\n [-13, -2, 14, -7, -1, -11, -10, -5, -2, 11, -3, 4],\n [-7, 0, -4, 2, 0, -10, -11, 6, 6, -8, -16, -2],\n [0, -10, -10, -2, 0, -5, 6, 0, -2, 2, -9, 9],\n [2, 6, 8, -2, -1, -2, 6, -2, -10, -2, 2, -12],\n [-2, 0, -2, 5, 0, 11, -8, 2, -2, -16, -1, 0],\n [4, -9, 2, -3, -10, -3, -16, -9, 2, -1, 8, -4],\n [-8, -1, -1, -4, 0, 4, -2, 9, -12, 0, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825216040246", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[1, -11, -1, 2, 14, 0, -5, 3, 7, -8, 5, 13],\n [-10, -2, -16, -2, 1, 4, -16, -6, -1, -1, -6, -8],\n [-13, -15, 5, -11, 12, -5, -12, 1, 16, -15, 6, 16],\n [-12, 14, -3, -12, 5, 5, 11, -8, 11, -14, 9, -3],\n [-16, -7, 14, 0, -13, -13, -2, 3, -5, -9, 13, 8],\n [-3, 16, 16, 1, 11, -11, 14, 7, 7, -1, -12, -11],\n [-7, 6, -8, -12, 1, -16, 1, 11, 8, -5, -1, -10],\n [8, -4, 2, 8, 7, -13, -8, -3, 8, -3, -7, 6],\n [-6, 1, 4, 13, 9, 6, -1, 13, -8, -6, 7, -9],\n [8, -8, -15, 16, -10, -9, -9, 5, -15, -13, 2, -12],\n [-2, -10, -5, -5, 8, -10, -8, -13, -3, 13, -10, -8],\n [-10, -7, -15, -6, -8, -11, 5, -3, -1, 2, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947034907203", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (2, 9) of the result:\nA =\n[[15, -8, 2, 16, 5, 13, 6, -2, 16, -5, -4, 10],\n [-8, 10, -4, -4, -6, -6, -10, 2, -14, 9, -9, 10],\n [2, -4, 7, -4, 9, -4, -6, 6, 5, 4, 0, 1],\n [16, -4, -4, -16, -6, -8, 8, 10, -2, 4, 12, -6],\n [5, -6, 9, -6, 3, 2, -2, 6, 0, -1, 2, 0],\n [13, -6, -4, -8, 2, 12, -5, 0, -1, 4, -8, 4],\n [6, -10, -6, 8, -2, -5, 0, 4, -4, -3, -6, -13],\n [-2, 2, 6, 10, 6, 0, 4, 6, 2, -3, 7, -1],\n [16, -14, 5, -2, 0, -1, -4, 2, 4, -12, 2, -10],\n [-5, 9, 4, 4, -1, 4, -3, -3, -12, -16, -10, -11],\n [-4, -9, 0, 12, 2, -8, -6, 7, 2, -10, -14, 14],\n [10, 10, 1, -6, 0, 4, -13, -1, -10, -11, 14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-106260720291", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (8, 12) of the result:\nA =\n[[5, -2, -4, 8, 4, 6, 2, 14, -10, -6, 10, 2],\n [-2, 12, -12, 2, -10, -10, 10, 14, 7, -13, 6, -2],\n [-4, -12, -4, -9, 5, -2, 3, 2, 4, 6, -5, 3],\n [8, 2, -9, -2, -6, -6, -14, 2, 6, -2, 0, -8],\n [4, -10, 5, -6, -13, 0, -2, 8, 2, 8, 10, 2],\n [6, -10, -2, -6, 0, 14, 7, 9, -9, -4, 11, -9],\n [2, 10, 3, -14, -2, 7, -11, 1, 0, 10, 0, -8],\n [14, 14, 2, 2, 8, 9, 1, 6, 4, 2, 0, 8],\n [-10, 7, 4, 6, 2, -9, 0, 4, -4, 1, -16, -4],\n [-6, -13, 6, -2, 8, -4, 10, 2, 1, -4, -4, -8],\n [10, 6, -5, 0, 10, 11, 0, 0, -16, -4, 15, -6],\n [2, -2, 3, -8, 2, -9, -8, 8, -4, -8, -6, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6078172399787", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[9, -7, 4, 4, 12, 10, -6, 2, 6, -6, -6, 6],\n [-7, -4, -9, -4, 2, 1, 4, -6, 2, 2, -3, -14],\n [4, -9, 6, -9, 2, 0, 6, 2, -14, 12, -6, 4],\n [4, -4, -9, -3, -2, -10, 0, 12, 8, 0, 2, 0],\n [12, 2, 2, -2, -8, 10, -9, -3, 14, 2, -4, 2],\n [10, 1, 0, -10, 10, 16, 4, -4, 10, 4, 14, -6],\n [-6, 4, 6, 0, -9, 4, -1, -12, 6, -10, 8, 6],\n [2, -6, 2, 12, -3, -4, -12, 0, 1, 8, 12, -7],\n [6, 2, -14, 8, 14, 10, 6, 1, -13, -10, 4, 10],\n [-6, 2, 12, 0, 2, 4, -10, 8, -10, 3, 4, 0],\n [-6, -3, -6, 2, -4, 14, 8, 12, 4, 4, -5, 2],\n [6, -14, 4, 0, 2, -6, 6, -7, 10, 0, 2, -8]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355427083597871", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[6, 1, 2, -1, -10, -6, -12, -4, 15, 2, -16, -9],\n [0, -12, -5, 10, -12, 1, -11, -10, 1, 6, 10, -14],\n [-8, 9, -2, 16, -13, 13, -1, -11, 10, -5, 13, 15],\n [7, 11, 5, 0, -3, -2, -2, -9, -3, -16, -16, 0],\n [-4, -3, -1, 5, 4, 2, -3, 8, -3, -16, 0, 5],\n [9, -13, -8, 10, 8, -6, -13, -4, 15, 3, 0, 6],\n [-13, 5, 15, 5, -6, -15, 8, -1, 13, -5, 15, -15],\n [16, -13, -9, 11, -6, 3, -4, -1, -16, -7, -4, 16],\n [0, -1, -1, -16, 4, 7, 3, -3, -16, 5, -10, 15],\n [-13, -1, 0, 13, -10, 3, 16, -5, -2, -2, 3, 0],\n [12, 7, -2, -5, 2, -4, 16, 13, -10, 1, 8, -5],\n [4, -10, 13, -1, 5, -1, -12, -8, 11, 14, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15741956874", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[0, 13, -3, 8, -13, -15, 13, 9, -6, -11, 2, 2],\n [-6, -11, 12, -3, -7, 9, 14, -7, 9, -7, 3, 4],\n [1, -5, -4, -13, 10, -8, 11, -6, -7, 10, 11, -7],\n [11, -14, -2, 16, 0, 10, 6, 11, 10, 2, -7, -3],\n [1, -16, -15, 1, 7, 4, -3, 16, -5, 0, 8, 14],\n [-13, 8, 16, 5, -5, -14, -13, -9, 15, -12, 6, -3],\n [2, 6, 4, -6, -6, 8, -1, 7, 7, -6, 7, 0],\n [1, 8, -9, -1, 12, -8, -10, -3, 8, 2, -15, 2],\n [-15, 7, -7, -4, -16, -2, -10, -1, -10, 1, 11, -3],\n [0, 6, 6, 7, 4, 5, 9, 12, -10, 0, -6, 8],\n [-9, -13, -8, -3, -3, 6, 16, 1, -7, -4, 7, 7],\n [-14, 3, -14, -7, 9, -1, -13, 16, -7, 6, 0, -9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "385146078834", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[14, -6, -6, -6, -2, -6, -2, 4, -8, 2, 5, 3],\n [-6, -6, -6, -10, 8, 0, 4, -2, 14, 0, 1, 2],\n [-6, -6, 14, -2, 0, -11, -10, 3, 5, -6, -2, 6],\n [-6, -10, -2, 11, -5, 0, -10, 6, -2, -8, 0, -6],\n [-2, 8, 0, -5, 13, -10, -11, 0, 11, 4, -3, 2],\n [-6, 0, -11, 0, -10, 12, -4, 0, 0, 6, -7, -2],\n [-2, 4, -10, -10, -11, -4, 15, 2, -8, 6, 8, -4],\n [4, -2, 3, 6, 0, 0, 2, -9, 0, 7, -3, 8],\n [-8, 14, 5, -2, 11, 0, -8, 0, -5, -15, -1, -6],\n [2, 0, -6, -8, 4, 6, 6, 7, -15, -5, -12, -6],\n [5, 1, -2, 0, -3, -7, 8, -3, -1, -12, 9, 8],\n [3, 2, 6, -6, 2, -2, -4, 8, -6, -6, 8, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2760463715122", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 8) of the 8th power of the matrix:\n[[2, 8, 12, -10, -13, 3, 10, -2, 11, 7, -7, -12],\n [-7, -15, 1, 1, 5, 11, -13, 3, 10, -16, -4, 6],\n [-10, 15, 15, -7, 2, -13, -11, -3, 13, 14, -2, 1],\n [5, -13, 4, 8, -6, -3, -5, 2, -5, -9, -15, 16],\n [11, -6, 9, 15, 5, -4, -13, -12, -9, 10, -4, 3],\n [5, 3, 15, 2, 11, 13, 12, -13, 11, -4, 3, 7],\n [-6, -14, -15, -7, 12, -13, -5, -3, -4, 8, 14, 12],\n [-11, -10, -16, 0, 13, 13, 0, 15, -15, 6, 6, -7],\n [11, -14, 13, -3, -7, 0, 1, 6, -14, -2, -11, -16],\n [-1, 7, 1, -13, -12, -11, -15, -8, 7, 15, 4, -13],\n [15, -1, 16, -15, -4, -15, -6, 2, 2, -7, -9, -4],\n [-7, -3, -16, -2, -16, -15, 16, -11, 13, 9, 4, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4909060011", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-7, -14, 2, 9, 14, -9, 5, -16, -10, -16, -16, -5],\n [11, 16, -16, 13, 0, 2, -6, 15, 14, -2, -12, 10],\n [1, -14, 5, 3, 9, 7, 9, -3, -12, 12, 9, 15],\n [6, 2, -14, -1, -6, 16, -9, -9, -10, -1, 9, -1],\n [11, 9, -13, 4, 12, 15, 9, 1, -14, -15, 13, 9],\n [-10, 6, 3, 9, 16, -14, 4, -11, 14, -9, 16, -16],\n [3, 2, -16, 15, 3, 11, -9, 2, -8, -4, -15, -16],\n [14, -15, 5, -9, -14, -6, 7, -7, -10, 4, -13, 6],\n [-1, -6, 1, -1, -2, -16, -3, 7, 12, -3, -13, -9],\n [-3, 2, 0, 16, 16, 14, 11, 9, -13, 12, 5, 2],\n [3, 15, -7, 13, -7, 10, 3, -1, 14, -15, -12, 16],\n [0, -12, -14, 13, -14, 16, 4, 0, 0, -11, -2, -9]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34406997718740", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-14, 6, -12, -11, 7, 5, -6, 16, 7, 7, 9, 9],\n [-16, -5, -11, 5, -7, 8, -15, -9, -14, 14, 15, -12],\n [-16, 3, -15, -9, 7, -3, 8, 0, 12, -8, -16, -13],\n [8, 11, -9, -11, 10, -11, -8, -12, 10, -16, 2, 7],\n [-16, -14, 7, 8, -3, 16, 7, 9, -6, -14, 3, -8],\n [3, -9, 3, 0, -6, 16, -4, -11, -15, 5, 8, 8],\n [-5, 4, -11, 13, 5, 0, 4, -6, -2, -3, 8, -3],\n [-9, -16, -14, 1, 6, -15, 15, -11, 3, -11, -12, 0],\n [-5, 15, 12, -12, -9, -2, -3, 7, 9, 10, -16, -7],\n [0, -8, -10, 11, 16, 7, 15, 10, 4, 5, 6, 6],\n [0, -12, -3, -4, -9, 14, -12, 14, -5, -5, 7, 10],\n [3, 8, 11, 6, 13, 9, 4, -16, 15, 10, 3, 11]], determine the value at position (11, 10).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30929087139", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-6, -16, -8, -4, 3, 12, 2, -9, 14, 4, -4, 7],\n [-1, -8, -7, 10, 15, -7, -5, 3, 2, 3, -7, -16],\n [13, 15, -10, -2, 5, -6, -12, -15, 14, -3, -8, -4],\n [-13, 5, 11, 0, -7, 3, 13, 1, -8, 16, 6, 5],\n [12, -16, 5, 8, -3, -13, -10, 12, 3, -9, -8, -11],\n [16, 14, -11, 6, 3, 6, -2, 16, -10, 16, 0, -12],\n [-13, -8, 10, -15, -6, 7, 12, -2, -14, 1, 4, -14],\n [-9, -14, -4, -1, 13, -8, 5, 12, -4, -13, 9, 13],\n [-15, -11, 0, -12, -5, -14, -6, 1, 5, -13, 6, 12],\n [11, -10, -1, 8, 9, -2, 10, 15, 16, -9, -11, 15],\n [-9, -14, 5, 15, 8, 11, 13, 13, -11, -1, 10, -7],\n [6, 3, 9, 2, 1, 13, 6, 2, -2, 16, 7, 10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8905357765", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[16, -11, -8, 11, -4, 0, -1, 15, 2, 8, -15, -16],\n [-13, -13, -2, 7, 5, -12, -5, 13, -16, 4, 9, 10],\n [-12, -15, -14, -2, -15, -12, 4, 15, 1, 13, -13, 9],\n [16, -9, -9, 15, 8, -10, 0, -15, 11, -1, 15, 4],\n [12, -10, 12, 8, 2, 7, -13, -2, 4, 5, 6, 1],\n [-10, 5, -7, 13, -11, 12, 9, -6, -13, -8, -8, 9],\n [-14, 11, 2, 9, 5, 6, 2, 10, -10, 15, -8, 16],\n [-14, -8, 10, 15, -4, -16, 5, -15, 9, -4, -9, 4],\n [14, -2, -8, 8, 7, -5, -1, -6, 16, -11, 11, 12],\n [-2, -10, 5, 15, 2, -16, -13, -10, -10, -14, -5, -13],\n [-6, 1, -15, 4, 1, -5, 0, 2, -1, 2, -15, 6],\n [-7, 5, -5, 12, -4, -1, 9, -2, -11, 7, 5, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3701300612483122", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[5, -4, -14, 10, -8, -5, 0, 7, -6, -2, 0, 1],\n [-4, 15, 6, 3, 6, -14, 2, -7, 6, 0, -6, 0],\n [-14, 6, 3, 6, 0, -6, 8, -12, -4, -1, 11, -4],\n [10, 3, 6, 10, -11, 6, 6, -12, -1, -2, -7, -15],\n [-8, 6, 0, -11, -3, 6, 14, 6, -11, 0, -6, 0],\n [-5, -14, -6, 6, 6, 14, -14, -2, -1, 4, 3, 0],\n [0, 2, 8, 6, 14, -14, -1, 8, -3, 6, -7, 14],\n [7, -7, -12, -12, 6, -2, 8, -8, 2, 3, -7, -4],\n [-6, 6, -4, -1, -11, -1, -3, 2, -8, -1, -9, 2],\n [-2, 0, -1, -2, 0, 4, 6, 3, -1, 2, -4, -6],\n [0, -6, 11, -7, -6, 3, -7, -7, -9, -4, -10, 12],\n [1, 0, -4, -15, 0, 0, 14, -4, 2, -6, 12, -11]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2310115629801", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[16, 1, -6, 6, -9, 2, 0, -4, 6, 2, -2, -10],\n [1, 6, 11, -2, -2, -11, -2, 2, 5, -5, 5, -10],\n [-6, 11, 11, -14, -4, -1, 6, 5, 6, 2, -8, 7],\n [6, -2, -14, 10, 9, -11, 0, -4, -4, -2, 6, 2],\n [-9, -2, -4, 9, -11, 0, 13, 8, -14, 5, -12, -4],\n [2, -11, -1, -11, 0, -12, 10, 10, 10, 7, 14, 0],\n [0, -2, 6, 0, 13, 10, 8, 14, 0, 7, -10, -5],\n [-4, 2, 5, -4, 8, 10, 14, 14, -2, 2, 4, -3],\n [6, 5, 6, -4, -14, 10, 0, -2, 10, 0, 6, 0],\n [2, -5, 2, -2, 5, 7, 7, 2, 0, -16, -5, -2],\n [-2, 5, -8, 6, -12, 14, -10, 4, 6, -5, 2, 10],\n [-10, -10, 7, 2, -4, 0, -5, -3, 0, -2, 10, -11]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-688348785906", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[15, -8, 3, 3, 11, 13, -12, 1, -11, -10, -14, -5],\n [16, 7, 3, 9, -13, 14, 8, 13, 0, 14, -3, 16],\n [-3, 2, 0, 16, -3, 12, -11, 7, 11, -14, -13, 15],\n [-8, -5, 16, 6, 10, -7, -1, 9, 14, -13, -3, -16],\n [-3, -7, -3, -12, -15, -13, -1, -1, -6, -13, -11, -9],\n [11, -11, 14, -6, -1, 15, -15, -5, 15, -5, 13, 2],\n [-16, -12, 0, 9, 12, -13, -5, 11, 6, 0, 6, 9],\n [-11, -7, 14, -4, 9, -6, 1, -6, 2, -15, 8, -15],\n [-14, 10, -11, 6, 0, -8, 1, 6, -1, -4, 16, -11],\n [-3, 8, -9, 16, -3, -13, -14, 0, 0, 1, 0, 16],\n [-12, 12, 11, -6, 16, 6, 5, -11, 15, -12, -7, 1],\n [-13, 1, 10, 3, -8, 0, -10, 1, -1, 11, -8, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76769237242370", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[0, -14, 13, 15, -16, -11, -1, 9, -10, 7, 0, -11],\n [0, -13, 2, 9, -6, 15, 8, 15, 7, 16, 12, 3],\n [6, 12, 14, 10, 13, 1, -8, -12, 1, -16, 3, -3],\n [4, -10, -2, -12, -11, 4, -16, -12, -7, -14, -8, 10],\n [-8, 5, -1, 15, 10, -9, 6, 5, -2, -11, -14, 0],\n [-11, -1, 10, -4, -1, 14, -13, 4, -16, -2, 3, -13],\n [11, -11, -14, -1, 6, 11, -14, 15, -3, -15, 0, 8],\n [14, 1, 0, -10, 5, 4, 16, 1, 14, -9, -10, -11],\n [7, -10, 12, 6, -6, 9, -8, -16, 12, 11, 2, -2],\n [14, -2, 6, 9, 13, 8, -3, 12, 0, -4, 11, 5],\n [-3, 2, -16, 13, -13, 0, -16, 11, 0, 4, -12, 12],\n [10, 6, -16, -10, 12, 14, -7, -1, -2, 15, -7, 10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4747914364158", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-11, -2, -4, -2, 4, 4, 0, 4, 6, 7, 0, -6],\n [-2, 3, 2, -6, 4, 0, 2, 4, -12, -6, -9, -5],\n [-4, 2, -15, -8, 1, -2, 12, -10, 8, 7, -7, 6],\n [-2, -6, -8, 3, 1, 8, -2, 1, 12, 10, 0, -6],\n [4, 4, 1, 1, -1, 2, 4, 10, -4, 2, -7, 8],\n [4, 0, -2, 8, 2, 13, 9, 6, -1, -6, -6, -2],\n [0, 2, 12, -2, 4, 9, 13, 2, 4, 10, 6, -8],\n [4, 4, -10, 1, 10, 6, 2, -1, -10, 2, -3, 4],\n [6, -12, 8, 12, -4, -1, 4, -10, -13, 10, 3, -4],\n [7, -6, 7, 10, 2, -6, 10, 2, 10, 12, -6, 0],\n [0, -9, -7, 0, -7, -6, 6, -3, 3, -6, -12, -3],\n [-6, -5, 6, -6, 8, -2, -8, 4, -4, 0, -3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37764322384385", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-1, -4, 4, 3, 0, 6, 0, 10, 0, 2, -4, 4],\n [-4, -13, 0, 6, -14, 8, -3, -6, -1, -10, -10, -4],\n [4, 0, 16, -2, 2, -3, -6, -12, 11, -9, -4, 2],\n [3, 6, -2, 9, -4, -2, 7, -4, -1, 8, -8, 4],\n [0, -14, 2, -4, -12, -12, 4, 7, 1, 2, 7, 10],\n [6, 8, -3, -2, -12, 4, -2, -2, -4, 6, 7, 14],\n [0, -3, -6, 7, 4, -2, 2, 7, 5, -7, -4, -4],\n [10, -6, -12, -4, 7, -2, 7, 12, -7, -8, 1, -2],\n [0, -1, 11, -1, 1, -4, 5, -7, 2, 4, -13, -8],\n [2, -10, -9, 8, 2, 6, -7, -8, 4, 1, -8, -8],\n [-4, -10, -4, -8, 7, 7, -4, 1, -13, -8, 8, 12],\n [4, -4, 2, 4, 10, 14, -4, -2, -8, -8, 12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-197136589428873", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[9, 6, 3, -12, -15, 7, 10, 11, 2, -14, -3, 14],\n [-11, 5, 8, 12, 8, -15, 2, -12, 16, 10, 1, -12],\n [-9, 2, -6, -1, 1, -5, -5, 9, 12, -8, 13, -6],\n [-6, 15, 3, -2, -15, 14, -12, 8, 11, -6, -16, 2],\n [10, 2, -14, -13, -13, -2, 13, -16, 16, -9, 5, -12],\n [0, 15, -8, -4, -2, 4, -2, -1, -15, 9, 6, 16],\n [-2, 4, -13, -12, 16, 11, -9, 5, -8, -1, 16, -12],\n [-5, 5, -14, -14, -10, -5, -6, -16, -12, 6, 2, -9],\n [-4, -4, 7, -6, 15, 11, -14, 11, 2, -2, -11, 8],\n [13, -12, -15, 6, 4, -12, 14, 9, -3, 9, -7, 0],\n [3, -11, -1, 14, -15, 16, -6, -3, -4, 7, -4, -9],\n [-3, 1, 13, 10, 13, -12, 4, -2, -1, -16, 0, 13]], determine the value at position (6, 9).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13286577109", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-9, -7, 2, 2, 3, -6, 15, 15, -5, -4, 5, 12],\n [-12, 8, -13, 8, -4, -14, -8, 7, -13, -9, -7, -7],\n [11, -16, 7, -4, 3, -10, 11, -4, -6, -10, -2, 16],\n [15, 8, -7, 4, 5, -5, 11, -16, 5, -14, -12, -14],\n [11, -4, 1, -1, 0, -14, -2, 0, 16, -13, 11, -9],\n [14, 16, -15, -13, -11, 16, 9, 9, -16, -5, 14, 12],\n [0, -7, -13, -15, 11, -11, 16, 1, -11, 15, 4, -16],\n [-4, 13, -13, -11, 15, 1, 7, -8, -12, 3, 14, 12],\n [-6, 14, -16, 1, -15, -16, 8, -14, 7, 2, -6, 3],\n [16, -7, -8, 3, 8, -12, 5, -6, 8, -15, 2, 4],\n [-8, 12, 8, -9, 7, 14, -7, 10, 2, -15, 14, -2],\n [9, -7, 10, -6, -6, -4, -8, -1, 0, -16, -15, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25285712967750", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (8, 10) of the 9th power of the matrix:\n[[13, -11, -2, 8, -10, -5, -1, 4, 0, -1, -2, -8],\n [-11, 8, 2, -8, 8, 8, 5, -3, -6, -10, 0, 2],\n [-2, 2, 0, -14, -2, 6, -4, 9, 5, 1, -7, -2],\n [8, -8, -14, 1, 12, -6, -6, -4, -13, 6, -2, 1],\n [-10, 8, -2, 12, 12, -4, 3, -6, 8, 4, -2, -14],\n [-5, 8, 6, -6, -4, 4, -2, -3, -5, 10, 8, 4],\n [-1, 5, -4, -6, 3, -2, 13, 2, -1, 6, -6, 4],\n [4, -3, 9, -4, -6, -3, 2, -3, 4, -5, 2, 12],\n [0, -6, 5, -13, 8, -5, -1, 4, -3, 6, 4, 8],\n [-1, -10, 1, 6, 4, 10, 6, -5, 6, 10, 12, 0],\n [-2, 0, -7, -2, -2, 8, -6, 2, 4, 12, 12, -14],\n [-8, 2, -2, 1, -14, 4, 4, 12, 8, 0, -14, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19141878804327", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[10, -1, 12, 0, 2, -2, -14, 4, -6, 16, 0, 0],\n [-1, -13, 1, 3, 6, 4, 8, 6, -11, -3, 6, -2],\n [12, 1, -9, -10, -2, -2, 4, 12, -12, 12, 2, -10],\n [0, 3, -10, 7, -4, -10, 6, -2, 7, 0, -5, -6],\n [2, 6, -2, -4, 4, 9, -12, -2, 10, 2, 2, -1],\n [-2, 4, -2, -10, 9, 8, 6, 8, 12, -8, 0, -3],\n [-14, 8, 4, 6, -12, 6, 10, -10, -2, 10, 8, 10],\n [4, 6, 12, -2, -2, 8, -10, 12, 12, 5, -4, -2],\n [-6, -11, -12, 7, 10, 12, -2, 12, 0, 2, 6, 4],\n [16, -3, 12, 0, 2, -8, 10, 5, 2, 6, -4, 0],\n [0, 6, 2, -5, 2, 0, 8, -4, 6, -4, -8, -2],\n [0, -2, -10, -6, -1, -3, 10, -2, 4, 0, -2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8482668270591", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 10) of the 9th power of the matrix:\n[[9, -15, -7, -9, -12, -6, -5, -5, 13, -11, -16, -11],\n [3, -7, 16, 13, -13, -1, 11, 14, -7, -16, 4, 11],\n [-8, 4, 0, -10, 2, -14, 1, 5, -7, 2, 6, -13],\n [-6, 2, 3, 3, 6, 9, -9, -13, -3, -16, -2, 2],\n [10, 0, 10, -1, 7, -4, 8, -11, -3, -5, -5, 5],\n [5, -10, 14, 15, 2, 10, 12, 0, -4, 13, -7, -16],\n [5, -11, 13, -14, 4, 10, 12, -6, -4, 3, -15, 11],\n [1, 14, 3, -3, -9, 9, 4, 6, -11, 2, 9, -14],\n [-15, -10, -4, -3, -7, 12, 11, 3, -11, 4, -7, -10],\n [-14, -5, 2, 10, 0, 3, -6, 6, 10, 13, 12, -15],\n [-16, 2, 8, -12, 9, 8, -10, -15, 10, -1, 16, 3],\n [2, -12, 6, 12, -13, 5, -2, 13, 11, 7, 13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-721509918292", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-4, -5, 7, 14, 10, 9, 4, -3, -7, -3, 0, -15],\n [9, 0, 16, -16, -15, -3, 14, 11, 1, -1, -6, -9],\n [2, 15, -9, -5, 1, 15, 9, -11, -4, -10, -10, -5],\n [-15, -14, 4, 13, 10, 10, -6, 1, -10, -15, 9, -9],\n [7, -16, 15, 1, -10, 6, 0, -11, -7, 7, 11, 14],\n [14, 16, 15, -6, -6, -13, -11, 15, 9, 15, 12, -12],\n [-14, 15, -3, 7, 16, 14, 8, -8, 7, -11, -3, 3],\n [13, -10, 6, 4, -15, 10, 13, 4, 6, 4, 14, -8],\n [3, 16, -1, 15, 2, 1, 11, 6, 16, -8, 3, 3],\n [-1, -1, -6, -3, 5, 3, -4, -12, 12, 5, -11, 10],\n [-1, -2, 6, 4, -8, -5, 5, 6, 15, -5, -6, 7],\n [9, 7, -5, -6, 14, -11, -3, -2, 1, -10, -14, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15285260784023", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-6, 5, -6, -4, -3, -11, -3, 0, -3, -16, -1, -9],\n [2, -12, 2, -6, -8, -6, -6, -6, -12, 14, 7, 16],\n [10, -14, -6, -8, -1, -6, -14, -16, -16, -7, 6, -9],\n [-7, 15, 2, -16, 12, 6, -16, -5, -13, -8, 2, 13],\n [-8, -14, -11, 4, 5, 14, 9, 8, 11, -1, -6, 7],\n [-7, 8, -4, -3, -6, -1, 1, 14, 10, -7, 15, 10],\n [-7, 2, 5, -11, 16, -8, 6, 15, 12, -6, 9, -10],\n [-2, 6, -16, -9, 9, -6, 15, -4, 15, -4, -10, 6],\n [-10, 11, -13, -13, 7, 5, 1, -8, -9, -15, 12, 4],\n [1, 0, -4, 3, 6, -3, -2, -14, 4, 9, -7, -1],\n [-14, -1, 6, 10, 0, 0, 16, -8, -13, -11, 3, -9],\n [-15, -6, -13, 1, 1, 1, 2, -12, 15, -12, 13, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250362980654", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (7, 4) of the 7th power of the matrix:\n[[-5, -10, 5, 2, 10, -8, -3, 12, -5, 4, -4, -10],\n [-10, 12, 4, -6, 2, 0, -12, -4, -2, -4, 8, 0],\n [5, 4, -9, -10, 4, -4, -2, 0, -4, 0, -9, 6],\n [2, -6, -10, -6, -10, -4, 7, 4, 10, 1, -2, 2],\n [10, 2, 4, -10, -9, 4, -11, 8, 8, -7, 2, 4],\n [-8, 0, -4, -4, 4, -2, 3, -1, 7, -2, 4, 6],\n [-3, -12, -2, 7, -11, 3, -14, -8, 0, 7, 4, -8],\n [12, -4, 0, 4, 8, -1, -8, -11, -4, -6, -12, 4],\n [-5, -2, -4, 10, 8, 7, 0, -4, -14, -1, 8, -4],\n [4, -4, 0, 1, -7, -2, 7, -6, -1, 7, -6, -12],\n [-4, 8, -9, -2, 2, 4, 4, -12, 8, -6, 12, -10],\n [-10, 0, 6, 2, 4, 6, -8, 4, -4, -12, -10, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16767576038", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-7, -10, -4, 7, 1, 11, -12, -1, -4, -4, -6, -13],\n [-10, 8, 1, 10, -7, 12, 6, 2, -6, -6, 9, 10],\n [-4, 1, 14, -7, 7, -6, -2, 2, 4, -4, 0, -10],\n [7, 10, -7, 2, -6, -4, -15, -8, -4, -4, -6, 6],\n [1, -7, 7, -6, -1, 11, 3, 4, 8, -6, 1, -2],\n [11, 12, -6, -4, 11, -16, 7, -6, 4, -8, -10, 14],\n [-12, 6, -2, -15, 3, 7, 15, 6, -10, 4, -10, 3],\n [-1, 2, 2, -8, 4, -6, 6, 6, -7, 6, 14, -8],\n [-4, -6, 4, -4, 8, 4, -10, -7, -10, -14, 7, 6],\n [-4, -6, -4, -4, -6, -8, 4, 6, -14, -2, -9, -2],\n [-6, 9, 0, -6, 1, -10, -10, 14, 7, -9, 1, 7],\n [-13, 10, -10, 6, -2, 14, 3, -8, 6, -2, 7, -14]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1770724951998", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[-12, -10, -7, -11, 3, 4, 10, 0, -8, 6, -2, 8],\n [-10, -13, -12, -2, 1, 0, 2, 7, 11, 5, 0, -8],\n [-7, -12, -6, -12, -6, -12, 4, 2, -4, -14, 0, -5],\n [-11, -2, -12, 4, 8, 4, -2, 11, -8, -10, -14, -2],\n [3, 1, -6, 8, 13, -6, 2, 2, -12, -9, 0, 10],\n [4, 0, -12, 4, -6, -10, 4, 6, -2, -2, -1, -1],\n [10, 2, 4, -2, 2, 4, 16, -4, 4, -7, 2, -14],\n [0, 7, 2, 11, 2, 6, -4, 14, -4, -12, -8, -11],\n [-8, 11, -4, -8, -12, -2, 4, -4, -9, 8, 2, -4],\n [6, 5, -14, -10, -9, -2, -7, -12, 8, 13, -8, -11],\n [-2, 0, 0, -14, 0, -1, 2, -8, 2, -8, 9, 2],\n [8, -8, -5, -2, 10, -1, -14, -11, -4, -11, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6708743208649989", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-1, 12, -4, -8, -13, 4, 0, -14, -5, 4, 11, -7],\n [12, -9, 14, 6, 2, -11, -2, 0, 3, -13, 5, 8],\n [-4, 14, 15, 11, -4, -7, 6, 3, 4, -1, -4, -3],\n [-8, 6, 11, -3, -2, 7, -1, -2, -8, -5, 8, 3],\n [-13, 2, -4, -2, 8, -10, -5, -12, 0, 4, 6, 2],\n [4, -11, -7, 7, -10, 14, 3, 2, 16, 0, 8, -4],\n [0, -2, 6, -1, -5, 3, -6, 1, 3, 6, 6, -10],\n [-14, 0, 3, -2, -12, 2, 1, -7, -4, -2, -6, -2],\n [-5, 3, 4, -8, 0, 16, 3, -4, -11, -14, 14, -4],\n [4, -13, -1, -5, 4, 0, 6, -2, -14, 15, 3, 3],\n [11, 5, -4, 8, 6, 8, 6, -6, 14, 3, 1, 3],\n [-7, 8, -3, 3, 2, -4, -10, -2, -4, 3, 3, 1]], determine the value at position (10, 10).