{"messages": [{"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[0, -3, 6, 4, 1, 6],\n [-2, 0, 3, -4, 0, 4],\n [4, 1, -2, -3, 1, 1],\n [-4, -1, -2, -5, 1, 5],\n [-1, -5, 5, -2, -6, 5],\n [3, -1, 6, 5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1120", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 5) of the result:\nA =\n[[4, 4, 3, 5, 5, -4],\n [5, 0, -3, 2, -4, -2],\n [-4, 0, -2, 2, 0, -5],\n [-3, 2, 5, -5, 3, 2],\n [3, -2, -5, -3, 5, 5],\n [0, 5, 6, 1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2122", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, -3, 2, -2, -5, 2],\n [-3, 3, 1, 2, 2, 0],\n [2, 1, -5, 2, -1, 4],\n [-2, 2, 2, 1, 0, 4],\n [-5, 2, -1, 0, 2, 6],\n [2, 0, 4, 4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95362", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 1) of the 4th power of the matrix:\n[[-6, 2, 0, 2, 1, -6],\n [5, 1, 1, 4, -4, -6],\n [1, -4, -4, -6, 4, -2],\n [3, 0, 3, 2, 5, 0],\n [2, 1, 5, -5, -6, 0],\n [0, 1, -2, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 0, 0, -5, -3, -2],\n [0, -6, 0, 2, 0, 3],\n [0, 0, 3, -2, 2, 3],\n [-5, 2, -2, -3, 6, 0],\n [-3, 0, 2, 6, 4, 1],\n [-2, 3, 3, 0, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67720", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 3) of the matrix A^4 where A is:\n[[5, -5, 3, 6, 2, -2],\n [-1, 5, 5, 5, 5, -3],\n [4, 3, 0, 5, 2, 0],\n [-6, -6, 2, 4, 2, -3],\n [6, 2, -4, 0, -1, 1],\n [4, 2, -2, -6, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-954", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 1, 4, -1, 1, 2],\n [-3, -6, -6, 3, -3, 5],\n [0, -5, -4, -6, -2, -6],\n [1, -6, 4, -6, -5, -5],\n [5, -1, 0, -2, -6, -6],\n [-4, -5, -2, 5, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124968", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, -3, 0, 4, 1, 4],\n [-6, -1, 1, -2, -3, -5],\n [-1, -1, 4, -6, 2, 5],\n [4, -1, 6, -4, -3, 5],\n [4, -3, -4, 3, -4, -4],\n [-3, 0, -3, 2, -6, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-122087", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -2, 0, -6, 4, 0],\n [-2, 2, 0, -2, 2, -4],\n [0, 0, 3, -2, 0, 3],\n [-6, -2, -2, 5, 0, -2],\n [4, 2, 0, 0, -4, -2],\n [0, -4, 3, -2, -2, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-142764", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, -3, 4, -6, 1, -3],\n [-1, 1, -3, -4, 2, -4],\n [2, 6, -5, -5, -5, -1],\n [-4, 6, 2, -3, -6, -3],\n [-6, -2, -3, 1, 1, 0],\n [-4, -6, -6, 5, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-277178", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[-1, -2, -2, 2, 2, 6],\n [-2, -1, -2, 0, 4, -2],\n [-2, -2, 5, -4, 2, 2],\n [2, 0, -4, -4, -4, -2],\n [2, 4, 2, -4, -1, 1],\n [6, -2, 2, -2, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5585", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, -3, 4, -6, -4, 5],\n [-3, 0, -4, -2, -1, 0],\n [4, -4, 3, -2, -2, 0],\n [-6, -2, -2, -5, 2, 4],\n [-4, -1, -2, 2, -6, 2],\n [5, 0, 0, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70824", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 0, -4, 4, 2, 2],\n [0, 3, -3, -2, 0, 0],\n [-4, -3, 1, 0, 1, -2],\n [4, -2, 0, 0, -1, 0],\n [2, 0, 1, -1, 3, 1],\n [2, 0, -2, 0, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206885", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 5, -2, -6, 1, -2],\n [5, 5, 5, -2, 0, -3],\n [-1, 6, -3, -4, 0, 1],\n [-3, 6, -5, 5, 3, -4],\n [-6, 1, -4, 5, 3, 0],\n [3, -2, 3, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1608150", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 2) of the 4th power of the matrix:\n[[5, -4, -6, 2, 1, -4],\n [-4, -1, 4, -2, 4, -2],\n [-6, 4, 0, 2, 2, 6],\n [2, -2, 2, 3, 0, 0],\n [1, 4, 2, 0, -2, -2],\n [-4, -2, 6, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5878", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[0, -3, -6, -2, 0, 3],\n [3, -1, -2, -3, -5, -3],\n [3, 3, -4, 3, -6, 1],\n [-2, 6, -3, 1, 0, -5],\n [-6, 5, 4, -3, 1, 5],\n [-5, -4, 5, -6, -6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "654667", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, 4, -2, 5, -4, -6],\n [-6, 1, 3, 4, 5, 6],\n [6, 5, -5, 6, -4, -5],\n [-4, 0, -6, 3, 1, 6],\n [3, 3, 3, -5, -4, 2],\n [0, -3, 3, -2, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-122267", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, 6, 1, -3, 2, -2],\n [6, 2, -3, 3, -2, 2],\n [1, -4, -6, -4, -3, -5],\n [-6, 0, 1, 0, -2, 5],\n [-6, 0, 6, 0, 2, -4],\n [2, -6, -6, -3, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "494882", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 3) of the 4th power of the matrix:\n[[6, 4, -4, -6, -3, 5],\n [6, 2, -4, 5, 2, 0],\n [5, -3, -4, 3, -2, -2],\n [-4, 5, 2, -3, 4, -2],\n [-3, -2, 0, 2, 0, 6],\n [-2, 3, 3, 0, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1514", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 2) of the matrix A^5 where A is:\n[[-4, 2, 6, 3, 5, -6],\n [2, 2, 1, -1, 2, -4],\n [6, 1, 0, 5, 0, 0],\n [3, -1, 5, 3, -4, -4],\n [5, 2, 0, -4, 1, 3],\n [-6, -4, 0, -4, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48257", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 5) of the matrix A^4 where A is:\n[[6, -3, -3, -1, 5, -4],\n [6, 5, -1, 0, 4, 3],\n [3, -4, 0, -4, 6, 6],\n [-5, 5, 3, -3, 5, 1],\n [6, 2, 0, -6, -4, 6],\n [5, 2, 5, -6, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3502", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-6, 2, 1, -2, 0, 4],\n [2, 6, 6, 0, -1, 2],\n [1, 6, -2, -4, -2, 0],\n [-2, 0, -4, 2, -5, -2],\n [0, -1, -2, -5, 0, 0],\n [4, 2, 0, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1028087", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[1, 5, -2, 1, 3, 5],\n [-3, 3, 1, 3, 5, -5],\n [5, 5, -2, 2, -3, 4],\n [-1, -6, 2, -6, -2, -3],\n [6, 5, 6, 6, -4, 6],\n [-1, -5, -4, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37286", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 1, -5, 4, 6, -2],\n [0, 1, -6, -1, -6, -5],\n [-6, 4, -2, 3, 2, -1],\n [4, 4, -6, 6, -6, -5],\n [2, -4, -6, -2, 0, -1],\n [5, -6, -2, -2, -1, -4]], determine the value at position (2, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1276", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 0, -2, -2, -2, 3],\n [3, -4, -6, -2, 2, -6],\n [-4, 6, 6, -3, -6, -6],\n [1, -5, 5, 1, 0, 3],\n [3, -5, -1, -1, -4, 4],\n [-5, 5, -6, -1, 5, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1163197", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 1) of the matrix A^4 where A is:\n[[4, -2, -6, -2, 0, -2],\n [-2, 4, -2, -2, 2, 6],\n [-6, -2, -5, -4, -2, 0],\n [-2, -2, -4, 2, 1, -2],\n [0, 2, -2, 1, -4, -2],\n [-2, 6, 0, -2, -2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -6, 4, 0, 1, -4],\n [-6, -1, 1, -3, 4, 5],\n [4, 1, -4, 2, -2, 2],\n [0, -3, 2, -3, -2, -4],\n [1, 4, -2, -2, 4, 1],\n [-4, 5, 2, -4, 1, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145417", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, -5, 5, 3, 6, -1],\n [-2, -1, -6, -2, 2, 5],\n [3, -5, -6, 3, 6, 4],\n [2, 3, 2, 2, -1, 1],\n [4, 6, -6, 3, -3, -6],\n [1, -6, -4, 6, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196467", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the 4th power of the matrix:\n[[-1, 3, 5, 0, 1, -5],\n [6, 3, 4, 1, -4, 0],\n [-4, 0, 4, 5, 6, -5],\n [3, -1, -4, -4, 2, 0],\n [-2, 5, 3, 0, 2, -6],\n [0, -1, 3, 5, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[6, -3, 2, -3, 3, -4],\n [2, 6, -5, -3, -1, -5],\n [1, 1, -6, 5, -4, 3],\n [2, -2, -1, -3, 3, -5],\n [4, 1, 4, 6, -1, -2],\n [2, -6, -2, -1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275252", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-1, 1, -3, 4, 0, 2],\n [1, 0, -2, -4, -2, -3],\n [-3, -2, -1, -3, 0, 6],\n [4, -4, -3, -1, -6, 3],\n [0, -2, 0, -6, 4, 0],\n [2, -3, 6, 3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-181424", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, -2, -2, -5, -2, -6],\n [-2, -6, 4, -4, 3, -2],\n [-2, 4, -3, 0, 4, -5],\n [-5, -4, 0, 1, -1, -2],\n [-2, 3, 4, -1, 6, 2],\n [-6, -2, -5, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1854421", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 4, 1, -1, 0, -4],\n [-6, -2, 5, 5, -5, -2],\n [1, 4, 2, -5, 5, -4],\n [-4, -6, 1, -1, 5, 6],\n [1, 4, 2, -2, 5, -4],\n [-2, -2, -2, -4, 4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-617", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 2, 6, 3, 2, -5],\n [1, 1, 0, 1, -4, 6],\n [-1, -6, 0, -6, 2, -6],\n [-6, 0, -5, -2, 1, 1],\n [-4, 0, -4, -1, -1, -4],\n [0, -4, 1, 3, -3, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12896", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 5th power of the matrix:\n[[-6, -3, 0, 4, -3, 6],\n [-1, 2, -6, 6, -2, 4],\n [0, -6, -3, -1, -5, 3],\n [-2, 4, 3, -6, -1, -1],\n [6, -3, 6, 1, -3, 1],\n [6, 1, -2, 6, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29723", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[6, -5, 4, -4, -4, -3],\n [-3, 3, 4, 4, -2, -3],\n [4, 3, 1, -1, -1, 1],\n [0, 3, 4, 5, 3, 6],\n [1, -5, 2, -6, 1, 5],\n [4, 5, 5, -3, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "647067", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 0, 2, 0, -6, 4],\n [0, 2, -1, 0, 2, 0],\n [2, -1, 4, -2, -3, 0],\n [0, 0, -2, -1, -2, 2],\n [-6, 2, -3, -2, 1, -2],\n [4, 0, 0, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70664", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 3, 2, -4, -3, 2],\n [3, 4, -1, -5, 0, -5],\n [4, -5, 4, -6, 4, 4],\n [5, 4, -4, -1, 1, 2],\n [0, -3, -1, -2, 1, -6],\n [-6, 6, 4, -1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57883", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, -2, -6, 0, -6, -3],\n [2, -6, -3, -1, -1, 5],\n [6, 1, -6, 0, -6, 6],\n [0, -4, 4, 1, -4, 6],\n [-6, 6, 6, 1, -4, -5],\n [-6, -4, -5, -5, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84642", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-6, -5, -1, -4, -3, -6],\n [1, 6, 0, 0, -4, 3],\n [3, -4, -5, 5, -6, 0],\n [0, 5, -5, 0, 6, 1],\n [-6, 2, 0, -4, 1, 0],\n [4, 6, 1, -1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1144", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, -4, -4, 4, 4, -5],\n [-4, 1, 0, 2, -4, -4],\n [-4, 0, -2, -3, -4, -1],\n [4, 2, -3, 0, 2, -4],\n [4, -4, -4, 2, 5, 0],\n [-5, -4, -1, -4, 0, 3]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4178", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -4, 0, 0, 5, -3],\n [-2, -2, -1, 2, -5, -2],\n [5, -4, -3, 3, -1, 5],\n [1, -6, 3, 1, 4, 0],\n [-6, -5, -4, -6, 2, 1],\n [-5, 6, 2, 0, 2, -1]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2777", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, 4, -3, 3, 3, 6],\n [6, -5, 0, -2, 4, -1],\n [-5, -2, 3, -3, 2, -1],\n [-5, -6, -2, 2, -1, 3],\n [5, 0, -2, 3, -1, -2],\n [4, 2, -1, 4, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "591501", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 6, 2, -2, 0, 3],\n [6, -6, 3, -2, 5, 3],\n [-5, 5, -1, 4, -6, -4],\n [-2, -3, -4, 3, 6, -2],\n [4, 1, 4, -3, -6, 4],\n [0, 1, -4, -1, -5, 0]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-446", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 6) of the result:\nA =\n[[1, 1, 2, 0, 1, -2],\n [1, -3, -4, 0, -5, 0],\n [2, -4, 4, 0, -1, -2],\n [0, 0, 0, -2, 2, 1],\n [1, -5, -1, 2, 6, 0],\n [-2, 0, -2, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1374", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[-5, -2, 5, 5, -4, -1],\n [-5, 5, -4, -2, 5, 4],\n [4, -6, 6, -6, 3, 2],\n [0, -6, 5, 1, -4, 1],\n [-2, -6, 0, -2, -1, -1],\n [1, 2, -5, 2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41223", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 2, 6, 3, 3, 0],\n [-6, 0, 3, -2, -1, 3],\n [0, -2, 0, 2, -4, 1],\n [-5, 4, 0, 6, -5, -3],\n [0, -4, -5, 4, 3, 0],\n [-6, 1, -4, 5, 5, 6]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1644", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-5, -4, -2, 4, 1, 3],\n [0, 0, 5, 0, 1, -6],\n [-3, 6, -1, 2, 6, -5],\n [-6, 6, 3, 5, -5, 0],\n [-4, 3, -5, 4, 0, 6],\n [6, -5, -4, 4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "646875", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 1) of the result:\nA =\n[[6, -6, 6, -2, 5, 2],\n [1, 5, 2, 3, 2, 0],\n [-3, -2, -6, -6, -4, 6],\n [1, -5, -3, -5, -2, 2],\n [-6, -2, 2, -6, 2, 1],\n [-3, 5, 4, 3, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26675", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 4, 5, -1, 0, 1],\n [1, 4, 6, -5, 2, 0],\n [-3, -3, 4, 1, -3, 6],\n [-1, -2, -4, 6, 3, 4],\n [-5, 2, 3, 2, -6, 3],\n [-4, 1, -1, -2, -2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "309", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -6, -2, 1, -2, 4],\n [-6, 6, -1, 2, -4, 0],\n [-2, -1, 1, 1, 0, 2],\n [1, 2, 1, 2, 2, 0],\n [-2, -4, 0, 2, 1, -4],\n [4, 0, 2, 0, -4, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31017", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 5, 3, 2, 1, 2],\n [-2, 4, 4, -5, 1, 5],\n [-1, 1, 4, -2, 3, -5],\n [-1, -2, 5, 6, 5, -2],\n [6, -6, -5, 1, 6, 6],\n [-4, 3, -4, 1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87768", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[1, 2, 5, 2, -3, -2],\n [2, -4, 2, 4, -4, 2],\n [5, 2, 6, 0, 5, 2],\n [2, 4, 0, 4, 2, 4],\n [-3, -4, 5, 2, 3, 3],\n [-2, 2, 2, 4, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1279185", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 0, 0, 0, 4, 2],\n [0, 0, -6, 1, 0, -4],\n [0, -6, 1, -3, 5, -1],\n [0, 1, -3, -4, 2, 0],\n [4, 0, 5, 2, -2, 0],\n [2, -4, -1, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-155949", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -4, 0, -2, -1, 2],\n [-4, -6, -3, 0, -2, 4],\n [0, -3, 6, 6, -2, 0],\n [-2, 0, 6, 5, -2, 0],\n [-1, -2, -2, -2, 4, 4],\n [2, 4, 0, 0, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30998", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, 1, 2, 2, -2, 2],\n [1, 6, 4, 1, -3, -4],\n [2, 4, 4, 1, -5, 4],\n [2, 1, 1, -2, 0, 4],\n [-2, -3, -5, 0, -2, -2],\n [2, -4, 4, 4, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43025", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[6, -4, -6, 2, 1, 5],\n [-5, 5, 4, 1, 5, 2],\n [-6, 6, -2, 1, 4, -5],\n [-3, 0, -4, 6, 5, -2],\n [1, 5, 3, -4, -3, 2],\n [0, -6, 5, -3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21882", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 2, 5, -1, -1, -2],\n [-2, -5, 1, 1, 4, 6],\n [-6, 1, -2, -5, -5, -1],\n [4, 6, 2, -6, 5, -1],\n [2, 1, 4, -1, -4, 1],\n [2, -6, 5, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63481", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[5, -3, -6, 3, 1, -5],\n [5, -6, -5, -6, -6, 2],\n [6, -6, 6, -3, 3, -1],\n [0, -5, -1, 0, 3, 3],\n [-5, -5, 3, 0, 5, -6],\n [1, 4, 6, -4, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3798", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 3) of the 4th power of the matrix:\n[[2, 2, 3, 2, 2, 0],\n [2, 1, 0, -3, 4, 2],\n [3, 0, 4, 0, -4, 0],\n [2, -3, 0, -4, 0, 6],\n [2, 4, -4, 0, 5, -2],\n [0, 2, 0, 6, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1220", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 0, -2, 4, -2, 6],\n [0, -2, -2, 0, 6, -6],\n [-2, -2, -4, -2, 2, 0],\n [4, 0, -2, 5, 1, 0],\n [-2, 6, 2, 1, -6, 3],\n [6, -6, 0, 0, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-928", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 2, -3, 0, 0, 2],\n [2, 1, -1, -4, 0, -2],\n [-3, -1, -2, -3, -2, -2],\n [0, -4, -3, 0, 4, -3],\n [0, 0, -2, 4, 5, -5],\n [2, -2, -2, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-259338", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, -2, 0, 1, 4, 2],\n [-2, 0, -2, -2, 0, 2],\n [0, -2, 5, 0, 2, -3],\n [1, -2, 0, 0, 2, -2],\n [4, 0, 2, 2, -5, 0],\n [2, 2, -3, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3610", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 2, -3, -1, 4, -5],\n [2, 3, 2, 2, 2, 2],\n [-3, 2, -3, 0, 1, 5],\n [-1, 2, 0, -3, 5, 2],\n [4, 2, 1, 5, -2, 0],\n [-5, 2, 5, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59781", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[5, 4, 6, -3, -5, -5],\n [2, -2, -3, 3, 6, -6],\n [0, -4, -1, -2, -2, 4],\n [-2, -6, -6, -4, 5, 3],\n [-3, -2, -5, 1, 4, 4],\n [-5, 2, -5, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2135412", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (6, 5) of the result:\nA =\n[[1, 0, 0, 0, 0, 1],\n [0, 0, 3, -1, -6, -1],\n [0, 3, 1, 0, -1, -6],\n [0, -1, 0, -1, -1, -4],\n [0, -6, -1, -1, 3, 4],\n [1, -1, -6, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90292", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, -4, 4, 3, 0, 4],\n [-4, -6, -2, -5, 2, -2],\n [4, -2, 5, -2, -2, -2],\n [3, -5, -2, 2, 5, 0],\n [0, 2, -2, 5, -3, -4],\n [4, -2, -2, 0, -4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31046", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 2) of the matrix A^4 where A is:\n[[-5, -5, 6, 2, 0, -4],\n [6, 4, -6, 1, -1, 0],\n [2, -2, -6, 5, 3, 0],\n [-2, -4, 5, 6, 2, -6],\n [-6, -6, -4, 5, -1, 3],\n [4, -4, 1, 3, -5, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2154", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[-4, 2, 0, 0, 0, 2],\n [2, -2, 0, 1, 0, 4],\n [0, 0, -2, 0, -2, 0],\n [0, 1, 0, 5, 4, 4],\n [0, 0, -2, 4, 0, -3],\n [2, 4, 0, 4, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-256", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 2, -2, -5, -2, 4],\n [2, -2, -1, 5, 6, 0],\n [-2, -1, 3, -3, -1, -1],\n [-5, 5, -3, 3, 1, 5],\n [-2, 6, -1, 1, 6, 2],\n [4, 0, -1, 5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "801159", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, -4, 2, 2, 2, -4],\n [-4, 5, 0, 4, 2, 4],\n [2, 0, -1, 1, 2, 2],\n [2, 4, 1, 2, 3, 0],\n [2, 2, 2, 3, 1, -1],\n [-4, 4, 2, 0, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "262024", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -1, -2, 0, -1, 2],\n [-1, -5, -4, -4, 0, 0],\n [-2, -4, -2, -3, 0, 6],\n [0, -4, -3, -2, -3, 0],\n [-1, 0, 0, -3, 4, 2],\n [2, 0, 6, 0, 2, -5]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8165", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 0, -1, -3, -3, -2],\n [0, 6, 0, 2, -6, 4],\n [-1, 0, 5, -2, -3, 1],\n [-3, 2, -2, 6, -4, 2],\n [-3, -6, -3, -4, 2, 0],\n [-2, 4, 1, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44140", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[6, -6, 5, -5, 5, -2],\n [5, 4, -2, 1, -1, 1],\n [-5, -4, -1, 5, 6, 3],\n [-4, -1, -1, -5, 0, 5],\n [-5, -1, -6, -4, -5, 0],\n [-3, 1, -1, 5, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87884", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 4, 2, 2, 2, 1],\n [4, 0, 0, -4, 0, -2],\n [2, 0, 6, -1, 4, -2],\n [2, -4, -1, -3, 0, 0],\n [2, 0, 4, 0, -3, -4],\n [1, -2, -2, 0, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25672", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[5, -4, -2, 0, 0, -2],\n [-4, 0, -5, 1, -2, 4],\n [-2, -5, 4, 0, 0, -4],\n [0, 1, 0, 0, 0, -3],\n [0, -2, 0, 0, -1, 4],\n [-2, 4, -4, -3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125879", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, 3, -1, -5, 6, -4],\n [1, 3, -1, -4, 0, -3],\n [2, -2, -4, -5, 4, -5],\n [-4, -5, -3, -5, 3, 2],\n [-5, 2, 6, -1, -6, -3],\n [-6, -1, 6, -3, -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": "164793", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -1, 2, 6, -2, -5],\n [1, -2, -5, -3, 2, -3],\n [6, 5, 5, 5, 6, -3],\n [-5, 6, 5, -1, 6, 4],\n [-5, 5, 0, -4, -4, -2],\n [-4, -5, 3, 2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21251", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 4, 0, 2, 3, -4],\n [4, -4, 2, -2, 1, -3],\n [0, 2, -6, -2, -3, -2],\n [2, -2, -2, 0, 5, 2],\n [3, 1, -3, 5, -1, -2],\n [-4, -3, -2, 2, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12560", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 2, -1, 0, 0, 2],\n [2, -2, 0, -2, 0, 2],\n [-1, 0, -2, 0, 3, 0],\n [0, -2, 0, -6, 2, -4],\n [0, 0, 3, 2, -2, -4],\n [2, 2, 0, -4, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47292", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 4, -2, -3, 0, -2],\n [3, -3, -5, -3, 5, -5],\n [1, -4, 2, 6, -3, 6],\n [-1, 3, -2, 3, 6, -6],\n [2, -6, 1, 2, 2, -6],\n [-5, 5, 6, -6, 3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9481", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 5, 1, -2, 5, 4],\n [0, -5, 1, 4, -1, 1],\n [-6, -6, 5, 0, 1, 6],\n [-4, -2, 5, -6, 0, -2],\n [1, 6, 1, 2, 0, 4],\n [-6, 6, -4, 1, -4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70956", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-6, -2, 1, -2, 1, 0],\n [-2, 4, -4, -2, 0, -5],\n [1, -4, 4, 3, 0, -2],\n [-2, -2, 3, -1, 4, -4],\n [1, 0, 0, 4, -5, -2],\n [0, -5, -2, -4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15866", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[2, 3, 0, -5, 3, -2],\n [-3, 5, 4, 1, -5, -1],\n [6, -2, 5, -5, 4, 3],\n [-6, 1, -5, 0, 2, 2],\n [1, 4, 5, 3, 2, -5],\n [-1, -3, -3, -2, 5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1037198", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-6, 1, -2, -4, 3, 0],\n [0, -6, 5, 2, -5, -2],\n [6, -2, 1, 1, 0, 0],\n [5, 4, -1, -1, 4, 2],\n [-1, 5, 6, 6, -5, -5],\n [6, -2, -3, 4, -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": "1442296", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 0, 0, 2, 2, 0],\n [0, 6, -3, 1, -3, 1],\n [0, -3, 6, 2, 0, -2],\n [2, 1, 2, 3, -2, -1],\n [2, -3, 0, -2, -3, 2],\n [0, 1, -2, -1, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2249", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 0, 4, 4, -5, 2],\n [6, 2, -3, -3, -1, 3],\n [3, 3, -1, 5, -6, 2],\n [-5, -2, 2, -3, 4, -4],\n [0, -1, 1, -4, -2, 3],\n [-3, 6, -3, -3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12555", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[-1, -2, 0, -1, -2, 0],\n [-2, 1, 2, -1, 3, -3],\n [0, 2, 2, 2, -2, -6],\n [-1, -1, 2, 6, -4, -2],\n [-2, 3, -2, -4, -3, 3],\n [0, -3, -6, -2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88546", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 0, 1, -3, 2, 0],\n [0, 3, -2, -2, 0, -2],\n [1, -2, 0, -6, 2, -4],\n [-3, -2, -6, 4, 2, 0],\n [2, 0, 2, 2, 6, -1],\n [0, -2, -4, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40010", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 6) of the 4th power of the matrix:\n[[5, 3, 3, -2, 3, -2],\n [3, -3, 5, 4, -4, -4],\n [3, 5, -6, 2, 4, -4],\n [-2, 4, 2, -4, -3, -3],\n [3, -4, 4, -3, -2, 4],\n [-2, -4, -4, -3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3481", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, -3, 1, 0, 0, -2],\n [-3, -4, -2, -1, 4, -2],\n [1, -2, -1, 3, 4, 5],\n [0, -1, 3, 2, -2, 0],\n [0, 4, 4, -2, 5, 2],\n [-2, -2, 5, 0, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71037", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 5) of the matrix A^4 where A is:\n[[3, 4, 4, -4, 4, 2],\n [4, -3, 2, 4, -3, 0],\n [4, 2, 2, -1, -1, -2],\n [-4, 4, -1, -1, -2, 2],\n [4, -3, -1, -2, -2, 0],\n [2, 0, -2, 2, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1152", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-2, -4, -2, -4, 0, 4],\n [-4, 1, 0, -3, -2, -2],\n [-2, 0, 2, 2, -2, 0],\n [-4, -3, 2, 3, -2, 2],\n [0, -2, -2, -2, 1, 5],\n [4, -2, 0, 2, 5, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "609709", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -1, -6, -6, -5, -1],\n [-1, -5, -6, 3, -2, -2],\n [-5, -1, 2, -5, 3, -5],\n [-4, 6, 0, -1, 5, 1],\n [1, -1, 5, 4, 3, -4],\n [-4, -6, 0, -2, -3, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102802", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, -3, -1, 1, 1, -2],\n [-1, -3, 5, 4, 6, 2],\n [1, 3, 5, 3, -6, -5],\n [2, 1, -4, 1, 5, -6],\n [3, -3, -4, -1, 0, -3],\n [0, 2, 4, -5, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "429518", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -2, 1, -2, 0, -1],\n [-2, 1, 2, 4, 1, 0],\n [1, 2, 1, 2, -1, 1],\n [-2, 4, 2, -3, 2, 2],\n [0, 1, -1, 2, -4, -1],\n [-1, 0, 1, 2, -1, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54994", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-6, -1, 3, -2, 2, 3],\n [-1, -3, 2, -2, 0, -1],\n [3, 2, 0, 0, 5, -3],\n [-2, -2, 0, -5, -2, 1],\n [2, 0, 5, -2, 4, 0],\n [3, -1, -3, 1, 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": "802842", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 6) of the result:\nA =\n[[-5, 3, -2, -4, 6, 5],\n [6, 2, -3, -1, -5, -1],\n [-4, 5, 5, 2, 4, -5],\n [5, 5, 2, -2, 1, -5],\n [-1, -4, 5, 5, 3, -2],\n [5, 1, 3, -6, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3592", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-3, 0, 4, 1, 0, -2],\n [0, 2, 2, -3, -3, 0],\n [4, 2, 4, -4, -4, -2],\n [1, -3, -4, -4, 2, 0],\n [0, -3, -4, 2, -3, 0],\n [-2, 0, -2, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2357", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, 0, 0, -3, 0, 0],\n [0, -2, 0, -4, 4, -2],\n [0, 0, -4, 2, 0, -4],\n [-3, -4, 2, 4, 2, -2],\n [0, 4, 0, 2, -1, 0],\n [0, -2, -4, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13323", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, 2, 1, 1, 3, -1],\n [0, -1, 2, -4, -4, -4],\n [3, -4, 2, 5, -3, 6],\n [0, 2, 4, 5, 0, 2],\n [5, -4, -3, 1, -1, -2],\n [6, -3, 1, -6, 2, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10689", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, -3, 2, 4, -2, -4],\n [2, 4, 2, -3, 4, -3],\n [5, 1, -5, 2, 6, -1],\n [2, 1, 0, 6, -6, 5],\n [-4, 4, -5, -2, -2, -2],\n [-3, -2, -4, 5, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1423172", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[6, -2, 3, -1, -2, -4],\n [-2, -5, 1, -2, -2, 2],\n [3, 1, 5, -2, 2, 1],\n [-1, -2, -2, 6, -2, 0],\n [-2, -2, 2, -2, 2, 6],\n [-4, 2, 1, 0, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1522240", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, -1, 5, 6, -4, -1],\n [5, -5, 1, -5, 4, 0],\n [2, -6, 1, 0, -1, -1],\n [-1, 2, -5, -6, 6, 5],\n [-1, 3, 4, 1, -4, 5],\n [3, -6, 2, 6, 6, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16298", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[-4, 1, -4, 6, -3, 1],\n [-6, 6, 6, -1, -6, -6],\n [1, 4, -3, 5, -6, 3],\n [0, -2, -2, -6, 3, 4],\n [-1, 2, 2, 1, -2, -6],\n [2, -6, 1, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1339", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, 0, 2, 0, 6, 4],\n [-4, 4, 6, 6, -6, 1],\n [5, -4, 5, 1, 1, 6],\n [-2, 6, 5, 6, -6, 6],\n [3, 0, 5, 3, -2, 1],\n [2, 4, 0, 6, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169603", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, -4, -4, -2, -4, -5],\n [-4, -5, -4, -2, 0, 0],\n [-4, -4, -6, 0, 4, -1],\n [-2, -2, 0, 6, 4, 2],\n [-4, 0, 4, 4, 3, -2],\n [-5, 0, -1, 2, -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": "2336959", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 4) of the matrix A^4 where A is:\n[[-4, 2, 0, 5, -1, -3],\n [2, -1, 0, 2, -2, -1],\n [0, 0, -4, 1, -2, -2],\n [5, 2, 1, -2, -4, 0],\n [-1, -2, -2, -4, 5, -3],\n [-3, -1, -2, 0, -3, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3710", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 6) of the 5th power of the matrix:\n[[0, 2, -2, -1, 3, 5],\n [5, -5, -4, -4, 5, 5],\n [2, 0, 1, 4, 3, 4],\n [2, -1, -3, 5, -6, 1],\n [0, -5, 1, 5, -2, 0],\n [-3, -2, 1, -6, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6010", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 1, 1, 5, -5, 4],\n [1, 4, 1, 2, -4, 0],\n [1, 1, 1, -6, -1, -1],\n [5, 2, -6, -3, -2, 4],\n [-5, -4, -1, -2, 4, 0],\n [4, 0, -1, 4, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "125756", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, 4, 3, -4, -5, -1],\n [4, 6, -2, 3, -2, 3],\n [6, -2, 3, 5, -2, -4],\n [0, -1, -3, -5, 5, 2],\n [-6, 6, 6, 4, -3, -6],\n [6, -1, -3, -2, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "738090", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-6, 6, -5, 6, -1, -2],\n [4, 0, -4, -4, 3, -5],\n [6, -4, 3, -6, -2, 5],\n [-2, 5, 4, 0, -3, -4],\n [-6, 5, 1, 6, -4, 6],\n [-5, 4, -3, -4, 6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12672", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 3, -2, 0, -1, 3],\n [3, 3, 0, -3, 3, -1],\n [-2, 0, -2, -1, 2, 1],\n [0, -3, -1, -2, -3, 1],\n [-1, 3, 2, -3, -2, -4],\n [3, -1, 1, 1, -4, 1]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-558", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 4) of the result:\nA =\n[[-3, -1, 1, 0, -2, -6],\n [-1, -4, 2, 3, 0, 1],\n [1, 2, 3, -2, -4, 0],\n [0, 3, -2, 4, 0, 0],\n [-2, 0, -4, 0, -2, 2],\n [-6, 1, 0, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4667", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 2, 1, -3, 6, -6],\n [-6, -6, -6, 1, -4, -1],\n [-4, 4, -2, 6, 6, 0],\n [-5, -1, 6, -1, 4, -4],\n [-1, 3, 3, -2, 5, -5],\n [2, 1, -4, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "445304", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, -2, 0, 0, -6, 0],\n [-2, 0, -5, 0, -1, 3],\n [0, -5, -2, 4, 0, -2],\n [0, 0, 4, -6, 0, -2],\n [-6, -1, 0, 0, -5, -4],\n [0, 3, -2, -2, -4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-622996", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[6, 5, -5, 0, 3, 0],\n [5, -1, -1, 2, -5, 0],\n [-5, -1, 5, 2, 3, 0],\n [0, 2, 2, 1, 2, -2],\n [3, -5, 3, 2, 1, -1],\n [0, 0, 0, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1030122", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, -5, -2, 0, 6, 2],\n [-5, -2, -2, 0, 0, 2],\n [-2, -2, 0, 0, 0, -2],\n [0, 0, 0, -3, -2, -2],\n [6, 0, 0, -2, -1, -4],\n [2, 2, -2, -2, -4, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136849", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -2, 0, 0, -4, 3],\n [-2, 5, -2, 2, 0, -2],\n [0, -2, -5, -3, 0, -1],\n [0, 2, -3, 1, 4, -2],\n [-4, 0, 0, 4, 5, 3],\n [3, -2, -1, -2, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54472", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-5, 6, -4, 2, -2, 1],\n [6, -4, -4, -4, 2, 2],\n [-4, -4, -6, 4, 0, -2],\n [2, -4, 4, 4, 0, 1],\n [-2, 2, 0, 0, -2, 4],\n [1, 2, -2, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120265", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 6) of the result:\nA =\n[[-6, -3, 2, 2, -2, -3],\n [-4, -4, 5, -2, 3, -6],\n [-2, -1, 0, 5, 2, -4],\n [-5, -4, 5, 2, 5, 0],\n [2, 6, -5, -2, 6, -3],\n [-5, 2, 2, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22933", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, -1, -6, -3, 6, 0],\n [6, 6, -5, 2, 1, 1],\n [0, -3, -5, -4, 5, -1],\n [5, 5, -2, 5, 1, -1],\n [-1, -6, -3, -2, 5, 4],\n [-4, 6, 2, -6, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-63852", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -2, 5, -2, 3, 6],\n [-2, -1, 1, -5, -1, -6],\n [-3, 3, -4, 2, -4, -1],\n [-6, 5, -1, -3, 1, 6],\n [4, 2, -3, 3, 5, 3],\n [-1, -6, -3, 0, 5, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98388", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, 2, 1, 4, 1, 0],\n [2, 3, 2, 1, -4, 1],\n [1, 2, -2, 0, 0, 0],\n [4, 1, 0, 2, 2, -1],\n [1, -4, 0, 2, -3, -2],\n [0, 1, 0, -1, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13401", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 1, 0, 1, 1, -2],\n [1, -4, 6, 0, 4, -2],\n [0, 6, 6, 4, -2, 0],\n [1, 0, 4, 1, -2, 2],\n [1, 4, -2, -2, 4, 4],\n [-2, -2, 0, 2, 4, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "679309", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 4, 2, -2, 4, -1],\n [4, 6, -2, -1, 4, -2],\n [2, -2, -3, 1, 3, 0],\n [-2, -1, 1, -1, -2, -2],\n [4, 4, 3, -2, 3, -2],\n [-1, -2, 0, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122421", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[1, -1, -6, -5, -1, 4],\n [-5, 6, 3, -2, -2, -1],\n [-1, -1, -5, 3, 6, -4],\n [-1, 6, 1, 5, 6, 4],\n [5, -6, -6, 4, 6, -5],\n [4, 5, 5, -1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-48558", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, 5, 1, 4, 3, 2],\n [5, 4, -2, 2, -5, -4],\n [0, 0, -1, -1, -5, 3],\n [-1, -3, 5, -4, 6, 4],\n [6, -5, -6, 4, 4, -2],\n [-5, -5, 0, 1, 6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8235", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, -3, -6, 4, 0, -6],\n [4, -3, 1, -5, -1, 6],\n [-1, 5, 2, -2, 3, -3],\n [-2, 5, 5, 3, 4, -2],\n [1, 3, 5, 1, -5, 0],\n [1, 4, -1, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4777", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[6, -4, 0, 0, 1, -1],\n [-4, 2, -2, -2, -3, 5],\n [0, -2, -6, 0, 3, -2],\n [0, -2, 0, -3, 1, 1],\n [1, -3, 3, 1, 3, -4],\n [-1, 5, -2, 1, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-503", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 6) of the result:\nA =\n[[4, -1, 0, -2, 0, -2],\n [-1, 3, 5, -4, 0, -2],\n [0, 5, 4, -2, 4, -2],\n [-2, -4, -2, -1, -4, -2],\n [0, 0, 4, -4, -2, 4],\n [-2, -2, -2, -2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, -4, 6, 5, 0, 0],\n [0, 3, 1, -2, -2, -3],\n [0, 3, -3, -5, -3, 6],\n [6, 1, 2, -4, 0, 5],\n [2, 4, -3, 3, -4, -2],\n [-6, -4, 1, 4, 1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43827", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, -4, 2, 0, 0, 2],\n [-4, -4, -2, 2, -4, 0],\n [2, -2, -3, 1, 2, -2],\n [0, 2, 1, 6, 2, 2],\n [0, -4, 2, 2, 3, 4],\n [2, 0, -2, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "512866", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -4, -1, -3, 5, 5],\n [-1, -4, -3, 2, -2, 6],\n [0, 3, -5, -2, 2, 4],\n [-4, 2, 4, -1, -3, 0],\n [1, -1, -2, -1, -2, 1],\n [-6, 4, 0, 3, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6732", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 2, -6, 4, 3, -1],\n [2, -6, -3, -3, 2, 4],\n [-2, -2, -1, -6, -6, 2],\n [-4, -3, -6, 2, 1, -5],\n [1, 0, 4, -1, -6, 0],\n [3, 0, 6, 2, -6, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78891", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 3) of the result:\nA =\n[[4, 0, 0, -1, 1, -4],\n [0, -3, 1, 0, 0, -6],\n [0, 1, 6, -2, -4, 0],\n [-1, 0, -2, -3, -4, -3],\n [1, 0, -4, -4, 1, 0],\n [-4, -6, 0, -3, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 0, 0, 2, 0, -5],\n [0, 1, -2, 1, 0, 0],\n [0, -2, 1, 5, -2, -3],\n [2, 1, 5, 3, -2, -1],\n [0, 0, -2, -2, 1, 0],\n [-5, 0, -3, -1, 0, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80623", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 4) of the 5th power of the matrix:\n[[0, -4, 0, -3, -3, -1],\n [-4, -3, 0, 2, -4, -5],\n [0, 0, 4, -4, 2, 2],\n [-3, 2, -4, -2, 3, 2],\n [-3, -4, 2, 3, -6, 0],\n [-1, -5, 2, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88448", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -2, -2, 4, -4, 0],\n [-2, 0, -2, -1, -3, 2],\n [-2, -2, 6, 1, -3, -1],\n [4, -1, 1, 3, 4, 3],\n [-4, -3, -3, 4, -2, 1],\n [0, 2, -1, 3, 1, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527636", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-6, 0, 0, 4, -2, 0],\n [0, 3, -2, 1, 0, -4],\n [0, -2, 3, 0, 0, 0],\n [4, 1, 0, 4, 2, -3],\n [-2, 0, 0, 2, -3, 2],\n [0, -4, 0, -3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9576", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -5, 2, 4, 0, -2],\n [-5, -1, -2, 3, -2, 3],\n [2, -2, 6, 0, -1, 1],\n [4, 3, 0, -2, 2, 2],\n [0, -2, -1, 2, -1, -4],\n [-2, 3, 1, 2, -4, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-179753", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, -4, 2, -1, 0, 0],\n [-4, -6, 1, -2, 2, 5],\n [2, 1, -1, -6, 4, -1],\n [-1, -2, -6, -4, -3, 0],\n [0, 2, 4, -3, 6, 2],\n [0, 5, -1, 0, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174516", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-6, 0, 1, -2, 3, -5],\n [0, 6, -1, 0, -6, -2],\n [1, -1, -6, 3, 1, 0],\n [-2, 0, 3, 6, -5, -4],\n [3, -6, 1, -5, 0, 4],\n [-5, -2, 0, -4, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240028", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[1, -2, 2, -4, -2, 3],\n [-2, 4, 4, 0, -1, -2],\n [2, 4, -1, 4, 2, 2],\n [-4, 0, 4, -6, 2, 1],\n [-2, -1, 2, 2, -2, 0],\n [3, -2, 2, 1, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "515890", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[3, 0, 0, 0, 0, -1],\n [0, 5, -2, 0, 0, 2],\n [0, -2, 6, -2, -2, 0],\n [0, 0, -2, 1, -2, 2],\n [0, 0, -2, -2, -5, 4],\n [-1, 2, 0, 2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-156", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-6, 0, 2, 0, -1, 0],\n [0, 6, -4, 0, -4, -2],\n [2, -4, -3, 2, 3, 0],\n [0, 0, 2, 2, 0, 4],\n [-1, -4, 3, 0, 6, -3],\n [0, -2, 0, 4, -3, 3]], determine the value at position (2, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "694", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, 1, -4, -6, 0, 3],\n [1, -1, -1, 6, 1, 3],\n [-4, -1, -1, -1, 0, -3],\n [-6, 6, -1, -4, 1, 0],\n [0, 1, 0, 1, 6, -1],\n [3, 3, -3, 0, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-130092", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-5, -2, 1, 4, -3, 2],\n [-2, -6, -2, 4, 0, 1],\n [1, -2, 5, 0, -2, -2],\n [4, 4, 0, 4, 2, -3],\n [-3, 0, -2, 2, 1, -2],\n [2, 1, -2, -3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79299", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, -1, -2, 4, 0, 4],\n [-1, -5, 1, 3, -2, -6],\n [-2, 1, 6, -2, 0, 3],\n [4, 3, -2, 3, -6, -1],\n [0, -2, 0, -6, -4, -3],\n [4, -6, 3, -1, -3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2861738", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-6, 5, 0, 5, 1, -4],\n [5, -2, 4, 2, 2, -2],\n [0, 4, 2, 0, 2, -2],\n [5, 2, 0, 2, -2, 6],\n [1, 2, 2, -2, 6, -4],\n [-4, -2, -2, 6, -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": "2569394", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, 2, -1, -5, 1, -4],\n [2, -1, 2, 0, 3, 0],\n [-1, 2, -3, 4, -2, 4],\n [-5, 0, 4, 6, 2, 0],\n [1, 3, -2, 2, -4, -2],\n [-4, 0, 4, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "599390", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 5, -3, 4, 3, 4],\n [4, 4, -5, -6, 2, 5],\n [5, -5, 6, 1, 2, -3],\n [1, 2, 3, 3, -2, 6],\n [0, 3, -3, -6, -4, -2],\n [-4, 5, 6, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95050", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 5, -1, 6, 3, -6],\n [0, -4, -2, 3, -3, 3],\n [-2, -2, -1, 3, 5, 3],\n [6, 6, 4, -1, 1, 1],\n [4, 2, 1, 6, 4, -5],\n [5, 3, 5, 4, -6, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37438", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, -5, 0, 0, 3, 0],\n [-5, -6, 2, 4, -2, 0],\n [0, 2, -6, 5, 2, -2],\n [0, 4, 5, -3, -2, 1],\n [3, -2, 2, -2, 0, -1],\n [0, 0, -2, 1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-199869", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[5, -4, 5, 2, 0, -4],\n [-4, -1, 4, 0, -2, -2],\n [5, 4, -5, 0, -2, 4],\n [2, 0, 0, 6, -2, 0],\n [0, -2, -2, -2, 1, 4],\n [-4, -2, 4, 0, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181123", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 2) of the matrix A^4 where A is:\n[[5, 0, 0, 0, 2, 2],\n [0, 6, 0, -2, 2, 5],\n [0, 0, -3, 4, 2, 0],\n [0, -2, 4, 5, -4, -4],\n [2, 2, 2, -4, -6, -4],\n [2, 5, 0, -4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1752", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the 4th power of the matrix:\n[[-2, 6, 3, -4, 2, -3],\n [6, 6, -4, 4, -5, 3],\n [6, 4, 2, -3, -4, 0],\n [1, 4, -5, 0, 5, -2],\n [4, -2, -4, -2, 5, -5],\n [-3, -1, -6, 3, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3899", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 2, 1, 4, -6, 2],\n [2, -1, 0, 2, 0, 2],\n [1, 0, -2, 0, 0, 0],\n [4, 2, 0, 3, -4, -5],\n [-6, 0, 0, -4, 1, 6],\n [2, 2, 0, -5, 6, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4300", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-3, 0, 0, -1, 4, 2],\n [0, 1, 0, -4, 2, -4],\n [0, 0, 3, 2, 4, -2],\n [-1, -4, 2, -5, 1, 2],\n [4, 2, 4, 1, 1, 2],\n [2, -4, -2, 2, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258404", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, -3, -3, 0, 4, 0],\n [6, 4, 1, 4, -2, 0],\n [1, 2, -4, -4, -3, -2],\n [3, -6, 0, 2, 1, -2],\n [-3, 5, 0, -2, 0, 5],\n [-6, -6, 3, 6, -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": "50651", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -5, 0, 5, 3, -5],\n [4, -3, -5, -1, 1, 3],\n [-3, -2, -3, -4, -2, 2],\n [1, 1, 1, 5, 1, 0],\n [1, 4, 1, 6, 1, 5],\n [3, 0, 5, -6, -3, 6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39326", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[6, -3, -2, 3, -1, -3],\n [-5, -1, 1, 1, 0, -1],\n [-5, 0, 4, 5, -2, -1],\n [3, 1, 1, -4, 5, 5],\n [0, -6, -6, 0, 3, 2],\n [0, 3, -2, 1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8038", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, 4, -2, -4, -2, 0],\n [4, -6, 2, -2, -2, 3],\n [-2, 2, 1, 2, 4, 2],\n [-4, -2, 2, 2, 2, 1],\n [-2, -2, 4, 2, 2, 0],\n [0, 3, 2, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11518", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 2, 2, 0, -4, -4],\n [2, -4, 2, 3, 0, 1],\n [2, 2, 5, 0, 3, 4],\n [0, 3, 0, -1, -2, 2],\n [-4, 0, 3, -2, 6, 0],\n [-4, 1, 4, 2, 0, 0]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "694", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 3, -2, -2, -1, -2],\n [3, 5, -2, 2, 0, -2],\n [-2, -2, 2, -2, 0, -4],\n [-2, 2, -2, 6, 2, -2],\n [-1, 0, 0, 2, 6, 0],\n [-2, -2, -4, -2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "509667", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[1, 3, 1, -5, 4, 6],\n [0, 1, 1, 4, 3, 4],\n [6, 0, -2, -6, 5, 2],\n [6, 0, -5, -1, -5, -6],\n [0, 6, -5, 6, -5, 6],\n [4, -2, -2, 0, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-315", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, -3, 2, -3, 3, 5],\n [-2, 0, -3, -6, 2, -3],\n [2, -1, -6, 5, -4, 4],\n [-5, 2, 5, -6, 6, 2],\n [2, 1, 1, 4, 5, -6],\n [4, 1, 3, -4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8435", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -6, -6, 3, 6, -2],\n [-2, 1, 0, 1, -1, -1],\n [-5, -1, -2, 6, -4, -1],\n [1, 2, -6, -4, -4, 4],\n [1, -6, -2, -4, -5, 1],\n [-4, 0, 5, 4, -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": "86215", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, 0, 1, 1, 0, 0],\n [0, -2, -5, 0, -4, 2],\n [1, -5, 4, -4, 3, 6],\n [1, 0, -4, 2, 1, -3],\n [0, -4, 3, 1, -4, 2],\n [0, 2, 6, -3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66495", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 1) of the 5th power of the matrix:\n[[1, -4, 5, -2, 2, -2],\n [-4, -1, 3, 4, 0, 0],\n [5, 3, 0, 4, 2, -4],\n [-2, 4, 4, -1, 3, 2],\n [2, 0, 2, 3, -4, 0],\n [-2, 0, -4, 2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11834", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 0, 0, -4, 0, 0],\n [0, 0, -2, -4, 1, 0],\n [0, -2, 0, -2, -1, 4],\n [-4, -4, -2, -2, 0, 0],\n [0, 1, -1, 0, 6, -2],\n [0, 0, 4, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33753", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, -2, 1, 2, 3, -2],\n [-1, -6, 4, 5, 0, -3],\n [4, -5, -2, 5, -4, -1],\n [1, 0, -4, 1, -5, 3],\n [2, -3, -6, 1, 0, 4],\n [6, -2, 3, 6, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53144", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 1, 4, 6, -1, 6],\n [-2, 2, 4, -5, -6, 1],\n [5, -4, 4, 5, 5, 5],\n [0, 3, 6, 4, 1, 6],\n [6, -1, 5, 3, 2, 0],\n [3, -2, 1, -5, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153384", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 2, -2, 3, 2, -2],\n [2, -6, -4, 2, -2, 0],\n [-2, -4, -6, -4, -1, 1],\n [3, 2, -4, -6, -4, 1],\n [2, -2, -1, -4, 6, 2],\n [-2, 0, 1, 1, 2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-578444", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, -4, 0, 0, -5, 0],\n [-4, -2, -3, 1, -2, 2],\n [0, -3, 3, 1, 4, 1],\n [0, 1, 1, -5, -2, -4],\n [-5, -2, 4, -2, 5, -3],\n [0, 2, 1, -4, -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": "1110220", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-4, -1, 0, -2, 4, 0],\n [-1, 1, 0, 4, -4, -2],\n [0, 0, -6, -3, 2, 2],\n [-2, 4, -3, -3, 2, 2],\n [4, -4, 2, 2, 5, 4],\n [0, -2, 2, 2, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2234", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 0, 4, -4, 2, 2],\n [0, 5, -4, -1, 4, 6],\n [4, -4, 3, 2, -2, 0],\n [-4, -1, 2, 0, 2, -4],\n [2, 4, -2, 2, -1, 4],\n [2, 6, 0, -4, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45067", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 3, -5, 1, 3, 2],\n [-2, 3, -3, -1, 1, 4],\n [-4, 3, 4, 4, -6, -3],\n [-3, -6, 2, -4, -2, -1],\n [1, -1, -4, -1, -6, -3],\n [-1, 0, 4, 6, 4, 3]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3297", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -2, 4, 4, 2, -2],\n [-2, -6, 0, 4, 2, -2],\n [4, 0, 6, -4, 0, -2],\n [4, 4, -4, 6, 2, -2],\n [2, 2, 0, 2, 0, 2],\n [-2, -2, -2, -2, 2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25888", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, 2, 0, -3, -1, 6],\n [2, 0, -6, -5, 4, 4],\n [0, -6, -1, 0, 4, -4],\n [-3, -5, 0, -2, 4, 2],\n [-1, 4, 4, 4, 3, 2],\n [6, 4, -4, 2, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "139723", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 2, -1, 2, 4, 3],\n [2, 1, 6, 2, 6, 0],\n [-1, 6, -6, 2, -2, 2],\n [2, 2, 2, -3, 2, 2],\n [4, 6, -2, 2, 3, -1],\n [3, 0, 2, 2, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1628568", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -3, -3, -4, 6, 3],\n [-2, -2, 4, 0, -3, 6],\n [-3, 2, -1, -3, -5, -1],\n [-5, -2, -1, -3, 6, -4],\n [0, -5, 6, 4, -1, 6],\n [-3, -1, -3, -3, -3, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1548835", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 4) of the result:\nA =\n[[0, -1, -3, 1, 1, 0],\n [-1, -3, 0, -3, -2, -4],\n [-3, 0, 0, 5, 0, 0],\n [1, -3, 5, 5, -2, 2],\n [1, -2, 0, -2, -3, 1],\n [0, -4, 0, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-564", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -5, 4, -3, -2, -1],\n [-5, 5, 1, -3, 2, -1],\n [4, 1, -6, 4, 2, -4],\n [-3, -3, 4, -5, 0, -2],\n [-2, 2, 2, 0, 5, 0],\n [-1, -1, -4, -2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1980926", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 0, 3, 0, 2, -6],\n [0, 4, 5, 0, 6, 1],\n [3, 5, -6, -1, -1, -2],\n [0, 0, -1, -3, 2, 4],\n [2, 6, -1, 2, 3, 0],\n [-6, 1, -2, 4, 0, 3]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -1, 6, -1, 2, -3],\n [-5, 4, 4, 2, -5, 3],\n [2, -5, 5, 1, 2, 5],\n [3, 2, 3, 2, -5, -3],\n [0, 5, -5, -6, -4, 5],\n [-3, 1, -1, 4, -5, 2]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 6, 0, 0, 6, -3],\n [6, 0, 1, -2, 0, -2],\n [0, 1, -5, 0, 3, -3],\n [0, -2, 0, 6, 0, -1],\n [6, 0, 3, 0, -6, 1],\n [-3, -2, -3, -1, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7322", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, 4, 4, -2, -3, -2],\n [1, -4, 0, -1, 5, -6],\n [6, 0, 6, 0, 5, -6],\n [2, -1, 5, -5, -2, 6],\n [4, -3, 0, 1, 4, 4],\n [-6, -2, -4, -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": "2209740", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[-1, 0, 1, 6, 4, -3],\n [-4, -2, 2, 6, -1, 2],\n [-1, -5, 6, -2, 5, 4],\n [2, 1, 0, -6, -3, 5],\n [0, 4, 0, -1, 1, 4],\n [6, -1, 3, -4, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[-6, 4, -4, 0, -3, 0],\n [4, -3, -2, 3, 2, 1],\n [-4, -2, 5, -4, -3, 4],\n [0, 3, -4, 6, -2, 4],\n [-3, 2, -3, -2, -4, 2],\n [0, 1, 4, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5268", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[2, -1, 5, -3, -2, 6],\n [-1, 4, -4, 1, -3, 1],\n [3, 3, -4, 3, 0, 4],\n [6, 5, 2, -3, 1, -4],\n [0, -4, 5, 0, 4, 3],\n [3, 4, 4, -1, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-258612", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 2, -3, 2, 0, 2],\n [2, -6, -2, -1, 2, 3],\n [-3, -2, 1, 1, 0, 3],\n [2, -1, 1, 5, 0, 0],\n [0, 2, 0, 0, -2, 2],\n [2, 3, 3, 0, 2, -1]], determine the value at position (6, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9110", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -2, 0, 2, -4, 0],\n [-2, 0, 2, 3, 0, -2],\n [0, 2, 6, 2, -4, 6],\n [2, 3, 2, 2, -2, 6],\n [-4, 0, -4, -2, 5, -2],\n [0, -2, 6, 6, -2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1513024", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, -1, 3, 4, -2, -1],\n [-3, 3, -1, 0, 2, 3],\n [0, -1, -6, -5, -6, 2],\n [3, 3, 2, 0, 6, -5],\n [-1, 4, -3, -6, -6, 5],\n [-2, 5, -5, -3, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27464", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, -1, 3, -3, -6, 0],\n [-5, 2, 6, -4, 1, 6],\n [1, -4, -3, -5, -3, 4],\n [4, 4, 2, -5, 5, 5],\n [6, -4, 4, 4, -3, -2],\n [-6, 0, 3, 0, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "757325", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 0, -1, 2, 2, 0],\n [0, 3, 0, 2, 0, -4],\n [-1, 0, 0, 2, 2, 2],\n [2, 2, 2, 1, 0, -2],\n [2, 0, 2, 0, 3, -1],\n [0, -4, 2, -2, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13296", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -4, -2, 4, -3, 5],\n [-4, 4, 2, -5, 1, -2],\n [-2, 2, -1, 0, 0, -2],\n [4, -5, 0, -1, 0, -2],\n [-3, 1, 0, 0, 4, -4],\n [5, -2, -2, -2, -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": "274150", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 0, -2, 4, -2, 2],\n [0, 0, 4, 0, 2, 4],\n [-2, 4, 5, 1, -1, -3],\n [4, 0, 1, -1, 1, 3],\n [-2, 2, -1, 1, 3, 4],\n [2, 4, -3, 3, 4, -4]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2703", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 4, 3, 1, 1, 0],\n [4, -1, 4, 2, -4, -2],\n [3, 4, 0, 0, 0, -2],\n [1, 2, 0, 6, 3, 0],\n [1, -4, 0, 3, 6, -4],\n [0, -2, -2, 0, -4, 2]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-306", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-1, 1, -6, -2, 5, -6],\n [3, 4, 1, 1, -6, 2],\n [-5, 5, 2, -6, 5, 3],\n [2, -3, 2, 0, 4, -1],\n [-2, 4, 2, -5, 6, 4],\n [5, -5, 4, 5, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174396", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, 3, 4, 4, -2, 1],\n [3, -6, -1, 0, -5, 1],\n [4, -1, -1, 2, 2, 0],\n [4, 0, 2, -3, 0, -2],\n [-2, -5, 2, 0, 6, -2],\n [1, 1, 0, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "655749", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, 1, 2, -3, 4, -2],\n [1, 5, 0, -2, -1, 1],\n [2, 0, -1, 2, -2, -4],\n [-3, -2, 2, 0, 0, 2],\n [4, -1, -2, 0, 5, 4],\n [-2, 1, -4, 2, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9315", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, -4, 1, -1, 6, 0],\n [5, -1, -1, 5, -4, 5],\n [6, 1, 5, 0, 0, -1],\n [-2, 3, 1, -2, 2, 2],\n [-6, -1, 0, -4, 0, 4],\n [4, 0, 6, 4, -5, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1286", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-6, -2, 2, 0, 0, 4],\n [6, 5, -5, 1, -4, 1],\n [-4, 3, 0, -5, -3, 4],\n [-1, 4, 2, -2, 6, 2],\n [-2, 3, 1, 6, 6, -6],\n [0, -3, -2, -1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60508", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-6, 5, 2, -5, 2, 3],\n [-5, 2, -1, 4, 2, 6],\n [-1, -1, 6, 4, -5, 1],\n [-4, 0, -2, -4, -6, 1],\n [-4, -5, -6, -3, 6, 1],\n [6, -4, -6, -3, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1904579", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, 6, 0, -5, 2, -3],\n [6, -4, 1, 0, 4, 0],\n [0, 1, -6, 2, 1, -1],\n [-5, 0, 2, 0, -3, -2],\n [2, 4, 1, -3, -2, 3],\n [-3, 0, -1, -2, 3, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110291", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 5) of the result:\nA =\n[[2, 2, -2, 1, -2, 0],\n [2, 2, 0, 0, 4, 6],\n [-2, 0, -3, -3, 1, 2],\n [1, 0, -3, -2, -3, -2],\n [-2, 4, 1, -3, 3, 1],\n [0, 6, 2, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5525", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 4, -4, -2, 6, 3],\n [6, -3, 1, 6, 5, -2],\n [3, 5, 1, 2, -3, 0],\n [-5, -1, 1, 5, 0, 0],\n [1, 0, -2, 0, 6, 3],\n [-4, -2, 0, 2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30654", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 3, -4, 2, 0, 4],\n [3, 3, -2, 1, 0, 0],\n [-4, -2, 3, -3, -2, 0],\n [2, 1, -3, -4, 0, 2],\n [0, 0, -2, 0, -3, -2],\n [4, 0, 0, 2, -2, -4]], determine the value at position (6, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1948", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-1, -3, 0, -4, -6, 2],\n [-1, 1, -4, 1, -5, 5],\n [-3, -4, 3, -6, 6, 6],\n [0, 4, 3, -5, -3, 2],\n [-1, 1, -5, 0, -1, 6],\n [2, 0, -6, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39532", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 0, 2, 0, 2, -2],\n [0, -4, 4, -1, 0, 0],\n [2, 4, 1, -1, -2, 2],\n [0, -1, -1, 6, -4, 4],\n [2, 0, -2, -4, -4, 2],\n [-2, 0, 2, 4, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54733", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-6, 3, -3, -2, 6, 0],\n [3, 4, 0, 0, 2, -6],\n [-3, 0, -2, -1, -1, -6],\n [-2, 0, -1, -3, 0, -2],\n [6, 2, -1, 0, 1, -4],\n [0, -6, -6, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-346007", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 0, -3, 1, 4, 0],\n [0, 2, -6, 4, 0, 2],\n [-3, -6, 6, -6, 0, 0],\n [1, 4, -6, -5, 0, -3],\n [4, 0, 0, 0, -1, 0],\n [0, 2, 0, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18022", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 6, -3, -2, 6, -2],\n [-1, -4, -2, -5, 3, -6],\n [4, -6, 3, 0, -5, -3],\n [-2, 0, -5, -1, -6, 0],\n [2, -2, -2, -3, -4, 2],\n [-2, 1, 2, -2, 3, 2]], determine the value at position (6, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9051", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, 2, 4, -3, -1, -1],\n [-1, -5, 0, 6, -1, 4],\n [-6, -5, 0, -6, -6, -6],\n [1, -3, -3, 6, -5, 4],\n [4, 4, -6, 5, 3, 2],\n [0, -3, 5, -1, -5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122474", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 4) of the matrix A^5 where A is:\n[[-5, 2, 2, 0, -4, 3],\n [2, -5, 0, 2, -5, 0],\n [2, 0, 6, 0, -3, -3],\n [0, 2, 0, 3, -2, 1],\n [-4, -5, -3, -2, -5, 3],\n [3, 0, -3, 1, 3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12711", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -6, -3, -5, 4, 6],\n [-2, 3, 2, 4, 5, 3],\n [-4, 1, -4, -1, -3, 1],\n [4, -1, 1, -6, -1, -6],\n [-6, 1, 0, -4, -1, 2],\n [0, 5, -4, 6, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59984", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 4) of the matrix A^5 where A is:\n[[-3, 0, -2, 1, -1, -3],\n [0, -5, 1, 0, 0, -2],\n [-2, 1, 1, 0, -5, -2],\n [1, 0, 0, 5, -4, -4],\n [-1, 0, -5, -4, -2, 0],\n [-3, -2, -2, -4, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20163", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -2, 5, 4, 6, -1],\n [1, 3, 5, -6, -3, 3],\n [4, -6, 2, 4, 0, 0],\n [5, -2, 0, 5, -5, 6],\n [-3, 0, -4, -5, 3, -5],\n [6, -6, -2, 5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1505359", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 5) of the matrix A^5 where A is:\n[[2, -3, -6, -1, -2, 3],\n [-1, -4, -5, -1, 6, -6],\n [0, 0, 3, 6, 0, 5],\n [4, 3, -6, -3, 6, 0],\n [4, 2, -2, 6, -5, 0],\n [3, -6, 0, -1, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39456", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[3, -5, 0, 3, 4, -6],\n [-5, 2, -2, -2, -2, 0],\n [0, -2, 4, 0, 0, -5],\n [3, -2, 0, 0, 0, 2],\n [4, -2, 0, 0, 5, -5],\n [-6, 0, -5, 2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 2, 4, 5, -6, 4],\n [-5, 3, -5, -3, -5, 0],\n [6, 2, 0, 5, -1, 3],\n [-6, 4, 3, 2, -2, 4],\n [-2, -1, 2, 6, 1, 1],\n [1, -6, -6, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810965", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[-5, -2, 4, 1, 0, -4],\n [-2, -6, -2, -1, 0, 4],\n [4, -2, -2, 0, 3, 2],\n [1, -1, 0, -6, -5, -1],\n [0, 0, 3, -5, -6, 3],\n [-4, 4, 2, -1, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2105", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 1) of the matrix A^4 where A is:\n[[1, 1, 4, 5, 2, 6],\n [4, 5, -2, 0, -4, 3],\n [-3, 3, 2, 3, 3, 5],\n [-6, -5, -2, -4, -5, -6],\n [3, -4, -6, 5, -6, 5],\n [-6, 1, -4, 4, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4460", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the 4th power of the matrix:\n[[3, -2, -2, -1, -2, -4],\n [-2, 0, -4, 4, 4, 1],\n [-2, -4, 2, 2, 2, 2],\n [-1, 4, 2, 5, 1, 2],\n [-2, 4, 2, 1, 3, -2],\n [-4, 1, 2, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-64", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, -3, 6, 3, 4, -5],\n [5, -6, 5, 3, 5, -6],\n [6, 1, -5, 5, 3, -2],\n [5, -3, 1, -5, 3, 2],\n [0, 6, 0, -6, 5, -5],\n [-3, -3, 4, -4, 0, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1611767", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, -5, -3, -4, -5, 5],\n [6, -1, 6, -3, -1, -5],\n [5, -3, 4, -1, -2, -4],\n [1, 0, -4, -1, -3, 4],\n [-2, 4, -2, 0, 4, -2],\n [4, -4, 3, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2046", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 2, -2, 3, 0, -6],\n [2, -2, 1, -1, -2, 0],\n [-2, 1, 3, 2, 4, -4],\n [3, -1, 2, 5, 1, 0],\n [0, -2, 4, 1, 3, 0],\n [-6, 0, -4, 0, 0, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61149", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 1, 0, -2, 2, -2],\n [1, 2, 1, 0, -4, -4],\n [0, 1, -6, 0, -2, 1],\n [-2, 0, 0, 4, 2, 2],\n [2, -4, -2, 2, 4, 1],\n [-2, -4, 1, 2, 1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35702", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 6, 3, 5, 6, -1],\n [-5, -2, -1, -2, 5, -5],\n [0, -3, 1, 0, 0, 2],\n [-6, 3, -1, -1, -1, 6],\n [5, -1, 5, 3, 0, 3],\n [-1, -6, -4, -5, -1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1853", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 1, 2, 3, 0, -2],\n [1, -2, -2, 2, 2, -2],\n [2, -2, 1, 4, 2, -3],\n [3, 2, 4, 3, 2, -1],\n [0, 2, 2, 2, 4, 0],\n [-2, -2, -3, -1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75926", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -2, -6, 2, -6, -6],\n [-2, -2, 0, 1, 0, 1],\n [-6, 0, -1, -4, -2, 1],\n [2, 1, -4, 3, 2, 0],\n [-6, 0, -2, 2, 3, -3],\n [-6, 1, 1, 0, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93836", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[-4, 0, -2, 0, 3, -2],\n [0, -1, -2, 2, 1, 0],\n [-2, -2, 1, 0, 3, 2],\n [0, 2, 0, -4, 4, 0],\n [3, 1, 3, 4, 3, 0],\n [-2, 0, 2, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5897", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 3) of the 4th power of the matrix:\n[[-2, 1, 5, -1, 0, -2],\n [1, 3, 2, 1, 0, 0],\n [5, 2, -2, 6, -1, 2],\n [-1, 1, 6, 2, 0, -6],\n [0, 0, -1, 0, 5, -4],\n [-2, 0, 2, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-212", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 3, 6, -2, 0, 6],\n [-2, 6, 6, -6, 4, 0],\n [1, 6, 0, 4, 6, -3],\n [1, -2, 3, 2, 5, 5],\n [3, -2, -6, 5, 2, 5],\n [-2, -1, -3, -1, 5, 1]], determine the value at position (3, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40550", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, -2, -5, -5, 6, 0],\n [3, 6, 3, 4, 3, -1],\n [-3, -2, -6, 0, 1, 2],\n [1, -2, -4, 3, 4, 2],\n [-1, -2, 6, -4, -1, -4],\n [3, 5, -1, -3, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4062", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 0, 2, 1, -1, -4],\n [0, -4, -1, 6, 2, -2],\n [2, -1, 2, 1, -4, 2],\n [1, 6, 1, 6, -4, 0],\n [-1, 2, -4, -4, -5, 4],\n [-4, -2, 2, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83970", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -4, 3, -1, 0, 3],\n [-6, -1, 0, -1, -3, -6],\n [4, 2, -3, 0, 0, -5],\n [-6, 1, 1, 0, 1, -4],\n [4, -5, 0, 1, -6, 5],\n [3, 2, 6, 4, -3, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45389", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 6) of the 5th power of the matrix:\n[[-3, -1, 0, -3, -2, -4],\n [-1, -5, -1, 2, -4, 6],\n [0, -1, 1, -2, 0, -1],\n [-3, 2, -2, -3, -2, 1],\n [-2, -4, 0, -2, -2, 2],\n [-4, 6, -1, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-89253", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, 2, 2, 2, 4],\n [0, -2, -2, 1, 0, -6],\n [2, -2, 3, 3, -1, 3],\n [2, 1, 3, 3, 0, -2],\n [2, 0, -1, 0, 1, -4],\n [4, -6, 3, -2, -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": "122998", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 0, -4, 4, 0, -2],\n [0, 1, -4, -1, -1, 1],\n [-4, -4, 6, -1, -6, 4],\n [4, -1, -1, 3, 2, 2],\n [0, -1, -6, 2, 3, 0],\n [-2, 1, 4, 2, 0, -3]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4053", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -2, -2, 0, -2, 4],\n [-2, -5, -4, 2, 6, -4],\n [-2, -4, 6, -2, 2, -2],\n [0, 2, -2, -4, 0, 4],\n [-2, 6, 2, 0, -3, 2],\n [4, -4, -2, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160963", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -1, 0, 2, -5, 0],\n [-1, -6, 3, -2, -5, 0],\n [0, 3, -1, -2, 0, 2],\n [2, -2, -2, 4, -2, -4],\n [-5, -5, 0, -2, -5, -1],\n [0, 0, 2, -4, -1, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1039133", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 6, -4, -2, -1, 2],\n [6, -3, 1, 6, 1, -1],\n [-4, 1, -2, -5, -2, 4],\n [-2, 6, -5, -6, -2, 5],\n [-1, 1, -2, -2, 5, -1],\n [2, -1, 4, 5, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52720", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 5) of the result:\nA =\n[[4, -4, 6, 5, -3, -6],\n [-2, -6, 6, -6, 3, 4],\n [4, 0, 5, -1, -5, 4],\n [5, -5, 4, 0, -6, 6],\n [-5, 5, 1, -1, -5, 0],\n [-3, -5, 5, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1854", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 2, 1, -4, -4, -5],\n [-2, 5, -3, 0, -3, 2],\n [5, 5, -5, 4, -1, 0],\n [-3, 6, -1, 0, -3, 1],\n [2, -6, 0, 2, 5, 3],\n [-2, 5, -5, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62906", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 5) of the 4th power of the matrix:\n[[5, 0, -5, -5, 3, 5],\n [3, -6, -3, 0, 2, -4],\n [5, 4, 0, 0, 0, -5],\n [-1, -5, -1, 6, 3, -4],\n [-5, 5, -1, -5, -2, -5],\n [-4, -4, -1, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2616", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, 6, 5, 6, -6, 0],\n [6, 1, -5, -3, 3, 0],\n [1, -6, -3, -1, -4, -2],\n [3, 2, 4, 6, -4, -2],\n [1, -1, -3, 1, 4, -4],\n [-4, -3, 2, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38052", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -1, 3, 2, 2, 1],\n [-1, 6, -1, 2, -1, -4],\n [3, -1, -4, -4, 2, 0],\n [2, 2, -4, -5, -2, 4],\n [2, -1, 2, -2, 4, 2],\n [1, -4, 0, 4, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6380", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[-2, -3, 0, 0, 6, 2],\n [2, -2, 6, 5, 6, 1],\n [3, -6, 2, 1, -1, 6],\n [-4, -4, 1, -2, 3, 4],\n [0, -2, 1, 3, 3, -3],\n [-5, -4, 1, 4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1313", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 4th power of the matrix:\n[[6, -5, -4, 3, 0, -2],\n [-5, -5, 4, 2, 2, -2],\n [-4, 4, 4, -1, 0, -3],\n [3, 2, -1, -5, 2, -2],\n [0, 2, 0, 2, 1, -4],\n [-2, -2, -3, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8613", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -4, 0, 2, -1, 0],\n [-4, 3, -2, 0, 5, 0],\n [0, -2, -1, 2, -3, 0],\n [2, 0, 2, 2, 2, 0],\n [-1, 5, -3, 2, 6, 2],\n [0, 0, 0, 0, 2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23712", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 0, 3, -2, 4, -1],\n [-2, 0, 5, -5, -2, 3],\n [-4, 2, 6, -1, 6, 3],\n [-4, 0, -3, -4, 1, 6],\n [-3, 4, -6, -1, 3, 4],\n [4, -6, -2, 0, -1, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39738", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -4, 4, -5, 0, -6],\n [-4, -4, 2, 2, -6, 4],\n [4, 2, -3, 1, 0, -4],\n [-5, 2, 1, 3, -2, 0],\n [0, -6, 0, -2, 6, 0],\n [-6, 4, -4, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215986", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -6, -4, 3, -2, 3],\n [6, -2, 6, 3, -1, 5],\n [3, 1, -2, 4, -6, -2],\n [-4, -3, 6, 1, 0, 4],\n [-2, -5, -1, 4, -1, 3],\n [3, 4, -1, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "323725", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, -6, -2, 0, -1, -2],\n [1, -4, -1, -2, 1, -3],\n [1, 3, -5, 2, 6, 2],\n [3, 3, 6, -1, -3, -3],\n [6, -1, -2, -1, 0, 0],\n [2, 1, 6, -1, 5, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "425289", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 1) of the result:\nA =\n[[-2, -6, 2, 2, 2, 4],\n [1, 6, 3, 6, -4, -6],\n [4, 5, 5, 1, 0, 6],\n [-2, 3, 0, 3, -3, 2],\n [4, 3, -5, 2, 2, -2],\n [4, -6, 0, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-675", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 1, 0, -4, -4, 4],\n [1, -1, -1, -2, 4, 0],\n [0, -1, -5, 3, -4, -1],\n [-4, -2, 3, -3, -4, -1],\n [-4, 4, -4, -4, -3, 4],\n [4, 0, -1, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26227", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, 4, 4, 5, -4, -2],\n [4, -4, -2, 0, -4, 0],\n [4, -2, -4, 1, 4, -2],\n [5, 0, 1, -4, 0, 4],\n [-4, -4, 4, 0, 4, -5],\n [-2, 0, -2, 4, -5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1354910", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[0, -1, 0, 0, 2, -2],\n [-1, 3, -4, 2, -4, -2],\n [0, -4, -3, -6, 0, -2],\n [0, 2, -6, 5, 0, -4],\n [2, -4, 0, 0, 2, 1],\n [-2, -2, -2, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-193018", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 6, -3, -2, -2, -3],\n [-3, -3, -3, -3, -2, -5],\n [-5, 2, -5, -1, -5, -2],\n [-3, 5, 0, 0, 6, -1],\n [3, -2, -6, 5, -4, 2],\n [-6, -2, -5, -3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1091289", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -1, -2, 4, 0, 0],\n [-1, -4, 0, -4, 4, -4],\n [-2, 0, 5, 2, -3, -3],\n [4, -4, 2, -6, 0, 0],\n [0, 4, -3, 0, 6, 0],\n [0, -4, -3, 0, 0, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1049383", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 0, 0, 5, 0, 2],\n [0, 1, -1, 1, 4, 0],\n [0, -1, 2, -5, 0, 0],\n [5, 1, -5, -5, 3, 2],\n [0, 4, 0, 3, -3, 0],\n [2, 0, 0, 2, 0, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52755", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-6, 0, 0, 2, 2, 6],\n [0, 5, 0, -2, -4, 3],\n [0, 0, -6, 0, -4, 5],\n [2, -2, 0, 2, 2, -1],\n [2, -4, -4, 2, 2, -2],\n [6, 3, 5, -1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1416069", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 0, 4, -3, -1, 2],\n [0, -5, 0, 2, 2, 1],\n [4, 0, 3, 0, 0, 3],\n [-3, 2, 0, -1, 1, 2],\n [-1, 2, 0, 1, 2, 2],\n [2, 1, 3, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6971", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[3, 5, -6, -3, -5, 4],\n [0, -5, 3, -5, -2, -3],\n [1, -3, 5, -1, -2, 4],\n [-5, 4, 6, 5, 1, -5],\n [2, 2, -4, -3, 1, 2],\n [-4, -2, 4, 1, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83412", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 5) of the matrix A^4 where A is:\n[[4, 1, 3, 4, -4, -5],\n [3, 6, 0, 5, 2, -6],\n [-4, -2, -4, -6, 0, 0],\n [3, 5, 1, -2, 3, 5],\n [-2, -2, -6, 3, -2, -1],\n [6, 5, -6, 4, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -5, -5, -2, 3, 6],\n [0, -6, 3, -6, -6, -1],\n [-5, -6, -1, -5, -1, 3],\n [1, -5, 4, 2, 1, 5],\n [3, -6, 0, 6, 3, -1],\n [-1, -1, -1, 3, 0, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1527998", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 3) of the result:\nA =\n[[-4, -1, -4, 0, 0, 1],\n [-5, 2, 6, -2, 2, 3],\n [-2, 0, 4, 2, -3, -5],\n [2, 6, -5, -4, 3, -5],\n [-4, -1, -4, 3, 1, 4],\n [-1, 0, -6, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22080", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[0, 2, -3, 5, -2, -4],\n [4, 2, -3, -2, -6, 4],\n [5, 6, -5, 5, 6, 2],\n [-5, -2, 6, 1, -4, -1],\n [-3, 4, 0, 3, 6, -4],\n [-1, 5, 3, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "262", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-6, -2, -1, 2, 1, -3],\n [-2, -4, 2, -1, 0, -2],\n [-1, 2, -6, 0, -3, 2],\n [2, -1, 0, -1, 2, -2],\n [1, 0, -3, 2, 3, 4],\n [-3, -2, 2, -2, 4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14049", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 5) of the result:\nA =\n[[-6, 4, 1, 3, -3, -4],\n [5, 0, 5, -5, 1, -1],\n [0, -2, 2, -2, 4, -2],\n [-4, 4, -6, -5, 1, -6],\n [0, -2, -4, 5, 5, 4],\n [0, 2, -5, 1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6218", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -4, 3, 0, -4, 4],\n [-4, -3, 2, 0, 0, 0],\n [3, 2, -3, -3, -1, -2],\n [0, 0, -3, 2, 0, -4],\n [-4, 0, -1, 0, 6, -4],\n [4, 0, -2, -4, -4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2435", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -3, 0, -2, 6, 4],\n [-3, -4, 3, -2, 2, 0],\n [0, 3, -1, 0, 2, 1],\n [-2, -2, 0, -5, -2, 0],\n [6, 2, 2, -2, 2, 0],\n [4, 0, 1, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "716657", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 4) of the result:\nA =\n[[6, 5, 4, -5, -3, -6],\n [-2, -1, 2, 3, 1, -5],\n [-6, -5, 0, -3, 3, -2],\n [5, 0, -4, 3, -5, 6],\n [0, -2, -6, -6, 2, -2],\n [-6, 0, 2, 4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13960", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[6, -3, -4, -2, 0, 1],\n [6, -5, 0, -6, 0, 1],\n [-5, 2, -6, 6, -1, -6],\n [-4, 4, -1, -4, 1, -2],\n [-5, -3, 2, -3, 3, 3],\n [1, -2, 4, 4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3908", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[6, 0, -2, -4, 4, -2],\n [0, -4, -6, 0, -3, 2],\n [-2, -6, 2, -3, -2, -1],\n [-4, 0, -3, 2, 1, -2],\n [4, -3, -2, 1, -1, 0],\n [-2, 2, -1, -2, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538748", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, 6, 3, 2, 3, -1],\n [0, 3, 1, 4, 6, 3],\n [-6, 1, -3, 3, 1, 6],\n [-1, 4, 2, 4, -3, -5],\n [-5, -2, 3, 2, 5, -4],\n [1, -3, -1, 3, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "237182", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, 5, -4, 4, 4, -6],\n [0, -3, 0, -4, 5, 4],\n [-2, -2, 6, -5, 4, 3],\n [5, -5, -3, -3, -3, -1],\n [-5, -1, 0, 4, 3, -4],\n [4, 5, 1, -5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11204", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[6, 4, -2, -5, 0, -5],\n [-1, 3, -4, 2, -4, 4],\n [5, 5, -4, -2, 0, 1],\n [5, 4, 0, 2, -2, 3],\n [4, -4, -1, -2, 5, -3],\n [5, -5, 0, 6, -2, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74676", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 4) of the matrix A^5 where A is:\n[[5, 0, -1, 0, -4, 0],\n [0, -2, -2, -4, -6, 3],\n [-1, -2, -6, 4, -2, -4],\n [0, -4, 4, -3, 6, 2],\n [-4, -6, -2, 6, -6, -2],\n [0, 3, -4, 2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-165627", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, 4, -5, 1, -2, 1],\n [1, -1, -5, 1, 4, -1],\n [-1, 1, -6, -5, 5, 5],\n [2, 4, 5, 1, 5, 0],\n [0, -2, -5, 4, -1, 3],\n [-4, -3, 6, 3, 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": "85020", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, -5, 5, 1, 1, 3],\n [-1, 6, -2, 1, -3, 4],\n [-3, -2, -6, -6, -5, 1],\n [0, 3, 2, -2, -5, 0],\n [1, 5, 0, 0, 5, -2],\n [-5, -1, -3, 3, -5, 5]], determine the value at position (6, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4920", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 2, 2, 6, 0, -1],\n [2, 3, 2, -2, -4, 1],\n [2, 2, -4, -2, -2, 2],\n [6, -2, -2, 3, -1, 2],\n [0, -4, -2, -1, 6, 0],\n [-1, 1, 2, 2, 0, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13246", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 4, 1, 3, -3, -4],\n [-4, 5, -2, 4, -6, 3],\n [-4, -1, -4, -2, 2, -5],\n [4, -5, 5, -1, -1, 4],\n [4, 1, 5, 6, 4, -5],\n [2, -5, 6, -6, 3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16314", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, 0, 1, -2, -1, 5],\n [-6, -1, 5, 1, 6, -4],\n [4, -6, 4, -3, -6, 1],\n [-2, -6, 1, 2, 3, -5],\n [2, 1, 0, -4, -5, 0],\n [-2, -1, -3, -5, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36808", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 0, 1, -5, 2, 5],\n [0, 0, 2, 0, -2, -2],\n [1, 2, -2, -1, 0, 2],\n [-5, 0, -1, -6, 1, -2],\n [2, -2, 0, 1, -6, 2],\n [5, -2, 2, -2, 2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31192", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, -1, -1, -2, 3, -6],\n [-1, 2, -2, -2, 0, -2],\n [-1, -2, 4, 4, 3, 0],\n [-2, -2, 4, 4, 0, -3],\n [3, 0, 3, 0, 1, 4],\n [-6, -2, 0, -3, 4, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22683", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, -4, 6, -3, -1, 4],\n [0, -3, -3, 0, -1, 6],\n [4, 1, -6, 3, 6, 4],\n [0, 5, 0, 4, 0, 0],\n [3, 3, 1, 2, 2, -5],\n [6, 6, 0, 0, -3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84236", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 5, -6, -5, 6, 6],\n [-5, 5, 5, 4, 1, -6],\n [-3, 3, 5, -2, 2, 0],\n [1, 4, 2, 6, 0, -2],\n [6, -2, 3, 4, -1, -2],\n [6, 5, 4, 2, -4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44445", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 0, -1, -4, 6, 0],\n [-2, 0, -5, -1, 1, -6],\n [-3, 4, -6, -6, 3, 5],\n [4, 1, 0, 5, 3, 6],\n [-6, 4, 6, -5, -3, -6],\n [-4, 1, 1, 1, -1, -1]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7104", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 6, 2, 0, 1, 3],\n [6, 5, 2, 0, 2, 1],\n [2, 2, 2, 2, -3, 1],\n [0, 0, 2, -3, -1, -4],\n [1, 2, -3, -1, -2, -3],\n [3, 1, 1, -4, -3, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "418476", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 1, 2, 5, -2, 5],\n [-1, 4, -3, -2, 0, 2],\n [3, 4, 6, -1, -1, 1],\n [4, -3, -4, 0, -2, -5],\n [-5, 4, -1, 1, -6, 4],\n [-1, 5, -5, -5, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-122538", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, 0, -2, 2, 2, 1],\n [0, 6, -5, 0, 2, 0],\n [-2, -5, 5, 1, -1, 2],\n [2, 0, 1, -5, 0, 2],\n [2, 2, -1, 0, -3, 2],\n [1, 0, 2, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60079", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[-5, -3, -2, -6, 1, 1],\n [-1, 5, -2, 1, -4, -4],\n [-5, -2, -4, -4, -1, 1],\n [-5, -3, 4, 0, -6, -6],\n [5, 6, 3, 0, 0, -6],\n [-6, -3, -2, -2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9881", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 2) of the matrix A^5 where A is:\n[[0, 1, 1, 2, -3, 5],\n [1, -6, 2, 4, 1, 5],\n [1, 2, -4, -2, -4, 6],\n [2, 4, -2, -4, 4, -4],\n [-3, 1, -4, 4, -5, 0],\n [5, 5, 6, -4, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7377", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 1) of the 4th power of the matrix:\n[[4, -5, 0, -3, 4, 6],\n [-5, 6, 0, 6, -2, -6],\n [-2, 5, 5, -4, 0, -1],\n [1, 6, -2, -5, 2, 4],\n [1, -1, 6, 3, 0, 2],\n [0, -4, -1, 4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4051", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 2) of the 5th power of the matrix:\n[[0, -6, -1, -4, 4, -3],\n [-6, 2, 0, 4, 2, 1],\n [-1, 0, -6, 0, -4, 2],\n [-4, 4, 0, 4, -6, -6],\n [4, 2, -4, -6, -3, -2],\n [-3, 1, 2, -6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12231", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, -2, 3, -2, -6, -1],\n [6, 2, -5, 0, -1, -2],\n [-3, -3, -1, -3, -2, 6],\n [-1, -2, 0, 2, 3, 0],\n [0, -3, -6, 1, -3, -6],\n [-2, 1, -3, 6, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47917", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -4, 2, -4, -6, -5],\n [-1, 5, 3, -5, -1, -6],\n [4, 6, -6, -2, 3, 6],\n [4, 2, 1, -4, -4, -6],\n [-4, 5, 5, 5, 6, 4],\n [-6, 1, -6, -2, 2, 0]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7398", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 6) of the matrix A^5 where A is:\n[[-3, 4, 4, 2, -5, 3],\n [4, 4, 4, 2, -2, 1],\n [4, 4, 0, -1, 3, 0],\n [2, 2, -1, -1, -2, 0],\n [-5, -2, 3, -2, 2, 2],\n [3, 1, 0, 0, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1393", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -2, 0, 0, -2, 4],\n [-2, 3, 0, -4, 2, 5],\n [0, 0, 0, 3, 3, -4],\n [0, -4, 3, -5, 1, 1],\n [-2, 2, 3, 1, 6, -1],\n [4, 5, -4, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83189", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 3) of the result:\nA =\n[[-1, 0, 0, 0, 3, -4],\n [0, 3, -3, 2, -3, -2],\n [0, -3, -5, -3, 2, -2],\n [0, 2, -3, -5, 1, 0],\n [3, -3, 2, 1, 4, -6],\n [-4, -2, -2, 0, -6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21593", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 6, 0, -1, 2, -4],\n [6, -1, -3, 0, -6, -5],\n [0, -3, -2, 2, 0, 4],\n [-1, 0, 2, 6, -2, 2],\n [2, -6, 0, -2, -6, 1],\n [-4, -5, 4, 2, 1, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140962", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 2, 2, 2, 3, 2],\n [2, -4, 0, 4, 2, -1],\n [2, 0, 3, 3, -2, -6],\n [2, 4, 3, 3, -4, -6],\n [3, 2, -2, -4, 4, 2],\n [2, -1, -6, -6, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27562", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -4, 0, 2, -2, 2],\n [-4, 2, 3, -2, -3, 3],\n [0, 3, 0, -2, -2, 1],\n [2, -2, -2, -4, 2, 3],\n [-2, -3, -2, 2, -6, -2],\n [2, 3, 1, 3, -2, -5]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2498", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 3, -2, 0, -1, 3],\n [3, 1, 2, -4, 0, 2],\n [-2, 2, -5, 4, 2, 2],\n [0, -4, 4, -4, 4, 5],\n [-1, 0, 2, 4, 3, -5],\n [3, 2, 2, 5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102086", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 1, 2, 2, 0, -2],\n [1, 1, 0, 0, -2, 1],\n [2, 0, 0, -6, 2, 3],\n [2, 0, -6, -4, 6, 1],\n [0, -2, 2, 6, 3, -3],\n [-2, 1, 3, 1, -3, -2]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1578", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 5) of the 5th power of the matrix:\n[[5, -3, -1, 5, -4, 1],\n [-1, 3, -2, 6, -5, 3],\n [3, 0, -5, -6, 0, -2],\n [-6, -3, 5, 6, -3, 3],\n [0, 2, -5, 5, -6, -5],\n [0, 6, 3, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15549", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[6, -6, -2, -6, 5, 0],\n [6, 4, -6, -6, -5, 6],\n [4, 5, 3, -4, 6, 4],\n [-6, 2, 3, 1, -2, 6],\n [4, -5, -2, -1, -6, 4],\n [-3, 2, -5, -2, -6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3134", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, -1, 3, 2, 1, -2],\n [-1, 0, 2, 4, -4, 0],\n [3, 2, -1, -6, 0, -3],\n [2, 4, -6, -2, 1, 0],\n [1, -4, 0, 1, 3, 1],\n [-2, 0, -3, 0, 1, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "917812", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[4, -4, 0, -2, -4, 2],\n [-4, 3, -2, 3, -2, 0],\n [0, -2, -3, 3, 2, 0],\n [-2, 3, 3, -6, 1, 4],\n [-4, -2, 2, 1, 4, 2],\n [2, 0, 0, 4, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25660", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, -4, 3, 3, 2, -3],\n [0, 6, 2, -5, -5, 2],\n [5, 6, -4, 2, 6, -2],\n [-1, -5, 1, 4, 2, -5],\n [-1, -1, 1, 3, 5, -2],\n [2, -6, 2, 3, 0, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9448", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 5) of the 5th power of the matrix:\n[[-4, -2, 0, -1, 4, 1],\n [-2, -4, 0, 4, 6, -1],\n [0, 0, -5, -1, -4, 0],\n [-1, 4, -1, 3, 2, -3],\n [4, 6, -4, 2, 5, -2],\n [1, -1, 0, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42828", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 2) of the matrix A^4 where A is:\n[[-6, 0, 2, 2, 1, 2],\n [0, -3, -4, 1, 4, 0],\n [2, -4, 4, 2, 4, 2],\n [2, 1, 2, -3, 2, 4],\n [1, 4, 4, 2, 2, -2],\n [2, 0, 2, 4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-872", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[6, -2, 2, 2, -2, 1],\n [-2, -6, 0, 0, 4, 1],\n [2, 0, 3, 2, 5, 0],\n [2, 0, 2, -3, -6, 0],\n [-2, 4, 5, -6, -6, 4],\n [1, 1, 0, 0, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44355", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 2) of the result:\nA =\n[[4, -2, -3, 2, 0, -4],\n [-2, -6, -1, 3, -2, 0],\n [-3, -1, 6, 1, -3, 1],\n [2, 3, 1, -1, 2, 0],\n [0, -2, -3, 2, 1, -2],\n [-4, 0, 1, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5954", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, 1, -4, 0, 2, 1],\n [1, 6, 4, -1, -4, 5],\n [-4, 4, -6, -3, -2, -4],\n [0, -1, -3, 2, -6, -3],\n [2, -4, -2, -6, 4, 1],\n [1, 5, -4, -3, 1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-682712", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 3, 4, 0, -3, -2],\n [3, -3, -1, -3, 0, 0],\n [4, -1, 3, -2, -3, 1],\n [0, -3, -2, 6, 2, 5],\n [-3, 0, -3, 2, -3, -2],\n [-2, 0, 1, 5, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7703", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[6, 0, 4, 1, -2, -1],\n [0, -4, 4, 0, 0, -4],\n [4, 4, 5, 0, 4, -6],\n [1, 0, 0, 2, 0, -4],\n [-2, 0, 4, 0, 2, -1],\n [-1, -4, -6, -4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61155", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -2, -2, 2, -4, -4],\n [0, 2, -1, -5, -6, -5],\n [-6, 3, 3, 2, 3, 5],\n [6, 1, 0, -4, 1, -5],\n [-5, 4, 3, -4, 0, -6],\n [1, 5, 0, -3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43720", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, -6, -3, -6, -6, 3],\n [-6, 0, 0, -3, 6, 5],\n [-5, 5, -4, 1, 6, 1],\n [4, 4, -1, 3, 2, 4],\n [5, 2, -3, 5, -6, -6],\n [5, 3, -2, 6, -5, -1]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105616", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, -6, -1, 1, 5, -2],\n [5, 0, 3, -1, -3, 0],\n [3, 2, 3, 3, 6, 0],\n [5, -2, 0, -4, -5, 4],\n [-2, -3, -2, 1, 5, -3],\n [2, 0, 3, 6, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20821", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[6, 1, 2, 4, 1, 2],\n [1, 3, -1, -2, 2, 0],\n [2, -1, 4, -3, 1, -1],\n [4, -2, -3, 0, 3, -2],\n [1, 2, 1, 3, 2, -2],\n [2, 0, -1, -2, -2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32775", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -3, -5, 2, -4, 1],\n [-1, 6, -2, -6, -3, -4],\n [-6, 5, -2, -1, -5, -4],\n [4, -1, -3, 2, -2, -3],\n [-5, -1, 3, -5, 5, 6],\n [0, -4, 2, 4, -2, 1]], determine the value at position (3, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -1, 5, 3, 1, 6],\n [6, 4, 5, -4, -4, -2],\n [4, 3, -4, 1, 3, 6],\n [5, 1, -5, 5, -3, 3],\n [6, -6, -3, 5, 6, 6],\n [4, 6, -3, 3, 2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123646", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 2, 2, -6, -1, 3],\n [1, -4, 4, 2, -5, -1],\n [-6, 6, 0, -4, 0, -3],\n [2, -2, -4, 1, -1, -5],\n [-4, 1, 3, 0, 3, -1],\n [-6, 2, -4, -2, 0, 0]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 5th power of the matrix:\n[[-4, 0, 2, -3, 2, -2],\n [0, 0, 2, -1, 2, 2],\n [2, 2, 4, 2, 2, 2],\n [-3, -1, 2, 4, 2, 4],\n [2, 2, 2, 2, -1, 1],\n [-2, 2, 2, 4, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11498", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -5, 4, -6, 6, 0],\n [5, 3, 2, 4, 5, 5],\n [2, -4, -1, 0, 3, 2],\n [-5, 1, 0, -3, -5, 1],\n [4, -2, -1, 4, 0, 3],\n [-6, 1, -3, 6, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44107", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 6) of the result:\nA =\n[[4, -6, 0, 2, 4, 0],\n [-6, -3, 2, 4, -4, 0],\n [0, 2, 4, -1, -4, 0],\n [2, 4, -1, 1, 1, 0],\n [4, -4, -4, 1, -2, 3],\n [0, 0, 0, 0, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9648", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-6, -4, 5, 4, -2, -2],\n [-4, -1, -2, -2, 2, 4],\n [5, -2, -2, 2, 2, -5],\n [4, -2, 2, -6, 0, -4],\n [-2, 2, 2, 0, 2, -5],\n [-2, 4, -5, -4, -5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5118", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 0, 0, -2, 2, 1],\n [0, 5, 1, 0, -6, 0],\n [0, 1, -3, -4, 0, 2],\n [-2, 0, -4, -6, -2, -4],\n [2, -6, 0, -2, -3, -4],\n [1, 0, 2, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67834", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 2, -1, 5, -6, 2],\n [5, 6, -4, 4, -1, 3],\n [6, 3, 4, 5, 2, 4],\n [6, -4, -2, 6, -2, 3],\n [0, -3, 4, -3, 0, 2],\n [4, -3, -3, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "869680", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-6, 2, -1, -4, 0, 2],\n [2, -2, 0, -4, 2, -2],\n [-1, 0, -3, 0, 3, 3],\n [-4, -4, 0, -6, 4, 0],\n [0, 2, 3, 4, 5, -6],\n [2, -2, 3, 0, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150412", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, -1, -2, 6, 2, 6],\n [4, 6, 4, -5, 3, 5],\n [1, 4, 3, 6, 2, -6],\n [0, 1, -4, -3, 6, -4],\n [0, 2, -4, 6, -1, 1],\n [-1, -5, 6, 0, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21890", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 4, -6, 4, -6, 0],\n [6, 5, -2, 4, -4, -6],\n [4, 3, -1, 4, -6, 2],\n [-5, -6, 5, 0, -1, -1],\n [-2, 4, -3, 4, -3, -4],\n [3, 1, 0, 2, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42024", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, -2, -2, 4, 1, -5],\n [-2, -4, -3, -2, -4, 4],\n [-2, -3, 6, -4, 2, 3],\n [4, -2, -4, 3, 1, 0],\n [1, -4, 2, 1, -6, 2],\n [-5, 4, 3, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10145", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-6, -5, 0, 3, 2, 1],\n [-5, -4, -5, -2, -4, 2],\n [0, -5, -3, 0, 3, 0],\n [3, -2, 0, -5, 1, -1],\n [2, -4, 3, 1, 2, -1],\n [1, 2, 0, -1, -1, 3]], determine the value at position (2, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28215", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 2, -4, -4, 0, 2],\n [2, 6, 3, 4, -5, -6],\n [-4, 3, -1, 0, 0, -4],\n [-4, 4, 0, 5, -3, 6],\n [0, -5, 0, -3, -4, -2],\n [2, -6, -4, 6, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32457", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -2, 2, 2, 0, 1],\n [-2, 2, 0, 1, 2, -3],\n [2, 0, -6, 0, -4, 3],\n [2, 1, 0, -5, 0, 4],\n [0, 2, -4, 0, 5, 0],\n [1, -3, 3, 4, 0, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9713", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-5, 1, -2, 0, -6, -2],\n [-6, 5, 6, 1, -3, -3],\n [-5, -2, -6, 2, -2, -1],\n [-5, 3, 3, -6, -3, 0],\n [-1, 3, -6, -6, 1, -3],\n [-2, 6, 0, 1, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-823754", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -3, 3, 5, -6, 3],\n [2, -4, 5, -4, 3, 2],\n [3, -4, 1, -5, 6, -4],\n [-5, -6, -5, 1, 2, 6],\n [-5, 0, -2, -4, 2, -1],\n [4, -6, -2, 0, -3, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5808", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -4, 4, 0, 2, 0],\n [-4, -4, -2, 0, 2, 2],\n [4, -2, -6, 0, 0, -4],\n [0, 0, 0, 0, -2, 0],\n [2, 2, 0, -2, -6, 2],\n [0, 2, -4, 0, 2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9278", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, 3, 1, -4, -2, 0],\n [-6, 0, 6, 5, 4, 1],\n [1, 2, -1, 5, -1, -5],\n [-4, -3, -3, 1, -6, 3],\n [-3, 4, 5, 6, 4, 4],\n [-3, -6, -4, -2, -1, 2]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5775", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 2, 4, -6, 5, 2],\n [6, 1, -5, 6, 4, -6],\n [-6, 5, -1, 2, 0, -2],\n [4, -5, -6, -5, -6, -4],\n [-1, 6, 1, -4, 3, 2],\n [3, -2, 0, 1, -4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81453", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 1) of the result:\nA =\n[[-5, -2, -6, -5, 6, 2],\n [0, -1, 2, 0, 4, -2],\n [2, -1, -1, 4, -3, 6],\n [5, -6, -2, 4, 2, 6],\n [1, 1, -2, 5, 2, -4],\n [-4, -6, 2, -1, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-286", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 1, -2, -5, -1, 2],\n [1, 4, -4, 6, -2, 4],\n [-2, -4, -2, 1, 3, 0],\n [-5, 6, 1, 0, 3, -4],\n [-1, -2, 3, 3, -5, 0],\n [2, 4, 0, -4, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71158", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 3) of the result:\nA =\n[[-3, -6, 2, -2, -2, 0],\n [-6, -2, 4, 2, 2, 4],\n [2, 4, -6, 0, 2, -4],\n [-2, 2, 0, 2, 1, -1],\n [-2, 2, 2, 1, -6, -2],\n [0, 4, -4, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113714", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 6) of the result:\nA =\n[[-2, 0, 6, 1, -2, -1],\n [0, 1, -2, 0, 4, 0],\n [6, -2, 6, -3, 0, 0],\n [1, 0, -3, -3, -4, 1],\n [-2, 4, 0, -4, 4, -1],\n [-1, 0, 0, 1, -1, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1799", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 4, 2, -3, -2, 0],\n [4, -6, 0, 1, -4, 2],\n [2, 0, -6, 0, 1, 0],\n [-3, 1, 0, 0, 0, -2],\n [-2, -4, 1, 0, -3, 0],\n [0, 2, 0, -2, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5211", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -4, 2, 0, 0, 0],\n [-4, 6, 1, 4, -4, 0],\n [2, 1, -6, 0, 2, 4],\n [0, 4, 0, 0, 4, -2],\n [0, -4, 2, 4, 1, 1],\n [0, 0, 4, -2, 1, -5]], determine the value at position (4, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, -2, -2, 3, 4, -4],\n [5, 1, 1, 5, -2, 1],\n [3, 1, -4, -5, 2, -5],\n [2, -3, 5, 6, -5, 3],\n [-6, -3, 2, 5, 2, -3],\n [2, 5, -1, -6, 3, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3977", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-1, 2, 6, -5, -1, -5],\n [-3, 1, 6, 0, 4, 5],\n [6, 2, 0, -6, -5, -1],\n [0, -4, 2, 6, 0, -1],\n [6, -1, -6, 6, -2, 3],\n [-4, 0, 3, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28188", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 6, 6, 3, -5, -1],\n [1, -3, 2, 5, 5, 1],\n [0, 0, -4, -1, 6, 6],\n [-2, -6, 4, -4, 6, 5],\n [-6, -3, 3, -4, 4, -3],\n [2, -4, 5, -1, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96044", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 4, 2, -2, -2, 2],\n [4, 3, 6, 4, -4, -4],\n [2, 6, -5, 2, 3, -5],\n [-2, 4, 2, -6, -2, 2],\n [-2, -4, 3, -2, -2, 5],\n [2, -4, -5, 2, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3292776", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[4, -5, -6, -5, 0, 0],\n [3, -1, -2, -4, 5, -4],\n [4, 6, 5, 2, -3, 2],\n [-3, -5, -3, -1, -1, -2],\n [-6, -4, -2, -1, -6, 2],\n [-4, 3, 6, -4, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439957", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, 6, 0, 1, 0, 2],\n [6, -3, 2, 2, 1, 1],\n [0, 2, -4, 5, 0, -3],\n [1, 2, 5, 1, 2, 4],\n [0, 1, 0, 2, 6, 3],\n [2, 1, -3, 4, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799704", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 4) of the matrix A^5 where A is:\n[[-5, -2, -4, 0, 2, 0],\n [-2, 4, -2, 2, 2, -2],\n [-4, -2, 6, -4, -4, -2],\n [0, 2, -4, -1, 0, 4],\n [2, 2, -4, 0, 5, -4],\n [0, -2, -2, 4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16431", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 3) of the matrix A^5 where A is:\n[[-6, 2, 4, 0, -4, -3],\n [6, -1, -4, 5, 0, 6],\n [-1, 2, 5, -2, -3, -4],\n [3, -6, -4, -4, 0, 0],\n [6, 5, -6, -4, 6, 1],\n [2, 0, 0, 5, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11244", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 4, -4, -6, 0, -6],\n [-6, 2, 6, 3, 0, 6],\n [4, 6, -3, -1, -6, 0],\n [5, -1, -3, 0, -4, -6],\n [-3, -4, -6, -5, 4, -2],\n [1, -6, -3, -3, -2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8377", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[6, 5, 1, -1, -6, 0],\n [-4, 6, 6, 6, -1, 1],\n [0, 3, -1, 2, 2, -6],\n [-6, -6, 1, 5, 6, 5],\n [3, 0, -4, 6, -5, -3],\n [-4, 0, 3, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1247691", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -5, 5, 0, 4, 3],\n [0, -3, 6, 1, -3, 0],\n [-3, 6, 5, -2, 0, 6],\n [6, 3, -4, 3, -2, 4],\n [-4, -2, -4, 4, 3, 4],\n [0, 6, -6, 2, 2, -2]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38956", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 0, 6, 2, -4, 1],\n [0, 4, 5, 2, -4, 0],\n [6, 5, -4, 2, 0, 0],\n [2, 2, 2, -2, 0, 3],\n [-4, -4, 0, 0, -5, -4],\n [1, 0, 0, 3, -4, -3]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2072", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 3) of the result:\nA =\n[[2, -5, 3, 4, 6, -6],\n [3, 1, 2, 0, 1, -3],\n [-3, 6, -5, 1, 4, -5],\n [2, -3, -6, 6, -3, -4],\n [5, -1, 0, 1, -5, -1],\n [-1, 3, 5, -2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13174", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, -4, -3, 3, 6, 2],\n [-3, -4, -5, -2, -3, 6],\n [6, 1, 0, -1, 4, 5],\n [-5, -4, 3, 2, 6, 2],\n [-2, -4, -5, 1, -1, 3],\n [4, 5, 0, -6, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86560", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 4) of the result:\nA =\n[[-5, 3, -4, 5, -6, -2],\n [-4, -6, 1, 5, 4, -1],\n [2, -4, 2, 2, 5, 6],\n [5, -6, -4, -1, 1, -3],\n [-2, 2, -1, 5, 0, 0],\n [-3, -3, -3, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1184", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 2, -5, 4, 0, -6],\n [-6, -3, 3, 0, -5, 4],\n [-5, -6, 3, -5, 6, 0],\n [2, -1, 3, -5, 5, 3],\n [3, 6, 2, 0, 4, -6],\n [5, 2, -5, -3, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2162", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 5) of the 5th power of the matrix:\n[[-4, -4, 2, 1, 3, -3],\n [-4, -1, 5, 2, 4, 2],\n [2, 5, 1, 6, 0, -2],\n [1, 2, 6, -6, 0, 4],\n [3, 4, 0, 0, 1, 0],\n [-3, 2, -2, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31869", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 0, -4, 0, -2, 0],\n [0, -1, 0, 1, -1, 2],\n [-4, 0, -5, 1, 1, 4],\n [0, 1, 1, -5, 1, 0],\n [-2, -1, 1, 1, -3, 4],\n [0, 2, 4, 0, 4, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555650", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 4) of the matrix A^4 where A is:\n[[-4, -5, 2, 5, -5, -1],\n [-2, -2, -3, -1, -2, 4],\n [-3, 6, 2, 6, -1, 4],\n [3, 3, 6, 3, 6, -4],\n [3, -1, -6, -2, 3, -1],\n [4, 1, 4, 2, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-553", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, 1, -2, 2, 2, -1],\n [1, -3, 0, -2, -4, 1],\n [-2, 0, 4, 0, -4, -5],\n [2, -2, 0, -6, 3, 1],\n [2, -4, -4, 3, 4, -2],\n [-1, 1, -5, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10646", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[0, 0, 5, 2, -1, -6],\n [1, -6, -4, 4, -2, 1],\n [2, 0, 2, 4, -4, 6],\n [-2, 3, 1, 5, -6, 1],\n [0, -6, 6, 6, 3, 5],\n [3, 5, -1, -6, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59873", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 2) of the matrix A^5 where A is:\n[[-5, 4, -5, -2, 0, 4],\n [4, 6, -2, 4, 1, 4],\n [-5, -2, -5, -4, 2, 4],\n [-2, 4, -4, -6, 1, -6],\n [0, 1, 2, 1, 1, -2],\n [4, 4, 4, -6, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50729", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, 3, 0, 1, 2, 2],\n [3, 6, -4, 0, -1, 5],\n [0, -4, 3, -2, 1, 0],\n [1, 0, -2, 4, 0, -3],\n [2, -1, 1, 0, 6, 2],\n [2, 5, 0, -3, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15004", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -6, -5, -5, 1, 1],\n [-5, 6, -1, -2, -4, -2],\n [-2, -2, -4, -4, -3, 0],\n [5, 5, 5, -5, 3, -3],\n [-3, -6, 3, 1, -6, 1],\n [0, 2, 1, -2, 1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "482415", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 6) of the result:\nA =\n[[3, 5, 5, -4, 3, 0],\n [5, -3, -2, 2, 0, -3],\n [-1, 3, 4, 0, 6, 3],\n [6, 2, -3, 3, -4, 1],\n [-6, 2, 6, -6, -5, 6],\n [1, 2, 0, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8499", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, 0, 0, 2, 6, 6],\n [0, 3, 0, 6, 0, 2],\n [0, 0, -3, 5, 0, 0],\n [2, 6, 5, 5, -1, -1],\n [6, 0, 0, -1, -5, 0],\n [6, 2, 0, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "605127", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, -5, 0, 1, 2, -1],\n [-5, -4, 0, 2, 3, 2],\n [0, 0, 6, 2, 0, -2],\n [1, 2, 2, -4, 2, 2],\n [2, 3, 0, 2, -3, -1],\n [-1, 2, -2, 2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3872", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -2, 1, 5, -2, -3],\n [1, 0, -1, -2, -2, 6],\n [3, -5, 6, -3, 1, 1],\n [4, -6, -5, -2, 2, 3],\n [4, 5, 6, 4, 0, 3],\n [-2, -6, -1, 5, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94883", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-5, 