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14649725149", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-12, 5, 14, 5, -7, -14, -2, 13, -3, 0, -13, -7],\n [-12, 12, -11, -3, 0, 14, 16, 16, 0, 13, -6, -12],\n [-15, -2, -4, -14, 15, -5, 2, 2, -6, -10, 0, -16],\n [7, 15, -7, -3, -1, -11, 15, 8, -6, -11, 15, -12],\n [-2, 9, -8, -12, 7, 14, -8, -16, 10, 13, 14, 9],\n [10, 6, -2, -4, -9, -1, 6, 1, 9, 8, 13, 1],\n [1, 10, -11, -15, 4, -13, -8, 3, 6, 15, 12, -3],\n [11, -11, -14, 13, 15, -5, 11, 14, -7, -7, -15, 14],\n [10, 15, 5, -1, 16, -12, -1, -11, -1, 6, -15, 12],\n [8, -14, -12, 7, -4, -5, 10, -4, 8, -9, -6, 3],\n [6, 0, -8, -4, 4, 6, 11, -7, 4, -13, 16, -7],\n [9, 12, 1, -3, 7, 12, -9, 14, 9, -9, 15, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5874329607725", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 5) of the matrix A^7 where A is:\n[[-8, 1, -3, 2, 4, -6, -3, -6, 6, -6, -4, -8],\n [-10, -11, -10, -6, -4, 14, -16, 13, -13, -12, 4, 7],\n [15, 7, -10, -8, 12, 5, -4, -14, 16, -12, -8, 9],\n [-6, -5, 9, -5, -5, -1, 6, 0, -9, 8, 4, 11],\n [10, -2, -10, 2, -14, 3, -12, 5, 16, -13, -13, -4],\n [-12, 13, 0, 2, 6, -6, 4, 6, 9, 13, -8, 5],\n [4, -8, 16, 9, -2, 3, 14, 11, 10, -16, -6, 4],\n [-13, 11, 11, 11, 2, 8, -11, 2, 2, 9, -2, 2],\n [-6, -6, 15, -9, -15, -5, -16, 12, -2, 12, 16, 11],\n [-3, 16, -2, 6, 2, -11, 10, -5, 10, 8, 3, -16],\n [13, -7, -9, -7, 12, -4, -8, 3, 11, 8, 4, -4],\n [4, -4, -4, -5, -1, -2, 4, 13, 0, -13, 11, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7143468632", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[10, -5, 6, 2, 4, 1, 2, 0, -4, -9, 2, 6],\n [-5, -12, 6, 2, 0, 2, -1, -2, 2, -13, -10, 1],\n [6, 6, -6, 4, 4, -3, -4, -11, 3, 0, 6, -4],\n [2, 2, 4, -7, -8, 5, -10, 6, -11, -11, 10, -9],\n [4, 0, 4, -8, -6, -5, -4, 0, 4, -3, -4, -11],\n [1, 2, -3, 5, -5, 11, -12, -6, 4, 0, -12, 1],\n [2, -1, -4, -10, -4, -12, 16, -2, -7, -10, 2, -1],\n [0, -2, -11, 6, 0, -6, -2, -1, -6, -2, 10, 0],\n [-4, 2, 3, -11, 4, 4, -7, -6, 9, -4, 8, 4],\n [-9, -13, 0, -11, -3, 0, -10, -2, -4, -15, -5, 4],\n [2, -10, 6, 10, -4, -12, 2, 10, 8, -5, -15, -2],\n [6, 1, -4, -9, -11, 1, -1, 0, 4, 4, -2, -16]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49096101447868", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^7 where A is:\n[[9, 1, 2, -12, 3, 0, 0, -2, 6, 1, 10, -3],\n [1, -11, 12, -10, -4, 10, -10, 4, 9, -4, 2, -2],\n [2, 12, 11, -6, 11, -12, -6, -1, 7, 2, -8, 10],\n [-12, -10, -6, -10, 4, 2, 16, -2, 2, -8, 10, 6],\n [3, -4, 11, 4, -2, -8, -13, 1, -2, 2, 0, -2],\n [0, 10, -12, 2, -8, 7, -1, 2, 0, 8, -4, 1],\n [0, -10, -6, 16, -13, -1, -13, 0, -4, 0, 8, -2],\n [-2, 4, -1, -2, 1, 2, 0, -7, 10, -9, -2, 0],\n [6, 9, 7, 2, -2, 0, -4, 10, 5, 4, -6, -6],\n [1, -4, 2, -8, 2, 8, 0, -9, 4, 13, 2, -10],\n [10, 2, -8, 10, 0, -4, 8, -2, -6, 2, 1, 0],\n [-3, -2, 10, 6, -2, 1, -2, 0, -6, -10, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28926634022", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-3, -14, 2, 10, -14, -4, -7, 2, 2, -4, -4, -9],\n [-14, 14, 3, 0, 6, -2, 9, 10, 6, -12, 2, 4],\n [2, 3, -16, 4, 4, 14, -7, 2, 14, -2, -14, -6],\n [10, 0, 4, -16, 2, 0, 9, 2, 4, 15, 8, -6],\n [-14, 6, 4, 2, 16, -5, 8, -10, -6, -7, 10, 2],\n [-4, -2, 14, 0, -5, -13, 0, -12, -15, 15, 8, -4],\n [-7, 9, -7, 9, 8, 0, 4, -3, 8, -6, 3, 2],\n [2, 10, 2, 2, -10, -12, -3, -4, -2, -2, -8, -2],\n [2, 6, 14, 4, -6, -15, 8, -2, 8, -6, 6, 10],\n [-4, -12, -2, 15, -7, 15, -6, -2, -6, -14, -8, 0],\n [-4, 2, -14, 8, 10, 8, 3, -8, 6, -8, -4, 4],\n [-9, 4, -6, -6, 2, -4, 2, -2, 10, 0, 4, 14]], determine the value at position (10, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-229818467882", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[10, 9, 5, 16, 15, -6, -11, 1, -7, 5, 6, 15],\n [-6, -14, -6, 5, 6, 8, 1, 13, 7, -16, 15, -5],\n [3, 16, 11, -5, 8, -2, 6, 16, 16, -14, 4, -15],\n [-5, 1, -7, 5, 13, -2, 15, 12, 16, 11, -15, -3],\n [6, -6, -11, -9, -4, 1, 11, 5, -13, -4, -15, -15],\n [1, -10, 8, -5, 8, -14, 11, -6, -8, -3, 3, 16],\n [4, -7, 11, 1, -12, 9, 16, -4, 14, 6, -16, 12],\n [3, 0, -3, 6, 4, -12, 10, 1, 4, -5, 16, -6],\n [-13, 4, -14, 7, -16, -16, -9, 6, -7, 9, -6, -6],\n [9, 1, -12, -3, 7, 2, -8, -12, 13, 1, 2, -8],\n [8, 5, 12, 1, 14, -3, 3, -9, -1, -8, 11, -9],\n [-14, 3, -7, -10, 0, 12, 14, 6, 16, 14, -3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26562816418825", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^9 where A is:\n[[2, -15, -1, -9, -2, -6, 10, 8, -15, -4, 4, 1],\n [12, -9, 3, 15, -8, 13, 3, 6, -9, -16, -11, -16],\n [-16, -5, -3, -13, 14, 8, 9, -5, 1, -15, -5, -16],\n [2, -12, -12, 4, -15, 14, -12, -15, -10, 14, -10, -12],\n [15, 12, 6, -9, 0, 15, 11, 3, 1, -2, -11, 0],\n [-3, -9, -9, 8, 16, 12, 3, -1, -1, -14, 8, -15],\n [-14, -11, -1, 15, 13, 15, 15, 9, -1, 4, 5, -4],\n [-8, -12, 11, 6, 10, -13, 0, 2, -15, -11, -15, 3],\n [-7, -5, 16, -9, -9, 10, 3, 16, 9, 0, -7, -13],\n [16, 6, 1, 5, 8, 1, 14, -16, -1, 15, 0, -6],\n [-4, -12, -6, 6, 0, -1, 3, 6, -10, 2, 1, -9],\n [7, 14, 0, 7, -4, 6, 10, 9, 6, -6, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3110880901600124", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[13, -9, -4, 10, -3, 0, 0, -10, 4, -4, -4, 7],\n [-9, 16, 4, -2, -6, 7, -9, -2, -2, -9, 0, 4],\n [-4, 4, 11, 6, 10, 10, 2, 6, 0, 4, 2, 10],\n [10, -2, 6, -10, 2, 2, 0, -13, 4, -7, 2, -7],\n [-3, -6, 10, 2, -12, -2, 2, -3, 8, 0, -4, 3],\n [0, 7, 10, 2, -2, -16, 8, -10, -8, 7, 2, 9],\n [0, -9, 2, 0, 2, 8, 13, 6, -4, 8, 0, -4],\n [-10, -2, 6, -13, -3, -10, 6, -12, -4, 3, 14, 12],\n [4, -2, 0, 4, 8, -8, -4, -4, 6, -10, 13, -6],\n [-4, -9, 4, -7, 0, 7, 8, 3, -10, -8, 2, -8],\n [-4, 0, 2, 2, -4, 2, 0, 14, 13, 2, -4, -2],\n [7, 4, 10, -7, 3, 9, -4, 12, -6, -8, -2, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1884640337112", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-10, 12, -5, 6, 11, -6, -6, 2, 2, -4, 2, -4],\n [12, -2, 0, -4, 0, 7, 0, -5, -1, 8, 2, -3],\n [-5, 0, 6, 0, -2, 0, -11, -5, -10, 2, -2, -1],\n [6, -4, 0, -12, -5, 4, 4, 14, 5, -6, 1, -8],\n [11, 0, -2, -5, -11, 0, 8, -6, 0, -7, 2, -4],\n [-6, 7, 0, 4, 0, 2, -2, 11, 0, 14, 2, -2],\n [-6, 0, -11, 4, 8, -2, -14, 12, -4, -2, 7, -9],\n [2, -5, -5, 14, -6, 11, 12, 12, -12, 0, 4, 5],\n [2, -1, -10, 5, 0, 0, -4, -12, -2, -6, -4, -3],\n [-4, 8, 2, -6, -7, 14, -2, 0, -6, 9, -2, -5],\n [2, 2, -2, 1, 2, 2, 7, 4, -4, -2, -5, 11],\n [-4, -3, -1, -8, -4, -2, -9, 5, -3, -5, 11, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56752144628739", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-5, -6, 3, -11, -5, -9, 1, -1, -7, -2, -9, -2],\n [-13, 14, -8, -2, 8, -16, 10, 9, -6, 4, 14, 16],\n [4, 11, -10, 11, 12, -15, -6, -14, -7, 7, 5, -7],\n [6, -14, -15, 4, -9, 0, 0, 3, -11, 6, -9, 12],\n [0, 9, -16, -12, 2, -4, 13, 16, 5, -13, 9, 6],\n [3, -14, -16, 11, -4, -3, 8, -3, 16, -8, -11, -14],\n [-14, -2, 11, -16, 14, -3, 14, 4, 14, -16, 9, -2],\n [-14, -3, 11, -10, 14, -9, -8, 16, 14, 13, -16, -5],\n [7, 7, 13, 14, 10, -10, 14, 11, -16, 8, -8, -2],\n [7, 1, 14, 10, 1, -1, -10, 1, -10, -16, 6, -10],\n [-12, 9, -5, -13, 4, -5, -9, 14, 7, 8, -13, -12],\n [-12, -1, 14, -1, 1, 0, -13, 16, -10, 10, 11, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6045414413288", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (7, 10) of the result:\nA =\n[[-1, 2, 4, 2, -7, 10, 4, -1, 4, -7, 10, -7],\n [2, 12, 2, 7, 14, 4, -3, 2, 0, 8, -8, 10],\n [4, 2, 16, 8, -3, 8, 5, -4, -4, 0, -6, -7],\n [2, 7, 8, -16, 1, 10, -14, 7, -10, 5, -11, -12],\n [-7, 14, -3, 1, -4, -4, -6, -4, 1, 4, -14, -6],\n [10, 4, 8, 10, -4, 9, -2, 4, -12, 10, 4, 0],\n [4, -3, 5, -14, -6, -2, -13, -7, 3, -5, 8, 4],\n [-1, 2, -4, 7, -4, 4, -7, -1, -6, 6, -10, -6],\n [4, 0, -4, -10, 1, -12, 3, -6, 15, 2, 0, -1],\n [-7, 8, 0, 5, 4, 10, -5, 6, 2, 2, -12, -2],\n [10, -8, -6, -11, -14, 4, 8, -10, 0, -12, -12, 6],\n [-7, 10, -7, -12, -6, 0, 4, -6, -1, -2, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2519079997914", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[5, 4, -13, -10, -16, 15, -11, -8, -3, 3, -7, -6],\n [-3, 13, 8, -5, 3, 13, 13, 9, -5, 0, -9, -3],\n [4, -10, 1, 0, -5, 7, 4, 10, 0, -16, -6, -2],\n [-5, -11, -16, -8, 4, -16, 6, 2, -5, -7, 1, 5],\n [-9, -7, -3, 2, -9, -14, -15, 2, -12, -7, 12, 16],\n [-2, -11, -5, -8, -11, 4, 13, 1, -1, -6, 5, -15],\n [-16, 14, -12, -15, 5, 5, 13, 8, 7, 4, 16, 16],\n [-8, 9, -15, 3, -12, 8, 1, -1, -14, 2, 13, -8],\n [-15, 6, -10, -11, -16, 12, -12, -4, -2, -16, 6, -4],\n [-6, -5, 14, 3, -8, 4, -4, -12, 12, 13, -6, 15],\n [13, 9, -12, -12, -13, -12, -5, -11, 13, -9, -8, -11],\n [0, 11, 12, 2, 10, 1, -12, -11, 3, 9, 9, -10]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13252145781282", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-13, 2, -6, -6, 8, 2, -16, 0, 4, 12, -3, -4],\n [2, 4, 3, -5, 1, -6, 6, -12, 4, -2, 8, 0],\n [-6, 3, -3, 0, 8, 4, 4, 3, 2, -8, 10, 4],\n [-6, -5, 0, 3, 6, 0, 5, -2, 3, 4, -6, -6],\n [8, 1, 8, 6, -4, -6, -11, 2, 9, 6, 6, 14],\n [2, -6, 4, 0, -6, 3, -2, 0, 6, -4, 13, -6],\n [-16, 6, 4, 5, -11, -2, 9, 9, 5, 3, 2, -12],\n [0, -12, 3, -2, 2, 0, 9, -4, 10, -11, 8, -15],\n [4, 4, 2, 3, 9, 6, 5, 10, -8, 5, 2, 2],\n [12, -2, -8, 4, 6, -4, 3, -11, 5, 11, -2, 0],\n [-3, 8, 10, -6, 6, 13, 2, 8, 2, -2, 10, -5],\n [-4, 0, 4, -6, 14, -6, -12, -15, 2, 0, -5, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3027772509758945", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-7, 2, -9, 8, -10, -12, -5, 15, 1, -9, 3, -1],\n [-15, 4, -15, 7, 7, -7, -7, 7, -6, -3, 12, -10],\n [-5, 0, -4, 10, 6, 10, -8, -13, -9, 2, 5, 2],\n [-15, -11, -8, -2, 4, 3, -6, -9, 12, 11, -8, -8],\n [11, -13, 2, 16, 8, 11, 1, -13, -9, -3, -16, -15],\n [-7, -4, -10, 4, 16, -2, 5, 11, 3, -8, 8, 2],\n [-7, -10, -5, -16, -14, 16, -3, 2, -6, 10, -12, -2],\n [-8, -11, 2, 14, 11, -9, 12, -16, 2, -12, -14, -9],\n [1, -10, 4, 9, 6, 4, 16, 3, 5, 7, -14, -15],\n [13, -14, -14, 2, -4, -9, 8, 5, 3, 10, -14, 2],\n [-4, -16, -16, 10, 5, 8, 5, -7, 3, -6, -4, 10],\n [-10, 9, 0, 4, -1, 8, 8, 13, -1, -1, 11, 10]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "465909309825", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 3) of the 9th power of the matrix:\n[[-14, -13, 15, -2, -12, 2, 3, 2, -5, 6, -12, 14],\n [-6, 5, -3, -2, -11, -3, 15, -11, -11, -11, 0, -16],\n [-2, 2, 9, -16, 9, -4, -10, -16, 16, -2, -15, -10],\n [9, 8, -7, -7, -7, 11, 13, 10, -9, -8, -7, 4],\n [8, 14, -15, 2, 13, 0, 12, -13, -8, 2, -15, 1],\n [-15, 10, -2, -3, -16, -12, 8, 15, -5, 12, 3, -14],\n [8, -6, 13, 15, 12, -9, -7, -1, 11, -6, -5, 0],\n [10, -11, 12, -9, -9, 1, -1, 6, -3, 2, -10, -4],\n [9, -11, -13, -6, 7, 13, -8, -11, -4, -9, -8, 15],\n [14, 2, 4, -15, 7, 11, 0, 11, -7, -4, 15, 16],\n [6, 9, -3, -4, 11, 8, 2, -4, -14, -13, -5, 6],\n [-13, -12, -1, 5, 8, 7, -10, -6, 15, -13, 3, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25942431191386", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[4, 5, 12, 10, -16, 11, 4, -7, 12, 3, -10, 16],\n [-4, 0, -8, -1, -10, -12, -5, -3, 10, -7, -11, 3],\n [7, 10, -12, -8, -10, -9, -7, 8, 16, -8, 14, 11],\n [-7, -9, -10, 13, 9, 15, 14, 7, 5, 0, 14, 3],\n [-12, 0, -9, 16, 14, 0, -3, 8, 3, -7, 0, 11],\n [10, -2, 1, -1, 15, 16, -10, 16, -15, 10, 13, 7],\n [4, -3, -14, 16, -13, 12, -13, 2, 16, 11, 9, 11],\n [-8, 4, -7, -10, -16, -13, 8, 1, -9, -9, 10, -14],\n [-13, 13, 14, -14, 6, -7, 6, -7, -8, 4, 15, -9],\n [1, 14, -16, 3, -1, -15, 8, 3, -2, -5, -1, -14],\n [-12, 0, 4, -12, 0, -5, -2, 8, -15, 7, 1, 2],\n [14, -3, 2, -16, 7, 7, 0, 0, -1, -16, -12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107524260068", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[11, 8, -14, 6, -10, -7, 16, -6, 5, -7, -2, 8],\n [8, 3, -6, -6, 2, -8, -8, -4, 11, 2, 6, -4],\n [-14, -6, -8, 4, 4, 6, 2, 3, -2, -1, 10, -9],\n [6, -6, 4, 9, -2, 11, -2, -2, -8, -3, 6, -1],\n [-10, 2, 4, -2, -8, 4, -4, 9, 4, -4, 6, 12],\n [-7, -8, 6, 11, 4, 8, -4, -2, 0, 1, 0, 6],\n [16, -8, 2, -2, -4, -4, -3, 15, 3, 6, 4, 6],\n [-6, -4, 3, -2, 9, -2, 15, -5, 2, 7, 5, 0],\n [5, 11, -2, -8, 4, 0, 3, 2, -14, 4, 0, -6],\n [-7, 2, -1, -3, -4, 1, 6, 7, 4, -1, 6, -2],\n [-2, 6, 10, 6, 6, 0, 4, 5, 0, 6, 14, -8],\n [8, -4, -9, -1, 12, 6, 6, 0, -6, -2, -8, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1373079528055", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-9, -2, 4, 0, -6, 0, 5, -6, 0, -10, -2, 1],\n [-2, 7, 12, -10, 10, -8, 8, 2, -1, 1, -6, 7],\n [4, 12, -9, 6, 6, -6, -11, -8, 10, 8, 0, -6],\n [0, -10, 6, -12, -2, -10, -3, 0, -2, -2, -8, -5],\n [-6, 10, 6, -2, -2, -6, 12, 13, 8, 9, -3, -5],\n [0, -8, -6, -10, -6, -12, 0, 3, -4, 2, 0, 14],\n [5, 8, -11, -3, 12, 0, 11, 10, -8, -8, 2, 4],\n [-6, 2, -8, 0, 13, 3, 10, 10, 6, -11, 6, 6],\n [0, -1, 10, -2, 8, -4, -8, 6, 9, 5, 4, 12],\n [-10, 1, 8, -2, 9, 2, -8, -11, 5, -9, 3, 3],\n [-2, -6, 0, -8, -3, 0, 2, 6, 4, 3, -11, 1],\n [1, 7, -6, -5, -5, 14, 4, 6, 12, 3, 1, 7]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60893810125064", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[7, 7, 16, 9, -5, 11, 10, 1, -10, -8, 7, 14],\n [-6, -9, -12, 15, -1, -16, 10, -1, 7, -1, -12, -6],\n [-8, 1, -16, -13, 13, -3, 5, -15, -13, -11, 15, 9],\n [-4, -5, -12, -16, 11, 5, -4, -10, 11, -2, 9, -5],\n [7, -13, 15, -11, -15, 15, 5, -10, -9, 12, 4, -7],\n [-9, 5, -2, -2, 15, 10, 14, -1, 9, -10, -5, -10],\n [-4, -1, -14, -2, -14, 4, 2, -5, 9, -15, 3, 12],\n [11, -14, -9, 7, 13, -1, 5, -9, -2, -8, 12, -3],\n [12, 11, -3, -13, 14, 0, -4, -3, 3, 6, -13, 0],\n [10, -16, 0, 2, 9, 1, -3, -12, 4, 16, 3, -1],\n [-11, 7, 5, 6, 16, 13, 3, 16, -1, -4, 10, -3],\n [-10, -7, -5, -4, -16, -3, -6, 10, -7, -16, -2, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161594246949478", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[6, 1, -12, -8, 2, -8, -12, -5, -2, -6, 2, 1],\n [1, -4, 0, 10, -1, 3, -2, -2, -2, 8, -3, 6],\n [-12, 0, 16, 4, -4, 2, -6, -2, 5, -8, -5, 6],\n [-8, 10, 4, 15, 2, 4, 14, -2, -10, -4, 3, -11],\n [2, -1, -4, 2, 13, -3, 4, -2, -5, -1, 6, 8],\n [-8, 3, 2, 4, -3, -7, 12, 0, 2, 5, 7, 1],\n [-12, -2, -6, 14, 4, 12, 5, 3, -4, -14, -13, 5],\n [-5, -2, -2, -2, -2, 0, 3, -7, 2, -2, 0, 12],\n [-2, -2, 5, -10, -5, 2, -4, 2, 13, 6, -14, -14],\n [-6, 8, -8, -4, -1, 5, -14, -2, 6, 1, -4, -12],\n [2, -3, -5, 3, 6, 7, -13, 0, -14, -4, 9, -6],\n [1, 6, 6, -11, 8, 1, 5, 12, -14, -12, -6, -15]], determine the value at position (8, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246828546213", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[16, -7, 0, 0, 0, 6, -1, 0, 14, -4, 0, 2],\n [-7, -6, 0, 1, -8, 4, -2, 4, 0, -4, -6, -12],\n [0, 0, -15, 10, 0, -2, -4, 4, 2, -6, 0, 8],\n [0, 1, 10, -16, 13, 14, 14, -11, 0, 7, -3, 3],\n [0, -8, 0, 13, -16, -6, 6, -4, -5, -8, 8, 14],\n [6, 4, -2, 14, -6, -15, -6, -10, -8, 0, -6, 2],\n [-1, -2, -4, 14, 6, -6, 0, 2, -13, 10, 2, 6],\n [0, 4, 4, -11, -4, -10, 2, 1, 9, -14, 10, -6],\n [14, 0, 2, 0, -5, -8, -13, 9, -3, -6, -2, -11],\n [-4, -4, -6, 7, -8, 0, 10, -14, -6, -16, -6, -3],\n [0, -6, 0, -3, 8, -6, 2, 10, -2, -6, -10, 2],\n [2, -12, 8, 3, 14, 2, 6, -6, -11, -3, 2, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34019742760884", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[4, -4, 11, -9, 4, 12, 2, -3, -8, 10, -16, -13],\n [14, -2, -16, -9, -11, 10, 9, -15, -4, 13, -10, 16],\n [10, 6, -1, 6, 8, -10, -15, 8, -3, 1, -13, -3],\n [14, 5, -10, 5, -13, 5, 0, 3, -8, -16, 6, 11],\n [-3, 5, 11, -13, -11, 0, 15, 14, -3, -4, -14, 4],\n [-4, -6, -13, -5, -2, -1, -9, -13, 3, -9, 8, -13],\n [16, 9, -12, 11, -13, 16, 7, 16, 10, 12, -14, 13],\n [-6, 11, -15, 6, -8, 14, -5, -9, -5, -16, -6, -13],\n [-3, 14, -14, -11, 3, 14, 6, 1, -3, 4, 12, -12],\n [1, -11, 4, -12, -8, 15, 8, 5, -13, 8, -5, 14],\n [-16, 5, 16, 6, 3, 15, -11, 5, -5, 6, -3, -5],\n [13, 5, -1, 5, 12, -10, -2, -15, 5, -2, 2, 10]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7938654629832", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 7th power of the matrix:\n[[6, 13, 8, 4, 10, 2, 9, 16, -14, 8, -4, -3],\n [-7, 7, 5, -3, -8, -5, 5, 16, 1, 14, -5, -2],\n [-16, 14, -7, -4, -7, 5, 9, -6, 16, -7, 14, 4],\n [8, -8, 1, 13, 4, 12, 0, -13, 16, 6, -10, 7],\n [-10, -9, -14, 10, -13, -15, -12, -7, -8, -9, -14, 12],\n [-2, 16, -1, -6, -11, -9, -8, -3, 7, -9, 16, 12],\n [-15, 1, 6, 14, 5, 3, -1, 6, 8, 2, 2, -15],\n [-10, 3, -13, 9, -6, 0, -2, -5, 0, -1, -1, -14],\n [11, -8, -6, 10, -7, -5, 14, 0, 1, -11, 0, -14],\n [16, 3, -1, -10, -15, -13, 0, -10, -5, -5, -7, 8],\n [-12, 0, -6, 5, 3, 15, 6, 6, -15, -14, 16, -12],\n [6, 8, 7, 13, 13, -9, 12, 4, -1, 6, 12, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13633795881", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (7, 9) of the result:\nA =\n[[7, 9, 10, -6, 10, 5, -16, 10, -16, -2, -6, 12],\n [13, 6, 9, 1, -2, 5, -15, -14, 9, 12, 12, 6],\n [6, 11, -15, 11, 7, -14, -7, 2, -16, -13, -10, -14],\n [-3, -1, 11, 11, -11, 11, 1, 1, -2, -3, 5, -3],\n [2, 13, 2, 16, 15, -3, 6, 2, 8, 9, 5, -6],\n [14, -12, 14, -14, 3, -2, 14, -12, -3, 5, 2, -10],\n [-12, 7, -3, 1, -2, 11, 16, 4, 0, -15, -16, -4],\n [-1, -2, 3, -3, -14, -2, -11, -8, -16, 14, 9, 5],\n [0, -7, 9, -7, -6, 14, 1, 11, 2, -4, 3, -11],\n [-4, 16, 3, 6, -7, -3, -13, -3, 14, 11, 14, 13],\n [-11, -10, 15, 9, -5, -3, 13, -8, -3, 3, -13, 8],\n [-14, 11, -7, -7, 3, -1, -12, -9, -4, 5, -9, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34730297834", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[15, 7, 5, 2, 8, -6, 7, 3, 4, 12, -8, 10],\n [-9, -8, -2, -1, 13, -10, -14, 15, -11, -7, -4, -12],\n [12, -7, 16, 14, 15, -4, 12, 6, 11, 14, -16, 13],\n [-13, -9, 5, -5, -5, 2, -4, -3, 16, -13, -12, 14],\n [-7, 8, 3, 3, -8, -5, -4, 16, -15, 6, -1, 5],\n [-13, 8, -13, -14, 5, 8, -2, 16, -4, 2, 2, -10],\n [-11, 11, 14, -16, -5, -4, -3, -3, -5, 14, -10, 0],\n [-9, -3, -7, 5, -1, -11, 7, 12, -8, -15, -12, -1],\n [-9, 5, -2, 11, 12, 15, -1, 16, 2, -13, -3, 8],\n [-10, 3, -9, 13, 3, 3, 11, -11, -8, 3, 6, 6],\n [-8, 5, 7, 1, -9, 4, 13, -9, 12, 0, -9, 5],\n [0, -13, 3, 12, -3, 14, 14, -14, 14, 5, 10, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5111970922518", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[7, 14, 15, -14, 10, 16, 13, -4, 3, -9, -9, -5],\n [4, -4, 13, 13, -15, 2, 10, -10, 10, -7, -5, 0],\n [-9, -4, 4, -8, -3, 5, -8, -11, 12, -1, 12, 4],\n [-15, -9, -14, 11, -3, 6, -15, 4, 12, 16, 8, -12],\n [13, 11, 7, 0, -16, -2, -15, -16, -9, -6, -14, -6],\n [-7, -5, -13, -16, -1, 8, 11, -10, -1, 0, 12, -6],\n [1, -5, 3, -6, -16, 11, 1, -14, -3, 8, 13, 3],\n [14, -6, -15, 11, -14, 3, -7, 11, -11, -14, 4, 6],\n [3, -11, -8, -6, -13, -11, -11, 0, 15, 7, -6, 9],\n [1, 13, 15, -10, -12, -11, -3, 3, 2, 16, -5, 2],\n [-2, -8, 0, -9, -14, -3, -6, -5, -13, 0, 12, 6],\n [-2, -5, 16, -4, 14, -7, 6, -4, 14, -5, 6, 9]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3158623487301", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[14, 5, 8, -3, 8, -7, -1, -9, 0, -7, 2, -6],\n [5, -10, -8, -6, -4, -4, 5, -5, -11, -2, 13, -12],\n [8, -8, 0, -6, 2, -1, -2, 0, -13, -2, -5, 6],\n [-3, -6, -6, 3, 8, -8, -6, -6, 2, 2, -4, 1],\n [8, -4, 2, 8, 9, 8, 1, -10, -4, -5, -1, -12],\n [-7, -4, -1, -8, 8, -16, 5, -5, -14, 5, 8, 2],\n [-1, 5, -2, -6, 1, 5, -5, -4, -12, 2, 1, -3],\n [-9, -5, 0, -6, -10, -5, -4, -10, -10, 4, 8, 6],\n [0, -11, -13, 2, -4, -14, -12, -10, -1, 2, -3, 6],\n [-7, -2, -2, 2, -5, 5, 2, 4, 2, -11, 0, -8],\n [2, 13, -5, -4, -1, 8, 1, 8, -3, 0, 7, -2],\n [-6, -12, 6, 1, -12, 2, -3, 6, 6, -8, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118018124707939", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-13, 0, 10, -10, 4, -8, -12, 0, -8, -5, -10, -2],\n [0, 1, 10, 6, 5, -4, 8, 8, -2, 9, -2, 12],\n [10, 10, 4, 0, 10, 2, 5, 3, 8, 1, 4, -14],\n [-10, 6, 0, -6, 0, 3, -2, -8, 14, 10, -14, -16],\n [4, 5, 10, 0, -11, -12, 0, -7, 0, 0, -4, 0],\n [-8, -4, 2, 3, -12, -1, -13, -7, -3, 10, 8, -12],\n [-12, 8, 5, -2, 0, -13, -12, 0, 12, -5, -10, 1],\n [0, 8, 3, -8, -7, -7, 0, -12, 6, 8, -11, 0],\n [-8, -2, 8, 14, 0, -3, 12, 6, -7, 1, -9, -4],\n [-5, 9, 1, 10, 0, 10, -5, 8, 1, 13, -14, 10],\n [-10, -2, 4, -14, -4, 8, -10, -11, -9, -14, -11, 0],\n [-2, 12, -14, -16, 0, -12, 1, 0, -4, 10, 0, 12]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191788364252359", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (10, 7) of the result:\nA =\n[[1, 2, 2, -6, 16, -10, -4, 14, 0, -2, 10, -2],\n [2, 11, 8, 0, -3, -1, -10, -10, -8, 10, -6, -2],\n [2, 8, 3, -1, -12, 6, 4, -12, -6, -4, 2, 0],\n [-6, 0, -1, 14, 0, -7, -2, 10, 6, -2, -8, 4],\n [16, -3, -12, 0, 15, -4, -8, 5, -2, 0, -4, 0],\n [-10, -1, 6, -7, -4, 2, -4, 2, -12, 6, 6, 14],\n [-4, -10, 4, -2, -8, -4, 4, 5, -6, 0, 4, 8],\n [14, -10, -12, 10, 5, 2, 5, 10, 6, 8, 2, 8],\n [0, -8, -6, 6, -2, -12, -6, 6, -13, 15, 5, -3],\n [-2, 10, -4, -2, 0, 6, 0, 8, 15, -8, 6, 8],\n [10, -6, 2, -8, -4, 6, 4, 2, 5, 6, -4, -8],\n [-2, -2, 0, 4, 0, 14, 8, 8, -3, 8, -8, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9949947987114", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 9) of the matrix A^9 where A is:\n[[-4, -9, -2, -5, 2, -2, 8, 10, 1, -12, -13, 1],\n [-8, 12, 13, -12, -1, 8, 14, 9, 10, 10, 13, -4],\n [15, 12, 15, -6, 12, 3, -2, 6, 11, 10, 5, -9],\n [12, 2, 15, -16, -14, 9, -10, 9, 10, 2, -13, 10],\n [-3, -9, -16, -9, 12, -10, -12, 3, 5, -13, -16, 15],\n [2, 6, 1, -11, -2, -5, 12, 7, -4, 13, -8, -15],\n [-7, -6, -3, -10, 7, -11, -9, 8, -12, 8, -13, -14],\n [-10, 5, 7, 1, 0, -9, -2, 15, -9, 11, 4, -13],\n [-12, 3, -8, -7, 13, -15, -16, -4, 7, 1, 16, -12],\n [-15, 0, 16, -8, 14, -10, -1, 13, -9, 7, -2, -4],\n [-2, -7, -14, 16, 11, 10, 4, -2, -9, -10, 13, 2],\n [-3, 13, -1, 7, 2, 2, 3, -5, 11, 2, -4, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3359751537536", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[7, 2, 2, -3, 0, 8, -1, 2, 2, 6, -5, 10],\n [2, -14, -2, -5, 7, -6, -3, 2, -2, 1, 6, 1],\n [2, -2, 16, 10, -2, -6, -14, -10, 2, -9, 5, 13],\n [-3, -5, 10, 6, -3, -4, 2, 12, -6, 8, -10, 8],\n [0, 7, -2, -3, 12, 16, 0, -3, -1, 5, 1, -3],\n [8, -6, -6, -4, 16, 9, -10, -4, -4, 2, -2, -5],\n [-1, -3, -14, 2, 0, -10, 16, -16, -5, 7, -9, 4],\n [2, 2, -10, 12, -3, -4, -16, 4, -3, -7, 4, 0],\n [2, -2, 2, -6, -1, -4, -5, -3, -6, 0, -3, -5],\n [6, 1, -9, 8, 5, 2, 7, -7, 0, -6, -3, -10],\n [-5, 6, 5, -10, 1, -2, -9, 4, -3, -3, 10, 6],\n [10, 1, 13, 8, -3, -5, 4, 0, -5, -10, 6, 10]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142632777878747", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-6, 15, 12, -9, -11, -14, -10, -10, -14, -9, 9, 14],\n [10, -16, 16, 0, 15, 4, 4, 11, -11, -12, -8, -7],\n [12, -3, -11, 5, -1, 2, -6, 13, -12, -10, -4, -2],\n [-13, -12, -4, 16, 3, -9, 0, -12, 14, -9, -15, -16],\n [9, -10, -5, -3, 6, 8, 8, -2, 5, -6, 9, 8],\n [7, 3, -11, 8, -2, -3, 8, -12, 16, 0, 16, 4],\n [14, -6, 9, 16, -4, 13, 16, 6, -7, -11, 13, 16],\n [4, -10, -7, -10, -8, -11, -13, 14, 9, -8, -16, -4],\n [13, 4, -13, -9, -1, -8, -3, -8, 15, 11, -1, -5],\n [15, 0, -7, -12, 12, 8, 10, -9, 5, 16, -9, -10],\n [14, -16, -14, 11, -7, 5, -12, 16, 4, 15, 6, 7],\n [6, -16, 8, 16, 14, -4, 12, 4, -2, 4, -13, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57400653847360", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (12, 11) of the matrix A^8 where A is:\n[[13, 2, 2, -6, 0, -2, 12, -9, 7, -9, -2, 7],\n [2, -11, 0, 12, 9, -4, 11, 3, 4, -8, 8, 8],\n [2, 0, 13, 2, -8, 10, 8, 2, 2, -4, -13, -8],\n [-6, 12, 2, 6, 7, -14, 10, -4, 4, 11, -7, 12],\n [0, 9, -8, 7, -15, 4, 2, -3, -10, -10, -5, -2],\n [-2, -4, 10, -14, 4, -6, -11, 3, 4, 6, -6, 8],\n [12, 11, 8, 10, 2, -11, -10, -12, -6, 6, -1, 5],\n [-9, 3, 2, -4, -3, 3, -12, 0, 1, 8, -5, 11],\n [7, 4, 2, 4, -10, 4, -6, 1, -6, 0, -4, 2],\n [-9, -8, -4, 11, -10, 6, 6, 8, 0, 3, 2, 8],\n [-2, 8, -13, -7, -5, -6, -1, -5, -4, 2, 15, -5],\n [7, 8, -8, 12, -2, 8, 5, 11, 2, 8, -5, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-350579246677", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[3, -16, 6, 7, -8, -5, 16, -14, 0, -15, 15, -14],\n [-12, 6, -8, 4, -3, 4, 11, -3, -15, 6, -6, -16],\n [-4, 6, -5, -11, -3, 5, 14, 7, -11, -13, 4, 12],\n [9, -11, 10, -4, 7, 1, -5, -16, 12, -3, -8, -1],\n [-5, -11, -6, 4, 2, -11, 5, 7, 12, 6, 11, 2],\n [-11, 4, 8, -12, 3, 6, -14, -5, 2, -15, 4, 12],\n [-3, 2, -10, 8, -10, 6, -12, 4, 7, -13, -6, -5],\n [7, -16, 11, -15, 5, 6, 12, 7, 6, -9, -16, -14],\n [2, -11, -13, 5, 13, -3, 4, -16, -15, 2, -15, 13],\n [-10, 8, -14, -9, -5, -1, -13, -16, 9, 16, -12, 11],\n [-6, -3, 6, 12, -12, 14, 6, -16, -3, -14, -16, 7],\n [4, -3, -8, 13, -9, 9, -13, 15, -6, -9, -12, -6]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12662798377", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[13, -1, 6, 8, 6, 12, -10, -4, 0, -14, -6, -2],\n [-1, -7, 6, 10, -11, 2, 0, -6, 10, 10, 8, 7],\n [6, 6, 14, -12, -14, 4, 2, -6, 4, 3, 2, 5],\n [8, 10, -12, 0, 12, 12, -10, 6, -15, 4, 11, 7],\n [6, -11, -14, 12, 15, -4, 10, -4, 11, 6, 0, 0],\n [12, 2, 4, 12, -4, -12, -8, 4, 2, 6, -4, 6],\n [-10, 0, 2, -10, 10, -8, 13, -12, 8, 10, 3, -6],\n [-4, -6, -6, 6, -4, 4, -12, -8, 0, -6, 0, 0],\n [0, 10, 4, -15, 11, 2, 8, 0, -12, 10, 0, 0],\n [-14, 10, 3, 4, 6, 6, 10, -6, 10, 12, -5, 9],\n [-6, 8, 2, 11, 0, -4, 3, 0, 0, -5, -12, 2],\n [-2, 7, 5, 7, 0, 6, -6, 0, 0, 9, 2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "744772264184926", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[15, 4, -1, -7, 2, 8, 2, -3, -6, -2, 1, 2],\n [4, 14, -2, 4, -4, 2, -9, 4, -2, -4, 12, 8],\n [-1, -2, -12, 1, -2, -10, 2, -2, -16, -4, -6, 2],\n [-7, 4, 1, 3, -10, 6, 4, 2, -5, 6, 0, 6],\n [2, -4, -2, -10, 4, 4, 6, 8, -4, -4, -14, 4],\n [8, 2, -10, 6, 4, 3, 4, 2, -5, 0, 6, -2],\n [2, -9, 2, 4, 6, 4, -7, -6, -6, 8, 6, 1],\n [-3, 4, -2, 2, 8, 2, -6, -4, 7, 0, 5, -8],\n [-6, -2, -16, -5, -4, -5, -6, 7, -9, -1, -6, 1],\n [-2, -4, -4, 6, -4, 0, 8, 0, -1, 16, 0, 10],\n [1, 12, -6, 0, -14, 6, 6, 5, -6, 0, -4, 4],\n [2, 8, 2, 6, 4, -2, 1, -8, 1, 10, 4, -15]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57001890536350", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 10) of the 8th power of the matrix:\n[[-8, 1, 2, -12, 8, 8, 2, -3, -10, 4, -14, 12],\n [1, 9, 9, -4, -12, -10, -6, -2, -2, -2, -2, -12],\n [2, 9, 11, 0, -3, -12, -11, -4, -1, 0, 4, -6],\n [-12, -4, 0, -5, -6, -11, -14, 4, -3, -12, 0, 16],\n [8, -12, -3, -6, 1, -8, 6, 4, 4, 8, 8, 14],\n [8, -10, -12, -11, -8, 7, 1, -4, -3, 2, -1, 7],\n [2, -6, -11, -14, 6, 1, -3, 14, 6, 0, 3, -4],\n [-3, -2, -4, 4, 4, -4, 14, -4, -10, 11, 0, 4],\n [-10, -2, -1, -3, 4, -3, 6, -10, -15, 8, 0, -8],\n [4, -2, 0, -12, 8, 2, 0, 11, 8, 14, -6, 8],\n [-14, -2, 4, 0, 8, -1, 3, 0, 0, -6, -3, -6],\n [12, -12, -6, 16, 14, 7, -4, 4, -8, 8, -6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2211347440409", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-1, -4, 2, -10, 4, 0, -10, -8, -8, -11, -2, 8],\n [-4, -10, -9, 11, 5, 14, 6, -10, -8, -10, 6, 4],\n [2, -9, 7, 2, 4, -10, 1, 11, -5, 10, 1, 1],\n [-10, 11, 2, -5, -10, 0, 8, 8, 0, 11, 7, 4],\n [4, 5, 4, -10, 7, 13, 8, 8, -2, -10, 5, -6],\n [0, 14, -10, 0, 13, -7, -8, -2, 1, -8, -5, 7],\n [-10, 6, 1, 8, 8, -8, 2, -7, 8, -2, -9, -8],\n [-8, -10, 11, 8, 8, -2, -7, 6, -2, -8, -1, -10],\n [-8, -8, -5, 0, -2, 1, 8, -2, -8, 2, 2, -10],\n [-11, -10, 10, 11, -10, -8, -2, -8, 2, 11, -8, -4],\n [-2, 6, 1, 7, 5, -5, -9, -1, 2, -8, -9, 4],\n [8, 4, 1, 4, -6, 7, -8, -10, -10, -4, 4, 6]], determine the value at position (4, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22960837356912", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[14, 2, -9, 0, 2, -4, -12, 1, -8, -12, -2, -6],\n [2, 14, 2, -4, -3, 12, 10, -2, 9, -2, 9, 6],\n [-9, 2, -16, 4, -1, 4, -8, -11, 1, 8, 1, -2],\n [0, -4, 4, 9, 2, 2, -6, 6, 4, 8, 7, 4],\n [2, -3, -1, 2, 12, 0, 6, 4, 13, -6, -4, -6],\n [-4, 12, 4, 2, 0, -8, -10, 0, -11, 2, 6, 2],\n [-12, 10, -8, -6, 6, -10, -12, 1, -4, 3, -10, -6],\n [1, -2, -11, 6, 4, 0, 1, -16, -6, -2, -12, 0],\n [-8, 9, 1, 4, 13, -11, -4, -6, 13, 3, -2, 10],\n [-12, -2, 8, 8, -6, 2, 3, -2, 3, 2, 2, 8],\n [-2, 9, 1, 7, -4, 6, -10, -12, -2, 2, -16, 3],\n [-6, 6, -2, 4, -6, 2, -6, 0, 10, 8, 3, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6491765946939382", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[13, 4, -2, 8, -10, 15, 6, 10, -12, 4, 6, 4],\n [16, -8, 8, 8, 2, -16, -13, 0, -4, -2, -14, -12],\n [-7, 1, -9, -1, -9, -10, -13, 7, 3, 13, 15, 8],\n [1, 14, 8, -15, -14, 4, 14, 3, -15, 13, -1, 11],\n [0, 2, -10, 1, 9, 11, -10, 9, -9, -13, 0, 4],\n [10, 5, 6, -14, 14, -9, -3, 10, 8, -16, 7, 9],\n [14, 10, 11, 14, -6, 13, -4, -5, 13, -8, -13, -4],\n [0, -16, -1, -7, -15, -6, -14, -9, -1, -8, 10, 5],\n [10, -11, 4, -10, -7, -1, 11, -10, -8, 9, 1, -7],\n [12, -3, -3, -9, -7, 12, 2, 1, 14, -3, 7, 12],\n [-12, 14, -10, 5, 0, -16, 15, -14, 11, -2, 5, 2],\n [11, 1, -6, -4, 11, -15, 13, 11, 16, 14, 14, -7]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3686045576563", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[1, 14, -16, 9, -2, -10, 3, 4, -5, 5, -8, -4],\n [-6, -3, 14, -14, 6, 5, -2, 14, -3, 13, 7, 2],\n [-10, 1, -6, 8, 13, -5, 4, -7, 8, 6, -6, 16],\n [4, 15, 5, 0, 11, 0, -3, 10, -10, 14, -5, -15],\n [5, -9, -1, 8, -14, 13, 2, 12, -12, 3, 16, -16],\n [15, 12, 6, -7, -5, -8, -6, -6, -13, 2, 4, -11],\n [6, -10, -2, -8, 5, -6, 0, -8, 2, 13, 5, 9],\n [13, -5, -10, -15, 4, 10, -16, -3, -15, 6, 9, 8],\n [-2, 12, 11, -13, 13, -7, -7, 5, -1, -4, 13, -4],\n [9, 14, 10, -13, -5, -16, -1, 5, 5, -3, -14, -4],\n [-15, -8, 10, 3, 4, -11, 12, 5, 6, 12, 10, -2],\n [10, -5, -9, -1, 0, 8, 9, 0, -5, -4, -11, -8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "428651520061212", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[5, -4, 8, -8, -2, -2, -2, -2, 0, 11, 4, -4],\n [-4, 5, -2, -4, -1, -4, -12, 1, 6, 6, -7, 6],\n [8, -2, 14, -4, 13, 6, -6, -4, 12, 6, -6, 8],\n [-8, -4, -4, 16, 0, -1, -1, 12, 0, -1, -9, 2],\n [-2, -1, 13, 0, -16, 0, -6, 0, 4, -7, 9, 6],\n [-2, -4, 6, -1, 0, 6, 3, 8, 6, 10, -9, -2],\n [-2, -12, -6, -1, -6, 3, -7, -2, -6, -2, 14, 6],\n [-2, 1, -4, 12, 0, 8, -2, 14, -3, -1, 3, 2],\n [0, 6, 12, 0, 4, 6, -6, -3, -1, -12, 6, 2],\n [11, 6, 6, -1, -7, 10, -2, -1, -12, 4, 2, -2],\n [4, -7, -6, -9, 9, -9, 14, 3, 6, 2, -2, -6],\n [-4, 6, 8, 2, 6, -2, 6, 2, 2, -2, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126994186891464", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 7) of the matrix A^7 where A is:\n[[2, -10, 2, 10, 6, 6, -1, 6, 9, 2, -8, 8],\n [-10, -6, 3, -4, 14, -4, 0, 0, 16, 2, 1, 6],\n [2, 3, 14, -8, -11, 8, 8, 4, 10, -4, 12, -14],\n [10, -4, -8, 6, 2, -12, -4, 8, -6, 8, 3, 11],\n [6, 14, -11, 2, -7, 6, -3, 15, 6, 14, 2, 3],\n [6, -4, 8, -12, 6, -6, 0, -5, 4, 2, 3, -2],\n [-1, 0, 8, -4, -3, 0, 2, 6, 11, -5, 4, -6],\n [6, 0, 4, 8, 15, -5, 6, 3, 0, -8, -1, 4],\n [9, 16, 10, -6, 6, 4, 11, 0, 10, 16, 10, -1],\n [2, 2, -4, 8, 14, 2, -5, -8, 16, 4, 14, 14],\n [-8, 1, 12, 3, 2, 3, 4, -1, 10, 14, 9, 8],\n [8, 6, -14, 11, 3, -2, -6, 4, -1, 14, 8, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31556888218", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (5, 8) of the result:\nA =\n[[-14, 2, -5, -12, 6, 2, 5, -2, 10, -3, -4, 4],\n [2, -8, 2, 8, 2, -6, -2, 16, 6, 8, -1, 2],\n [-5, 2, -3, 1, -6, 8, -4, -1, 9, 12, 4, 0],\n [-12, 8, 1, 11, -4, -8, 4, -4, 10, 2, 10, 4],\n [6, 2, -6, -4, 14, 0, 2, 10, -4, 12, -11, 2],\n [2, -6, 8, -8, 0, -1, -1, 2, -1, -6, -4, 6],\n [5, -2, -4, 4, 2, -1, 15, 6, 2, -4, -2, -2],\n [-2, 16, -1, -4, 10, 2, 6, -4, -14, 0, -7, 2],\n [10, 6, 9, 10, -4, -1, 2, -14, 16, -11, -12, 2],\n [-3, 8, 12, 2, 12, -6, -4, 0, -11, 9, -13, -6],\n [-4, -1, 4, 10, -11, -4, -2, -7, -12, -13, 0, 6],\n [4, 2, 0, 4, 2, 6, -2, 2, 2, -6, 6, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2033765480186", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (10, 10) of the result:\nA =\n[[-3, 12, -4, 6, 4, -2, -11, -2, 6, 6, -4, 2],\n [12, 16, 8, -2, 0, 10, -10, -4, -5, -6, -10, -5],\n [-4, 8, -9, -6, 14, 8, -2, -13, 2, 0, 9, 12],\n [6, -2, -6, 9, -6, -8, -7, 5, 7, -2, -2, 0],\n [4, 0, 14, -6, -7, -8, -6, -8, -2, -2, -6, 7],\n [-2, 10, 8, -8, -8, 5, 2, 0, 0, 6, 7, 9],\n [-11, -10, -2, -7, -6, 2, -15, 11, -6, 6, 8, 5],\n [-2, -4, -13, 5, -8, 0, 11, -4, -2, -6, -12, 0],\n [6, -5, 2, 7, -2, 0, -6, -2, -10, 0, 4, 7],\n [6, -6, 0, -2, -2, 6, 6, -6, 0, 0, 7, 5],\n [-4, -10, 9, -2, -6, 7, 8, -12, 4, 7, 0, -6],\n [2, -5, 12, 0, 7, 9, 5, 0, 7, 5, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3862195562", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[3, 0, -4, 4, 9, -8, 8, 7, -2, -12, 6, -1],\n [0, 8, -5, 6, 0, 5, 2, 0, 8, -2, -4, -12],\n [-4, -5, 5, -10, 0, -6, 0, 2, 8, -12, 5, 0],\n [4, 6, -10, 0, -1, 2, -10, -9, 8, -14, 6, -4],\n [9, 0, 0, -1, -13, 6, 2, -12, -6, 4, -8, -8],\n [-8, 5, -6, 2, 6, -3, 12, 0, -11, 12, -8, 2],\n [8, 2, 0, -10, 2, 12, 11, 1, -9, -8, 2, 0],\n [7, 0, 2, -9, -12, 0, 1, 4, -2, 2, 3, 4],\n [-2, 8, 8, 8, -6, -11, -9, -2, -11, 1, -7, -2],\n [-12, -2, -12, -14, 4, 12, -8, 2, 1, 7, 6, 4],\n [6, -4, 5, 6, -8, -8, 2, 3, -7, 6, 8, -4],\n [-1, -12, 0, -4, -8, 2, 0, 4, -2, 4, -4, 0]], determine the value at position (2, 11).