4, 0, 3, -2, 4],\n [4, -6, 2, 0, -4, -1],\n [0, 2, 6, 0, 0, 1],\n [3, 0, 0, -3, 2, -2],\n [-2, -4, 0, 2, -1, -1],\n [4, -1, 1, -2, -1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1527227", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[6, -3, 2, -5, -4, -5],\n [-5, 3, 4, 4, 1, -4],\n [0, 1, -4, -5, 6, 6],\n [1, -4, 0, 5, -6, 5],\n [-1, 5, 5, 6, 2, 5],\n [-4, 0, 6, -1, 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": "144233", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -2, -3, 2, 1, 0],\n [-2, 1, 2, 3, 0, -4],\n [-3, 2, 3, 3, 0, 2],\n [2, 3, 3, -3, 0, -2],\n [1, 0, 0, 0, 5, 2],\n [0, -4, 2, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "243945", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 4, 5, 3, -3, 5],\n [1, 4, 2, -4, -2, -3],\n [5, 3, -1, 4, 3, -3],\n [1, -4, 4, -2, 6, -6],\n [6, -1, 4, -2, 1, 2],\n [1, 1, 5, 6, -4, -3]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33354", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 5) of the 4th power of the matrix:\n[[4, 1, 2, -3, 4, 4],\n [1, 2, -2, 3, 4, -3],\n [2, -2, -5, 3, -2, 0],\n [-3, 3, 3, 2, 1, 1],\n [4, 4, -2, 1, -6, -2],\n [4, -3, 0, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2875", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[0, 4, -2, -2, 0, 4],\n [-4, -1, 0, -6, 5, -5],\n [5, -3, 6, 1, 4, 6],\n [3, -1, -6, 3, -2, 0],\n [6, -1, 6, 6, 5, 2],\n [1, -3, 6, 4, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31860", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -1, -2, 0, 2, 2],\n [-1, -3, 6, 1, -5, 4],\n [-2, 6, 4, -4, 1, 0],\n [0, 1, -4, -6, -2, -1],\n [2, -5, 1, -2, -1, 1],\n [2, 4, 0, -1, 1, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23702", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 1) of the matrix A^5 where A is:\n[[-6, -2, 5, -1, 1, 6],\n [-6, -2, -4, -5, 4, 1],\n [0, 3, 0, -2, 5, 6],\n [2, -2, -5, -4, -3, -2],\n [6, -4, 5, 0, -2, -2],\n [-1, 0, 3, 3, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17021", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[4, -3, -2, -2, 1, 2],\n [0, -2, -4, -6, 4, 2],\n [-2, 2, 3, 5, 6, -3],\n [-2, -3, -5, 5, -6, 1],\n [-3, -2, -1, 1, 4, 1],\n [0, -3, -1, -3, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2773", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[6, 5, 6, 6, 4, -6],\n [-2, 3, 5, 3, -3, 4],\n [0, 6, 2, -2, -3, 2],\n [-2, 2, 1, -3, 4, 4],\n [0, -2, 3, -3, -2, -2],\n [4, 2, 5, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-662", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, -3, 0, -2, 0, 0],\n [-3, -5, 4, -4, 2, -2],\n [0, 4, -5, -5, -3, 0],\n [-2, -4, -5, 0, -2, -2],\n [0, 2, -3, -2, -4, 6],\n [0, -2, 0, -2, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43723", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, 4, 4, -2, -6, 2],\n [-6, -1, -6, -4, 3, -2],\n [3, 0, 3, 1, 5, 2],\n [-1, 4, 2, 1, 2, 3],\n [-3, 2, 0, -2, -2, -6],\n [-5, 3, -4, 1, -1, 5]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-421", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^5 where A is:\n[[3, 4, 6, -2, 6, -6],\n [5, 4, 5, 2, -4, -4],\n [-5, -3, 5, -5, 6, 2],\n [5, 3, 0, 1, -4, -1],\n [3, -1, 6, -6, -1, 6],\n [-4, 4, -4, -4, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-140190", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 0, 2, 3, 6, -2],\n [0, 6, 0, 0, 0, -4],\n [2, 0, 0, -1, 0, 2],\n [3, 0, -1, 5, -4, 3],\n [6, 0, 0, -4, 2, 4],\n [-2, -4, 2, 3, 4, 6]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "667", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -4, -4, -1, -4, 4],\n [-2, -3, -4, 1, 3, -4],\n [-1, 6, 0, 0, -5, -4],\n [5, 3, 3, -3, 0, -5],\n [-4, 0, 0, 3, -4, 5],\n [-6, 5, -4, -2, 0, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-155", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[6, 0, 2, 4, 0, 0],\n [0, 5, -3, -1, 1, 2],\n [2, -3, 0, -6, -4, 3],\n [4, -1, -6, 5, -6, 0],\n [0, 1, -4, -6, 3, 0],\n [0, 2, 3, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1253864", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-6, 4, 3, 4, 1, 2],\n [4, -6, -1, 5, -3, 6],\n [3, -1, 4, -2, 0, -4],\n [4, 5, -2, 3, -1, -1],\n [1, -3, 0, -1, -6, 1],\n [2, 6, -4, -1, 1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "189723", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, 2, -2, 4, -2, 3],\n [2, 5, -2, 2, -3, 2],\n [-2, -2, 3, 4, 4, 2],\n [4, 2, 4, 1, -4, 3],\n [-2, -3, 4, -4, 2, 0],\n [3, 2, 2, 3, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "398116", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 6, -4, 5, 2, -3],\n [-3, -4, -2, -4, 2, -4],\n [-5, 5, -2, -1, -6, 5],\n [4, -1, 3, -4, -3, -1],\n [1, 2, -1, 0, -2, 5],\n [2, -3, 3, 4, -1, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127522", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-6, -2, 6, -2, 2, -6],\n [-2, 0, 4, -1, -1, 5],\n [0, -1, -2, 3, -2, 2],\n [1, 5, 3, -3, -3, 3],\n [-2, 6, 6, -4, 1, 0],\n [-2, 3, -4, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181816", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -6, -1, 3, -3, -3],\n [1, -5, -3, -5, -6, 3],\n [6, 6, -4, 5, 1, -1],\n [5, 0, -5, -1, 1, 1],\n [-3, -1, -2, 2, 1, -5],\n [5, 6, 0, 0, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23987", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-6, -3, 2, 0, -4, -2],\n [-3, -4, 0, 5, 0, -3],\n [2, 0, 1, 3, -2, 2],\n [0, 5, 3, 6, 2, 0],\n [-4, 0, -2, 2, 1, 2],\n [-2, -3, 2, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-58485", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 4, -2, -2, 4, -1],\n [4, -5, -4, 2, 1, -2],\n [-2, -4, -2, 0, -2, -4],\n [-2, 2, 0, -2, -2, -2],\n [4, 1, -2, -2, 1, 5],\n [-1, -2, -4, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29074", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[0, 4, 4, 4, 2, 2],\n [4, 4, 2, -2, 0, 4],\n [4, 2, 0, -4, 0, 4],\n [4, -2, -4, 0, 4, -2],\n [2, 0, 0, 4, 6, -6],\n [2, 4, 4, -2, -6, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4557301", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -1, 2, -4, 0, -1],\n [-1, 1, -2, -2, 5, 2],\n [2, -2, -3, 0, 3, 4],\n [-4, -2, 0, 0, 1, 2],\n [0, 5, 3, 1, -3, 0],\n [-1, 2, 4, 2, 0, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5426", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 2, 0, -2, 2, 0],\n [2, -1, 4, 2, -6, 4],\n [0, 4, -6, 2, 0, 4],\n [-2, 2, 2, 2, 1, 2],\n [2, -6, 0, 1, -1, 4],\n [0, 4, 4, 2, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11504", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -5, -1, -1, -5, -3],\n [1, 1, 6, 1, 1, -6],\n [-5, 5, -3, 5, 2, -4],\n [-1, 0, 1, 6, 0, -4],\n [-1, -2, 6, 5, 3, -3],\n [-6, 6, 0, 1, -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": "84629", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -2, 6, 0, -2, 0],\n [-2, -2, 0, 2, 0, 2],\n [6, 0, 2, 5, 1, -4],\n [0, 2, 5, -6, 1, 0],\n [-2, 0, 1, 1, 0, 0],\n [0, 2, -4, 0, 0, -3]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6025", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 4) of the matrix A^5 where A is:\n[[-6, 2, 5, -3, 5, -1],\n [6, 0, 1, 5, 6, 4],\n [2, 2, 1, 3, 4, 5],\n [5, -4, 5, -5, -2, -6],\n [-4, -6, 6, -4, 6, -3],\n [0, 5, 5, -2, -2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7453", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-6, 1, 6, -3, 3, -2],\n [-5, 5, 6, -6, 2, -5],\n [-1, -6, -6, 2, -3, 2],\n [4, -2, 0, -6, -1, 1],\n [-6, 2, -4, -6, -6, 6],\n [4, -1, 4, -1, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-63004", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 2, -1, 1, -2, 6],\n [2, -3, -4, -2, 0, 0],\n [-1, -4, -3, -2, 0, 0],\n [1, -2, -2, -3, 4, -2],\n [-2, 0, 0, 4, -3, 1],\n [6, 0, 0, -2, 1, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57546", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (6, 5) of the result:\nA =\n[[5, -1, -2, 1, 0, 0],\n [-1, -5, 2, 2, -2, 0],\n [-2, 2, 5, -2, -2, -4],\n [1, 2, -2, 4, -4, 0],\n [0, -2, -2, -4, -5, -2],\n [0, 0, -4, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9338", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, 1, 0, -1, -5, -1],\n [6, 5, 4, 2, -5, -6],\n [4, 6, -2, 4, -1, -4],\n [1, 0, -5, 5, 0, -6],\n [2, 6, 0, -1, 6, -5],\n [-4, -6, 3, 6, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146402", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[6, 0, 0, 4, -2, -1],\n [0, 5, -2, 1, -1, 1],\n [0, -2, -2, 1, 1, 0],\n [4, 1, 1, -1, -4, -2],\n [-2, -1, 1, -4, 0, -2],\n [-1, 1, 0, -2, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61046", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-6, 0, -4, 2, 3, 4],\n [0, -5, 5, 2, 3, 0],\n [-4, 5, 1, 5, -5, 4],\n [2, 2, 5, -5, 2, -2],\n [3, 3, -5, 2, 6, 2],\n [4, 0, 4, -2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9982", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-6, -6, -3, -2, 5, 0],\n [-3, 3, 5, -6, 4, 3],\n [0, -5, 6, 4, -5, 1],\n [5, 3, 3, 3, -2, 3],\n [-5, -2, 1, -1, -4, 1],\n [2, -2, 6, -5, -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": "337562", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-6, 3, 5, -5, 3, -3],\n [-6, -3, 6, 5, 4, 6],\n [3, -2, 2, -6, 5, -2],\n [-5, 2, -1, -5, -4, 1],\n [-6, 5, -4, 6, 3, -6],\n [4, 4, 1, -6, 6, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136091", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 3) of the matrix A^5 where A is:\n[[-3, 0, -2, 1, 5, 4],\n [-6, -2, -3, -4, -2, 3],\n [-4, 1, 6, -4, -6, 2],\n [2, -1, 3, -6, 1, -5],\n [2, 1, -4, 6, -2, 2],\n [6, -6, 2, -3, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 5, 0, -2, 1, -2],\n [5, -3, -2, -4, 3, 2],\n [0, -2, -4, -5, 0, -3],\n [-2, -4, -5, -4, 0, 0],\n [1, 3, 0, 0, 6, -4],\n [-2, 2, -3, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1045452", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 4) of the matrix A^5 where A is:\n[[-1, -2, -1, 2, 0, 3],\n [-2, -3, -1, 6, -2, -1],\n [-1, -1, -4, 4, 1, 4],\n [2, 6, 4, 2, 4, 2],\n [0, -2, 1, 4, 0, -2],\n [3, -1, 4, 2, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25910", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 5, 4, -2, 5, -5],\n [6, -1, -4, -1, 5, -2],\n [-5, 5, 6, -2, -2, 2],\n [4, 1, 5, 5, 0, 5],\n [6, -4, 3, -3, -1, -4],\n [4, 2, 1, -1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "482008", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, 4, -4, 3, 1, -6],\n [-4, 4, -2, -2, 3, -5],\n [3, 1, -2, 0, 0, -2],\n [1, 2, -3, -3, 1, -6],\n [-3, -1, 6, -3, -1, -2],\n [2, 3, 2, -3, 6, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19265", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[5, 1, 3, -3, -5, 6],\n [6, -5, -6, -2, -1, 2],\n [-2, 6, -1, -1, -4, 5],\n [-3, -6, -3, -6, -2, 4],\n [4, 1, 1, -2, 3, -5],\n [5, -1, -6, 0, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16476", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, -1, 4, -6, 2, 3],\n [-3, 1, -2, 4, 1, -6],\n [1, 4, 6, 4, -3, -5],\n [4, -1, -5, -2, -5, -4],\n [4, -1, -6, -1, -4, 0],\n [-5, -1, 1, -6, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50127", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[6, 0, 0, -3, 4, 3],\n [0, -1, 0, 1, 1, -2],\n [0, 0, 4, 3, 0, -2],\n [-3, 1, 3, 4, -4, -2],\n [4, 1, 0, -4, 4, 4],\n [3, -2, -2, -2, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "195911", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 1) of the 5th power of the matrix:\n[[3, 2, 0, 4, 4, 2],\n [2, 3, -2, 4, 4, 2],\n [0, -2, -1, -3, 0, 1],\n [4, 4, -3, -5, -2, 0],\n [4, 4, 0, -2, 3, 3],\n [2, 2, 1, 0, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61200", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 4, -5, 6, -3, -6],\n [-4, 4, 2, 0, 0, -6],\n [0, 3, 0, -3, 0, 1],\n [-4, 6, 3, -5, 0, -2],\n [-2, -2, 0, 2, 4, 1],\n [-1, 0, 2, 4, -1, -6]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1540", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, 2, 0, -2, -2, 1],\n [2, -4, 0, 0, -2, -5],\n [0, 0, -2, 0, 0, -2],\n [-2, 0, 0, -1, 1, -2],\n [-2, -2, 0, 1, 6, 2],\n [1, -5, -2, -2, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43242", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 2) of the 5th power of the matrix:\n[[0, 2, 3, 2, -3, 0],\n [2, 2, 0, 2, -1, -2],\n [3, 0, -3, 0, 2, -3],\n [2, 2, 0, 2, 0, 2],\n [-3, -1, 2, 0, -2, -4],\n [0, -2, -3, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3168", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 2, 2, 4, -2, -6],\n [2, -3, 0, 0, -2, -1],\n [2, 0, 4, 2, 4, 2],\n [4, 0, 2, -2, 4, -2],\n [-2, -2, 4, 4, -2, -3],\n [-6, -1, 2, -2, -3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-561837", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 4) of the matrix A^4 where A is:\n[[2, 1, 3, -4, -3, 1],\n [1, 0, 2, -4, 1, -4],\n [3, 2, -1, 3, 2, 0],\n [-4, -4, 3, -5, 4, -2],\n [-3, 1, 2, 4, 2, 3],\n [1, -4, 0, -2, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6020", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 3) of the matrix A^5 where A is:\n[[-2, 4, -2, -2, 3, -4],\n [4, -1, 2, 2, -4, -4],\n [-2, 2, -5, 1, -1, -2],\n [-2, 2, 1, 4, -3, -2],\n [3, -4, -1, -3, 0, 0],\n [-4, -4, -2, -2, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17122", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[6, -5, -6, -6, 6, 4],\n [-3, 3, 6, -5, -6, -1],\n [-3, 3, 6, 5, 0, 4],\n [-1, -2, 3, 5, 6, 5],\n [5, 5, -5, -2, 2, 2],\n [-5, 0, 3, -3, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5456160", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 4, -6, -4, 4, 2],\n [2, 0, -4, 6, -4, -3],\n [0, 0, 5, 5, -5, 5],\n [-2, 0, 0, -1, 3, 3],\n [5, 1, -4, -6, -4, 4],\n [-5, -5, -5, -2, 6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69877", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, -3, 3, -2, -5, -2],\n [3, -3, 1, -6, 5, -2],\n [4, 5, 3, -6, 3, 3],\n [-3, 1, -6, 4, -5, -6],\n [4, 0, -5, -6, 5, -1],\n [-1, 3, -5, -6, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1773870", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, -2, 0, -2, -2, 1],\n [-2, 6, 0, 4, -4, 4],\n [0, 0, -1, 0, -1, 1],\n [-2, 4, 0, -5, 4, 2],\n [-2, -4, -1, 4, 0, 4],\n [1, 4, 1, 2, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38508", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -4, -2, 1, 3, -2],\n [-4, 0, 1, -2, 1, -3],\n [-2, 1, -3, 4, 2, 3],\n [1, -2, 4, 1, -4, 4],\n [3, 1, 2, -4, -5, -2],\n [-2, -3, 3, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7681", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[5, -2, -4, 2, 6, -2],\n [-4, -4, -4, -1, -6, 4],\n [-3, 6, 1, -4, -2, -5],\n [-5, 4, 6, 0, 3, -4],\n [-2, -4, -1, 6, 3, -4],\n [1, -5, -4, 1, 1, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3282", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, 3, -5, 5, 0, -1],\n [-5, -2, 0, 1, -4, -6],\n [6, 0, 6, -2, -2, 0],\n [-6, 1, 5, 3, -2, 1],\n [3, 3, -2, 5, 0, 3],\n [-4, -5, -1, -2, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71033", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[-3, -1, 0, 4, 0, 0],\n [-1, 3, 2, 0, 0, -4],\n [0, 2, 6, 1, -2, -3],\n [4, 0, 1, 4, -1, 0],\n [0, 0, -2, -1, 5, 5],\n [0, -4, -3, 0, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, 2, -1, 2, 2, -2],\n [2, 3, -6, 0, -5, 0],\n [-1, -6, -4, -4, 5, -4],\n [2, 0, -4, -4, -2, -3],\n [2, -5, 5, -2, 1, -2],\n [-2, 0, -4, -3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1545558", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 4, -1, 2, -2, -1],\n [4, 6, -2, -2, 3, -4],\n [-1, -2, 3, 1, 0, 0],\n [2, -2, 1, -3, 3, -2],\n [-2, 3, 0, 3, 6, 3],\n [-1, -4, 0, -2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1001469", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 6) of the result:\nA =\n[[1, 1, 2, 3, -1, 5],\n [-3, 5, 4, -4, 5, -2],\n [-1, -4, -5, 0, 4, -2],\n [2, -4, 1, -1, -3, 5],\n [5, 2, -2, 3, -1, 6],\n [2, 0, 5, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1089", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, -4, 3, 5, -4, -3],\n [-1, 5, -4, 3, -6, -6],\n [2, 2, -2, 2, 4, 0],\n [2, 5, 0, 2, -5, 4],\n [4, 1, 0, -1, -2, -3],\n [0, -4, 1, -5, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123620", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-5, 1, 2, 3, -2, -2],\n [1, -5, 2, 2, 1, -4],\n [2, 2, -3, -4, 0, 0],\n [3, 2, -4, 6, 0, 4],\n [-2, 1, 0, 0, -2, 3],\n [-2, -4, 0, 4, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10658", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[6, -5, 6, 2, -3, -1],\n [5, -6, 5, 2, -2, -4],\n [-3, -6, 2, 1, -3, -5],\n [2, -3, 2, 3, -4, 0],\n [0, 3, 6, -3, -5, 4],\n [2, -3, 1, -5, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33116", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, -3, 2, -2, 0, 2],\n [-3, 3, -2, -1, -1, 2],\n [2, -2, -1, 0, 3, -2],\n [-2, -1, 0, 5, 4, -4],\n [0, -1, 3, 4, -6, 2],\n [2, 2, -2, -4, 2, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "878158", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 2, -1, -4, 3, -3],\n [3, -2, 5, 5, -6, -2],\n [-6, 2, 0, -4, 2, -5],\n [5, 0, 2, -1, 3, -2],\n [5, 0, -1, -2, -5, 1],\n [6, 0, -1, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166596", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-6, 2, -1, -3, 3, 0],\n [2, -2, -2, 1, 0, 6],\n [6, 1, 4, 5, 3, -5],\n [2, -4, -1, -1, -5, 5],\n [6, 0, 2, 5, 3, 4],\n [-6, 1, -5, -6, 1, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11242", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 1, 0, 4, -1, 6],\n [1, -3, -2, 2, 6, 2],\n [0, -2, 4, 6, 0, 0],\n [4, 2, 6, 2, 0, 4],\n [-1, 6, 0, 0, 2, -2],\n [6, 2, 0, 4, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64970", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 1, 1, 0, -4, 3],\n [1, -6, -3, -2, 1, -2],\n [1, -3, -1, 6, -2, 0],\n [0, -2, 6, -2, -2, 2],\n [-4, 1, -2, -2, 4, -4],\n [3, -2, 0, 2, -4, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23353", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-6, -3, -3, 0, 0, 4],\n [-3, 3, 4, 4, -2, 1],\n [-3, 4, 6, -1, 3, 0],\n [0, 4, -1, 1, -4, -3],\n [0, -2, 3, -4, -5, 2],\n [4, 1, 0, -3, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92177", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -3, 4, 3, 3, 6],\n [0, -2, 2, -3, -4, 6],\n [-5, -6, 4, -1, 3, -5],\n [1, -1, 5, 5, -2, 6],\n [-5, 0, -5, 6, -2, -5],\n [4, 3, 4, 4, -5, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29600", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, -4, 0, -4, -4, -5],\n [-4, -2, -2, -2, -5, -4],\n [0, -2, 0, 2, 1, 0],\n [-4, -2, 2, -4, 3, 2],\n [-4, -5, 1, 3, -1, 0],\n [-5, -4, 0, 2, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83919", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, 0, 0, 2, -2, -2],\n [0, -2, -1, 2, 0, 0],\n [0, -1, -4, 1, 0, 0],\n [2, 2, 1, -6, 1, 4],\n [-2, 0, 0, 1, -1, 2],\n [-2, 0, 0, 4, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30865", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (6, 5) of the result:\nA =\n[[1, -2, 2, 0, 2, 0],\n [-2, 4, 0, 6, -1, 6],\n [2, 0, 2, 0, -6, -1],\n [0, 6, 0, 3, 1, 0],\n [2, -1, -6, 1, 6, -2],\n [0, 