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "565615648", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[11, 16, -2, 8, -4, -2, 11, -4, 5, -10, 6, -6],\n [16, 14, 4, 1, 4, 4, 10, 11, -4, -4, 1, 4],\n [-2, 4, 1, -4, 0, 2, 2, -8, 13, 14, 2, 0],\n [8, 1, -4, 10, -9, 0, -10, -12, -14, -6, 4, -2],\n [-4, 4, 0, -9, 16, 2, 6, 6, -2, 8, 4, -2],\n [-2, 4, 2, 0, 2, -6, 4, -10, 4, 1, 13, 12],\n [11, 10, 2, -10, 6, 4, 3, 1, 10, 13, 3, -2],\n [-4, 11, -8, -12, 6, -10, 1, -16, -4, 12, -7, 0],\n [5, -4, 13, -14, -2, 4, 10, -4, -13, 2, 2, 14],\n [-10, -4, 14, -6, 8, 1, 13, 12, 2, -8, 10, -2],\n [6, 1, 2, 4, 4, 13, 3, -7, 2, 10, -1, 8],\n [-6, 4, 0, -2, -2, 12, -2, 0, 14, -2, 8, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87709276021346", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[12, 7, 14, -15, -9, -11, 12, 6, 16, -1, 11, 7],\n [-13, -4, 11, 13, 5, 14, -10, -4, 12, 11, 0, 7],\n [-3, -10, -16, -12, -6, 4, 11, -4, 14, 4, -10, 13],\n [14, 9, 6, 14, 16, 7, -7, -13, -7, -4, 10, 2],\n [11, 15, 11, 3, 5, 9, 7, -15, -14, -1, 10, -1],\n [-8, 15, 2, 1, 4, -14, 7, 11, 4, -13, -16, 10],\n [1, 3, 13, -12, 0, 3, 0, -5, 14, 3, -6, 14],\n [7, 9, -2, -6, 11, -5, 16, -1, -4, 4, 1, -3],\n [2, -9, 13, -5, -6, -12, 11, -8, -12, -6, 7, 5],\n [-1, -15, 4, -16, 9, -8, 3, -10, 14, -8, -4, -12],\n [10, 2, -2, 2, 12, 11, -3, -3, -2, 2, -1, 16],\n [3, 7, 8, -7, 7, 0, -3, -1, 9, 14, -16, -10]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "841487242162", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[14, 4, 2, -4, 13, -12, 2, 3, 11, 3, 2, 12],\n [4, 6, 6, 16, -10, 0, -6, 5, 6, -1, -12, 4],\n [2, 6, 16, 8, -8, -1, -2, -6, 10, 4, 11, 0],\n [-4, 16, 8, 7, -2, 6, -4, -2, -10, 13, -8, -3],\n [13, -10, -8, -2, 12, -10, -6, 0, -2, 7, 0, 4],\n [-12, 0, -1, 6, -10, -3, 4, 4, -12, -4, 0, -6],\n [2, -6, -2, -4, -6, 4, 8, 8, -10, 2, -4, 3],\n [3, 5, -6, -2, 0, 4, 8, -4, -7, 2, 4, 2],\n [11, 6, 10, -10, -2, -12, -10, -7, -12, 5, -10, -3],\n [3, -1, 4, 13, 7, -4, 2, 2, 5, 6, -8, 2],\n [2, -12, 11, -8, 0, 0, -4, 4, -10, -8, -14, 12],\n [12, 4, 0, -3, 4, -6, 3, 2, -3, 2, 12, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2999479703127", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 8th power of the matrix:\n[[-15, 8, 7, -10, -15, 5, 5, 10, -6, -4, 1, -12],\n [9, 10, -10, -10, -8, 3, -6, -6, 10, 0, -14, -14],\n [-5, 3, 9, 13, -3, -7, -8, -6, -10, -9, 6, -10],\n [11, 12, -7, -5, 1, 2, 9, -10, 15, 6, -10, -1],\n [-12, 0, -11, 8, 15, -16, -10, -10, -1, -11, 14, -3],\n [-2, 1, 14, -13, 12, -4, -7, -4, 15, -8, 15, 3],\n [-16, 0, -6, -8, -15, 10, -11, -16, 1, 2, -16, 15],\n [-16, -3, 0, -8, -8, -6, -6, 9, -8, -8, -9, -12],\n [-12, -2, 9, -4, 11, -3, -16, 1, -14, -3, 10, -10],\n [-1, 15, -12, -15, -14, -10, -15, -4, -11, -12, -6, 1],\n [2, -12, -9, 10, -3, -14, -13, 16, 9, -5, -7, 10],\n [-16, 3, 1, -11, -10, -11, 12, -12, -14, 3, -12, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37202769972017", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-16, 0, -4, -3, -7, 8, 8, -5, -2, -6, 0, 4],\n [0, 13, 8, 9, 0, -2, 4, -6, 11, 10, 2, 2],\n [-4, 8, 9, -2, 7, 6, -6, 0, -10, -8, 8, -4],\n [-3, 9, -2, 6, 6, -4, -10, -3, -2, 6, -6, -16],\n [-7, 0, 7, 6, -10, -3, 0, 6, 4, -8, 9, 2],\n [8, -2, 6, -4, -3, 11, -6, 6, 0, -4, 9, -2],\n [8, 4, -6, -10, 0, -6, -8, -2, -2, -1, -8, -12],\n [-5, -6, 0, -3, 6, 6, -2, 3, 10, 10, -1, -8],\n [-2, 11, -10, -2, 4, 0, -2, 10, -4, 0, 8, 1],\n [-6, 10, -8, 6, -8, -4, -1, 10, 0, 7, 12, 6],\n [0, 2, 8, -6, 9, 9, -8, -1, 8, 12, 8, 2],\n [4, 2, -4, -16, 2, -2, -12, -8, 1, 6, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145761747300562", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[16, 0, -4, 2, -15, -2, 10, -12, 5, 10, 6, 8],\n [0, -4, -2, -8, 10, 8, 4, -2, 0, 2, -14, -6],\n [-4, -2, -14, -13, 0, -4, 2, -1, -8, 8, 5, -6],\n [2, -8, -13, 0, -6, -4, 3, -8, -10, -2, 10, -2],\n [-15, 10, 0, -6, 12, 6, -4, 0, -1, 3, -4, -13],\n [-2, 8, -4, -4, 6, 12, -8, 8, 11, -4, -10, -2],\n [10, 4, 2, 3, -4, -8, 10, 0, -4, -2, 0, 0],\n [-12, -2, -1, -8, 0, 8, 0, 16, 12, 7, 0, 12],\n [5, 0, -8, -10, -1, 11, -4, 12, 3, -9, 2, -2],\n [10, 2, 8, -2, 3, -4, -2, 7, -9, -14, 8, -10],\n [6, -14, 5, 10, -4, -10, 0, 0, 2, 8, -2, 5],\n [8, -6, -6, -2, -13, -2, 0, 12, -2, -10, 5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11207152368432", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[13, 16, 11, 13, -7, -2, 2, -5, 14, -5, -5, 5],\n [9, -10, -14, 15, -10, -1, 6, -4, -9, 5, 14, -3],\n [-12, 14, -8, -9, -5, -12, 15, 9, -5, 16, -8, -16],\n [-2, 10, -9, -11, 5, -4, -6, -4, -10, 14, -13, -10],\n [16, -6, 11, -1, 7, 8, 9, 5, -1, 2, -6, -16],\n [14, -3, -7, -14, 11, -7, 9, 5, 14, 15, -10, -9],\n [12, -9, -11, 8, 11, 15, -4, -6, -10, -7, 10, -11],\n [-10, 1, -4, -4, -3, -1, 1, 13, -4, 6, 2, -9],\n [0, -9, 13, -11, -14, 7, 11, 7, -5, 2, 1, -14],\n [-8, 5, 4, -2, -6, 10, 13, -11, -5, -3, 5, -2],\n [15, 13, 6, -1, -5, 3, 16, -3, 14, 13, 9, 1],\n [-7, 1, -16, -14, -11, 9, 5, 3, 12, 10, 6, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3394779931210", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-6, 0, -6, 13, 2, -4, 8, -2, -8, -1, -8, -1],\n [0, 10, 0, -12, 2, -2, 4, 4, -3, 1, 7, 8],\n [-6, 0, -16, -11, 0, -8, -6, -8, 6, 6, 6, 8],\n [13, -12, -11, 10, 6, -1, 8, 0, 9, -7, -2, -6],\n [2, 2, 0, 6, 1, 6, -7, 14, 0, -10, -6, -10],\n [-4, -2, -8, -1, 6, 13, -2, 0, 4, 1, -2, -8],\n [8, 4, -6, 8, -7, -2, 2, 0, -10, 0, -4, 8],\n [-2, 4, -8, 0, 14, 0, 0, -3, 0, 8, 0, -8],\n [-8, -3, 6, 9, 0, 4, -10, 0, -16, -8, -4, -6],\n [-1, 1, 6, -7, -10, 1, 0, 8, -8, -15, 7, -11],\n [-8, 7, 6, -2, -6, -2, -4, 0, -4, 7, -12, -4],\n [-1, 8, 8, -6, -10, -8, 8, -8, -6, -11, -4, -10]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5004129624502292", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[15, 4, 2, -4, -3, 0, 12, -8, -6, -9, 2, -2],\n [4, 15, -6, 2, 8, 0, 2, 6, -9, 2, 7, -8],\n [2, -6, -5, 0, 0, 11, 2, 8, -8, 5, -6, 5],\n [-4, 2, 0, -1, -8, -4, -12, -4, 8, 6, 0, -10],\n [-3, 8, 0, -8, -12, -2, 7, 4, 2, 2, -3, 7],\n [0, 0, 11, -4, -2, -6, -8, 8, 2, 4, -10, 8],\n [12, 2, 2, -12, 7, -8, 16, -12, 4, 8, -6, 5],\n [-8, 6, 8, -4, 4, 8, -12, -5, 6, -8, 5, 2],\n [-6, -9, -8, 8, 2, 2, 4, 6, 0, 10, 10, 0],\n [-9, 2, 5, 6, 2, 4, 8, -8, 10, -4, 2, -6],\n [2, 7, -6, 0, -3, -10, -6, 5, 10, 2, -12, -4],\n [-2, -8, 5, -10, 7, 8, 5, 2, 0, -6, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45185857610389", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[-16, -9, -15, -14, 0, 14, -7, -7, 1, -12, -11, 14],\n [-3, 16, 12, 2, -7, 6, -9, 7, -11, 10, 15, 13],\n [-14, -7, 1, -4, 0, -1, 4, -5, -1, -3, -7, 0],\n [2, -8, -11, 1, 16, -12, 11, -9, -1, -3, 0, -12],\n [12, 2, 9, 12, -6, 8, 12, 1, 12, 13, 5, 15],\n [12, 5, -14, -4, -15, -8, -16, 0, -6, -6, -15, -9],\n [-3, -13, -1, -10, 16, 8, -11, -9, 13, -10, 2, -14],\n [-7, 14, -4, 14, -8, 2, 10, 2, 1, -16, 12, -5],\n [-11, 2, 9, 8, 0, -5, 3, 11, -11, 6, 14, -15],\n [16, -8, 9, 0, 0, 13, 13, -1, 4, 1, 10, -12],\n [-4, 9, 3, -12, -4, 9, -2, -8, 6, 4, -15, 1],\n [10, -16, 3, 6, 11, 12, 16, -12, -9, 2, -6, 13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80137566698982", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (4, 1) of the result:\nA =\n[[-16, 0, -7, -5, 13, -9, 16, -4, 5, -1, -7, 9],\n [8, -4, -14, 12, -13, 5, -3, -16, 7, -8, 2, -9],\n [-15, 13, 13, -16, 10, -16, 14, -8, -14, 6, -9, -3],\n [-4, -5, -6, -5, -3, -5, -8, 6, 3, 10, -15, -2],\n [4, -4, 8, 5, 12, -13, -1, 11, 5, -4, 1, 12],\n [4, -4, 10, -12, -8, -1, 2, 6, 15, -14, -5, -9],\n [0, -6, 16, 10, 14, -8, 2, 8, 2, -7, -8, -9],\n [-16, 4, -13, 1, -3, 3, -15, -2, 1, 8, 13, -9],\n [13, 8, -10, 0, 15, 8, 11, -9, 5, -11, -5, 12],\n [13, 15, -9, 9, 4, -4, -11, 5, -1, 1, 15, 0],\n [-3, 0, 0, -1, 0, 5, 11, -2, 5, 4, -6, -4],\n [3, -11, -16, 0, 5, 6, -11, 2, 13, -6, 0, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28210537397", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 5) of the 7th power of the matrix:\n[[2, -5, 4, -2, 13, -16, 0, 13, 4, 11, 3, 2],\n [7, -6, 9, 0, 9, -2, -4, 0, -3, 2, 10, -3],\n [-15, -10, -16, 4, 15, -12, 11, -6, -4, 10, -16, -8],\n [-11, -6, -11, -14, 11, -11, -9, 7, -2, 11, -8, 16],\n [11, -7, 8, -13, 14, -4, 9, -10, -15, -8, 0, 4],\n [12, 15, -1, -9, 4, -10, -4, 4, -12, -12, 11, 16],\n [-13, 3, -8, 15, 16, 10, 16, 7, 0, -6, 1, 4],\n [2, 2, -14, 9, 10, -14, -10, -14, 4, 1, 10, -7],\n [-14, 8, 14, 16, 3, -5, 13, -8, -12, 7, -12, -10],\n [16, -10, -4, -13, 1, 10, 11, 7, -3, -5, -8, -4],\n [10, -9, -7, -12, 16, -5, 15, -13, -8, -8, -8, -10],\n [-15, -7, 7, -5, -14, -14, -1, 6, -16, 13, 15, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15289169089", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 5) of the 8th power of the matrix:\n[[11, 15, 3, -13, 15, -1, -3, 3, 11, -3, -14, 7],\n [11, -10, -2, 8, -10, 7, -6, -2, -7, 12, -5, 7],\n [-10, 12, 4, 11, 12, 2, 13, 8, 13, 14, 6, -7],\n [-9, -11, -15, -2, 8, -2, -9, -10, -7, -1, 6, -14],\n [-15, 13, 12, -8, 7, -15, -15, 2, -6, 7, -1, 15],\n [8, -10, 1, -9, 15, -13, 4, -4, 16, 7, -11, 4],\n [14, -8, -16, 2, -15, 3, -12, 0, -5, 5, 8, 13],\n [-8, 2, -10, 5, 4, 11, 9, 9, 9, 1, 1, 0],\n [9, -8, -1, 4, 0, -3, -16, 4, -13, 1, -7, 12],\n [-15, -9, -6, -7, 16, -13, 8, 5, -12, 11, -5, -13],\n [2, 8, 1, 15, 0, -1, 1, 12, 8, -7, -8, 1],\n [6, -11, 5, 11, -9, -6, -9, -8, 9, 13, 10, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "924408512499", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-11, 1, -16, -9, -5, -16, 12, 0, -11, 5, -9, 4],\n [-12, 14, 11, 13, -4, 12, 16, -7, 2, -8, -1, 10],\n [-11, 2, 14, 2, 15, -14, 5, -6, 15, -13, -5, 12],\n [-13, -14, 6, -7, 0, 12, -5, 1, 5, 2, 0, -12],\n [-2, 9, 7, 3, 4, 10, -7, 9, -6, 3, 16, -11],\n [-15, -8, 15, 2, 8, 13, 0, -4, 8, -3, 1, -1],\n [-9, 4, -2, -16, -2, 0, 9, -3, 16, -2, 7, 4],\n [1, -10, 1, 1, -16, 6, -10, 3, 15, -12, 5, 15],\n [-10, -10, 4, -8, -2, 9, -9, -15, -8, 1, 7, -14],\n [4, -6, -16, -5, -11, -10, -13, -9, 6, -3, 16, -12],\n [-11, 6, -2, -14, 13, -1, -3, 4, -15, 3, 1, 2],\n [0, -3, -4, 10, -11, 1, 5, -13, 12, 15, -4, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2372204879874", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (10, 9) of the matrix A^9 where A is:\n[[-1, -7, 10, 1, 4, -2, 12, -2, -2, 4, -8, 6],\n [-7, 2, -10, -2, -3, 0, -12, 8, 4, 3, 0, 4],\n [10, -10, 0, -8, 0, 1, -10, 5, 4, 0, 0, 13],\n [1, -2, -8, 7, 0, 1, 0, -7, -2, -1, 3, 6],\n [4, -3, 0, 0, -1, 6, -6, 4, -10, -3, -2, 14],\n [-2, 0, 1, 1, 6, 0, 10, 4, 9, -6, 4, 7],\n [12, -12, -10, 0, -6, 10, 4, 4, 0, -6, -6, 8],\n [-2, 8, 5, -7, 4, 4, 4, 2, 0, 4, -10, -14],\n [-2, 4, 4, -2, -10, 9, 0, 0, 7, 0, 0, -2],\n [4, 3, 0, -1, -3, -6, -6, 4, 0, -14, -2, 4],\n [-8, 0, 0, 3, -2, 4, -6, -10, 0, -2, -3, 3],\n [6, 4, 13, 6, 14, 7, 8, -14, -2, 4, 3, -12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3278928217364", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[-11, 4, -6, -14, -4, -10, -10, -4, -12, -2, 0, 3],\n [4, -8, -14, -13, 8, -6, -4, 0, 8, 2, -6, 8],\n [-6, -14, -6, 6, -2, -1, 16, 0, -2, -1, 0, -1],\n [-14, -13, 6, -9, 2, 0, 11, 9, 12, -10, 0, 6],\n [-4, 8, -2, 2, -2, 4, -8, 0, 4, -2, -14, -6],\n [-10, -6, -1, 0, 4, 4, -10, 4, 0, 10, -2, 6],\n [-10, -4, 16, 11, -8, -10, 16, -1, -2, -1, -1, -14],\n [-4, 0, 0, 9, 0, 4, -1, -7, 0, -5, 4, -2],\n [-12, 8, -2, 12, 4, 0, -2, 0, 4, -13, -8, 10],\n [-2, 2, -1, -10, -2, 10, -1, -5, -13, 16, -8, -8],\n [0, -6, 0, 0, -14, -2, -1, 4, -8, -8, -11, -4],\n [3, 8, -1, 6, -6, 6, -14, -2, 10, -8, -4, -7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3885768873465", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 8th power of the matrix:\n[[-2, 12, -3, 10, -2, -2, 2, 2, 9, -3, 0, 2],\n [12, -7, 6, 8, 11, -3, -8, 3, 6, -2, 12, -4],\n [-3, 6, -12, 6, -3, -11, -2, 2, -4, 12, 2, -13],\n [10, 8, 6, 12, 0, 5, 0, -6, 2, 2, -10, 0],\n [-2, 11, -3, 0, 0, -4, 11, 7, 3, -6, -1, 0],\n [-2, -3, -11, 5, -4, -16, -4, 6, 2, 4, -10, 8],\n [2, -8, -2, 0, 11, -4, 13, -2, -2, 0, -3, 6],\n [2, 3, 2, -6, 7, 6, -2, -8, -4, 7, -2, -2],\n [9, 6, -4, 2, 3, 2, -2, -4, 13, 3, 1, 10],\n [-3, -2, 12, 2, -6, 4, 0, 7, 3, -3, 8, -10],\n [0, 12, 2, -10, -1, -10, -3, -2, 1, 8, -12, 4],\n [2, -4, -13, 0, 0, 8, 6, -2, 10, -10, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6846781076451", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 7th power of the matrix:\n[[-3, 10, -6, -3, 2, 1, 6, 10, -2, -7, 6, 4],\n [10, -5, 6, -8, 1, 1, -2, 6, -8, -5, -6, 0],\n [-6, 6, 5, 4, -9, -9, 4, -4, 8, -2, 0, -6],\n [-3, -8, 4, 12, -2, -4, 3, -4, -1, -3, -5, 6],\n [2, 1, -9, -2, -7, 5, -5, 2, -4, -11, 9, 0],\n [1, 1, -9, -4, 5, 16, -4, -3, 6, -4, 2, -11],\n [6, -2, 4, 3, -5, -4, -14, -11, -9, 3, 1, 6],\n [10, 6, -4, -4, 2, -3, -11, -5, 2, 15, -2, -3],\n [-2, -8, 8, -1, -4, 6, -9, 2, -14, 1, 2, 1],\n [-7, -5, -2, -3, -11, -4, 3, 15, 1, -5, 4, 0],\n [6, -6, 0, -5, 9, 2, 1, -2, 2, 4, 14, -9],\n [4, 0, -6, 6, 0, -11, 6, -3, 1, 0, -9, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22329736246", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 10) of the 7th power of the matrix:\n[[-10, -15, 16, 1, -2, -16, 9, 16, -12, 8, 7, 15],\n [-8, 8, 9, -16, -3, 13, 11, 10, -8, 15, -13, 1],\n [-1, -11, 13, -6, -14, -15, -10, -9, 14, -16, -6, -12],\n [14, 2, -6, -6, -9, 9, -11, 15, 12, 2, -1, 7],\n [12, 2, -13, 8, 14, -16, 0, -15, 15, -9, 2, 12],\n [-14, -15, 15, -2, 4, -4, 5, 14, -4, 5, -9, 14],\n [10, 8, 1, 15, 2, -11, -12, 9, 2, -10, 12, -11],\n [-12, -6, -13, 16, 8, 12, -2, -16, 4, -2, -7, 0],\n [8, -16, 13, 2, -16, -11, 15, -12, 16, -10, -3, 15],\n [10, 6, -5, 13, 7, -10, -13, -9, 14, 10, 8, -12],\n [-3, -13, 10, 5, -14, 4, -10, -10, 12, 4, 3, -11],\n [14, -10, 10, -15, 12, 6, 12, 1, 11, 13, 12, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22438199711", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-14, 8, 6, -16, 4, 13, 15, 7, 10, -1, -13, 13],\n [1, -11, -2, -10, 9, -16, 9, 13, 6, -14, 2, 14],\n [-4, 12, -7, 0, 14, 11, -9, 13, 12, -4, 10, -14],\n [9, 11, -7, 2, -1, 12, 16, 9, 4, 8, -1, -15],\n [5, -15, -6, 0, 11, -13, 10, -15, -12, 11, -8, -3],\n [4, -5, -2, 11, -6, 3, 10, 15, -4, -13, -3, -11],\n [-14, 13, -5, -11, 8, 10, -10, 3, -7, -6, -10, -1],\n [-14, 8, 6, 11, 4, -13, -9, 13, 14, 15, 13, 10],\n [-9, -2, 12, -10, -13, -9, 6, 14, 9, -1, 4, -4],\n [-12, -6, -16, -7, 1, -3, -11, 6, 10, -15, 0, 8],\n [12, -15, -6, -4, -2, -13, -8, 14, 16, 6, 10, -16],\n [7, 1, -3, -11, -14, 15, -13, -10, -14, -14, 0, -16]], determine the value at position (11, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-319185039911", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (1, 10) of the result:\nA =\n[[-15, -6, -3, -5, -3, 4, 8, 13, 8, 0, -5, -2],\n [-6, 6, -2, -4, -12, -6, 10, -3, -4, -2, -13, 4],\n [-3, -2, -9, 0, 8, -10, 0, 2, -6, -1, -8, 5],\n [-5, -4, 0, -12, 6, 0, 12, 9, -10, -4, 3, 8],\n [-3, -12, 8, 6, 0, -12, 6, -10, -6, -1, -2, 1],\n [4, -6, -10, 0, -12, -15, -1, -5, -1, 4, 4, 8],\n [8, 10, 0, 12, 6, -1, 2, -4, 4, -2, 4, 3],\n [13, -3, 2, 9, -10, -5, -4, -3, -10, -4, 8, -5],\n [8, -4, -6, -10, -6, -1, 4, -10, -14, -6, 4, 14],\n [0, -2, -1, -4, -1, 4, -2, -4, -6, 8, -8, 8],\n [-5, -13, -8, 3, -2, 4, 4, 8, 4, -8, 15, -5],\n [-2, 4, 5, 8, 1, 8, 3, -5, 14, 8, -5, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12084930679562", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-1, -3, -5, 16, 0, 16, 11, 4, 15, -2, 8, 6],\n [-5, -10, 15, 7, 6, -12, 15, -4, 15, -6, -9, 15],\n [1, 2, -10, 1, 0, -8, -8, -2, 5, 16, 16, 10],\n [15, 16, 16, 7, -11, -16, -8, 6, -9, 12, 1, -9],\n [-7, -1, 7, -9, -6, -12, 7, -12, 13, -6, 9, -14],\n [-4, -3, 9, -7, 6, -6, -13, -4, 14, 1, -3, 8],\n [8, -15, 1, 1, 6, -15, 4, -16, 12, 15, -4, -4],\n [-14, 13, 8, -3, 5, -16, 6, 9, 4, -12, -11, 3],\n [4, -3, 8, 0, -14, -7, -11, -5, 11, -16, 14, 0],\n [5, 12, 5, -1, 14, -7, -11, 2, -5, 10, 16, 9],\n [7, 14, -15, 5, 1, 3, 1, 12, 8, -6, -5, -9],\n [11, -14, 16, -6, 3, 13, 11, 15, -2, -1, -12, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7082179829266", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[10, -13, 0, -3, -16, -8, 14, -5, -9, 6, -16, -16],\n [-3, 15, 11, 16, 10, 16, -14, 3, -3, -6, -15, -13],\n [-7, -10, 2, -10, 10, -12, 13, 9, -8, -11, 8, -7],\n [2, 9, -14, -12, -8, 12, 3, -1, 16, 5, -2, 5],\n [8, 11, 4, 10, -16, 12, 15, -4, -4, -4, -12, -7],\n [-3, 0, -15, -1, 8, -10, 5, 9, 3, -16, -8, 5],\n [14, 0, -15, -1, -7, -7, 8, -2, 2, -13, 5, 5],\n [2, -8, -6, -9, -16, 5, -15, -2, 12, -2, 1, -7],\n [2, -7, 10, 5, 13, 8, -2, -14, -8, 16, 6, -7],\n [-16, -9, -3, -14, -5, -3, 1, -8, -15, -2, -8, -6],\n [4, -16, 3, 9, -8, -1, 9, -9, 10, -7, -2, 2],\n [7, -4, -10, -10, 11, -2, -5, 11, 14, 14, -5, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35169755903119", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-13, -6, 16, 6, -3, -6, 5, -8, 5, 14, 14, -11],\n [3, -8, 3, 3, -16, -6, -14, -11, 4, -8, 3, 2],\n [9, -3, 7, -14, 11, -16, -8, -16, 14, -6, 13, 7],\n [10, 6, -10, -9, 10, 10, -8, -11, -15, -8, -11, -6],\n [-16, -7, 3, 2, -6, 10, 12, 3, -9, -4, -9, 2],\n [16, 7, 16, -14, -14, -16, 10, 9, 14, 11, -1, 3],\n [-8, 15, -16, -16, 16, 7, -15, 13, 1, 11, -2, -3],\n [-15, -15, 7, -6, 2, -16, 11, 10, -5, 16, 0, -3],\n [13, 9, -1, 15, -10, 7, -16, 4, 9, 13, 9, 13],\n [6, -6, -3, -5, 13, -2, 8, -14, -14, 6, -7, 9],\n [16, 12, -16, 3, -9, 11, 14, -2, -5, -12, -16, 13],\n [-14, 2, -12, -4, -12, -12, -13, -3, -1, -16, -7, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5881961508827168", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (11, 11) of the result:\nA =\n[[-1, 14, -5, -1, 7, 4, -1, 8, 4, -13, 7, -11],\n [-10, -13, 14, 8, -3, -12, -5, -13, 13, 12, 12, 5],\n [9, 5, -16, 16, 9, 16, 10, -8, -9, -14, 9, -9],\n [-2, -9, -15, 13, 10, 10, -11, -8, 12, 2, 7, 3],\n [15, -13, -4, -12, -6, -1, 10, 2, 9, -14, 12, 4],\n [15, 5, -13, -1, -16, 11, -6, -14, -7, -1, 11, 12],\n [5, -8, -5, 11, -12, 2, -5, -5, -16, -15, 11, 2],\n [14, -7, -16, -5, 15, -4, 7, 13, -11, 13, 11, 15],\n [-12, 7, -12, 15, 1, 14, -15, 10, 11, -5, -15, -10],\n [3, -15, -7, -4, -1, 11, 12, -6, -1, -9, 4, -11],\n [-6, 9, -5, -15, 3, 11, -10, -1, -4, 12, 5, -15],\n [-3, 11, -4, -13, -1, -15, 3, 1, -9, 6, 6, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22631042321", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 11) of the matrix A^8 where A is:\n[[-14, -4, 7, 2, 4, -7, 13, 5, 3, 3, 0, 4],\n [-4, 12, 4, 11, 2, 2, -7, -6, -4, 14, 0, -8],\n [7, 4, -7, 10, -8, 8, -10, 4, -13, 0, 1, 4],\n [2, 11, 10, -9, 8, 8, 0, -8, 8, 2, -8, 2],\n [4, 2, -8, 8, -1, 7, 9, -4, -6, 6, -3, -1],\n [-7, 2, 8, 8, 7, 14, -2, -6, 13, 2, 1, 4],\n [13, -7, -10, 0, 9, -2, 2, 5, -8, -2, 8, -4],\n [5, -6, 4, -8, -4, -6, 5, 14, -8, -6, 3, -4],\n [3, -4, -13, 8, -6, 13, -8, -8, -6, -2, 6, -4],\n [3, 14, 0, 2, 6, 2, -2, -6, -2, 15, -5, 7],\n [0, 0, 1, -8, -3, 1, 8, 3, 6, -5, -5, 8],\n [4, -8, 4, 2, -1, 4, -4, -4, -4, 7, 8, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1406919186207", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-12, 7, -14, -6, -12, -15, -4, -5, -1, -1, -6, -8],\n [7, 7, 13, 4, 0, 7, 10, 13, -4, -14, 11, 5],\n [1, -7, 4, 16, 7, -4, 6, 14, -7, -16, -15, -15],\n [8, 13, -1, 3, 0, -11, 11, -11, -16, 7, -3, 10],\n [-4, -3, 7, -8, 5, -12, 11, 13, -8, 9, 4, -13],\n [0, 12, 2, -8, -6, -3, 11, 2, -7, -1, -2, 1],\n [-11, 7, 6, 12, 6, 14, 10, 10, 8, -12, 4, -6],\n [2, -1, -11, 9, 11, 5, -10, -16, -4, 0, 4, -16],\n [0, 3, 13, 0, 10, 10, -13, 16, -16, -6, -9, 13],\n [7, -14, 14, -13, -13, -9, -15, -14, 14, -7, 9, -15],\n [-3, -15, 1, 10, -8, 15, -6, 4, 16, 16, 1, 7],\n [-5, -2, 4, -11, -10, 1, 5, 15, -10, 3, -4, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9405350868844", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[4, -6, -2, 0, -6, 3, 0, -8, -14, 4, -2, -2],\n [-6, 7, 0, -8, -4, -8, 3, -4, -10, 0, -14, -2],\n [-2, 0, -10, 0, 0, 2, 1, -12, 4, 10, -12, 1],\n [0, -8, 0, 2, -4, 0, 2, -4, 12, 6, 4, -10],\n [-6, -4, 0, -4, -7, -2, -6, -1, 1, -8, 0, -6],\n [3, -8, 2, 0, -2, 11, -2, 9, -10, 6, 2, -10],\n [0, 3, 1, 2, -6, -2, -12, -1, -11, 5, -4, 0],\n [-8, -4, -12, -4, -1, 9, -1, -4, 0, -3, 4, 2],\n [-14, -10, 4, 12, 1, -10, -11, 0, -8, 12, 5, 7],\n [4, 0, 10, 6, -8, 6, 5, -3, 12, -2, 1, -4],\n [-2, -14, -12, 4, 0, 2, -4, 4, 5, 1, 10, -5],\n [-2, -2, 1, -10, -6, -10, 0, 2, 7, -4, -5, -8]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-128014572018", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[15, 16, -10, 4, -2, -13, -5, 7, 4, 11, -14, -16],\n [-6, 3, -11, 7, 13, -16, 9, -7, 3, 0, -1, 15],\n [-8, 14, 10, 5, 4, 8, -14, -14, -13, -7, 14, 8],\n [-15, -8, 13, 8, 14, 12, -3, 11, -9, 10, -8, -4],\n [3, -1, -7, 8, -14, -2, -16, -2, -1, -6, -16, 2],\n [-7, -9, 3, -8, -10, -5, 6, 9, -7, 8, 13, 16],\n [-14, 15, 1, 13, 2, -5, -13, 7, -10, 0, 7, -1],\n [8, 2, 9, 16, -3, 6, 14, 2, 13, 9, -9, 5],\n [10, 13, -15, -4, -7, 8, 16, 10, 12, 10, -1, 12],\n [-1, -2, 10, 16, 8, 16, -5, -3, -7, -5, 4, -10],\n [-5, 3, 14, -11, -13, -1, 13, 15, 11, -14, -14, 10],\n [12, -4, -6, -9, 12, -7, -10, -9, 9, -15, -6, 7]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-177545317171514", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (7, 5) of the 8th power of the matrix:\n[[12, 6, -12, 7, -3, 0, -16, -5, -1, -14, -12, 15],\n [0, -9, -14, 16, 2, -1, -14, 7, 9, -6, 10, -6],\n [-11, -14, -2, 16, 16, -12, -12, -14, 14, 11, -12, 13],\n [0, -1, -9, 15, -2, -2, 13, 16, 8, 0, -14, 1],\n [-10, 8, -2, -7, -1, 9, 4, -7, -6, 3, 3, -4],\n [6, -3, 11, 6, -13, 2, 9, -6, 13, 1, 13, 1],\n [-6, -15, 2, 4, 0, -2, 3, -13, 0, 8, -9, 10],\n [14, -9, 8, -8, -16, 13, -3, -13, 9, -3, -14, 3],\n [-11, 4, -6, 10, 13, -3, 1, -11, 15, 16, -5, -13],\n [-6, -2, 7, 16, 11, -13, -5, -1, -5, 4, 9, -8],\n [3, 4, -12, -6, -12, -1, -5, 5, -2, 15, 16, -13],\n [-1, -7, 16, -5, -2, 14, 6, 15, 8, -12, -3, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684120241678", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-3, -3, -11, 8, 11, 0, -13, 11, -10, -11, 12, 11],\n [2, -3, -4, 12, -15, -15, 9, -16, 11, 7, 12, 11],\n [16, -12, 13, 5, -14, 12, 14, 13, 12, 14, 7, 6],\n [7, 8, -15, -11, 15, -4, -1, 9, -7, -13, -3, 7],\n [6, -6, -9, -11, 16, -7, -10, 0, 3, 11, 7, -8],\n [13, 0, -1, -10, 10, -10, 15, -1, 2, 9, -16, 13],\n [-2, -14, 3, 2, 10, -16, -4, 16, 7, -6, -12, 15],\n [2, -16, -2, 2, -13, 8, -9, 9, 1, 11, 16, -12],\n [11, 0, -3, 12, -2, -14, -14, 2, 16, 9, -1, 7],\n [12, 10, -10, -8, -13, -10, -13, -8, -15, 10, 15, 3],\n [4, 0, -4, 7, -11, 9, 15, -15, -12, -12, -3, -11],\n [3, 0, -14, 16, -8, -11, -8, 1, -9, 0, 8, 8]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9166124448422472", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-8, -4, -1, -9, -11, -2, 0, -4, -4, -6, -15, 9],\n [-4, 0, 2, 10, -9, -15, -8, 0, -4, -14, 2, 4],\n [-1, 2, 16, 1, -6, -14, -4, 0, -10, 10, -6, 2],\n [-9, 10, 1, -13, -3, 4, 12, -12, -6, 10, -10, 4],\n [-11, -9, -6, -3, 5, 4, 5, -10, -8, -3, 8, -5],\n [-2, -15, -14, 4, 4, -15, -6, -2, 0, -1, -8, -2],\n [0, -8, -4, 12, 5, -6, -15, -7, 4, -6, 2, 2],\n [-4, 0, 0, -12, -10, -2, -7, 2, 10, -2, 0, 2],\n [-4, -4, -10, -6, -8, 0, 4, 10, -15, 1, 1, -4],\n [-6, -14, 10, 10, -3, -1, -6, -2, 1, 16, -12, -8],\n [-15, 2, -6, -10, 8, -8, 2, 0, 1, -12, 8, -3],\n [9, 4, 2, 4, -5, -2, 2, 2, -4, -8, -3, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33941444814531", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[6, 11, -1, 12, 16, 15, 6, 16, 16, -14, 11, -9],\n [-8, -12, 14, -12, 16, -4, 8, 7, -6, 2, -6, 16],\n [13, -3, -16, 14, -14, 8, 8, 1, -3, 10, 14, -15],\n [15, 13, 16, 7, 16, 9, -11, 0, 7, -1, 7, -12],\n [7, 9, 3, 11, 3, 12, 11, 9, 15, 4, 1, -5],\n [5, 12, 2, 1, 1, -1, 2, -8, 16, -4, -6, 16],\n [13, -8, 6, 7, 15, -13, 10, -6, 4, -3, 1, 7],\n [3, 9, 14, -1, 2, -10, -1, 7, -11, -1, -2, -13],\n [-15, -3, 5, -15, 3, -13, 1, 3, 9, -10, 2, 7],\n [-6, -1, -16, 11, -4, -6, -11, 13, 11, -8, 14, -11],\n [-11, 3, 15, 15, -12, -7, -15, -10, -6, -16, -3, 4],\n [-11, 9, 0, 9, -10, -16, -2, 14, -11, 2, -11, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "478245664364293", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[0, -1, 2, -6, 2, 0, -4, 4, -2, 8, 0, -3],\n [-1, 10, -1, -2, -12, -4, -6, 2, 8, 2, -3, 0],\n [2, -1, 1, -5, -14, 9, -1, -4, -10, -1, -4, -8],\n [-6, -2, -5, -2, 3, 0, 12, -10, -5, 0, -3, 2],\n [2, -12, -14, 3, 12, 0, -6, -7, -6, -4, 5, 10],\n [0, -4, 9, 0, 0, -11, 10, 2, -8, -7, 6, 2],\n [-4, -6, -1, 12, -6, 10, 16, 6, 0, 8, -7, 6],\n [4, 2, -4, -10, -7, 2, 6, -15, -2, 0, 6, 4],\n [-2, 8, -10, -5, -6, -8, 0, -2, 7, 6, 12, 1],\n [8, 2, -1, 0, -4, -7, 8, 0, 6, 3, 4, 12],\n [0, -3, -4, -3, 5, 6, -7, 6, 12, 4, -15, -4],\n [-3, 0, -8, 2, 10, 2, 6, 4, 1, 12, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24142404980", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 8) of the matrix A^8 where A is:\n[[2, 13, -6, 5, 15, -12, 2, 3, 6, -2, 16, -14],\n [3, -12, 5, 0, 0, -11, -1, -15, -2, -11, -15, -14],\n [-12, 9, 5, -7, 7, -2, -4, 15, -12, -4, -6, -8],\n [10, 13, -14, 7, 12, -5, 3, -15, -9, -1, 10, 16],\n [7, -4, 6, 11, -5, -15, -4, -3, 9, 5, -16, -13],\n [-1, -8, 14, 5, -15, -11, -2, 1, -9, 11, 10, 10],\n [10, -7, 15, -5, 9, 10, -5, 14, 16, -16, -4, 13],\n [5, -7, -2, -10, -15, -15, 3, -10, 12, -12, -13, -3],\n [-16, -1, 7, 7, -15, -3, -13, -2, -15, 8, 16, -15],\n [10, -8, -16, -7, -2, -10, -16, -2, -16, -11, 4, 9],\n [-10, 13, 16, 0, -8, -13, 0, -13, -16, -7, 4, 15],\n [13, -6, 3, 11, -8, 3, -11, 8, -10, -9, -10, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1465499764308", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-12, -7, -5, 6, 0, -14, 2, -6, 4, -6, 8, -13],\n [-7, -12, -12, -8, -12, -11, -9, -2, 11, -4, 10, 0],\n [-5, -12, -8, -4, 4, 4, 4, 2, 3, -10, 2, -8],\n [6, -8, -4, -11, 8, -8, -4, 3, 4, 0, 14, 0],\n [0, -12, 4, 8, 14, -2, -11, 0, 3, -2, -1, 1],\n [-14, -11, 4, -8, -2, -2, -6, -2, 6, 0, 9, -4],\n [2, -9, 4, -4, -11, -6, -5, 0, 0, -8, 6, 2],\n [-6, -2, 2, 3, 0, -2, 0, -16, 2, -8, 4, 10],\n [4, 11, 3, 4, 3, 6, 0, 2, -1, 1, 8, 0],\n [-6, -4, -10, 0, -2, 0, -8, -8, 1, -6, -10, -4],\n [8, 10, 2, 14, -1, 9, 6, 4, 8, -10, -15, 1],\n [-13, 0, -8, 0, 1, -4, 2, 10, 0, -4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "237360396085541", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[0, -6, -11, 14, -5, 10, -12, 12, 13, -4, -4, 12],\n [-12, -3, 5, 0, 2, -5, 8, 6, 0, 7, -5, -3],\n [-3, -7, -16, 6, 11, -10, 15, -6, -8, 7, -13, 0],\n [4, 8, 16, -14, -13, -4, 12, -11, -3, -16, -10, 14],\n [3, 12, 10, 5, -2, -14, -4, 14, -6, 14, 13, 6],\n [-2, -14, 6, 4, -12, 8, -7, -5, 15, 5, 14, 13],\n [1, -6, 11, 1, -16, -15, -12, -10, 1, 5, 12, 11],\n [4, -3, 8, -16, 4, 15, 13, -9, -13, 7, -8, -16],\n [10, 16, 12, -12, 12, -8, -12, -3, -15, -10, -2, -5],\n [14, -8, 5, 13, 7, 11, -1, 0, -2, -5, 16, 11],\n [-13, 4, 4, -12, -5, -9, -5, -6, 14, -4, 15, -2],\n [13, -11, -9, -2, 14, -3, -8, 11, 2, -8, -3, 11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3125767452253", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (2, 2) of the result:\nA =\n[[4, -14, -2, -14, -3, 3, 4, 4, 3, 2, -6, -3],\n [-14, -2, 2, -10, -9, -1, 8, 8, 0, 1, 12, 6],\n [-2, 2, 13, 0, 3, 4, -2, -5, 6, -2, -2, 6],\n [-14, -10, 0, 11, 2, 8, 0, -4, -2, 3, 0, 6],\n [-3, -9, 3, 2, -6, -6, -2, 3, 2, -10, -2, 8],\n [3, -1, 4, 8, -6, 10, -6, 5, -6, -8, -4, 3],\n [4, 8, -2, 0, -2, -6, -12, -2, 10, 8, 6, 7],\n [4, 8, -5, -4, 3, 5, -2, -15, -12, -8, -9, -6],\n [3, 0, 6, -2, 2, -6, 10, -12, -4, -4, -4, 2],\n [2, 1, -2, 3, -10, -8, 8, -8, -4, -3, -12, 8],\n [-6, 12, -2, 0, -2, -4, 6, -9, -4, -12, 9, 10],\n [-3, 6, 6, 6, 8, 3, 7, -6, 2, 8, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1005882997515", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (11, 3) of the matrix A^7 where A is:\n[[4, -16, -1, -3, -7, 11, 2, -5, 1, -2, 2, 1],\n [11, 0, 4, 11, -1, 9, 2, -16, 12, 5, 15, 1],\n [-10, -9, -4, -11, -3, -16, 3, 2, 6, -10, 6, 8],\n [-10, 16, -5, 1, 16, -13, 9, 6, 11, 5, -9, -11],\n [-15, -5, 12, -6, 2, -14, 4, 9, 10, 12, -3, -16],\n [2, -11, -4, 2, -13, 7, 15, 5, 15, 0, -3, -4],\n [6, 4, 10, -11, -5, -7, 2, -5, -6, -5, -11, 9],\n [-5, -14, 8, -13, 6, -16, -13, 0, -8, 1, 0, 0],\n [2, 4, 14, 11, 5, -6, -10, 5, 4, -6, -10, -14],\n [1, -10, 13, 10, -15, 1, 4, 13, -7, 8, 2, -4],\n [8, -12, -13, 1, -5, 0, 4, -2, 0, 0, -3, 12],\n [16, -2, 0, -5, -12, -2, 3, -15, 9, -16, -12, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2180298494", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (5, 12) of the result:\nA =\n[[-15, 5, -10, 2, 4, 2, 0, -1, 2, -4, 2, 3],\n [5, -8, 2, -12, -2, -5, 0, 9, 4, -4, 5, 3],\n [-10, 2, -1, -6, -4, -1, 1, -9, -4, 10, 10, -3],\n [2, -12, -6, 7, 4, 9, 4, -2, 0, -1, 6, -8],\n [4, -2, -4, 4, -7, -2, -5, 2, -2, 8, 1, 8],\n [2, -5, -1, 9, -2, 0, -8, 4, -10, -1, 0, -3],\n [0, 0, 1, 4, -5, -8, 0, -10, -2, 4, -6, -8],\n [-1, 9, -9, -2, 2, 4, -10, 8, 5, -6, 5, 9],\n [2, 4, -4, 0, -2, -10, -2, 5, 15, 2, 0, -11],\n [-4, -4, 10, -1, 8, -1, 4, -6, 2, -14, 6, 1],\n [2, 5, 10, 6, 1, 0, -6, 5, 0, 6, -16, -8],\n [3, 3, -3, -8, 8, -3, -8, 9, -11, 1, -8, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123830509477", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[0, -1, 3, -6, 5, -4, -8, 0, 0, 2, 4, -6],\n [-1, 10, -9, -10, 12, 8, 2, 14, -2, -6, 13, 4],\n [3, -9, 2, -2, 10, -5, -10, -7, 8, 0, 14, 7],\n [-6, -10, -2, 15, 4, 2, -2, 0, 6, -9, 7, 10],\n [5, 12, 10, 4, -7, 6, -4, 4, 5, 5, 2, -7],\n [-4, 8, -5, 2, 6, -2, -2, 3, 3, 2, 11, -5],\n [-8, 2, -10, -2, -4, -2, -15, -4, 11, 4, 2, -5],\n [0, 14, -7, 0, 4, 3, -4, 8, 10, -4, -2, -4],\n [0, -2, 8, 6, 5, 3, 11, 10, 8, 0, -10, 7],\n [2, -6, 0, -9, 5, 2, 4, -4, 0, -1, 2, -2],\n [4, 13, 14, 7, 2, 11, 2, -2, -10, 2, 13, 2],\n [-6, 4, 7, 10, -7, -5, -5, -4, 7, -2, 2, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19558160474420", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[-7, 3, 10, 3, -4, 4, 4, 0, 14, -1, -2, 8],\n [3, 12, 7, 7, -6, -6, -2, -4, -6, 12, -2, 0],\n [10, 7, 14, 0, -14, 0, 4, -6, 9, 0, 0, 3],\n [3, 7, 0, -13, 0, -5, -2, 6, -11, 0, -4, -2],\n [-4, -6, -14, 0, 7, -12, -4, 10, 0, -14, 5, 5],\n [4, -6, 0, -5, -12, 15, 5, -9, -4, 0, 4, 0],\n [4, -2, 4, -2, -4, 5, -12, -6, 11, -1, -4, -2],\n [0, -4, -6, 6, 10, -9, -6, 4, -4, 0, -4, 12],\n [14, -6, 9, -11, 0, -4, 11, -4, -3, -7, -4, -6],\n [-1, 12, 0, 0, -14, 0, -1, 0, -7, 9, 4, -6],\n [-2, -2, 0, -4, 5, 4, -4, -4, -4, 4, 16, 6],\n [8, 0, 3, -2, 5, 0, -2, 12, -6, -6, 6, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215758357074583", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-12, 4, 3, -6, -6, -7, 5, 11, -6, -9, -10, -4],\n [4, -6, 0, 5, -5, 12, 1, -7, 12, 0, -10, -6],\n [3, 0, -2, -12, -2, -3, -5, -4, 1, -4, -5, -6],\n [-6, 5, -12, 10, -2, 1, -12, -8, -12, 10, -2, -1],\n [-6, -5, -2, -2, 4, 5, -1, 10, -8, -4, 10, -2],\n [-7, 12, -3, 1, 5, -14, -2, -3, -5, -6, 0, 0],\n [5, 1, -5, -12, -1, -2, -13, -9, 2, -4, -6, 12],\n [11, -7, -4, -8, 10, -3, -9, -7, 9, 8, 3, -2],\n [-6, 12, 1, -12, -8, -5, 2, 9, -10, 5, -6, 13],\n [-9, 0, -4, 10, -4, -6, -4, 8, 5, 5, -10, -13],\n [-10, -10, -5, -2, 10, 0, -6, 3, -6, -10, -9, -10],\n [-4, -6, -6, -1, -2, 0, 12, -2, 13, -13, -10, -11]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5607319908582137", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[15, -13, -7, 6, -12, -7, -3, -12, -12, -7, -3, 7],\n [11, 11, 3, -12, -12, -9, 13, 13, 16, 13, 16, 6],\n [10, -6, 3, -10, -11, 12, 16, -9, 7, 5, 5, 4],\n [4, -11, 8, 15, -8, 8, 8, -9, 12, -15, 3, 6],\n [14, 10, 4, -13, -1, -8, 14, 6, -5, -15, 12, 2],\n [-3, 6, -12, 11, 3, -7, -6, -5, -10, 7, -12, 6],\n [6, -9, -15, -15, -15, 14, -9, -9, 4, -2, 3, -12],\n [-4, -1, -14, -16, -11, 10, -16, 7, -4, 13, 5, -16],\n [12, 9, -9, 6, 6, -15, 1, 2, -4, 12, -15, -9],\n [3, -7, 7, 7, 10, 3, 2, 2, 2, -14, -16, 15],\n [13, 7, 6, -7, 9, -1, -16, -10, -4, 4, 3, 3],\n [-7, -16, 10, 16, -3, 2, 10, 7, -6, 14, -5, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91183487403", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[4, -14, 8, -11, 6, -9, -12, 2, 9, 1, -8, 15],\n [6, -1, -15, -10, -11, 9, -13, 13, 12, -16, 16, 9],\n [11, 12, -14, -4, -15, -8, -12, -15, 7, 8, -12, 15],\n [13, -3, 0, -7, 2, 3, -5, 9, -6, -7, -8, 10],\n [-7, 15, -12, 11, 11, -7, -7, -9, -2, -10, -6, 15],\n [12, -10, -4, 9, 8, -4, -4, -8, 13, 6, 8, 10],\n [-11, -9, 16, 6, -13, -4, 0, -5, -3, 15, -16, 16],\n [-7, -3, -7, -16, 7, -9, 1, -12, -2, -12, 5, 10],\n [8, -15, 6, 4, -12, 10, 1, 10, 11, -2, 8, 2],\n [0, 16, -16, 10, -7, -7, 15, 4, -9, -8, 1, -12],\n [5, -3, 15, 15, -5, -12, 11, 11, 12, 0, -3, -1],\n [4, 10, -3, -15, -10, 2, 5, 1, 12, 7, -9, -7]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1088056607015", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (7, 6) of the result:\nA =\n[[15, 8, 6, 5, 0, 6, -6, -6, -4, 12, 0, -10],\n [8, -8, 0, 10, -3, 7, 0, -2, -2, -4, -4, -14],\n [6, 0, 16, -10, 0, 8, -6, -2, 2, -3, -3, -1],\n [5, 10, -10, -7, -6, 8, -4, 14, 0, -9, -1, 12],\n [0, -3, 0, -6, -3, 6, 3, 6, -10, 12, -2, 12],\n [6, 7, 8, 8, 6, 5, 2, 10, -12, 0, 4, 4],\n [-6, 0, -6, -4, 3, 2, 1, -6, -13, 5, -7, 8],\n [-6, -2, -2, 14, 6, 10, -6, 16, -6, 6, -2, -8],\n [-4, -2, 2, 0, -10, -12, -13, -6, 8, -6, -3, 2],\n [12, -4, -3, -9, 12, 0, 5, 6, -6, 7, -4, 0],\n [0, -4, -3, -1, -2, 4, -7, -2, -3, -4, -11, 4],\n [-10, -14, -1, 12, 12, 4, 8, -8, 2, 0, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8689815565", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-13, -4, 9, -8, 4, -1, 9, 13, 9, 3, 6, 15],\n [13, 9, 7, -14, 7, 14, 5, 5, -8, 6, 6, 3],\n [10, 10, 12, -13, -2, -10, 3, -8, 12, -6, -15, 7],\n [-15, -5, 5, -12, -1, -10, -9, 3, 10, 0, 1, 0],\n [-5, 14, -14, -11, -9, -1, -1, 12, 3, -1, -7, 6],\n [16, 13, 2, -8, 16, 8, -13, 3, -10, -11, -10, -11],\n [-15, -6, 7, -11, 7, -15, -2, -10, 9, 16, -6, 6],\n [8, -5, 6, 16, 4, -8, -3, 10, -8, 10, -7, -13],\n [-15, 7, -7, 5, 2, -12, 12, 15, -1, -14, 16, -6],\n [-8, 11, 12, 12, -1, 12, 6, 6, -4, -2, 10, -11],\n [-16, -16, -14, -9, 14, 15, 10, -1, -1, 16, -1, -10],\n [12, 11, -1, -15, 12, -12, -4, -11, -9, -8, 0, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72278962956762", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-7, -10, 5, 0, -12, 0, 0, 0, -2, 1, -3, 6],\n [-10, 4, 10, 2, -2, -6, -10, 12, -1, 11, 6, 2],\n [5, 10, 15, -2, -2, 0, -5, 8, 0, 2, -4, 13],\n [0, 2, -2, -6, 8, -8, 8, -6, 2, -12, 8, -15],\n [-12, -2, -2, 8, 6, -4, -12, 9, -6, 2, 8, 10],\n [0, -6, 0, -8, -4, -4, -4, 13, 8, -9, -4, 4],\n [0, -10, -5, 8, -12, -4, -5, -4, 0, 0, -4, -10],\n [0, 12, 8, -6, 9, 13, -4, -13, 4, -4, 6, -14],\n [-2, -1, 0, 2, -6, 8, 0, 4, 4, 10, 2, 0],\n [1, 11, 2, -12, 2, -9, 0, -4, 10, 6, -2, 6],\n [-3, 6, -4, 8, 8, -4, -4, 6, 2, -2, 11, -11],\n [6, 2, 13, -15, 10, 4, -10, -14, 0, 6, -11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10634963002795", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-16, 6, 4, -6, 6, -4, -5, -16, 3, -4, 4, -2],\n [6, -5, -14, 14, -4, 9, -1, 6, 6, 5, -1, 2],\n [4, -14, -1, -3, -2, -11, -8, 2, -5, 1, 8, 12],\n [-6, 14, -3, -12, 5, 2, 0, -4, 4, -13, 2, -6],\n [6, -4, -2, 5, -11, 10, 10, -16, -8, 4, -4, 2],\n [-4, 9, -11, 2, 10, -14, -3, 0, -7, -6, -1, -6],\n [-5, -1, -8, 0, 10, -3, 14, 4, 10, -8, 7, 1],\n [-16, 6, 2, -4, -16, 0, 4, 15, 8, 4, -8, -9],\n [3, 6, -5, 4, -8, -7, 10, 8, -10, 4, -6, 2],\n [-4, 5, 1, -13, 4, -6, -8, 4, 4, -1, -10, -12],\n [4, -1, 8, 2, -4, -1, 7, -8, -6, -10, -5, -7],\n [-2, 2, 12, -6, 2, -6, 1, -9, 2, -12, -7, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15769813311094596", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 5, 12, 13, -14, -10, 12, -11, -7, 14, -9, -11],\n [-10, -11, 2, 10, -15, 5, 16, -5, 12, -8, 6, 9],\n [11, -9, -6, -6, 14, -4, -1, -6, 16, 1, 14, 14],\n [-6, -10, 13, 1, 2, 0, 9, 3, -14, -8, 5, 2],\n [-13, -14, 9, -15, 2, 5, -11, 15, -12, 1, 3, -1],\n [-3, 7, -9, 5, -11, -15, -16, -2, 12, -9, -5, 9],\n [1, -9, -8, 15, -7, 7, -9, 8, 9, -5, 9, 7],\n [-1, -11, 1, -4, 5, -10, 1, 4, 10, -9, 15, -12],\n [-3, -15, 7, -4, 5, -6, 2, 13, -13, 11, -6, -13],\n [-1, 9, 11, 14, -10, -1, 10, -4, 5, 6, 2, -11],\n [-5, -6, -5, -9, -6, -7, 12, -2, -16, -11, 12, 10],\n [-4, 1, -3, 4, 15, 14, 12, 7, 12, -7, -14, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2045057723909937", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 8) of the matrix A^9 where A is:\n[[5, 3, -12, 10, -2, 7, -2, 6, 0, -7, -6, -6],\n [3, 7, 10, -2, -6, -4, 4, 7, 3, 12, 3, 4],\n [-12, 10, -7, 0, -2, 0, 11, 0, -14, 2, 4, 8],\n [10, -2, 0, 9, -6, 4, -2, -10, -14, 6, -14, -4],\n [-2, -6, -2, -6, 10, -3, -2, -4, 6, 1, 4, -4],\n [7, -4, 0, 4, -3, -12, 10, -7, 8, -3, -2, -6],\n [-2, 4, 11, -2, -2, 10, -6, -6, 2, -10, 6, -10],\n [6, 7, 0, -10, -4, -7, -6, -16, -2, 10, 8, -1],\n [0, 3, -14, -14, 6, 8, 2, -2, -15, -12, -12, 14],\n [-7, 12, 2, 6, 1, -3, -10, 10, -12, -4, -7, -3],\n [-6, 3, 4, -14, 4, -2, 6, 8, -12, -7, -6, 1],\n [-6, 4, 8, -4, -4, -6, -10, -1, 14, -3, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13990644634142", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (10, 1) of the result:\nA =\n[[-5, 4, 9, 2, 10, 3, 8, -6, 11, -2, -4, -2],\n [4, -12, 2, -9, 2, 2, -2, 6, -6, -6, 6, 2],\n [9, 2, -9, 4, 2, 2, 12, 4, 2, 13, -12, -6],\n [2, -9, 4, 4, 1, -2, 4, -8, 4, -10, 8, -2],\n [10, 2, 2, 1, -6, 2, 2, 8, 4, 2, 2, 2],\n [3, 2, 2, -2, 2, -4, -6, 0, 7, 2, 1, -2],\n [8, -2, 12, 4, 2, -6, -11, -10, -6, 0, -10, -10],\n [-6, 6, 4, -8, 8, 0, -10, -8, 0, 14, 7, 10],\n [11, -6, 2, 4, 4, 7, -6, 0, -14, -16, -4, -2],\n [-2, -6, 13, -10, 2, 2, 0, 14, -16, 4, -6, -8],\n [-4, 6, -12, 8, 2, 1, -10, 7, -4, -6, -4, -12],\n [-2, 2, -6, -2, 2, -2, -10, 10, -2, -8, -12, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17294165803", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[4, 1, 10, -5, -9, -10, -14, -9, 13, 11, -13, -14],\n [2, 2, 4, -12, 14, 8, 12, 0, 4, -15, -5, -14],\n [12, 10, -2, -5, -13, -1, -7, 1, 0, -10, -14, 4],\n [-10, 6, -13, 6, 13, -6, 8, -6, -7, -13, -11, 15],\n [-13, -8, -7, 11, -4, 15, 0, 1, -10, -3, 15, -7],\n [10, -11, -16, 16, -7, 1, -1, -6, 2, 11, -16, 7],\n [14, 14, -6, -4, -13, 8, 0, -11, 7, 10, -8, -2],\n [1, 8, -3, -10, 12, -15, -13, -9, -9, 6, 11, -13],\n [7, -9, -16, -1, 14, 7, 9, -5, 1, -2, 9, -7],\n [7, 4, -10, -11, 16, 4, 4, -8, 13, 11, 4, -7],\n [-10, 6, 8, -2, 10, -14, 1, -8, -12, 8, -2, -2],\n [-1, 7, -3, 14, 14, 4, 5, 4, 16, 16, 14, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1306243506057914", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[13, -1, -6, 9, -5, -13, 6, 16, 6, 15, 2, 3],\n [-10, 15, -10, -11, 15, -8, 9, 10, 1, 7, 7, 3],\n [-1, 2, -8, 0, -7, -14, 1, -6, 10, -13, -15, -7],\n [3, 14, 0, 10, -12, 1, 3, -12, 2, -8, 1, -14],\n [11, -14, -4, -5, -12, -1, 2, -8, 10, -7, 8, -5],\n [-8, 10, 9, 16, 11, 0, 2, 8, 6, 2, -1, 8],\n [0, -4, -8, 11, 14, -10, -10, -8, 2, -5, 10, 9],\n [5, 4, -10, -10, 14, -3, 15, 9, -9, -3, -2, 0],\n [1, 9, -1, -12, 1, 15, -2, 9, -14, -16, 0, -7],\n [-2, -14, 0, -12, 13, 3, 0, -7, -12, -11, 10, 6],\n [14, 0, -11, -16, -5, -12, -14, -14, -13, -12, 6, -8],\n [-1, 14, 3, 15, 12, -7, 9, -11, -7, 1, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "925140863986", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -3, 5, 8, 16, -16, -11, 3, -11, 10, -6, 7],\n [3, 6, -12, 14, -14, 14, 12, 14, -4, 6, -6, 8],\n [13, 0, 4, -15, -1, 5, 0, -15, 8, 9, 14, 16],\n [1, 7, -3, 7, -12, 9, -15, -5, 12, 15, 13, -1],\n [-15, 1, -8, -16, 5, 4, 1, 10, 0, -7, 14, 9],\n [-13, -1, -6, -16, -2, 15, -7, -11, 6, 9, -12, 7],\n [-4, -3, 2, -15, 9, 14, 14, 3, 10, 2, 11, -3],\n [-11, -5, -10, -1, 2, 14, -9, -7, 0, 13, 3, 10],\n [11, -15, 7, 14, -15, 11, 15, -10, -7, -13, 2, -4],\n [14, 14, 6, 14, -1, 5, -8, 4, -16, -2, -10, 10],\n [16, 1, -11, 7, 9, -9, -10, 13, 4, -5, -2, 3],\n [-5, -11, 11, 8, -12, 7, 12, 12, -5, -9, -15, 14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84429414640572", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (7, 7) of the 9th power of the matrix:\n[[-15, 0, 4, -5, -14, -14, 8, 7, 14, -14, -7, 11],\n [16, 5, 0, -13, 1, 5, -12, -1, -5, -12, -14, 15],\n [-16, -15, -9, -14, 7, 7, 6, 5, -15, -4, -8, 6],\n [8, 5, 3, 0, 11, -2, -3, -8, -11, 5, -16, 15],\n [8, 10, -2, 16, 14, -12, 16, -2, 12, -3, 3, 12],\n [-10, -14, -7, 6, 8, 15, -1, -5, 2, -9, -15, -11],\n [9, 12, -13, 10, -13, 16, 12, 8, 9, -8, 10, 16],\n [-10, 15, 0, -15, -15, 11, 2, 6, -13, 9, -2, -8],\n [16, -4, -10, -10, 0, 9, -13, -1, 15, 7, 3, -9],\n [-14, -9, -3, 3, 4, -14, -8, 9, 2, 0, 15, -14],\n [7, -5, -1, -4, 8, 13, -4, 15, -13, -12, 10, -7],\n [3, -13, -7, -16, -14, 4, -6, 8, -11, 3, 3, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25939097206363", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[12, -15, -13, 0, 4, -14, 9, 4, 3, 11, -10, 6],\n [0, 14, -9, -9, -4, 6, -2, 8, 4, 11, -10, 8],\n [-7, 10, 1, 13, 14, -2, -2, -13, -11, 5, -13, 6],\n [14, 9, -6, 4, -3, 10, -7, -9, -13, -10, 12, 8],\n [-16, -1, -14, 16, -10, -2, -9, 8, -16, -7, -1, -5],\n [8, 6, -3, -9, -9, 9, -15, -8, 3, 6, -3, 11],\n [14, 11, -15, -14, 14, -1, 12, -10, -6, 1, 9, -4],\n [-15, 16, 11, 5, 6, 6, 14, 6, -9, 14, 0, 6],\n [8, 11, -2, 4, -11, -9, 16, 4, 4, -7, -13, -8],\n [13, 11, 13, 6, 7, -7, 2, 16, 8, 4, 3, -1],\n [-15, -6, -10, 3, -10, -6, 10, 16, -9, -9, -16, 15],\n [14, -14, 4, -12, -3, 7, 15, -1, -4, 7, -8, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41403314799319", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^8 where A is:\n[[8, -2, 13, -4, 4, -2, -16, -1, 12, 6, 2, 10],\n [-10, -5, -7, 5, 16, -5, 11, 4, -2, 15, -11, 16],\n [2, 13, 10, 9, 6, 11, -13, -6, 4, -8, -5, -16],\n [-5, 6, -11, 15, 11, -7, -1, 3, 5, 7, 13, -3],\n [9, -9, 9, 5, -5, -8, 13, 1, 3, -5, 13, -14],\n [-9, 11, -16, 0, -2, 0, -5, 2, 8, -14, 7, -14],\n [-5, -9, 15, 5, -3, -1, 6, -3, -1, 1, 8, -3],\n [-14, -15, 5, 8, 9, -9, 10, 8, 12, 2, -11, -16],\n [16, 13, -1, 1, -2, 12, -1, -1, 4, 7, -2, -2],\n [-2, 4, -16, 8, 8, 1, -13, 6, 8, 13, 14, 5],\n [-3, 11, 0, -5, 16, -14, 13, 8, -8, -15, -3, 7],\n [12, 6, -4, 9, 5, 6, 14, 13, 9, -12, -11, -16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19962601338703", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the value at position (11, 1) of the result:\nA =\n[[3, 10, 16, 4, -6, -16, -3, 2, -14, -2, 12, -16],\n [1, 13, -7, 10, -14, -1, -7, -9, 11, 12, -4, 9],\n [-13, 1, 5, -6, -8, 1, 5, -7, 11, 6, -14, -10],\n [-9, 15, -16, 8, 9, -4, 11, -6, -5, 11, 8, 12],\n [-16, 6, 8, 0, -10, 13, -11, 14, -9, 12, 8, -8],\n [14, 12, -1, -9, -12, 1, -14, -12, -9, -5, 1, 10],\n [-10, 2, 1, -9, 12, 1, -12, -12, 8, -16, -6, -3],\n [-8, -12, 7, -11, 0, -6, 13, -5, -2, -3, -9, -4],\n [11, 3, 9, 6, -2, 11, -16, 1, -8, -15, -4, -3],\n [-8, 9, 15, -14, 1, 4, 14, 7, -12, 15, 4, 10],\n [16, -14, 2, -16, -13, 10, 6, -13, 3, -5, 14, -8],\n [-4, 16, 13, 5, -10, 0, -8, -13, 11, 15, 1, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126529288970", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-15, -2, 14, 6, -5, 4, 0, -3, 4, -12, 2, -4],\n [-2, -8, -4, 0, -4, -2, -1, 2, 3, 0, 10, -8],\n [14, -4, 1, 6, 9, 4, 0, 6, 9, -3, 2, 0],\n [6, 0, 6, 4, 0, 1, 8, -10, 11, -8, -5, -8],\n [-5, -4, 9, 0, -1, -1, -6, -7, -10, 10, 0, -6],\n [4, -2, 4, 1, -1, 15, 0, 12, 0, -7, -4, -8],\n [0, -1, 0, 8, -6, 0, -10, -8, -10, -2, -13, 3],\n [-3, 2, 6, -10, -7, 12, -8, 15, 0, 7, 11, 0],\n [4, 3, 9, 11, -10, 0, -10, 0, 4, 3, -2, 0],\n [-12, 0, -3, -8, 10, -7, -2, 7, 3, -11, -6, 3],\n [2, 10, 2, -5, 0, -4, -13, 11, -2, -6, -6, 2],\n [-4, -8, 0, -8, -6, -8, 3, 0, 0, 3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6519509569247", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (11, 5) of the 9th power of the matrix:\n[[12, -15, 16, 15, -16, -15, 13, 10, 1, -13, -1, 15],\n [5, 14, -2, 7, -8, -14, -14, -15, 14, 10, 0, -7],\n [8, -6, 12, -6, 14, 11, -4, 16, -3, 14, 10, 14],\n [-5, 14, -15, -14, 14, 11, 15, -1, 0, 2, 11, 15],\n [-14, 16, 3, 8, 9, 10, 1, 9, -3, -10, 0, -7],\n [-7, -6, -1, -11, 11, 8, 8, -16, -6, 13, -16, 12],\n [12, -8, 2, 5, -1, 5, -15, 3, -12, 11, 3, 10],\n [-1, 4, 14, 11, -6, 16, -10, -13, -4, 16, 4, -8],\n [8, -6, 6, 12, 8, 8, -4, -11, -10, 3, -11, -10],\n [-14, 16, 0, -12, -9, 4, 3, -3, -3, 2, -11, 13],\n [-14, -14, -14, 12, 4, 4, -14, 0, 5, -7, -9, -5],\n [-5, -3, 0, 0, 13, -4, -11, 2, 9, -4, 13, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37164185256627", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-12, -6, -2, 2, -3, 7, -5, -5, 4, -4, -5, -2],\n [-6, -1, -2, -4, 2, 6, 6, -2, -2, 12, 7, 0],\n [-2, -2, 0, -4, -10, -4, 8, -6, 10, 4, 0, 2],\n [2, -4, -4, 16, 3, 6, 4, -8, 14, 1, 5, 14],\n [-3, 2, -10, 3, 8, 4, -2, 0, -2, 8, 2, -7],\n [7, 6, -4, 6, 4, 12, -5, -7, -14, 10, 3, -12],\n [-5, 6, 8, 4, -2, -5, 3, 14, -8, 2, -1, 2],\n [-5, -2, -6, -8, 0, -7, 14, -2, 4, 0, -6, 4],\n [4, -2, 10, 14, -2, -14, -8, 4, 6, 6, -13, 0],\n [-4, 12, 4, 1, 8, 10, 2, 0, 6, -4, 11, 4],\n [-5, 7, 0, 5, 2, 3, -1, -6, -13, 11, -2, -14],\n [-2, 0, 2, 14, -7, -12, 2, 4, 0, 4, -14, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191407761809982", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[5, -10, -12, -7, -16, -9, 5, 5, -2, 13, 1, -11],\n [-5, -15, -11, 5, -13, -2, 16, 13, 1, -3, 3, 4],\n [11, 0, 1, 9, 13, -14, 15, -2, -12, 9, 15, 7],\n [4, -8, 9, 6, 9, 12, -5, 4, -13, -11, 2, -12],\n [12, 2, -9, -10, -4, 11, 13, 2, -2, -12, -12, -4],\n [-5, -16, 16, 4, -13, -16, 7, 4, 1, -14, 12, -15],\n [7, -11, 9, 6, 3, 12, 15, 3, -9, 7, -10, 9],\n [1, -5, 7, -9, -8, -8, 2, -1, -16, 3, 11, 11],\n [4, -6, 7, -5, 9, -8, -13, -13, -2, -7, 11, -7],\n [-1, -3, -13, -9, 6, -1, 10, 7, 5, 10, 7, -6],\n [-1, 11, -6, 3, 16, -10, -7, 4, -14, -12, -16, -5],\n [14, 9, -1, 7, -12, -16, 4, -7, -9, 3, 13, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57290378249358", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[11, 9, 6, 0, -4, -12, -10, 4, 2, 0, -14, 0],\n [9, -14, 1, -4, 2, 6, 2, 0, 0, -1, 0, -6],\n [6, 1, -5, 12, -11, 2, -14, 0, 4, 4, -6, 4],\n [0, -4, 12, -1, -5, 8, 1, 14, -4, -2, -11, 0],\n [-4, 2, -11, -5, -12, 8, 0, 10, -7, 10, -3, -7],\n [-12, 6, 2, 8, 8, 12, 8, -4, 6, -2, -7, 0],\n [-10, 2, -14, 1, 0, 8, 6, 0, -2, 10, 8, -10],\n [4, 0, 0, 14, 10, -4, 0, 13, 2, 14, -11, -2],\n [2, 0, 4, -4, -7, 6, -2, 2, 12, 3, 4, 0],\n [0, -1, 4, -2, 10, -2, 10, 14, 3, 5, -4, -10],\n [-14, 0, -6, -11, -3, -7, 8, -11, 4, -4, -7, 2],\n [0, -6, 4, 0, -7, 0, -10, -2, 0, -10, 2, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3367754334588817", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[-10, -2, -5, 8, 1, -10, -14, 1, 12, -4, -4, -12],\n [6, -11, 8, -3, 11, 2, -3, -2, 4, -2, 9, 0],\n [1, 12, 12, 2, 14, -7, -1, -11, 11, -13, 4, -16],\n [-1, 15, -12, -1, 15, -11, 12, -14, 3, -12, -3, -6],\n [-14, 8, 0, -5, 8, -15, 11, 4, -13, -13, 2, -5],\n [10, -1, -4, -4, -4, 12, 2, -7, 1, -9, -9, -3],\n [10, 5, -13, 9, -3, -9, 11, 16, 5, -3, -8, 7],\n [15, -6, -2, -11, 1, -9, 8, -6, 12, 10, -12, -8],\n [6, -4, 4, -8, -15, 8, -16, -9, 15, 15, 4, 5],\n [-15, -7, -16, -7, -9, -13, 9, 12, -9, 2, -9, -5],\n [1, -4, -15, 2, 6, -3, 15, 7, -8, -7, -5, -3],\n [4, 6, -16, 0, 16, -2, -14, 7, 0, -6, 9, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46390614312452", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 9) of the matrix A^8 where A is:\n[[-5, 2, -5, -2, 7, -6, 2, -10, -6, 15, -4, -8],\n [2, -12, -3, 0, 2, 6, 6, 4, 3, 10, 4, -6],\n [-5, -3, -4, -4, -5, 2, 8, -6, 3, 0, -4, 2],\n [-2, 0, -4, 14, -2, 0, 0, 8, 0, -12, -4, 2],\n [7, 2, -5, -2, -14, -2, -5, 4, -12, 4, 0, -5],\n [-6, 6, 2, 0, -2, 8, 10, -4, -2, -1, 10, -14],\n [2, 6, 8, 0, -5, 10, -7, 2, 7, 0, -3, -6],\n [-10, 4, -6, 8, 4, -4, 2, 16, -2, 14, 8, 0],\n [-6, 3, 3, 0, -12, -2, 7, -2, -8, -6, -10, 5],\n [15, 10, 0, -12, 4, -1, 0, 14, -6, 0, -10, -10],\n [-4, 4, -4, -4, 0, 10, -3, 8, -10, -10, -6, 11],\n [-8, -6, 2, 2, -5, -14, -6, 0, 5, -10, 11, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84276334922", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-9, 12, 16, 8, -15, -12, -3, -3, 2, -1, 1, -15],\n [-14, -10, -5, -1, 1, 15, -7, 16, -1, 6, 13, -9],\n [-16, -8, 16, -1, -13, -10, 13, -14, -10, 9, 7, -1],\n [-9, 14, 4, -6, 13, 13, -6, -5, 9, 11, -8, -7],\n [-2, 15, -5, 0, -8, 1, 12, -10, 8, -4, -5, 5],\n [-2, -10, -11, -11, 2, 16, -12, 16, 4, -2, 10, 13],\n [-12, 6, 4, -16, -8, 15, -11, 6, -1, 0, -3, -2],\n [-13, 9, -11, 9, 15, 2, 6, -7, -3, -7, 12, -8],\n [5, -13, 8, 0, -12, 0, -3, -8, 8, 11, -16, -11],\n [-13, 1, -1, -12, -13, -6, -1, 6, -13, 4, 9, 10],\n [-5, 3, 7, 2, 1, -11, -2, 8, 16, 10, -8, 16],\n [0, -14, 13, -1, 4, -8, -11, 13, 7, -7, 15, 9]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27480533700", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (12, 7) of the result:\nA =\n[[11, -12, -14, -10, 5, 13, 11, 7, 8, 10, -9, 15],\n [-3, -15, 7, -14, -16, 11, 9, 8, 10, -7, 7, 15],\n [-6, -16, -15, -2, -9, -4, 9, 7, -16, -12, 2, -5],\n [-8, -15, -9, -7, 12, 6, 10, -1, 15, -4, -11, 6],\n [7, -6, 13, -2, 0, 13, 5, -2, -14, 4, -8, -2],\n [5, 16, 4, 5, -10, 10, -12, 7, -15, 5, -11, 9],\n [-14, -13, -4, 2, -9, -7, 4, 2, -6, -8, 3, -7],\n [-16, 12, 14, 9, 3, -11, 14, -5, 0, 7, -11, 2],\n [-14, 0, 2, -13, -4, -8, 13, -13, 7, -2, -8, 3],\n [14, 15, -10, -12, -15, -8, 9, 0, 15, 13, -12, 3],\n [-11, -9, 15, -5, 9, 3, -4, 7, -9, -1, 4, 5],\n [14, 4, -6, 4, 7, 0, -12, -6, -9, -11, -8, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9535319534063", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-11, -4, -2, 0, 6, 2, -7, 2, 0, -6, 2, -12],\n [-4, 8, 3, 6, -1, -9, 3, -5, -5, 6, 8, 4],\n [-2, 3, 8, 4, -4, -12, -8, -4, 4, 4, 8, -7],\n [0, 6, 4, -8, 5, 6, 10, 10, -12, -7, -6, -10],\n [6, -1, -4, 5, -13, 2, 8, 0, 12, -7, -2, 2],\n [2, -9, -12, 6, 2, 8, -1, 2, 5, -2, 4, -10],\n [-7, 3, -8, 10, 8, -1, 8, 2, 1, -10, 6, -8],\n [2, -5, -4, 10, 0, 2, 2, 11, -4, 2, 4, 2],\n [0, -5, 4, -12, 12, 5, 1, -4, 11, 8, 0, -9],\n [-6, 6, 4, -7, -7, -2, -10, 2, 8, -7, 6, 11],\n [2, 8, 8, -6, -2, 4, 6, 4, 0, 6, 0, 11],\n [-12, 4, -7, -10, 2, -10, -8, 2, -9, 11, 11, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-181509326851584", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[8, 1, 4, 8, -5, 14, -5, 14, -14, 10, 4, 4],\n [-16, 12, -2, 13, -12, 6, -15, -13, -15, 9, 16, 11],\n [-14, 13, -8, 3, 0, 3, -3, -3, -14, -7, -14, -3],\n [-8, 16, 16, -1, -10, 3, 11, 13, 9, 9, -7, 1],\n [11, -9, -13, -2, 4, -2, -5, -12, -14, -10, -7, -15],\n [-6, 4, -14, 6, -5, 16, -13, -11, 5, -8, 15, -16],\n [-12, 3, 13, -16, 10, -2, -15, -8, 15, -12, -8, -9],\n [-14, -14, -14, 16, 2, 15, 13, -2, 13, -9, -13, -14],\n [12, 5, 7, -10, -5, -14, -4, 15, -8, 13, 14, -11],\n [-5, 6, -1, -1, 4, -3, -11, -9, -16, 3, 9, -9],\n [-11, -11, 10, 0, 12, 4, -13, -15, 3, -16, -8, 14],\n [-13, -13, -10, 7, -2, 0, 14, -8, 11, -12, 16, 14]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706763022709", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-14, -14, -16, -4, -8, -12, -10, -10, -15, -16, -15, 13],\n [8, 0, -12, -12, 6, 0, 0, -12, 10, -1, -15, -12],\n [-6, -15, 14, -16, -1, 16, 1, 11, 6, 16, -6, -13],\n [-2, 2, 11, 11, -6, -10, 1, -2, 1, -7, 11, -5],\n [-1, 13, -14, 1, -6, -14, -9, -15, 0, -16, -2, -7],\n [0, -14, 11, 0, -13, 2, -2, 8, -1, 13, 6, -3],\n [-4, 12, 7, 8, 1, -13, 13, -5, 11, 4, 9, 5],\n [1, 13, -8, 4, 12, 3, -16, 15, 0, 4, 9, 16],\n [11, 11, -3, 16, 10, 15, 3, -5, -12, 13, 10, 5],\n [-8, 13, 13, 14, -11, -14, -4, -8, -11, 15, 14, 5],\n [14, 8, 14, 1, 4, 15, -15, 5, 13, 0, -1, 14],\n [-7, 2, -14, -5, 2, 10, 6, -15, 15, -16, 12, -12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3009157684476989", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (11, 10) of the result:\nA =\n[[-10, -4, 0, -3, -10, 8, 10, 4, 6, -2, 2, -8],\n [-4, -9, 0, -8, 8, 2, 0, 8, 0, 0, 6, -10],\n [0, 0, -11, -12, -4, 11, 10, -1, 0, -12, 2, 4],\n [-3, -8, -12, 13, 8, 2, -8, 3, -6, 2, 11, -10],\n [-10, 8, -4, 8, -9, 0, 8, 3, -2, -13, -3, 10],\n [8, 2, 11, 2, 0, 13, -6, -12, -6, -8, -13, -6],\n [10, 0, 10, -8, 8, -6, 11, 2, 2, -4, 2, -2],\n [4, 8, -1, 3, 3, -12, 2, 12, -9, -3, 4, 1],\n [6, 0, 0, -6, -2, -6, 2, -9, -7, 5, 8, 3],\n [-2, 0, -12, 2, -13, -8, -4, -3, 5, -14, 4, -8],\n [2, 6, 2, 11, -3, -13, 2, 4, 8, 4, -14, -2],\n [-8, -10, 4, -10, 10, -6, -2, 1, 3, -8, -2, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8340515343", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (10, 9) of the 8th power of the matrix:\n[[2, -2, -2, 0, -4, 2, 2, 1, -4, 0, -4, 4],\n [-2, -10, -2, 1, -9, 0, 2, -4, -3, 0, -7, 2],\n [-2, -2, -10, -15, 10, 0, 1, -4, -10, 0, -11, -12],\n [0, 1, -15, 11, 4, 10, 5, 0, 4, -1, 2, 2],\n [-4, -9, 10, 4, 1, 4, -4, 11, 16, -4, -4, 0],\n [2, 0, 0, 10, 4, 11, 10, 7, 5, -8, 8, -5],\n [2, 2, 1, 5, -4, 10, -6, 2, -6, -9, 4, 8],\n [1, -4, -4, 0, 11, 7, 2, -14, -10, 6, -10, -2],\n [-4, -3, -10, 4, 16, 5, -6, -10, -2, -12, -2, 8],\n [0, 0, 0, -1, -4, -8, -9, 6, -12, 9, 10, 4],\n [-4, -7, -11, 2, -4, 8, 4, -10, -2, 10, -1, 12],\n [4, 2, -12, 2, 0, -5, 8, -2, 8, 4, 12, -16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-827001281408", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-1, -8, -2, 2, -2, 3, 15, -14, 12, 1, -4, 8],\n [-8, 4, -7, 2, 3, -9, 2, 2, -4, -6, -8, -12],\n [-2, -7, 11, -4, 8, -7, 0, -8, 12, 4, -7, -6],\n [2, 2, -4, 4, 5, 2, -8, 5, 8, -8, -10, -6],\n [-2, 3, 8, 5, 16, 4, -6, -6, -2, 4, 6, 3],\n [3, -9, -7, 2, 4, 12, -4, -6, -4, 10, -4, -2],\n [15, 2, 0, -8, -6, -4, 15, 3, -4, -2, 12, -9],\n [-14, 2, -8, 5, -6, -6, 3, 9, 8, 2, 4, -2],\n [12, -4, 12, 8, -2, -4, -4, 8, -15, 0, 10, -4],\n [1, -6, 4, -8, 4, 10, -2, 2, 0, 2, -1, -14],\n [-4, -8, -7, -10, 6, -4, 12, 4, 10, -1, -15, -2],\n [8, -12, -6, -6, 3, -2, -9, -2, -4, -14, -2, -6]], determine the value at position (12, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16094781474", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-11, 0, 2, -10, -6, 10, 7, -3, -7, 12, -12, 4],\n [0, -9, -4, -3, 10, 5, -1, 10, 8, 8, -9, -1],\n [2, -4, 0, -8, 8, -4, 12, -2, -2, 0, 2, -2],\n [-10, -3, -8, 9, -8, -2, 11, 0, -5, 0, 0, 8],\n [-6, 10, 8, -8, 16, -12, -14, 0, 6, 7, -2, -11],\n [10, 5, -4, -2, -12, -8, 0, 8, -7, -4, -10, 2],\n [7, -1, 12, 11, -14, 0, 10, 10, -6, 2, -6, -3],\n [-3, 10, -2, 0, 0, 8, 10, 16, 10, -4, -2, 2],\n [-7, 8, -2, -5, 6, -7, -6, 10, -4, 8, -2, 4],\n [12, 8, 0, 0, 7, -4, 2, -4, 8, -6, 4, -6],\n [-12, -9, 2, 0, -2, -10, -6, -2, -2, 4, -13, 0],\n [4, -1, -2, 8, -11, 2, -3, 2, 4, -6, 0, -13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-117551302849866", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-6, -13, -1, 0, 15, 4, -16, 3, 6, -9, -3, -8],\n [-7, -8, 4, -1, 6, 12, 2, 14, 14, 0, 9, 0],\n [-6, -4, -14, 1, 12, 11, 9, 9, 12, -12, 12, 8],\n [15, 2, 8, 14, 8, -7, 4, -9, -11, -10, 13, 7],\n [-9, -9, 14, -13, -15, 5, 4, 15, -12, -16, 14, 9],\n [9, 6, 0, 2, -14, -12, 12, 8, 11, 12, -8, -7],\n [-1, 14, -2, 2, 3, 0, 2, 13, 1, 12, 8, -8],\n [16, -13, 8, -8, -15, 8, -3, 2, 8, -15, -7, -14],\n [10, 13, 1, 10, 2, 0, -13, 4, -6, -1, 1, 0],\n [-3, -3, -15, -1, 11, -5, 12, -8, 2, -13, -7, -8],\n [12, 9, 11, 7, 14, -11, -4, 12, 13, -3, 5, 11],\n [-2, -11, -3, 11, 13, 13, -16, -9, 6, -4, 7, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1791805903183", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (12, 4) of the matrix A^8 where A is:\n[[-16, -2, 8, -2, -10, 6, 8, -1, 3, -9, 6, -5],\n [-2, -15, -3, 0, -1, -12, 0, -1, 13, -8, 4, 8],\n [8, -3, 2, 6, -2, -14, -1, -8, 8, -9, 2, -6],\n [-2, 0, 6, 4, -8, -3, 6, -4, 14, -6, 6, 6],\n [-10, -1, -2, -8, -2, -4, 3, 0, -6, -2, -6, 0],\n [6, -12, -14, -3, -4, 11, 2, -1, -2, 4, -14, 16],\n [8, 0, -1, 6, 3, 2, 6, -4, 1, 14, 1, -1],\n [-1, -1, -8, -4, 0, -1, -4, -5, -4, 10, -12, 4],\n [3, 13, 8, 14, -6, -2, 1, -4, -5, 8, -8, 15],\n [-9, -8, -9, -6, -2, 4, 14, 10, 8, 15, -2, -2],\n [6, 4, 2, 6, -6, -14, 1, -12, -8, -2, 14, -5],\n [-5, 8, -6, 6, 0, 16, -1, 4, 15, -2, -5, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-787231642402", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-15, 2, -9, 1, -14, -6, 1, -5, 1, -10, 5, 2],\n [2, 4, 12, -5, -7, 8, 6, -10, 4, -8, -4, -3],\n [-9, 12, 4, 12, 0, 2, -5, 5, 12, 12, -2, -8],\n [1, -5, 12, -12, 10, 8, -2, -3, 8, -4, -6, -3],\n [-14, -7, 0, 10, 8, -8, -6, 6, -10, -6, -8, -3],\n [-6, 8, 2, 8, -8, -12, 0, 13, 6, 0, -6, 1],\n [1, 6, -5, -2, -6, 0, -7, -6, 4, 3, 4, 5],\n [-5, -10, 5, -3, 6, 13, -6, 6, 4, -7, -8, -12],\n [1, 4, 12, 8, -10, 6, 4, 4, 15, -8, 5, -6],\n [-10, -8, 12, -4, -6, 0, 3, -7, -8, 11, -10, 8],\n [5, -4, -2, -6, -8, -6, 4, -8, 5, -10, -1, -4],\n [2, -3, -8, -3, -3, 1, 5, -12, -6, 8, -4, 7]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105412307185648", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[-10, -8, -16, -11, -5, 11, 11, 9, 1, 10, -7, -1],\n [-9, -10, -4, -6, -12, 12, 6, 4, 0, -4, -12, 14],\n [0, 7, 0, -1, 9, 4, -6, 7, 14, -13, -11, 6],\n [1, 0, 15, 5, -6, -6, 3, -7, 11, 15, -10, -14],\n [7, -10, -12, -7, 4, 0, -3, 13, -11, 10, -13, 9],\n [-16, -9, 10, -13, -8, 2, -13, 10, -9, 12, 15, -7],\n [2, 1, 9, 13, 12, 5, -5, 6, -8, -6, 4, -6],\n [14, 15, -1, -5, -7, -11, 3, -6, -15, 2, 9, -15],\n [1, 13, 4, -4, 10, -15, 12, 10, 5, 14, -1, 1],\n [-16, -14, -14, -8, -5, 7, -14, 10, -12, 9, -1, -4],\n [-10, 10, 9, -14, -6, -12, -5, 8, 14, -1, 3, 14],\n [1, -1, -12, 6, 15, 2, 6, -12, 13, -13, -14, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1776030504036", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 11) of the 9th power of the matrix:\n[[-4, 1, 4, 1, 2, 0, 2, 16, -8, 10, -6, 8],\n [1, 11, 6, -6, 2, 1, -2, 1, 2, 10, 0, -3],\n [4, 6, 11, -8, 12, -10, 8, -4, 6, 0, 3, 10],\n [1, -6, -8, -5, 0, 10, -6, -8, 1, 13, -2, -3],\n [2, 2, 12, 0, 6, 0, -8, 6, -3, 2, 12, 0],\n [0, 1, -10, 10, 0, 15, 0, 10, -7, 2, 1, -5],\n [2, -2, 8, -6, -8, 0, 9, 3, 6, 6, -6, -5],\n [16, 1, -4, -8, 6, 10, 3, -7, 12, 0, -2, 4],\n [-8, 2, 6, 1, -3, -7, 6, 12, -13, 10, -4, 4],\n [10, 10, 0, 13, 2, 2, 6, 0, 10, 5, -1, 4],\n [-6, 0, 3, -2, 12, 1, -6, -2, -4, -1, -3, 1],\n [8, -3, 10, -3, 0, -5, -5, 4, 4, 4, 1, -10]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8568109638809", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (12, 5) of the matrix A^7 where A is:\n[[-10, -9, -5, -12, 15, 2, 13, 9, 15, 7, 5, 13],\n [15, -7, 14, 15, 8, -10, -4, 15, -6, -9, -10, 4],\n [-13, -16, 3, -3, -10, -7, -5, -1, 16, -16, -4, 4],\n [13, -3, 15, 2, -1, 3, -13, 0, -9, 5, -3, 11],\n [8, 2, -10, 14, -11, -5, 5, 1, 11, 13, -7, 8],\n [2, -1, -1, -12, -5, -3, -16, -2, 14, 6, -6, -3],\n [-7, -1, 5, -9, 14, -7, 13, -3, -13, -7, -12, 13],\n [-6, -13, 12, 10, 7, -2, -13, -3, -4, -12, -11, -15],\n [-5, 5, -13, -2, 3, 15, 14, 7, 11, 3, 12, -11],\n [9, -1, -3, 12, 6, -6, 15, -16, -4, -10, -10, -3],\n [9, 0, 12, -6, -7, -10, 3, -2, -15, -13, 10, -14],\n [-16, -10, 10, -14, 2, -11, 16, -5, 7, -3, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-176889407", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 9) of the matrix A^9 where A is:\n[[-9, 8, -13, 12, -14, 14, -7, -5, -14, -8, -3, -3],\n [2, 0, 5, 4, 14, -5, -3, 1, -7, 15, 6, -7],\n [1, -13, -14, 12, -5, -11, 7, 11, 15, 2, -12, -13],\n [13, 10, -11, -2, 4, 13, -12, -3, 7, -2, 7, 11],\n [7, 6, -10, -7, 16, -8, 4, 12, 12, -11, -13, 2],\n [-6, 2, -10, 3, -10, -5, -2, -1, -7, -1, 8, -8],\n [-16, -4, 4, 9, -1, -16, -2, -14, -3, 3, 10, 15],\n [14, -11, 16, 12, 4, 8, -2, 7, -9, -3, 3, 16],\n [-10, 7, -5, -1, 0, 6, 5, -2, 8, 3, -12, 12],\n [-13, 15, 8, 8, -9, 5, 2, 8, -13, 15, 15, -1],\n [8, 12, -11, -2, -10, 2, 8, 5, -1, -10, 10, -14],\n [11, -3, 8, -14, -1, -6, -10, 2, -15, -8, 13, 16]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3295610062633", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-8, -4, -14, 1, -8, -16, -16, -14, -12, -7, 14, 11],\n [11, -9, -6, 0, 7, 15, 12, -10, 6, -1, 11, -2],\n [-13, -2, 10, 8, -16, 11, -5, -14, 4, 10, 8, 12],\n [10, 14, -3, -5, -11, -2, -16, -2, 11, -3, 6, -12],\n [11, 2, 5, -10, 3, -6, -14, 7, 4, 12, -10, -6],\n [-2, 7, -5, 5, 9, -7, 6, 5, 1, 9, -12, 13],\n [10, -14, -15, 5, 6, -14, 2, -11, 15, -15, -6, 9],\n [4, 13, -7, -5, 7, 2, 14, -8, 5, 9, -14, -5],\n [-11, 6, -3, 7, -9, 3, 5, 14, -10, -8, 12, 0],\n [7, -1, 16, 0, 16, 8, 10, 0, 16, 14, -11, 12],\n [-13, 1, 7, 5, -15, 8, -3, 2, 8, -16, -2, 8],\n [-7, 1, -8, -15, 6, -9, -11, 4, -10, 9, -13, 1]], determine the value at position (8, 10).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149648155847", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[-7, 12, 8, 2, -2, 9, -3, -3, 5, -4, 0, -2],\n [12, -4, 8, -4, 2, -1, 0, 7, -12, -2, 4, 10],\n [8, 8, -9, 12, -8, -4, 2, -6, 1, 12, -8, 2],\n [2, -4, 12, -3, 1, -14, 1, 2, 5, -2, -6, 7],\n [-2, 2, -8, 1, -16, 4, 1, -14, -2, -10, -9, 9],\n [9, -1, -4, -14, 4, 4, 1, -4, -2, 3, 0, -2],\n [-3, 0, 2, 1, 1, 1, -8, -7, 5, -8, -15, 4],\n [-3, 7, -6, 2, -14, -4, -7, 5, 8, 4, 4, 4],\n [5, -12, 1, 5, -2, -2, 5, 8, -8, 6, 2, 6],\n [-4, -2, 12, -2, -10, 3, -8, 4, 6, -4, -2, -2],\n [0, 4, -8, -6, -9, 0, -15, 4, 2, -2, 1, -12],\n [-2, 10, 2, 7, 9, -2, 4, 4, 6, -2, -12, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9652215452253", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of all entries of the result:\nA =\n[[2, 6, -11, -2, 0, -2, 10, -9, 14, 0, 6, -12],\n [11, 0, 12, 11, 16, 8, -1, -14, 13, 11, -16, -2],\n [8, -14, 3, -4, -14, 14, -8, 10, 1, 14, -16, 13],\n [-11, 16, 10, -12, -13, -2, -3, -15, 2, 16, -9, -16],\n [-7, -4, 6, -15, -13, -16, 2, -10, -8, 8, -13, -3],\n [5, -5, -7, 11, -7, -10, -12, 4, -10, -16, 16, 8],\n [7, -9, 13, -3, 13, -8, 7, -16, 3, 13, 9, -3],\n [-11, -1, 7, -14, -2, 16, 8, -11, 10, 12, 1, -11],\n [16, -13, 12, -10, -7, -3, 3, 16, -7, -6, 10, -3],\n [-14, 4, 1, 14, 8, 10, -15, 10, 3, -6, -5, 7],\n [-3, -6, 3, 15, 10, 6, 5, 5, -6, -5, -13, -4],\n [4, 2, 5, -1, 5, 16, -3, -7, 1, -1, 9, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26827121792044", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 7th power of the matrix:\n[[16, -12, -6, 2, -11, 14, 0, -6, -1, -10, 16, 1],\n [-14, 15, 12, 14, -4, -13, -7, 3, 13, 9, 12, 8],\n [16, -8, -1, -8, -2, -8, 5, -2, 10, -16, -10, -7],\n [7, 9, -8, -11, -8, 5, 5, -7, -9, 16, 16, 9],\n [8, 14, 1, 15, -3, -8, -10, -3, 2, 0, 5, -9],\n [-7, -7, -15, -11, 11, 0, 16, -4, 12, -11, 2, 3],\n [16, 5, -9, -15, 3, -7, 13, 15, -13, 14, -6, -4],\n [-13, 5, -8, 2, 13, -13, 5, 8, 2, -15, 2, 2],\n [-14, 7, 8, -4, -14, -11, 16, -13, 10, 14, -6, 14],\n [15, 10, -7, -15, 11, -10, -2, -13, 5, -5, -7, 1],\n [-5, 14, 11, -1, -14, -11, 7, -6, -4, -4, 8, -10],\n [10, -4, 10, 16, 5, 5, 2, -4, -16, -3, -10, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1303327512092", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[2, -2, 4, 1, -10, -8, 4, 4, 7, 0, 1, -1],\n [-2, -10, 8, -10, 4, -3, -4, 4, -9, -4, 2, 8],\n [4, 8, -5, -5, -10, -8, -10, 0, -6, -4, 3, 8],\n [1, -10, -5, -8, -10, -3, -1, 5, 5, 12, 4, -4],\n [-10, 4, -10, -10, -13, -2, -6, 0, -4, -2, -12, 0],\n [-8, -3, -8, -3, -2, 9, 0, -10, -6, -2, -2, 14],\n [4, -4, -10, -1, -6, 0, 15, -2, 0, -4, -2, 7],\n [4, 4, 0, 5, 0, -10, -2, -13, 2, 10, -4, -6],\n [7, -9, -6, 5, -4, -6, 0, 2, -15, 1, -14, 1],\n [0, -4, -4, 12, -2, -2, -4, 10, 1, 4, 4, 8],\n [1, 2, 3, 4, -12, -2, -2, -4, -14, 4, 11, 12],\n [-1, 8, 8, -4, 0, 14, 7, -6, 1, 8, 12, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2270683869781847", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-3, 2, 1, 15, 16, -9, 8, 16, -13, -6, -6, 4],\n [4, -3, -4, 16, 0, -9, 8, 0, 9, -12, 4, -1],\n [1, -13, -6, -5, 8, 9, 16, 15, 10, -8, 9, -6],\n [-16, 6, -15, 11, 5, 9, 5, 12, -12, -3, -11, -3],\n [1, -5, 16, -3, 10, 1, -14, -3, -10, 7, -16, 13],\n [-13, 11, -7, 13, 3, 16, 5, 4, -13, -9, 0, -16],\n [7, 0, 12, -10, 5, -4, -3, -6, -2, 9, 9, -12],\n [1, -16, -15, -14, -1, 0, 4, 12, 3, 14, -10, 0],\n [-1, 8, 6, 7, -6, -15, 11, 15, -11, 5, -1, -5],\n [-4, -15, -2, -15, 5, -3, 13, 5, -4, -8, 8, 3],\n [-2, 7, 8, -16, -11, -7, -8, 14, -15, 9, 3, -15],\n [9, 2, -11, 12, 5, -3, -3, -3, -12, 8, -8, -11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4826661775242039", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[6, 15, -2, -7, -9, 11, 14, 10, -5, 4, 10, 11],\n [15, -9, 2, 3, -5, 15, -9, -13, -16, 11, -2, -6],\n [2, 10, -5, -6, 2, -16, -7, 9, 14, -3, -13, 2],\n [13, 9, 4, 2, -5, 10, -5, -10, 0, -8, 0, -3],\n [16, -6, 5, 6, 8, 5, -4, 6, 0, -16, -3, -8],\n [13, 8, 15, 7, 15, -3, -10, 12, -7, 2, -3, 1],\n [-6, 9, -3, 7, -8, 9, -4, -9, -2, 10, -14, 9],\n [8, 13, 13, 9, 2, 10, -12, 16, -1, 8, -14, 6],\n [-4, 5, -15, -1, 16, -16, -9, 2, -4, 11, -9, 5],\n [6, -6, -6, 4, 16, -1, -12, 14, -3, -11, 11, 1],\n [5, -11, -5, -13, -2, 7, -1, -14, 7, -1, 1, 13],\n [-16, -5, -14, -11, 12, -14, 12, -16, -6, -4, 4, 13]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34681593112851", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 7) of the 9th power of the matrix:\n[[4, -6, -16, -7, -15, 15, 1, 0, 15, -10, -10, 15],\n [-12, 3, 2, 9, 12, 7, -11, 13, 11, -6, 2, -10],\n [0, -5, 3, -10, -10, 3, 11, -13, -8, 15, 16, 11],\n [0, -1, 14, -11, -7, 2, 8, -15, 5, 4, 14, -3],\n [-2, 14, -3, 3, 5, -16, 15, -4, 5, -15, 12, 10],\n [-8, 5, 1, 0, 7, 3, -12, -15, -3, -6, -3, -15],\n [5, 5, 8, -7, 15, -12, -2, -10, -2, -15, -4, -6],\n [-4, 10, -12, -12, 1, -1, -4, 9, 1, 13, 9, 5],\n [-11, 8, -9, 4, -14, -15, -11, 11, 16, -8, 14, -16],\n [3, -9, -3, -13, -3, 0, 8, 2, -11, -2, -8, -3],\n [-5, -12, 15, -15, 7, 11, 4, -12, 14, -8, 14, 0],\n [-6, -6, 16, -2, -12, -6, 2, 14, 13, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6584543046849", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[-12, 10, 4, 2, -11, -6, 4, 5, 4, 8, 7, 16],\n [10, -15, 12, 2, -6, 0, 6, 6, -7, 2, -11, -2],\n [4, 12, 6, -10, 2, 4, -13, 4, 4, 10, 4, -14],\n [2, 2, -10, 8, 2, 16, 10, -6, 1, 10, -15, -8],\n [-11, -6, 2, 2, -6, 0, -4, 3, 8, -4, -9, -11],\n [-6, 0, 4, 16, 0, -10, 0, 12, 6, -4, 8, 0],\n [4, 6, -13, 10, -4, 0, 9, -14, 0, -6, -6, 4],\n [5, 6, 4, -6, 3, 12, -14, 8, 4, -15, 4, -6],\n [4, -7, 4, 1, 8, 6, 0, 4, 13, 0, 4, -2],\n [8, 2, 10, 10, -4, -4, -6, -15, 0, 14, -2, 6],\n [7, -11, 4, -15, -9, 8, -6, 4, 4, -2, -4, -2],\n [16, -2, -14, -8, -11, 0, 4, -6, -2, 6, -2, -11]], determine the value at position (1, 7).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38617635868438", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 10, -10, 13, -6, -1, -6, -12, -2, -14, 2, 12],\n [10, -4, 12, 1, -11, 0, 4, -6, 0, 10, 6, 2],\n [-10, 12, 12, 8, -3, 2, -8, 10, 15, -4, 2, -8],\n [13, 1, 8, 14, -6, 2, -4, -2, 8, -8, 12, 1],\n [-6, -11, -3, -6, 12, -6, -12, -14, -2, -10, -2, 0],\n [-1, 0, 2, 2, -6, 0, 8, -11, -6, 2, 6, -4],\n [-6, 4, -8, -4, -12, 8, -11, 9, -4, 7, 4, -10],\n [-12, -6, 10, -2, -14, -11, 9, 2, 0, 6, 2, 2],\n [-2, 0, 15, 8, -2, -6, -4, 0, -9, 8, 4, -8],\n [-14, 10, -4, -8, -10, 2, 7, 6, 8, -3, -2, 2],\n [2, 6, 2, 12, -2, 6, 4, 2, 4, -2, 2, 6],\n [12, 2, -8, 1, 0, -4, -10, 2, -8, 2, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5611116039703369", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[-3, -3, -7, -7, 13, -13, 0, -3, 5, -6, -11, 8],\n [10, -12, 5, 8, -1, -15, -15, 10, -7, 6, -2, -4],\n [-12, -15, 10, 10, -12, -12, -10, -4, 0, 16, -9, -13],\n [-13, -16, -14, 9, 4, -14, 10, 10, -14, -3, 13, -9],\n [-8, 9, 0, 0, -12, 4, 7, 1, -1, 3, -2, 15],\n [14, 10, -10, -8, 3, -1, -13, 9, -16, 13, 6, -15],\n [14, -4, -4, 3, -8, 1, 8, -2, -5, -3, -10, 7],\n [-10, 14, 16, -11, 16, 5, 1, -6, -3, 9, -7, 15],\n [-5, 15, 16, -4, 14, -2, 0, 7, -3, -3, 8, -7],\n [-2, -10, 0, -2, -13, -7, 2, 2, -7, -9, 15, 5],\n [-8, -10, -4, 4, 7, -3, 8, -4, -16, 0, -14, 9],\n [-3, -13, -5, -7, -6, -13, -2, -13, 0, 12, -14, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "717556742860114", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (12, 12) of the matrix A^7 where A is:\n[[-6, -8, -1, 14, 8, -2, -2, 2, 6, 9, -4, -5],\n [-8, 3, -14, 4, 0, 12, 2, -8, 12, 6, -14, -14],\n [-1, -14, 11, 2, -8, -3, 10, 4, 12, -12, 6, 6],\n [14, 4, 2, -11, 12, -6, -4, 4, 0, 6, -2, -7],\n [8, 0, -8, 12, 2, -4, -2, 0, 0, 8, -4, 1],\n [-2, 12, -3, -6, -4, 8, -1, -4, 11, 6, 1, -9],\n [-2, 2, 10, -4, -2, -1, 3, -8, -2, 10, 6, 8],\n [2, -8, 4, 4, 0, -4, -8, 12, -4, -3, 1, -4],\n [6, 12, 12, 0, 0, 11, -2, -4, 9, -10, 0, 8],\n [9, 6, -12, 6, 8, 6, 10, -3, -10, 7, 10, 8],\n [-4, -14, 6, -2, -4, 1, 6, 1, 0, 10, -13, 4],\n [-5, -14, 6, -7, 1, -9, 8, -4, 8, 8, 4, -11]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23665890945", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[3, -1, -14, 6, 10, 8, 9, 12, 13, -4, -10, -4],\n [-16, 15, 6, 0, 3, 15, -6, 3, 11, 14, -13, 5],\n [-13, 9, -14, 4, -2, 9, 10, 11, 13, 6, -13, 16],\n [0, 4, 2, -5, 15, -13, -9, -13, 5, -7, 4, 16],\n [6, -1, 13, 2, -10, -8, 12, -12, 1, -15, 10, -9],\n [8, 5, 7, -14, -7, -2, 4, 2, 4, -9, 0, 11],\n [4, -9, -6, -4, -2, 11, -15, 4, 4, 10, -2, 11],\n [16, -10, 15, -14, -14, -1, 4, -8, -14, 13, -9, 12],\n [-3, 6, 11, 11, 12, -1, 5, -15, -8, -13, 6, 7],\n [-14, -5, 12, 5, 2, -1, 10, -3, 12, -14, 13, 16],\n [9, -14, 13, -1, -12, 14, 9, 13, 10, -4, -6, 9],\n [16, 12, 5, 10, 16, -1, -1, -9, -13, -7, 15, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11728719244436", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 3) of the 7th power of the matrix:\n[[0, 1, 4, -8, 5, -6, 8, 2, 6, -5, -8, -2],\n [1, -7, -4, 2, -4, 12, 4, 10, -7, 8, -6, 3],\n [4, -4, -12, 2, 4, -9, 12, -4, 8, 10, 10, -4],\n [-8, 2, 2, 12, 4, 0, 6, 8, -6, 0, -2, 4],\n [5, -4, 4, 4, 1, -2, -10, 4, -2, 12, -12, 0],\n [-6, 12, -9, 0, -2, 11, -4, -14, 2, -9, 4, -4],\n [8, 4, 12, 6, -10, -4, 4, 2, 12, 2, -4, 11],\n [2, 10, -4, 8, 4, -14, 2, 8, 0, -6, 7, -4],\n [6, -7, 8, -6, -2, 2, 12, 0, -13, 3, 6, 0],\n [-5, 8, 10, 0, 12, -9, 2, -6, 3, -16, -11, -4],\n [-8, -6, 10, -2, -12, 4, -4, 7, 6, -11, 11, 4],\n [-2, 3, -4, 4, 0, -4, 11, -4, 0, -4, 4, -15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3890123065", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-3, -8, 1, -6, 0, 10, -12, 10, 1, -16, -1, 2],\n [16, 13, 10, 15, 12, -9, -3, 15, -7, 12, 14, -9],\n [6, -11, 4, -12, -12, -11, -12, -16, 10, -5, -14, -11],\n [-16, -7, -7, -9, -5, 8, 7, -16, -13, -4, 6, -6],\n [2, -12, 2, -14, -11, -12, 13, 16, -7, 10, -11, 5],\n [6, -2, -10, -13, -16, 3, -15, -14, -1, -5, 9, 5],\n [13, 13, 0, -11, 13, -5, 2, 6, -9, -9, 6, 9],\n [-8, -14, -12, 5, 14, -1, 7, 1, -4, 9, 9, -8],\n [16, -1, -7, -9, -8, 11, -13, 11, 2, 10, -12, 4],\n [-5, -4, 1, -7, 3, -13, -16, 0, 10, 13, -10, 2],\n [-5, 11, 7, -2, -14, 11, 2, 8, -9, 15, -9, 16],\n [-11, 5, -7, -13, 12, 8, 3, 2, -5, 4, -16, 7]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2225929869951", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 9th power of the matrix:\n[[11, -1, 7, 10, 3, 5, -4, 3, -8, -10, 2, 0],\n [-1, 11, -4, 12, 10, 0, 4, -6, 10, -10, 0, -8],\n [7, -4, 12, 12, 7, -2, -9, 6, -9, -5, 0, -9],\n [10, 12, 12, 9, -3, -2, -4, -8, -15, 8, 10, 2],\n [3, 10, 7, -3, -15, -10, 14, 0, -8, 3, 10, 3],\n [5, 0, -2, -2, -10, -13, -8, 10, 4, 4, -8, -8],\n [-4, 4, -9, -4, 14, -8, 0, 10, -10, -10, 2, 6],\n [3, -6, 6, -8, 0, 10, 10, -2, 6, 3, 3, 15],\n [-8, 10, -9, -15, -8, 4, -10, 6, 2, -8, 0, 2],\n [-10, -10, -5, 8, 3, 4, -10, 3, -8, -3, -2, -2],\n [2, 0, 0, 10, 10, -8, 2, 3, 0, -2, -12, -2],\n [0, -8, -9, 2, 3, -8, 6, 15, 2, -2, -2, 16]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7389459052777102", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 6, 4, -13, 5, 3, 1, -10, 1, 14, -13, -8],\n [15, -10, 1, 15, -3, 9, -15, 2, 15, 7, 8, 8],\n [12, 16, 5, 10, 10, 12, 1, -7, -12, -1, 12, 15],\n [11, 10, 16, -13, 2, 5, 6, 7, -14, -12, 13, -8],\n [-3, -16, 16, -6, 3, -2, 10, 2, 3, 10, -9, -9],\n [14, -4, 5, 7, 15, -10, -3, 1, -2, 10, -16, -2],\n [5, -7, 9, 7, -2, -2, -3, -7, 16, 9, 0, -1],\n [0, -6, 13, -5, -3, -1, -1, -6, -14, 15, 6, 0],\n [-5, 13, 15, -15, 3, -8, 5, 13, 11, -13, 11, 2],\n [16, 2, 5, 15, 6, 12, 13, -3, 10, 6, -16, 15],\n [-4, 12, -1, 3, 10, 15, -6, 3, 6, 3, -10, -10],\n [1, -1, 10, -6, 12, -14, -11, 4, 16, 13, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2471034252629989", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 8th power of the matrix:\n[[2, -3, -10, 2, -6, -10, -1, 9, 8, -6, 4, 3],\n [-3, 9, -6, 4, 2, 6, -2, -7, -10, -6, 4, -8],\n [-10, -6, -11, -2, -8, 6, 0, 11, 0, 2, -3, 0],\n [2, 4, -2, -13, 1, 3, 8, -2, 2, 3, -14, -4],\n [-6, 2, -8, 1, 6, 0, 2, -8, -5, -4, -13, 4],\n [-10, 6, 6, 3, 0, -1, 6, 8, -8, 4, 2, 4],\n [-1, -2, 0, 8, 2, 6, 7, 12, -2, -10, -2, -8],\n [9, -7, 11, -2, -8, 8, 12, 11, 2, -10, -4, 4],\n [8, -10, 0, 2, -5, -8, -2, 2, -7, 8, -6, -7],\n [-6, -6, 2, 3, -4, 4, -10, -10, 8, 14, 0, -2],\n [4, 4, -3, -14, -13, 2, -2, -4, -6, 0, -8, 2],\n [3, -8, 0, -4, 4, 4, -8, 4, -7, -2, 2, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146995888174", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[-9, -8, -2, -2, 6, 0, 3, -8, 4, 0, 1, 0],\n [-8, 15, -6, 0, 6, -14, -2, 9, 10, -14, 0, -5],\n [-2, -6, 15, -2, -8, 0, -6, -2, -4, 0, -2, -8],\n [-2, 0, -2, 9, 2, -11, 4, 2, -1, 12, 3, -2],\n [6, 6, -8, 2, 7, 4, 5, -6, -12, 6, -6, -4],\n [0, -14, 0, -11, 4, 1, -5, -4, 9, 8, 4, 14],\n [3, -2, -6, 4, 5, -5, -12, -9, 2, -5, -4, -8],\n [-8, 9, -2, 2, -6, -4, -9, 9, 1, 8, -4, -12],\n [4, 10, -4, -1, -12, 9, 2, 1, 1, 5, 0, 4],\n [0, -14, 0, 12, 6, 8, -5, 8, 5, -16, 1, 4],\n [1, 0, -2, 3, -6, 4, -4, -4, 0, 1, -4, -6],\n [0, -5, -8, -2, -4, 14, -8, -12, 4, 4, -6, -10]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-136345276378506", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 2) of the matrix A^9 where A is:\n[[14, -3, -12, -2, -2, 7, 2, 0, -10, 6, 8, 4],\n [-3, 3, 3, 1, -6, -12, 10, -4, -4, 6, 12, -2],\n [-12, 3, 4, 8, -5, 12, -8, -10, -2, 8, -2, -3],\n [-2, 1, 8, 3, 8, -9, -2, 4, 0, 6, -6, 4],\n [-2, -6, -5, 8, -8, -6, -10, 2, 0, 0, 4, 2],\n [7, -12, 12, -9, -6, -4, 9, 4, -5, -2, -4, 4],\n [2, 10, -8, -2, -10, 9, -13, 6, -2, 8, -4, 2],\n [0, -4, -10, 4, 2, 4, 6, -15, -1, 8, -2, -10],\n [-10, -4, -2, 0, 0, -5, -2, -1, 11, -9, -2, 4],\n [6, 6, 8, 6, 0, -2, 8, 8, -9, -15, -4, -4],\n [8, 12, -2, -6, 4, -4, -4, -2, -2, -4, -9, -2],\n [4, -2, -3, 4, 2, 4, 2, -10, 4, -4, -2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11894032013465", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 9) of the 7th power of the matrix:\n[[-5, -1, -1, 4, 10, -2, -1, 6, 8, 11, 7, -13],\n [-11, -3, -14, 4, -15, -10, 6, 3, 16, 8, -13, -10],\n [1, -1, -6, -4, -15, 7, -11, 11, 8, 4, -5, -3],\n [4, 4, 10, 8, -10, -6, -6, 9, 8, -9, 9, -9],\n [-3, 7, -7, 5, -2, -14, 12, -12, 10, -15, 5, 4],\n [-7, -1, -11, -9, 14, -16, 9, 16, 9, -9, -5, -11],\n [1, 3, 10, -3, 15, 13, 7, 0, 8, -14, -1, -12],\n [-12, -16, 8, 16, -14, -10, -12, 11, 8, -2, 14, -4],\n [2, -3, 3, 4, -2, 12, 10, 10, -10, 15, 2, 11],\n [-10, 3, 7, 12, -3, 10, -12, 0, -5, -13, -4, -10],\n [16, -2, 2, 8, 1, 1, 14, 16, -14, -14, -15, -13],\n [-5, -10, 10, -7, -16, 14, -8, 8, 12, -13, 10, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9213202677", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (7, 2) of the matrix A^9 where A is:\n[[-16, 6, 10, -8, 8, -2, -3, -14, 11, -4, 1, 0],\n [6, 4, 6, 3, -6, -6, 10, -12, 0, 6, 0, 2],\n [10, 6, 15, -6, 8, -4, -12, -4, 0, 2, -6, 2],\n [-8, 3, -6, -14, 8, -6, -14, -2, -2, 2, -3, 6],\n [8, -6, 8, 8, 9, 10, -6, 4, 0, -4, 0, 2],\n [-2, -6, -4, -6, 10, 8, 10, -3, -4, 9, -2, 10],\n [-3, 10, -12, -14, -6, 10, -7, -3, -2, -5, 7, -14],\n [-14, -12, -4, -2, 4, -3, -3, 0, 0, -6, 1, -6],\n [11, 0, 0, -2, 0, -4, -2, 0, -3, 4, 8, 0],\n [-4, 6, 2, 2, -4, 9, -5, -6, 4, 3, -9, 0],\n [1, 0, -6, -3, 0, -2, 7, 1, 8, -9, 11, 2],\n [0, 2, 2, 6, 2, 10, -14, -6, 0, 0, 2, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29394438450213", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 6) of the matrix A^7 where A is:\n[[-8, 1, -3, -7, 1, 9, 10, 2, 6, -3, -10, -16],\n [14, 3, 6, 10, 14, 9, -13, 13, 2, 14, -3, 1],\n [-12, 1, 5, -1, -4, 4, 16, 1, 12, 6, 15, 3],\n [-10, 2, -14, -11, 0, 15, -10, 1, 0, 16, -12, 5],\n [-6, 0, 6, -15, 15, -10, -2, -1, -3, 5, 6, 5],\n [2, -16, 5, 15, 1, -2, 16, 10, -12, -11, -9, 10],\n [-9, 0, 13, 5, 4, 9, 4, 1, -3, -2, -14, 14],\n [-11, 0, -15, -12, 7, 13, -2, 2, -9, -3, -5, 16],\n [16, 2, 4, -2, 2, 15, -3, 14, 3, 3, -7, -10],\n [-14, 6, -7, 0, 4, 13, -14, -15, 8, -12, -10, -16],\n [15, 16, -5, -14, 2, 7, 6, 6, -9, 7, -7, -13],\n [-4, 11, 7, 10, 15, 1, -11, 12, 10, 10, -16, -13]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1026199805", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (9, 8) of the result:\nA =\n[[15, 10, -4, -8, -8, -9, -4, 1, -2, -5, 4, -8],\n [10, 0, -6, -5, 4, -12, 8, 0, 0, 2, 6, -4],\n [-4, -6, -7, 0, 8, 0, 1, 2, 6, -4, 1, -12],\n [-8, -5, 0, 4, 13, 8, -4, -7, -4, -2, -10, -1],\n [-8, 4, 8, 13, 14, 16, 8, -6, 10, -2, 2, -6],\n [-9, -12, 0, 8, 16, -15, -6, 8, 5, 3, 3, -4],\n [-4, 8, 1, -4, 8, -6, 10, 4, -14, 2, 10, 12],\n [1, 0, 2, -7, -6, 8, 4, -1, -13, 3, 8, 2],\n [-2, 0, 6, -4, 10, 5, -14, -13, 2, -6, 10, 11],\n [-5, 2, -4, -2, -2, 3, 2, 3, -6, -1, -4, -2],\n [4, 6, 1, -10, 2, 3, 10, 8, 10, -4, -2, -6],\n [-8, -4, -12, -1, -6, -4, 12, 2, 11, -2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37506782858", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^9 where A =\n[[10, -10, 11, -3, -2, 8, -13, 8, -3, -8, 0, 14],\n [1, -2, 16, -3, -11, 9, 15, 2, 6, 9, -6, -4],\n [4, 6, 13, -2, -14, -9, -10, 6, 2, -14, -6, 3],\n [4, 0, 14, 13, -1, -9, 7, 8, -8, 5, 15, -8],\n [2, 4, 10, 10, 5, -12, -6, 3, -13, 6, 0, -13],\n [11, -7, -6, -10, -16, 16, 0, 4, 11, -1, -1, 11],\n [12, -15, -1, 2, 10, -15, 1, 6, -5, 9, 13, -3],\n [-2, -16, 0, -9, 14, 9, 1, -3, -5, -11, 4, 5],\n [1, -4, -15, 7, 16, 4, 10, 2, 0, 3, 8, -1],\n [13, 4, -4, -16, -7, -6, 16, 1, 10, 6, 14, -7],\n [9, -2, 2, -9, -8, 1, 9, -13, -3, 15, 11, 14],\n [15, 5, -4, -8, 3, -11, 3, 7, 5, 7, 6, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "441013684213411", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (10, 4) of the result:\nA =\n[[-1, 10, 8, 11, 7, -7, 7, -3, 13, 16, -12, -5],\n [-1, 6, 0, -16, -11, 11, -12, -8, -16, -14, 13, 4],\n [0, -13, 16, 13, 11, 7, 6, 0, 11, 16, -3, 11],\n [-15, -2, 5, 14, -3, 2, 14, -8, 4, 15, 3, -12],\n [-9, 6, 1, -11, -7, -6, 9, -12, -15, -16, -7, -15],\n [-14, 14, 14, 4, 10, 5, 1, -11, -1, 15, -15, -16],\n [16, 2, -6, 13, 12, -6, -2, 10, 13, 10, 5, 1],\n [11, 9, 6, 12, -13, 14, 12, 10, 1, -5, 0, -9],\n [-9, -9, 13, -15, -4, -11, -13, 9, 14, -6, -14, -14],\n [-16, -11, 5, -6, 9, 6, -11, 14, 5, -14, 9, -15],\n [5, 11, -2, -11, 15, 4, 8, 4, 2, -5, -7, 8],\n [-1, 11, 5, -15, -4, 16, -15, -7, -8, 3, 7, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40103390225783", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-7, 2, -7, 4, -14, -2, -3, -6, 9, -4, -8, -8],\n [2, 12, -9, 4, 2, -2, 8, 12, -3, 6, -2, -10],\n [-7, -9, 10, -6, 8, 10, -10, 4, -6, -11, -6, -13],\n [4, 4, -6, -8, -7, -10, 10, 10, 0, -8, -1, -4],\n [-14, 2, 8, -7, 0, -4, 5, 5, -10, -4, -3, -13],\n [-2, -2, 10, -10, -4, -10, -6, -7, 3, 10, -10, 6],\n [-3, 8, -10, 10, 5, -6, -14, -14, 12, 8, -6, -10],\n [-6, 12, 4, 10, 5, -7, -14, -11, 2, -4, -4, 8],\n [9, -3, -6, 0, -10, 3, 12, 2, -16, 10, 4, 4],\n [-4, 6, -11, -8, -4, 10, 8, -4, 10, -12, 10, 4],\n [-8, -2, -6, -1, -3, -10, -6, -4, 4, 10, 2, 6],\n [-8, -10, -13, -4, -13, 6, -10, 8, 4, 4, 6, 9]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16368867572997", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 1) of the matrix A^9 where A is:\n[[-10, -9, 2, -3, -4, 4, 8, 8, -4, 8, 2, 2],\n [-9, 10, 1, 2, 9, -6, 12, -13, 2, -2, 5, -8],\n [2, 1, 9, -9, 1, 4, 6, 0, -2, -6, -6, -9],\n [-3, 2, -9, -7, 12, 10, 8, -2, -4, 4, -2, -6],\n [-4, 9, 1, 12, 0, 12, 7, 0, 4, 4, 10, -6],\n [4, -6, 4, 10, 12, -8, 6, -10, 2, 0, 10, -4],\n [8, 12, 6, 8, 7, 6, -16, -11, 2, 1, 8, 2],\n [8, -13, 0, -2, 0, -10, -11, -14, -7, 7, -2, 2],\n [-4, 2, -2, -4, 4, 2, 2, -7, 4, -4, -6, -2],\n [8, -2, -6, 4, 4, 0, 1, 7, -4, -15, -6, -6],\n [2, 5, -6, -2, 10, 10, 8, -2, -6, -6, 3, -1],\n [2, -8, -9, -6, -6, -4, 2, 2, -2, -6, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24859258509954", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^8 where A is:\n[[11, 0, -6, 4, -11, -6, 8, 12, 8, 8, 6, -8],\n [0, 16, -10, 4, -12, 6, -7, 2, 9, 0, -1, 5],\n [-6, -10, -3, -2, -4, -4, -5, -4, 6, -1, -7, 8],\n [4, 4, -2, 5, -4, 3, -2, -8, -10, 10, 10, -2],\n [-11, -12, -4, -4, -14, 4, -2, 0, 0, -6, -8, 8],\n [-6, 6, -4, 3, 4, -6, -10, 12, -6, 14, 2, -6],\n [8, -7, -5, -2, -2, -10, 15, 4, 8, -4, 7, 3],\n [12, 2, -4, -8, 0, 12, 4, 4, -1, -4, -7, 9],\n [8, 9, 6, -10, 0, -6, 8, -1, -15, 0, -8, 4],\n [8, 0, -1, 10, -6, 14, -4, -4, 0, -5, 12, -8],\n [6, -1, -7, 10, -8, 2, 7, -7, -8, 12, -3, 6],\n [-8, 5, 8, -2, 8, -6, 3, 9, 4, -8, 6, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12214757304477", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the 8th power of the matrix:\n[[7, 12, -2, -8, 0, 12, 9, 13, 10, -3, -12, -13],\n [16, 13, 6, -2, -11, 13, -4, -11, 1, 8, -13, 7],\n [8, 5, -16, -13, 10, 16, -10, -11, -4, 13, -3, 3],\n [-4, -15, 13, 10, -10, 5, -1, 3, 4, -4, 1, 7],\n [-1, 14, 12, -16, 12, -2, -16, 7, 1, 16, -12, 14],\n [2, 5, 9, -10, 13, 8, 1, -15, 7, 12, -7, 14],\n [-10, 12, 12, 6, -6, 5, -15, -13, 16, -3, -4, -6],\n [-16, 4, 16, 2, -15, 4, -1, -10, -13, -2, 11, 14],\n [3, 10, 3, -6, 9, -16, 11, 3, -16, 14, -14, 0],\n [-6, -4, -12, 1, 1, 11, -5, 9, 11, 12, 14, -13],\n [-11, 11, 5, 0, 14, 14, 16, 13, 3, 7, 9, 7],\n [13, 10, -11, -6, -2, -4, 0, 4, -16, -1, 6, -14]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-973533410348", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 9th power of the matrix:\n[[-5, 12, -8, 10, 3, 15, 15, 16, -2, -9, -13, 15],\n [2, 9, -9, 3, 13, -5, 13, 7, 5, -3, 6, -15],\n [-3, 15, 1, 8, 8, -15, -13, -9, -16, -8, 10, 11],\n [-16, -11, -2, -7, 7, -16, 10, 3, 13, -7, 6, 7],\n [3, 1, -16, 2, 0, -16, 16, 16, 13, -3, 2, -10],\n [4, 1, -5, -5, -9, -1, 10, 2, -2, 16, 15, 10],\n [-2, 8, 15, -9, -7, -2, 9, 8, 14, -4, -10, 1],\n [-15, -5, -16, -13, 11, -10, 7, 13, 5, 5, 11, 3],\n [-8, 11, -12, 5, 6, -7, -10, 13, 2, -2, 12, -15],\n [8, -9, 2, -12, 14, -10, 11, -5, 16, -15, -2, -4],\n [-12, -6, -13, 16, 0, -16, 14, -4, 11, 11, -8, -7],\n [-8, -8, 4, 14, 1, -4, 9, 8, -9, -2, 12, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11829440161316", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of absolute values of all entries of the result:\nA =\n[[15, 10, -4, -12, 14, -5, 2, 4, -14, -7, 13, -10],\n [16, 0, -11, -15, -10, -4, -1, 0, -9, 11, -5, 6],\n [3, -16, -12, -7, 12, 1, -9, -10, 4, -16, -3, -6],\n [16, -2, -4, 1, 16, -15, -16, 8, 5, -16, -5, -1],\n [2, -4, -2, 11, -12, 14, -3, 8, -13, 12, -14, 16],\n [-10, 4, -11, -8, -10, -10, -12, -15, -10, 15, -10, -9],\n [-11, 1, 2, -14, 6, -12, 2, -1, 7, -13, 4, -16],\n [2, 6, 14, -10, 6, -5, 13, -2, 16, 13, 9, 14],\n [6, -8, 11, 5, -12, -3, -10, -2, 2, -14, 1, -4],\n [-4, 12, -14, 9, -13, 7, -8, -4, 10, -15, 3, -2],\n [-5, -15, -1, 11, 6, -10, -2, -14, 8, -7, -4, 7],\n [-12, 0, 8, -4, -4, -5, 12, -5, 8, 12, -14, 15]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1382796385601437", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (12, 7) of the result:\nA =\n[[4, -10, -14, -9, -10, -1, 4, -2, 13, 11, -10, 12],\n [15, 4, -9, -11, 13, -14, -2, 11, -1, 12, 11, -12],\n [13, -5, -15, 5, -2, 1, -12, 16, -14, 12, -9, 10],\n [11, -10, -11, -11, 5, 6, 11, 9, 16, 7, -2, -6],\n [4, 5, -5, -4, 7, -14, 7, -4, 10, -7, 6, -5],\n [1, 2, -15, -13, 15, 2, 16, 7, 8, -16, 14, -13],\n [13, -5, -6, 3, 1, -6, -15, -9, -8, 9, 16, -10],\n [13, -7, -16, 12, -14, 15, 14, -13, 13, -1, 2, 5],\n [14, -12, -13, -15, 3, -16, 1, 11, 4, -9, -11, 1],\n [-2, -10, 16, -13, -5, 2, -1, 12, -8, -2, -10, -11],\n [10, -7, 4, -9, 2, 13, 15, -11, 13, -5, -14, -4],\n [1, -9, 15, -13, 2, 1, -5, -4, -16, 1, 10, 7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19435912682659", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^7 where A is:\n[[1, -8, -16, -13, 16, 10, -15, -12, 2, -2, 9, 5],\n [2, -13, 3, 6, -11, 4, 8, 8, 9, 10, 12, 5],\n [1, 7, -2, -11, -10, 12, -15, -3, 5, -2, -4, -16],\n [-1, -4, -5, -4, 1, -9, -6, -11, -13, 11, 6, 7],\n [4, -11, 8, -4, 0, -2, -4, -1, -9, -8, -14, -4],\n [-3, 13, 4, -5, 8, 3, -11, 6, 4, 15, -13, 1],\n [15, 0, 11, 12, -6, -4, 5, 0, -7, -13, -16, 15],\n [16, 14, -12, -12, -8, -16, 1, -3, 1, 1, 7, 7],\n [-3, 1, 5, -16, 4, 10, -4, -6, -15, -13, 11, 13],\n [0, 16, 6, 12, 4, -3, -14, -3, 16, -14, -1, -13],\n [-8, -9, -14, 16, -13, 7, -15, -16, 3, 8, 13, -7],\n [-6, -4, -4, -1, -3, -16, -13, -16, 14, -16, 13, -8]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1415432385029", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the sum of all entries of the result:\nA =\n[[-4, -5, -8, 13, 7, -1, -13, 13, 3, 9, 16, -2],\n [-2, 0, 6, 8, -12, -6, -3, -14, 7, 16, 10, 8],\n [3, -6, -4, 0, -11, -7, 8, -12, -10, 2, -13, -7],\n [1, 8, 13, 11, 8, 13, -14, -8, -5, -9, -11, -10],\n [-10, -8, -16, 3, -1, 9, -5, 3, 13, 6, 13, -2],\n [8, 11, 0, -3, 1, -8, 9, 14, 11, -1, 6, -14],\n [7, -12, -15, 14, 13, 10, -8, 12, -2, 13, 6, 4],\n [2, -3, -15, -6, 15, -8, 13, -15, -6, -2, 8, 7],\n [-2, -2, 13, 13, -14, -15, 8, -10, 10, -10, -8, -12],\n [13, 0, 11, -7, -14, -6, 8, -9, 11, -4, 5, -12],\n [16, -12, 15, -4, 16, -11, -15, -2, -16, -14, -7, -7],\n [5, -3, 8, 6, -15, 7, -1, 4, 0, 15, -3, 11]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4001868956", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 10) of the 8th power of the matrix:\n[[16, -10, -3, -11, -6, 10, 9, 8, 1, 11, -7, -8],\n [4, 9, 16, 8, -14, 2, -5, 13, -9, -3, -6, -9],\n [2, 4, 2, 16, 5, -14, -8, 14, 10, 3, -6, 0],\n [11, -14, -14, 5, -1, -7, -15, -5, -3, -1, -6, 6],\n [12, -6, -7, -1, -2, 8, -13, -5, -1, 5, -11, 16],\n [2, -2, 11, -1, -10, 8, -5, -14, -5, 3, 8, 12],\n [13, 11, 2, -15, 4, -4, -3, 14, 0, -5, -1, 6],\n [-1, 4, -6, -5, 9, 9, -1, -2, -11, -7, 2, -11],\n [-6, -14, -5, 16, 14, 9, 16, -8, 13, -10, -7, 1],\n [0, 11, -10, 9, -3, -14, 16, -9, 16, 12, -9, 7],\n [-3, -4, -11, -10, 4, -14, 5, -4, 14, 12, -3, -3],\n [-12, -15, 1, 0, -11, 11, 2, 11, 9, -13, 15, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "265532554360", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^8 where A =\n[[-11, 6, -5, 1, -5, -1, -8, 2, 10, 8, 2, -2],\n [6, -8, -2, -4, -2, -4, -4, -10, -5, -4, -2, -9],\n [-5, -2, -1, -1, -2, -6, -2, 3, 9, -7, 4, -4],\n [1, -4, -1, 6, 6, 4, 1, 4, 0, 4, 4, -6],\n [-5, -2, -2, 6, 1, -7, 2, -8, -13, 4, -2, 16],\n [-1, -4, -6, 4, -7, 16, 2, -8, 12, -9, -14, 8],\n [-8, -4, -2, 1, 2, 2, 3, 8, 7, 9, 2, -3],\n [2, -10, 3, 4, -8, -8, 8, 6, 16, 12, 0, 3],\n [10, -5, 9, 0, -13, 12, 7, 16, 12, 4, -3, -5],\n [8, -4, -7, 4, 4, -9, 9, 12, 4, -8, 14, -4],\n [2, -2, 4, 4, -2, -14, 2, 0, -3, 14, 15, -10],\n [-2, -9, -4, -6, 16, 8, -3, 3, -5, -4, -10, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187910447354627", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 4, 4, -6, -6, -4, -11, 4, 3, 4, -9, 12],\n [4, 1, 4, 8, -9, 5, -10, -12, 2, 10, 13, -8],\n [4, 4, 10, -4, -4, 0, 6, -10, -4, 3, 4, 8],\n [-6, 8, -4, 13, 2, 0, 12, -10, -6, 3, 0, -3],\n [-6, -9, -4, 2, -15, -8, 0, 6, -2, -10, 1, 9],\n [-4, 5, 0, 0, -8, -9, -12, 10, 8, 0, 6, -1],\n [-11, -10, 6, 12, 0, -12, 8, 8, -2, -9, -6, -12],\n [4, -12, -10, -10, 6, 10, 8, -15, -6, 2, 4, 3],\n [3, 2, -4, -6, -2, 8, -2, -6, 11, -4, -6, 11],\n [4, 10, 3, 3, -10, 0, -9, 2, -4, 16, 1, -14],\n [-9, 13, 4, 0, 1, 6, -6, 4, -6, 1, 1, 10],\n [12, -8, 8, -3, 9, -1, -12, 3, 11, -14, 10, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135124279884355", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the sum of all entries of the result:\nA =\n[[13, 6, -10, 0, -2, -8, 0, -4, 6, -2, 8, 8],\n [6, -5, -12, -2, 8, 8, 2, 0, -2, 0, -12, 4],\n [-10, -12, -7, 7, -6, 2, 4, 4, 10, -4, -1, -7],\n [0, -2, 7, -15, -2, -11, 4, 15, 0, -6, -2, 2],\n [-2, 8, -6, -2, -3, -2, -3, -3, 1, -2, 4, 0],\n [-8, 8, 2, -11, -2, -6, 8, -1, -5, -8, 0, 12],\n [0, 2, 4, 4, -3, 8, -7, -4, 10, 8, 0, 0],\n [-4, 0, 4, 15, -3, -1, -4, -2, 7, 3, 4, 11],\n [6, -2, 10, 0, 1, -5, 10, 7, -14, 9, -2, -6],\n [-2, 0, -4, -6, -2, -8, 8, 3, 9, -8, 10, -6],\n [8, -12, -1, -2, 4, 0, 0, 4, -2, 10, 15, -4],\n [8, 4, -7, 2, 0, 12, 0, 11, -6, -6, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-65847444067847", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^9 and find the value at position (1, 12) of the result:\nA =\n[[6, 5, 16, 8, -12, 12, 2, 2, -9, 14, -13, 5],\n [14, -13, 13, 1, 9, 15, 14, 3, -8, 13, 0, -12],\n [13, -15, 14, 13, 9, -8, -3, 4, 14, -9, 11, 4],\n [16, 6, -2, 13, 6, 5, 3, 6, -11, -13, -7, -5],\n [7, -12, -11, 8, -12, -9, -1, 14, -1, -14, 2, -4],\n [-4, -11, 6, -11, -13, 0, 8, 12, -11, -3, 10, -11],\n [-9, 13, 11, 10, 16, 9, -1, -3, 7, 14, -16, 3],\n [15, 5, 7, -15, -11, -16, 14, -16, 15, 8, -15, 10],\n [-11, 0, -13, -1, 3, 14, 12, -16, 3, 10, -14, 15],\n [0, -10, 1, -12, -14, -2, -5, -14, -9, -15, 2, 15],\n [6, 0, -2, 9, -12, 11, 8, -3, -2, -1, 5, 2],\n [-3, 10, -3, 13, -15, 1, -3, -8, 5, -5, -6, -9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11144371089702", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[15, -4, 4, 9, -1, 4, 8, -6, -8, 4, 8, 3],\n [-4, 12, 12, 0, -10, -4, -8, 6, -10, 0, -7, 4],\n [4, 12, -9, 2, 6, 4, 6, 11, 8, 0, 3, -14],\n [9, 0, 2, -3, 2, 2, -10, 4, -4, 2, 0, 14],\n [-1, -10, 6, 2, 8, 0, 10, -7, -2, 4, -4, -6],\n [4, -4, 4, 2, 0, -13, -3, -2, -6, 0, 1, -10],\n [8, -8, 6, -10, 10, -3, -8, -5, 4, -6, 8, 6],\n [-6, 6, 11, 4, -7, -2, -5, -8, -14, -2, -4, 2],\n [-8, -10, 8, -4, -2, -6, 4, -14, 6, -13, 2, 2],\n [4, 0, 0, 2, 4, 0, -6, -2, -13, 5, -8, -10],\n [8, -7, 3, 0, -4, 1, 8, -4, 2, -8, -6, 10],\n [3, 4, -14, 14, -6, -10, 6, 2, 2, -10, 10, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-309365886082199", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[-8, 8, -7, 2, -2, 6, 6, 6, -8, -2, -12, -2],\n [8, -6, -6, 12, -9, 1, -2, 6, 0, 4, 0, -6],\n [-7, -6, -8, -10, 1, 3, 6, -9, -6, -10, 14, 2],\n [2, 12, -10, -1, 4, 0, 6, -3, 4, 6, -4, 6],\n [-2, -9, 1, 4, 14, 6, 2, -6, 2, 13, -6, 6],\n [6, 1, 3, 0, 6, 12, -10, -2, 4, -13, 5, 6],\n [6, -2, 6, 6, 2, -10, 2, 4, 7, -8, 4, 12],\n [6, 6, -9, -3, -6, -2, 4, 1, 2, -6, 4, 12],\n [-8, 0, -6, 4, 2, 4, 7, 2, -5, -1, 0, -2],\n [-2, 4, -10, 6, 13, -13, -8, -6, -1, 6, -2, 0],\n [-12, 0, 14, -4, -6, 5, 4, 4, 0, -2, -14, -2],\n [-2, -6, 2, 6, 6, 6, 12, 12, -2, 0, -2, 15]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111222226774190", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^8 and find the sum of absolute values of all entries of the result:\nA =\n[[6, 6, -6, 5, -11, -2, 8, -12, 6, 1, 2, -13],\n [6, -8, 1, 8, 3, -6, -10, 3, -2, 2, 5, 6],\n [-6, 1, 4, 3, 1, -10, 2, 12, -13, 0, -6, -4],\n [5, 8, 3, 4, 4, 1, 6, 10, 4, -4, 5, -3],\n [-11, 3, 1, 4, -16, -6, 4, -2, 10, 4, 2, -14],\n [-2, -6, -10, 1, -6, 2, 4, 3, 2, 9, -8, -7],\n [8, -10, 2, 6, 4, 4, -1, -7, -5, 4, 3, -10],\n [-12, 3, 12, 10, -2, 3, -7, 15, -3, -8, 12, 9],\n [6, -2, -13, 4, 10, 2, -5, -3, -16, -2, 2, -2],\n [1, 2, 0, -4, 4, 9, 4, -8, -2, 9, 5, 4],\n [2, 5, -6, 5, 2, -8, 3, 12, 2, 5, 10, 0],\n [-13, 6, -4, -3, -14, -7, -10, 9, -2, 4, 0, 9]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140185749176248", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^7 where A =\n[[-10, -4, 2, 6, 4, 12, -2, 5, 0, 2, -2, -5],\n [-4, -2, 0, -6, 0, -4, 8, 10, -6, -6, -8, -8],\n [2, 0, 11, 2, 0, 4, 0, 2, 16, -1, -4, 0],\n [6, -6, 2, -7, -5, -8, -5, 4, 8, -7, -2, -6],\n [4, 0, 0, -5, 15, -1, -3, 8, 10, -3, 10, 1],\n [12, -4, 4, -8, -1, 15, -7, 1, 6, 6, -5, -7],\n [-2, 8, 0, -5, -3, -7, -5, -7, -3, -2, -6, 4],\n [5, 10, 2, 4, 8, 1, -7, 14, -1, 4, -1, -5],\n [0, -6, 16, 8, 10, 6, -3, -1, -2, 0, -3, -14],\n [2, -6, -1, -7, -3, 6, -2, 4, 0, -13, 4, 1],\n [-2, -8, -4, -2, 10, -5, -6, -1, -3, 4, 8, 6],\n [-5, -8, 0, -6, 1, -7, 4, -5, -14, 1, 6, -15]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4289999525", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^9 where A is:\n[[-7, 0, -14, 6, -2, 1, -4, -7, 2, 0, -8, -6],\n [0, -6, -6, -11, 0, 2, -10, 10, -9, -4, 2, -9],\n [-14, -6, -12, 1, 10, -8, -14, 6, 0, 1, -11, 6],\n [6, -11, 1, 7, 4, 6, -1, -2, 0, -6, -5, 8],\n [-2, 0, 10, 4, -12, 0, 3, -2, 0, 9, -3, 6],\n [1, 2, -8, 6, 0, 4, 4, 4, 8, 0, -11, -4],\n [-4, -10, -14, -1, 3, 4, 12, 2, -4, -14, -2, -2],\n [-7, 10, 6, -2, -2, 4, 2, -12, -4, -9, 1, 11],\n [2, -9, 0, 0, 0, 8, -4, -4, 10, -1, 0, 2],\n [0, -4, 1, -6, 9, 0, -14, -9, -1, -2, -6, 3],\n [-8, 2, -11, -5, -3, -11, -2, 1, 0, -6, -7, 8],\n [-6, -9, 6, 8, 6, -4, -2, 11, 2, 3, 8, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1449119609217276", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (9, 3) of the result:\nA =\n[[1, -12, 8, 4, 4, 6, 12, 5, 8, -6, -5, -11],\n [-12, -1, 0, -4, -2, 11, 1, 2, 8, 8, 0, 15],\n [8, 0, 10, 5, 2, -6, -7, -4, 6, -10, -8, 0],\n [4, -4, 5, 14, -2, 4, -6, -8, -1, 16, -4, -9],\n [4, -2, 2, -2, -7, -8, -7, 7, 12, -7, 4, -7],\n [6, 11, -6, 4, -8, 11, -4, 2, 2, -10, 2, 6],\n [12, 1, -7, -6, -7, -4, -11, -13, -2, 6, 2, 4],\n [5, 2, -4, -8, 7, 2, -13, -3, -4, 2, -13, 9],\n [8, 8, 6, -1, 12, 2, -2, -4, 6, -1, -4, 9],\n [-6, 8, -10, 16, -7, -10, 6, 2, -1, -16, 8, -14],\n [-5, 0, -8, -4, 4, 2, 2, -13, -4, 8, 16, 3],\n [-11, 15, 0, -9, -7, 6, 4, 9, 9, -14, 3, -7]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10350097464", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^7 and find the value at position (10, 7) of the result:\nA =\n[[3, -13, 2, 16, -10, -3, 0, 0, -9, -10, 6, 6],\n [9, -6, -1, 3, 2, -7, 8, 11, -11, 8, 3, 14],\n [-14, -2, -7, -11, -12, -16, 15, 0, -12, 5, -8, 11],\n [0, 5, -3, 10, 3, 2, -4, -4, -13, -5, 16, 1],\n [14, 3, 12, -13, -10, -11, 4, 8, -15, 15, -13, -14],\n [-2, 16, -10, -13, 16, -1, -10, 8, -1, -7, 5, -15],\n [10, 11, -5, 8, 14, 16, 7, -14, -10, 2, 15, -10],\n [-7, 5, 12, 2, -1, 7, 9, 7, -8, 7, 16, 16],\n [-15, -8, -12, -13, -16, 0, -10, 10, -6, -5, 6, -10],\n [2, 13, 9, -10, 0, -11, -13, -11, 12, 5, -2, -10],\n [4, -8, 12, 11, -6, -6, -12, 7, 12, 10, 10, -11],\n [-4, -5, 10, 5, 10, 4, -3, 10, 6, -6, 13, 12]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3967512703", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (12, 12) of the matrix A^7 where A is:\n[[0, -9, -2, 10, -1, -4, 0, -1, -4, 0, 6, -10],\n [-9, 1, 12, -4, 11, 12, 15, -11, -10, -8, 2, 0],\n [-2, 12, 13, -4, 12, 6, -6, -5, -6, 2, 2, 10],\n [10, -4, -4, -1, 4, 8, 12, 9, 4, -2, 8, 5],\n [-1, 11, 12, 4, -7, -4, 3, -6, 5, 0, 6, -7],\n [-4, 12, 6, 8, -4, 6, 10, 2, -2, -3, -8, -6],\n [0, 15, -6, 12, 3, 10, 15, 2, 3, -6, 11, 4],\n [-1, -11, -5, 9, -6, 2, 2, 13, -8, 6, 12, 10],\n [-4, -10, -6, 4, 5, -2, 3, -8, 16, 6, 0, 2],\n [0, -8, 2, -2, 0, -3, -6, 6, 6, -3, -4, -11],\n [6, 2, 2, 8, 6, -8, 11, 12, 0, -4, -15, -3],\n [-10, 0, 10, 5, -7, -6, 4, 10, 2, -11, -3, 12]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11052079984", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (9, 3) of the 8th power of the matrix:\n[[9, -4, -1, -14, 4, -11, -2, 8, 12, 14, -4, 6],\n [12, 13, 13, -4, -11, 9, -5, 0, 3, -1, 3, -3],\n [-1, -11, 6, -14, 9, -5, -13, -10, 8, -16, -9, -13],\n [0, 13, 2, -12, -8, 2, 13, -16, 5, -13, 16, 0],\n [13, -9, 12, -13, -6, 1, 15, -2, -9, -8, -14, 15],\n [-2, 5, -11, -6, 4, 0, -2, 3, -13, -13, -16, -3],\n [13, -11, -2, -14, 14, 16, -13, -6, 6, -10, 16, -7],\n [2, 11, 6, 6, -1, -2, -6, -3, 8, 6, 4, 15],\n [4, 11, 7, 16, -3, 13, 1, -8, 4, 11, 4, -12],\n [3, 9, 5, -7, -8, 9, -1, -11, 2, 5, -12, -1],\n [-11, -7, 2, 10, -4, 4, 11, 14, 7, 3, -13, -9],\n [13, -1, 12, -6, -6, 13, 14, -8, 7, 8, -13, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350576589456", "dataset": "MATH"}