6, -1, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27480", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 1) of the result:\nA =\n[[3, -2, 5, 0, 0, 0],\n [-2, 0, 1, -2, -4, 4],\n [5, 1, -4, -2, -2, -1],\n [0, -2, -2, -5, -2, 2],\n [0, -4, -2, -2, -2, -2],\n [0, 4, -1, 2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5702", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 2, 2, -2, -2, 6],\n [2, -5, 0, 0, -4, 4],\n [2, 0, -1, 0, -4, -1],\n [-2, 0, 0, -3, -5, 2],\n [-2, -4, -4, -5, 3, -2],\n [6, 4, -1, 2, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81171", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 3) of the 4th power of the matrix:\n[[-3, 0, -2, -2, 0, -2],\n [0, 5, -2, 0, 0, -2],\n [-2, -2, -6, -3, -2, -5],\n [-2, 0, -3, -5, -1, 1],\n [0, 0, -2, -1, -1, -4],\n [-2, -2, -5, 1, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15878", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-6, 6, -4, 0, 4, 2],\n [-5, 0, -6, -5, -1, 4],\n [-2, 1, 5, 4, -5, -6],\n [0, -1, 1, 4, 6, 1],\n [-5, 1, -1, 2, 5, 0],\n [-5, 1, 2, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37896", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 3, -1, 0, -1, -2],\n [3, 1, 0, 4, 2, -2],\n [-1, 0, -2, 0, 2, 4],\n [0, 4, 0, 4, -2, 2],\n [-1, 2, 2, -2, 0, 2],\n [-2, -2, 4, 2, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136236", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, -1, -4, -6, 2, 2],\n [-4, -3, 6, 0, -5, 5],\n [-4, -1, 4, 1, -6, -3],\n [-6, -5, 1, -1, 2, -5],\n [-4, 2, 2, 6, -1, -4],\n [-2, -5, 0, 3, 4, 1]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1256", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[-1, 3, -4, 1, 0, 0],\n [3, -6, -2, -3, -1, -1],\n [-4, -2, -4, -2, 0, 3],\n [1, -3, -2, -6, 0, -4],\n [0, -1, 0, 0, -3, -1],\n [0, -1, 3, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1563", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -4, 4, -4, 1, -3],\n [-4, 3, -2, -3, 2, 1],\n [4, 0, 1, 6, -2, -3],\n [0, -6, -1, 1, 0, -5],\n [6, 0, 6, -1, 6, -2],\n [-3, -6, 6, -5, 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": "91930", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[-4, -2, 1, 6, 6, 1],\n [-1, -2, 6, -5, 2, -6],\n [4, -5, 6, -6, 5, -3],\n [-3, -2, -2, 1, 4, 4],\n [-4, -1, 5, 6, 5, -4],\n [6, -5, 1, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "633", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, 1, 3, 0, 4, 2],\n [1, -4, -2, 0, -2, -2],\n [3, -2, 4, 0, 4, 0],\n [0, 0, 0, 1, 0, 2],\n [4, -2, 4, 0, -5, 2],\n [2, -2, 0, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39110", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 5, 1, -2, 5, -2],\n [5, -1, 0, -4, 5, -2],\n [1, 0, 3, 2, 4, -1],\n [-2, -4, 2, 3, 1, 0],\n [5, 5, 4, 1, -3, 0],\n [-2, -2, -1, 0, 0, 3]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48643", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 3, -3, 4, -4, 0],\n [3, -6, 0, 4, -1, -1],\n [-3, 0, -1, 2, 0, 0],\n [4, 4, 2, -1, -6, 1],\n [-4, -1, 0, -6, 5, 3],\n [0, -1, 0, 1, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132620", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, 3, -5, 6, 2, -5],\n [-4, 5, 6, 3, 5, 5],\n [-5, 2, -6, -2, -6, -2],\n [1, 1, 4, 1, -5, 1],\n [5, -2, -6, 0, 6, -1],\n [-2, -6, -6, -1, 3, 5]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "519", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 0, -1, 0, 2, 0],\n [0, -5, 0, 0, 4, 1],\n [-1, 0, 5, 1, -4, -3],\n [0, 0, 1, -1, -2, 0],\n [2, 4, -4, -2, -5, -2],\n [0, 1, -3, 0, -2, 0]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, 4, 1, 2, 5, 2],\n [-4, -2, -1, -1, 3, 1],\n [-1, -1, -3, 0, 1, -4],\n [0, -4, 1, -6, -6, -1],\n [3, 2, 5, -3, -1, 5],\n [-2, 5, -6, -1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739862", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 4, -4, -5, 6, -3],\n [3, -4, 5, -5, -6, -4],\n [3, -1, 2, 4, -2, -4],\n [-2, -2, -2, 5, 5, 0],\n [-2, 0, 2, -2, -5, -2],\n [1, 5, -3, -5, 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": "383147", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 2, -2, 0, 2, -1],\n [2, -6, 2, 5, 1, -1],\n [-2, 2, -6, -3, 0, -2],\n [0, 5, -3, 4, 0, -1],\n [2, 1, 0, 0, 6, -4],\n [-1, -1, -2, -1, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1075534", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, 5, 3, 0, -3, 4],\n [-1, -4, 0, -1, -4, -3],\n [3, -2, 2, -1, 6, -3],\n [4, 4, 0, -5, -3, -2],\n [-3, -3, 4, 6, 2, 4],\n [6, -5, -1, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80322", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[0, 3, 2, 0, -2, 0],\n [3, -1, 4, 0, 0, 4],\n [2, 4, 0, 2, 1, 0],\n [0, 0, 2, -5, 4, 3],\n [-2, 0, 1, 4, 3, 1],\n [0, 4, 0, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, 2, 4, -4, 1, 3],\n [2, 0, 1, 0, 0, -2],\n [4, 1, -6, 1, -5, -2],\n [-4, 0, 1, -4, -2, -2],\n [1, 0, -5, -2, 5, -5],\n [3, -2, -2, -2, -5, -4]], determine the value at position (6, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-63638", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 5, 2, 0, 0, -1],\n [5, 1, 4, -2, -1, 0],\n [2, 4, 3, -4, 4, -4],\n [0, -2, -4, -2, -2, 0],\n [0, -1, 4, -2, 1, 0],\n [-1, 0, -4, 0, 0, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23727", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 1, 4, -2, 3, 1],\n [1, 0, -4, 0, 3, 0],\n [4, -4, 6, 2, 2, -4],\n [-2, 0, 2, 2, 5, 2],\n [3, 3, 2, 5, 1, -2],\n [1, 0, -4, 2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79150", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[-4, -4, 5, 4, -2, -2],\n [-1, -2, 5, -1, 1, -5],\n [-3, 6, -1, 5, -2, -6],\n [2, -4, -5, 2, 0, -2],\n [5, -1, 5, 4, -3, -6],\n [-3, 2, -6, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1552", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, 2, -1, -4, 6, 0],\n [-3, -4, 0, 4, 4, 0],\n [-3, 5, 0, 4, -5, -6],\n [5, -5, -3, 1, -4, 3],\n [-1, -1, 6, 2, 2, -3],\n [2, 6, -1, -5, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4736", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (6, 6) of the result:\nA =\n[[-1, -5, 1, -3, -2, 1],\n [4, 1, 5, 5, -1, -3],\n [-6, 5, 0, 1, 2, -5],\n [-6, -3, 6, -2, 3, 5],\n [-6, -2, -1, -4, 5, 0],\n [-1, -3, -4, -2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24191", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 2, -1, 6, 4, -1],\n [5, -3, -3, -5, 3, -3],\n [1, 6, 3, -5, 2, -6],\n [6, -5, -5, 4, 6, -1],\n [0, 6, -4, 4, 2, -2],\n [-2, 4, 5, -3, 2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148214", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, -3, -3, -5, 2, -4],\n [-3, 0, 3, 1, 1, -3],\n [0, 3, -6, -1, -1, -1],\n [5, -5, 1, -2, -2, -5],\n [-3, 5, 2, 2, -1, 4],\n [2, -3, 4, -6, -5, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3243", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^4 where A is:\n[[-6, -2, -2, 4, 1, 2],\n [-2, -1, 3, 4, 0, 2],\n [-2, 3, -2, 3, -4, 2],\n [4, 4, 3, 0, 4, 0],\n [1, 0, -4, 4, 1, 3],\n [2, 2, 2, 0, 3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3036", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, -5, 6, 4, 2, 0],\n [3, 1, -1, 2, -1, 0],\n [0, 2, 4, 1, 6, -6],\n [-3, 0, 4, 1, 0, 5],\n [-4, -3, 5, 0, 1, 0],\n [-1, 2, 2, 4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-87445", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 0, -4, -3, 0, -5],\n [0, -6, 6, -4, 3, 0],\n [-4, 6, 3, -4, -2, -1],\n [-3, -4, -4, 1, 1, 0],\n [0, 3, -2, 1, 3, -2],\n [-5, 0, -1, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "805304", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 1) of the matrix A^5 where A is:\n[[-4, 0, -5, -4, -6, 1],\n [-5, 0, 4, 2, -1, -5],\n [-5, 2, 3, 1, 2, -3],\n [-3, -5, 3, -6, 3, 6],\n [-3, 3, 3, 4, 1, -5],\n [6, 5, 4, 1, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-171631", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-3, 0, 4, -2, -2, 5],\n [0, 4, -2, 4, 2, 0],\n [4, -2, 4, 0, 1, -3],\n [-2, 4, 0, -3, -2, 2],\n [-2, 2, 1, -2, -4, -2],\n [5, 0, -3, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24791", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -2, 0, 2, -2, 4],\n [-2, -6, 0, 0, 0, -4],\n [0, 0, -6, 4, -4, 1],\n [2, 0, 4, -6, -3, 4],\n [-2, 0, -4, -3, 2, -1],\n [4, -4, 1, 4, -1, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57883", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 5, -4, -1, 6, -3],\n [6, 5, 3, -5, 6, -4],\n [2, 4, 4, 2, -1, 3],\n [3, 2, -3, 4, -2, 3],\n [-1, 6, 2, 6, -2, 1],\n [4, -6, -2, 3, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158908", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-1, 2, 2, -3, -2, 0],\n [2, -2, -3, 0, 0, 2],\n [2, -3, 5, -4, 0, -2],\n [-3, 0, -4, -2, 2, 4],\n [-2, 0, 0, 2, -2, -2],\n [0, 2, -2, 4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3382", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 0, -2, -2, -4, -4],\n [0, -3, 0, 0, -1, 0],\n [-2, 0, 2, 0, 4, -2],\n [-2, 0, 0, -2, -2, 0],\n [-4, -1, 4, -2, -1, -4],\n [-4, 0, -2, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44974", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-6, -2, 0, 2, -2, 0],\n [-2, -5, -4, -4, -5, 0],\n [0, -4, 4, -2, 0, 4],\n [2, -4, -2, -1, -4, 0],\n [-2, -5, 0, -4, 5, 2],\n [0, 0, 4, 0, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108646", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -5, 6, 1, -5, 3],\n [-5, -6, 0, 5, -5, 3],\n [-2, -2, -4, -4, 6, 5],\n [-4, -1, -3, 6, -4, -5],\n [6, -4, -3, -1, -3, 1],\n [-4, 5, -4, -4, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2820", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-6, -5, 4, 2, 2, 4],\n [-5, -4, -4, -2, 1, 0],\n [4, -4, 3, -2, -4, 0],\n [2, -2, -2, 2, 1, 0],\n [2, 1, -4, 1, -3, -2],\n [4, 0, 0, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11374", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[6, 4, 0, 4, 6, 5],\n [1, 2, -5, -4, 5, 5],\n [-5, 3, 0, 5, -5, 5],\n [-5, -5, 5, 6, -3, -6],\n [-5, -4, 0, 3, -6, -1],\n [-4, -4, -3, 6, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96727", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, -2, 4, 0, 0, 2],\n [-2, -2, 1, 4, 4, 1],\n [4, 1, -2, -2, 0, 1],\n [0, 4, -2, -5, 0, 0],\n [0, 4, 0, 0, 4, 4],\n [2, 1, 1, 0, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21421", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, -4, 5, -6, 4, -2],\n [3, 3, -5, -3, -5, -5],\n [6, -4, -2, -3, -5, 4],\n [3, -5, -1, 0, 5, 3],\n [-1, 0, -6, -1, 4, -4],\n [-6, 1, -3, 3, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-120953", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -2, -1, 4, 2, -1],\n [-2, 2, 0, 2, 4, 0],\n [-1, 0, -3, 2, 0, 0],\n [4, 2, 2, -2, -1, 0],\n [2, 4, 0, -1, 2, 0],\n [-1, 0, 0, 0, 0, -1]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "494", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, -4, -1, 6, -4, 2],\n [-4, 4, -1, 2, 0, -4],\n [-1, -1, 2, 0, -3, 2],\n [6, 2, 0, 2, 3, 0],\n [-4, 0, -3, 3, 3, 2],\n [2, -4, 2, 0, 2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "723083", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -5, 2, 2, 0, 0],\n [-5, 2, -6, 2, -2, -4],\n [2, -6, 0, -2, 6, 4],\n [2, 2, -2, 6, 4, 0],\n [0, -2, 6, 4, -1, 3],\n [0, -4, 4, 0, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2860129", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, 0, -2, 0, -4, -4],\n [0, 1, -4, -2, 3, 2],\n [-2, -4, -5, 2, -2, -4],\n [0, -2, 2, -2, 0, -2],\n [-4, 3, -2, 0, -1, 4],\n [-4, 2, -4, -2, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-272889", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, -1, -3, -2, 2, -4],\n [-1, -3, 1, 1, -2, 2],\n [-3, 1, -5, 0, 1, -1],\n [-2, 1, 0, 5, -2, 0],\n [2, -2, 1, -2, -1, -4],\n [-4, 2, -1, 0, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25132", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 1, -6, 6, 0, 2],\n [5, 6, -4, -4, 1, -3],\n [1, -2, -4, -3, -3, 1],\n [-1, 0, 2, -1, -4, 6],\n [-4, 4, -4, 5, 3, -5],\n [-6, 4, 3, -6, -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": "48038", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 5, 0, 2, 6, 1],\n [5, 2, 6, 1, 2, 0],\n [0, 6, -4, -2, 2, -4],\n [2, 1, -2, -1, -2, -2],\n [6, 2, 2, -2, -1, -3],\n [1, 0, -4, -2, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56511", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 4) of the matrix A^5 where A is:\n[[-3, -2, -5, 3, 3, 1],\n [3, 0, 3, -1, 0, 5],\n [-6, -2, 0, -6, -5, 2],\n [5, -4, -1, 0, 2, -2],\n [-3, 4, 5, -5, -4, -2],\n [4, 6, -5, 6, -3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5736", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 0, 0, 0, 4, 0],\n [0, -1, -2, 0, -1, 1],\n [0, -2, 0, -2, 0, 3],\n [0, 0, -2, 6, 3, 0],\n [4, -1, 0, 3, -3, 0],\n [0, 1, 3, 0, 0, 1]], determine the value at position (6, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[-4, 3, 2, -2, 0, 4],\n [3, 5, -2, 0, -2, -2],\n [2, -2, -3, -4, 2, 0],\n [-2, 0, -4, -3, 0, 6],\n [0, -2, 2, 0, -2, 2],\n [4, -2, 0, 6, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-174", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 1) of the result:\nA =\n[[-2, 2, -2, -5, -2, 0],\n [2, 0, 0, 4, -3, 0],\n [-2, 0, 1, 0, -2, 3],\n [-5, 4, 0, 0, 2, 4],\n [-2, -3, -2, 2, 1, 0],\n [0, 0, 3, 4, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3386", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, 0, 6, 4, 6, -4],\n [-4, -2, 4, -1, -5, -4],\n [-1, -4, -2, 2, 5, -4],\n [5, 4, 6, 6, -1, 4],\n [-2, -2, 4, -1, -1, -6],\n [4, 2, -2, -6, 1, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20408", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, -2, -6, 2, 4, 2],\n [1, -2, -4, 1, -6, -4],\n [5, 4, 0, -3, 0, 5],\n [4, 6, -2, -1, 0, 6],\n [3, 5, 0, 0, 0, 4],\n [6, 6, 0, -4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29173", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[0, -5, -5, -4, -3, -1],\n [6, 1, 3, 3, 0, -3],\n [-5, -5, -3, -1, -4, -1],\n [-2, -2, -5, 1, -2, 4],\n [-5, 0, 6, 2, 2, -6],\n [0, 2, -1, -6, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1567", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, -2, 0, -2, -3, -4],\n [-2, 3, -2, 2, 4, 2],\n [0, -2, -2, -2, -2, 1],\n [-2, 2, -2, -4, -2, 0],\n [-3, 4, -2, -2, -5, -2],\n [-4, 2, 1, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-743414", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, -2, -3, 0, 0, -4],\n [-2, -4, -6, 5, -1, 1],\n [-3, -6, 5, -5, 4, -2],\n [0, 5, -5, 4, 2, 4],\n [0, -1, 4, 2, 5, 0],\n [-4, 1, -2, 4, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52352", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 0, 6, 1, -2, -4],\n [0, -6, 1, -2, 0, -2],\n [6, 1, 0, 4, -2, 2],\n [1, -2, 4, -5, -2, 2],\n [-2, 0, -2, -2, -6, -6],\n [-4, -2, 2, 2, -6, -1]], determine the value at position (6, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6745", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, 3, -2, 3, 5, 5],\n [-3, -6, -4, 6, 5, -3],\n [-5, 5, -5, -5, 4, -6],\n [3, -5, -1, -4, 3, -2],\n [-6, 1, 6, -3, 2, -3],\n [-5, -4, -2, 5, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6035", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^4 where A is:\n[[6, -1, 0, -3, 0, 3],\n [-4, 0, -3, 6, 6, 1],\n [2, 0, 1, 1, -5, 2],\n [-1, 4, -3, -2, 3, -2],\n [0, 2, 0, 2, -3, 3],\n [3, -3, -1, 1, 2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-644", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-6, 5, 0, 0, -2, 4],\n [5, -4, 3, 6, 1, -4],\n [0, 3, -6, 2, -3, 0],\n [0, 6, 2, 1, 0, 3],\n [-2, 1, -3, 0, -2, 6],\n [4, -4, 0, 3, 6, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24918", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 6) of the 5th power of the matrix:\n[[-6, 0, -6, -2, 0, 0],\n [0, -2, 2, 2, -4, -2],\n [-6, 2, -4, -3, 4, -1],\n [-2, 2, -3, 2, 2, -2],\n [0, -4, 4, 2, 0, -2],\n [0, -2, -1, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4234", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 1) of the result:\nA =\n[[5, 2, -6, 2, 0, -1],\n [2, 5, 0, 3, 4, 4],\n [-6, 0, 0, 4, 2, -2],\n [2, 3, 4, -3, 1, 2],\n [0, 4, 2, 1, 3, 1],\n [-1, 4, -2, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2140", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, 4, -1, -2, 4, -4],\n [4, 1, 0, 1, -1, -4],\n [-1, 0, 6, -2, 4, 1],\n [-2, 1, -2, 2, 0, -2],\n [4, -1, 4, 0, 6, -5],\n [-4, -4, 1, -2, -5, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2079544", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -3, 5, -3, -1, -1],\n [3, -1, -6, 3, 2, 4],\n [0, 0, 4, 0, -5, -5],\n [-1, 0, -4, 6, -3, 5],\n [-4, 0, 0, -3, 6, 0],\n [-2, -6, 3, -3, 0, 6]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3040", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 5) of the result:\nA =\n[[-5, 0, -2, 0, -1, 2],\n [0, 1, -1, -5, -3, 4],\n [-2, -1, -1, 0, 2, -4],\n [0, -5, 0, 3, -1, 2],\n [-1, -3, 2, -1, 1, 2],\n [2, 4, -4, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4783", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 4) of the matrix A^4 where A is:\n[[5, -6, -3, -5, 2, -2],\n [-4, -3, -1, 3, -6, 0],\n [1, 0, 0, 2, 6, -3],\n [0, 2, -2, -5, -2, -3],\n [1, -2, 2, 2, -4, 6],\n [3, -1, -1, -3, 4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4640", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 5) of the result:\nA =\n[[3, -4, -6, 5, 0, -2],\n [3, 0, -6, 1, -4, 0],\n [5, -4, -4, 3, 2, 6],\n [-5, -3, -1, -4, 5, 3],\n [3, 0, 0, -2, -4, -5],\n [-3, 6, -3, 4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1273", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[6, -2, 6, -1, 1, -6],\n [-2, -3, -3, 4, -5, 3],\n [-6, -1, 0, -2, 1, 2],\n [4, 4, -5, 4, 6, -3],\n [4, 2, -2, -4, -1, -4],\n [-2, -4, -1, 5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-99533", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, -4, -1, 1, 0, -1],\n [-5, 0, 1, -6, 2, -3],\n [1, 3, 0, 6, 3, 0],\n [-5, -6, -3, 5, -5, 1],\n [3, 0, 1, 4, -1, -6],\n [6, 6, 5, 2, -1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196610", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 6) of the matrix A^4 where A is:\n[[6, 3, -6, -6, 1, -1],\n [1, 1, 4, 1, 3, 0],\n [0, 3, -3, 2, 5, -5],\n [4, 2, 3, -4, 6, -5],\n [6, -3, -2, -5, 6, -6],\n [3, 4, -2, 2, 5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6731", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 1) of the matrix A^4 where A is:\n[[-2, 5, -1, 2, -2, 0],\n [5, 3, -2, 0, -2, -1],\n [-1, -2, -4, 0, -3, 4],\n [2, 0, 0, 2, -1, 0],\n [-2, -2, -3, -1, -6, -4],\n [0, -1, 4, 0, -4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, 2, -3, -2, 6, 4],\n [2, -1, 3, 5, 2, 2],\n [0, 5, 3, 2, -2, -2],\n [5, 1, 3, -3, 2, 0],\n [0, 6, -4, -3, 0, 4],\n [4, -2, 5, -4, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26232", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 3, 0, -5, 6, 5],\n [-3, -5, 1, 0, -6, -5],\n [-5, -3, -4, -6, 5, -5],\n [4, 2, 6, -6, 2, 0],\n [-5, -5, -2, 6, -2, -3],\n [5, 3, 3, 6, 5, -4]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9911", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, 0, -4, -4, 1],\n [0, 4, 0, -1, -4, 2],\n [0, 0, 0, -2, 2, -3],\n [-4, -1, -2, -4, 0, 0],\n [-4, -4, 2, 0, 1, 0],\n [1, 2, -3, 0, 0, -1]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-4, -3, -6, 1, -6, -2],\n [-1, -5, 0, 0, -6, -3],\n [5, 6, -3, -2, -6, -6],\n [0, 2, -6, -5, -1, -1],\n [-5, 2, -3, 6, 0, -1],\n [4, 6, 4, -4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56432", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[2, 0, -5, -1, 0, 2],\n [0, -6, 2, -2, 0, 0],\n [-5, 2, 3, 2, 1, -4],\n [-1, -2, 2, 0, 6, 0],\n [0, 0, 1, 6, 2, 2],\n [2, 0, -4, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-312", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 6, -6, -6, -3, -4],\n [0, 4, -4, -6, 5, 4],\n [3, -5, 3, 6, -3, -6],\n [-6, 5, 1, 0, 1, 6],\n [-3, -1, 6, -4, 4, 6],\n [1, -3, -4, -3, -1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13326", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[0, 0, 5, -3, 1, 0],\n [-5, 6, 1, 2, -2, -3],\n [-3, 6, -3, -1, 4, -3],\n [0, 0, -2, 6, -2, 3],\n [1, 0, 0, -1, 0, 0],\n [3, -5, 3, -5, 3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "390379", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 0, 0, -2, -6, -5],\n [6, 2, 1, 1, 3, -6],\n [-1, 2, 1, -4, -3, -4],\n [-1, 2, 1, 6, 3, -3],\n [-5, 6, 1, 1, 5, 4],\n [-1, 1, 2, 6, -6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "314", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 2, -2, 1, -2, 4],\n [2, 1, -2, 6, -6, 0],\n [-2, -2, -4, -2, -4, 4],\n [1, 6, -2, 0, 0, 0],\n [-2, -6, -4, 0, -6, 2],\n [4, 0, 4, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3173097", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 4, 2, 0, -6, -6],\n [-3, -3, -6, -1, 3, -5],\n [4, -2, 1, -4, 2, 0],\n [2, -6, -2, 5, 6, -4],\n [-3, -3, 4, 5, 0, 3],\n [4, 1, 4, 3, -2, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1843", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[6, 0, 4, 2, 0, -3],\n [0, 5, 2, -3, -1, 2],\n [4, 2, -2, 4, 0, -2],\n [2, -3, 4, 4, 5, 2],\n [0, -1, 0, 5, -1, 2],\n [-3, 2, -2, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350082", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 5) of the matrix A^5 where A is:\n[[1, 1, 0, 1, -5, -4],\n [2, -6, 1, 1, 0, 6],\n [4, -2, -3, 3, 3, 6],\n [3, 3, -1, 5, 4, -6],\n [6, -2, -3, -3, 0, 2],\n [1, 4, 6, 5, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4679", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, -5, 2, 1, -3, -2],\n [-5, -4, 2, 2, 0, 3],\n [2, 2, -5, 2, 4, -4],\n [1, 2, 2, -6, 1, -1],\n [-3, 0, 4, 1, 1, -6],\n [-2, 3, -4, -1, -6, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95958", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[2, -4, -3, 0, 0, 2],\n [-4, -1, 2, 1, -2, 6],\n [-3, 2, 5, 4, 0, -1],\n [0, 1, 4, -1, -3, 3],\n [0, -2, 0, -3, -2, 0],\n [2, 6, -1, 3, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-56", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[6, -3, 6, -4, 2, 2],\n [-3, 1, 0, -1, -3, -2],\n [6, 0, -3, -2, -4, -2],\n [-4, -1, -2, 1, 0, 2],\n [2, -3, -4, 0, -4, 0],\n [2, -2, -2, 2, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25973", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-6, 4, 4, -2, 2, 5],\n [4, -5, 2, 2, -6, 2],\n [4, 2, 4, -1, 0, 5],\n [-2, 2, -1, -4, -4, -5],\n [2, -6, 0, -4, 4, 0],\n [5, 2, 5, -5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1663486", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -5, -2, 0, 4, 4],\n [-4, 4, -3, -6, -4, 2],\n [3, -2, 1, -5, -4, 0],\n [3, -3, 2, 0, 4, 5],\n [-6, -3, 3, 4, -1, -1],\n [3, -1, -2, -4, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53376", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 0, -5, -3, -4, 2],\n [0, -4, -3, -2, 0, 0],\n [-5, -3, -5, 4, -3, 0],\n [-3, -2, 4, -4, 0, 0],\n [-4, 0, -3, 0, 2, 3],\n [2, 0, 0, 0, 3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "885713", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 0, 0, -4, -4, 2],\n [0, -4, 0, 0, -2, 3],\n [0, 0, 2, 0, 0, -3],\n [-4, 0, 0, -4, 0, -4],\n [-4, -2, 0, 0, 3, 0],\n [2, 3, -3, -4, 0, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-152012", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-6, 1, -5, -4, 5, -5],\n [-3, -6, -4, -2, 3, -6],\n [-3, -1, -3, 0, 0, -1],\n [2, -5, 6, 3, 1, 1],\n [4, 3, 4, -3, -1, 4],\n [-1, -2, -6, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1356320", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, -3, 0, 2, -4, 0],\n [-3, 1, 2, 0, -3, 1],\n [0, 2, -5, 2, -5, 0],\n [2, 0, 2, 5, 2, 4],\n [-4, -3, -5, 2, -2, 0],\n [0, 1, 0, 4, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77858", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-6, -2, -2, 2, 1, -3],\n [-2, -6, 1, 0, -6, -2],\n [-2, 1, 0, 2, 1, 4],\n [2, 0, 2, -5, 0, 0],\n [1, -6, 1, 0, -5, -4],\n [-3, -2, 4, 0, -4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1614664", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -4, 0, 1, -1, -2],\n [-4, -1, 2, 0, -2, -1],\n [0, 2, 6, 0, -3, -2],\n [1, 0, 0, 1, 0, 2],\n [-1, -2, -3, 0, -2, -3],\n [-2, -1, -2, 2, -3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51267", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, -3, 2, 0, -2, 0],\n [2, 3, -1, -6, -1, -6],\n [6, 5, -3, 1, -2, -2],\n [6, 3, 4, 1, 1, -6],\n [6, 6, -2, 5, -2, 1],\n [-6, 0, 0, 6, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "688702", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -4, -6, 1, -2, -1],\n [-4, -4, 2, 0, 2, 4],\n [-6, 2, 3, -6, 4, 2],\n [1, 0, -6, -6, -2, 1],\n [-2, 2, 4, -2, 1, -2],\n [-1, 4, 2, 1, -2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1523416", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-3, -2, -1, 2, 6, 4],\n [5, -3, -1, 6, -6, -5],\n [1, -3, 3, 0, -3, 2],\n [2, -3, 6, 1, -1, -6],\n [0, -6, -4, 1, 2, -4],\n [-6, -6, 0, -2, 6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "428069", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-1, 0, -2, -3, 0, 1],\n [0, 5, -4, 0, 1, 0],\n [-2, -4, -3, 0, 4, -4],\n [-3, 0, 0, -5, -2, 1],\n [0, 1, 4, -2, 2, -4],\n [1, 0, -4, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-61922", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 6) of the 4th power of the matrix:\n[[1, 2, 4, 1, 0, -4],\n [-5, -4, -3, -3, -1, 5],\n [0, 5, -3, 3, -1, 2],\n [-1, -4, -6, 4, 3, 3],\n [6, -2, 3, 3, -4, 1],\n [3, -6, 4, -5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4743", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 0, -2, 2, 2, 3],\n [0, 5, -4, 2, 2, 2],\n [-2, -4, -2, 1, 2, -2],\n [2, 2, 1, -2, -2, -4],\n [2, 2, 2, -2, 0, -3],\n [3, 2, -2, -4, -3, 1]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11254", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, 1, -3, -4, 0, -5],\n [-2, 6, 0, -6, -3, -5],\n [-1, 5, -6, 0, -4, 5],\n [-6, 1, 0, -5, 0, -4],\n [6, 2, 1, -2, 0, -4],\n [-6, -6, 4, -5, 1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2245856", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 5, -2, 2, 5, 2],\n [-5, 0, 4, -6, -4, -1],\n [2, 3, -5, 0, -3, -5],\n [-4, -1, 3, 2, 1, 3],\n [4, 2, -3, 5, -3, 2],\n [1, 5, -5, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1109260", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 6, 2, 2, -4, -4],\n [6, -4, -2, -4, -2, 4],\n [2, -2, -4, 1, -2, -2],\n [2, -4, 1, 2, 0, -2],\n [-4, -2, -2, 0, 5, -2],\n [-4, 4, -2, -2, -2, -6]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4232", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 5) of the result:\nA =\n[[3, -4, 4, -6, 2, 3],\n [5, 2, 0, 6, 5, 1],\n [-6, -2, -5, 6, -6, -4],\n [0, -6, 4, -5, -5, -3],\n [5, -4, -4, 3, -2, -4],\n [4, 0, -2, -3, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6439", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 3) of the 4th power of the matrix:\n[[5, -3, 5, -5, -6, -4],\n [4, -5, -6, -6, -5, 6],\n [6, 2, 6, 6, -2, 2],\n [1, 6, 4, -1, -6, 3],\n [-2, 5, -6, 0, 3, 4],\n [1, 1, 0, -5, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2838", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 3, 2, -3, 5, 1],\n [1, -5, -1, -2, -5, 5],\n [3, -3, 0, 6, -6, 2],\n [3, 5, -6, 5, -2, 0],\n [1, -5, -3, -5, -3, -1],\n [-1, 5, 6, -5, 4, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3146794", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -6, -5, -4, 6, 4],\n [-2, 4, 1, -1, -4, -1],\n [0, -1, 3, -1, -6, -4],\n [0, -3, 5, -3, 0, 2],\n [4, 6, 6, -5, 2, -4],\n [-1, -3, -6, 2, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3224", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, -5, 0, -1, -5, -5],\n [-3, -3, -4, 1, 0, -5],\n [-4, 3, 2, 6, -2, -5],\n [-4, 1, -3, -5, -5, -1],\n [1, 0, -3, -5, 2, -3],\n [2, -2, 5, 5, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27858", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 6) of the 5th power of the matrix:\n[[0, 4, 0, -2, 0, -2],\n [4, 6, -2, 5, -2, 4],\n [0, -2, -2, 1, 0, -2],\n [-2, 5, 1, -2, -6, -2],\n [0, -2, 0, -6, -1, 6],\n [-2, 4, -2, -2, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70670", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -1, -2, -2, 0, 2],\n [-1, 2, 2, 0, 2, 6],\n [-2, 2, 6, 2, 3, 2],\n [-2, 0, 2, 0, 2, 0],\n [0, 2, 3, 2, 3, 2],\n [2, 6, 2, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114543", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, -2, 2, 0, -2, -2],\n [-2, 6, -2, -1, -2, 0],\n [2, -2, 2, 2, 0, -1],\n [0, -1, 2, 6, 2, -2],\n [-2, -2, 0, 2, -3, 2],\n [-2, 0, -1, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5688", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-6, 1, 1, -4, 6, 2],\n [4, 6, 6, 4, 1, -4],\n [3, -2, -4, -2, 2, 5],\n [-3, -1, -4, -4, -2, 1],\n [1, -4, 1, 6, 4, 6],\n [1, -4, 3, 6, 3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1449334", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -2, 0, 0, -1, 0],\n [-2, 5, -4, -2, -4, -2],\n [0, -4, -3, -4, 4, 2],\n [0, -2, -4, -6, -1, 1],\n [-1, -4, 4, -1, -4, 2],\n [0, -2, 2, 1, 2, -6]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4710", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 4) of the matrix A^5 where A is:\n[[6, 1, -1, -6, -3, -2],\n [0, 1, 2, 5, 5, -1],\n [3, 2, -3, 1, -4, -3],\n [3, -3, -1, 2, -1, -6],\n [-2, 2, -2, -1, -4, 1],\n [3, 4, 6, -3, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7668", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, -2, 3, 2, 6, 1],\n [0, -2, 2, 2, 3, 3],\n [-5, -3, 1, 6, -6, 6],\n [-2, 1, -5, -5, 6, 1],\n [3, 5, 2, 0, 1, -2],\n [-6, -3, -5, -4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-188001", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 6) of the 5th power of the matrix:\n[[2, 6, 3, -3, -5, -4],\n [-4, 0, 1, 6, 4, 6],\n [-1, -3, -1, 6, 4, -6],\n [6, 3, 1, -6, -2, -5],\n [-1, 2, -2, -3, -5, 5],\n [-4, -1, 1, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11484", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 6, -4, 0, 6, -1],\n [-6, -3, -1, 4, -1, 4],\n [5, 5, -4, -1, 5, 3],\n [-1, 5, 2, 2, -5, -3],\n [2, 6, -3, 1, 3, 5],\n [-4, -4, 2, 4, 3, 1]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2393", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-6, 0, -2, 0, 4, 0],\n [0, 1, 4, 0, 4, 0],\n [-2, 4, 6, 4, 2, -2],\n [0, 0, 4, -6, 4, 0],\n [4, 4, 2, 4, -2, -2],\n [0, 0, -2, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98209", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -5, -6, 5, 3, -5],\n [1, 4, 1, -4, 0, 0],\n [-5, 2, -4, -5, 5, -4],\n [-5, 1, -2, -4, -2, 4],\n [4, 1, 0, -1, 6, -6],\n [3, -6, -6, 3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872745", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 4) of the result:\nA =\n[[0, -1, -3, -6, 2, -6],\n [-3, -4, 0, -2, -2, -3],\n [-6, -2, -3, 3, 6, 1],\n [-5, 1, -6, 6, -3, -4],\n [-2, 6, -2, -2, 5, -3],\n [1, -4, 5, -3, -6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21666", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, -5, 4, 0, -6, 4],\n [-4, 6, -1, -1, -1, 4],\n [6, -5, -5, -1, 3, -2],\n [0, 0, -2, 1, 3, -1],\n [-2, -3, 0, -3, -2, -2],\n [-6, -6, -4, 4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91841", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, -5, -1, 6, -6, -1],\n [-2, -1, -2, 0, -6, 6],\n [-4, -1, -6, 6, 4, 4],\n [0, -3, -4, 3, 2, -6],\n [1, -6, 6, -2, 3, 1],\n [-1, 0, 4, 1, 6, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73970", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[4, -1, 4, -1, -2, 1],\n [6, -5, 0, -3, -6, 6],\n [-2, -4, -3, 0, -2, -3],\n [-6, -1, 4, 3, -1, 0],\n [-6, -3, 5, 2, 5, 3],\n [-1, -5, -3, -1, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-90686", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 5, 5, -4, -2, 0],\n [5, -3, -4, 4, -5, 0],\n [5, -4, 6, 1, 2, -3],\n [-4, 4, 1, -4, 0, 0],\n [-2, -5, 2, 0, -5, 0],\n [0, 0, -3, 0, 0, -4]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36956", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -1, -1, 0, 4, 4],\n [-6, 0, -5, -1, 6, 1],\n [6, -2, 3, -4, 4, 1],\n [1, -3, 1, -2, 6, 4],\n [-2, -4, 0, 4, 4, 2],\n [2, -6, -6, 3, 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": "1134690", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 1) of the 5th power of the matrix:\n[[4, -2, -6, -3, 5, -6],\n [-5, -5, -3, 1, -5, 2],\n [5, 2, -5, -6, 3, 3],\n [2, -5, 1, -4, -6, 4],\n [-6, 3, -5, 0, 5, -1],\n [5, 4, -5, -3, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30179", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, -2, -2, 2, 0, 2],\n [-2, 3, 2, 0, 4, -2],\n [-2, 2, 1, 0, 2, 4],\n [2, 0, 0, 2, 4, 0],\n [0, 4, 2, 4, -4, 2],\n [2, -2, 4, 0, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27635", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[6, -1, -2, -2, -5, 0],\n [5, -3, -4, 1, -3, 4],\n [-3, 1, -6, 2, 0, 5],\n [-5, 4, 5, -1, 1, 4],\n [-2, -1, 5, 3, 1, 6],\n [-1, 5, 2, 5, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133347", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 0, 6, 4, -5, -2],\n [0, 5, 2, 0, 2, 2],\n [6, 2, -1, 2, -1, 2],\n [4, 0, 2, 0, 0, -2],\n [-5, 2, -1, 0, -1, 0],\n [-2, 2, 2, -2, 0, -5]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3106", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -3, 1, 2, 0, -3],\n [-3, 2, -1, 1, 2, -2],\n [1, -1, -1, -6, 1, -2],\n [2, 1, -6, -5, -2, 0],\n [0, 2, 1, -2, 2, 0],\n [-3, -2, -2, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38133", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[5, -4, 3, 4, -1, -4],\n [-6, -3, -6, -5, -4, 1],\n [3, -3, -3, 6, 3, 2],\n [0, -5, -4, -3, -3, 3],\n [1, 3, 3, -1, -4, 4],\n [2, 3, 1, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "665376", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 6, 5, -2, 2, 2],\n [-4, 0, -1, -3, -2, 3],\n [-5, 4, 0, -3, -5, 4],\n [-1, 4, 5, -5, 3, -5],\n [0, -6, 0, 3, -2, -6],\n [-1, 0, -6, 2, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488255", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -1, -2, -1, -5, 1],\n [-1, 4, 1, 0, 0, 3],\n [-2, 1, -6, 2, -3, 0],\n [-1, 0, 2, 6, 2, 4],\n [-5, 0, -3, 2, -4, 1],\n [1, 3, 0, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78702", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, -1, 3, 6, -3, 1],\n [2, 3, -2, -5, -1, 4],\n [5, 1, 6, -2, -6, 1],\n [2, -6, 1, 3, 5, -5],\n [-3, 6, -5, -5, 3, -4],\n [1, -3, 0, 5, 3, -4]], determine the value at position (5, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2400", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 6, 6, 5, -2, -5],\n [6, 5, -2, 2, -2, -2],\n [6, -2, 6, 2, 6, -4],\n [5, 2, 2, -5, -1, 2],\n [-2, -2, 6, -1, 6, -2],\n [-5, -2, -4, 2, -2, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4653463", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[6, 2, -2, -2, -4, -1],\n [2, 6, 1, -2, -3, 0],\n [-2, 1, 1, -4, 2, 3],\n [-2, -2, -4, 3, 2, -2],\n [-4, -3, 2, 2, -4, -5],\n [-1, 0, 3, -2, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33055", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, 0, 5, 0, -2, 3],\n [1, -5, -5, -2, -6, -1],\n [-3, -1, 0, 6, -4, 4],\n [6, 1, 0, 6, -6, -1],\n [0, 4, -3, -5, 3, 2],\n [0, -6, 1, -4, -3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175234", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -6, -1, 3, -1, -5],\n [4, 3, -1, 1, -1, -3],\n [-3, 2, -1, 1, 1, 0],\n [-4, 3, -6, -2, 6, 3],\n [3, -5, 5, 3, 6, -5],\n [0, 4, 6, -4, 6, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109212", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[2, 1, 0, 2, -3, -2],\n [1, 0, 4, -2, 5, 2],\n [0, 4, -6, 4, 1, 6],\n [2, -2, 4, -1, 2, -4],\n [-3, 5, 1, 2, 4, -2],\n [-2, 2, 6, -4, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 4) of the result:\nA =\n[[-3, -5, -6, -4, -4, -2],\n [-6, 0, 6, -6, -3, -1],\n [-6, 0, 3, 0, -4, -3],\n [-1, 4, 0, 6, -3, 3],\n [4, 2, 2, 2, 5, 3],\n [-1, -5, -5, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21168", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -1, -5, -6, 5, -2],\n [1, 3, 3, -5, 3, 2],\n [5, 1, -4, -6, -3, 1],\n [-4, 3, 5, -5, 0, -3],\n [-1, -2, -5, 3, -5, 2],\n [4, 3, -5, 1, 1, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35049", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-6, 4, -2, -3, 2, 0],\n [4, 6, 0, -1, 0, 0],\n [-2, 0, 0, 0, 0, -4],\n [-3, -1, 0, -3, 0, -2],\n [2, 0, 0, 0, -1, 3],\n [0, 0, -4, -2, 3, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-159879", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 1, -4, -4, 1, -5],\n [2, -3, -1, -4, -4, -4],\n [4, 6, 3, 5, 5, -5],\n [1, 2, 1, 3, -4, 0],\n [4, 3, -5, -3, 5, 6],\n [6, -1, 4, -2, 6, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2885", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[3, 2, -4, 0, 3, 2],\n [2, 1, -4, -2, 0, -2],\n [-4, -4, 1, 1, 2, 1],\n [0, -2, 1, 1, -4, 0],\n [3, 0, 2, -4, 3, -2],\n [2, -2, 1, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2001", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[-1, -3, -3, -5, 6, 4],\n [-3, -2, 6, 5, -2, -2],\n [-3, -6, 3, 1, -4, -5],\n [2, 0, 2, 6, -5, 2],\n [3, 2, 4, 2, 3, 6],\n [3, -3, 3, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16409", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, 2, -5, -2, -2, 0],\n [2, 6, -3, 1, 2, 2],\n [-5, -3, 6, 4, 2, 6],\n [-2, 1, 4, 3, -1, 0],\n [-2, 2, 2, -1, 1, 2],\n [0, 2, 6, 0, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2821086", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[6, -4, -5, -6, -3, -5],\n [-5, 6, 4, 4, -2, -3],\n [-6, 2, -3, -2, 0, -5],\n [1, 4, -5, 4, 3, -2],\n [6, 5, -5, -5, -3, -3],\n [6, 1, 6, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143615", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[6, 1, 0, 0, -2, -4],\n [1, -5, -3, -2, 4, 4],\n [0, -3, -5, -3, 6, 4],\n [0, -2, -3, -5, -2, 4],\n [-2, 4, 6, -2, 4, 2],\n [-4, 4, 4, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15995", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-5, 3, -2, 2, 0, 5],\n [3, 5, -2, 0, 2, -5],\n [-2, -2, 0, 0, -1, 0],\n [2, 0, 0, 0, -6, 4],\n [0, 2, -1, -6, 0, -2],\n [5, -5, 0, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5136", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, -2, -4, 0, 1, -3],\n [-2, -5, 2, -2, 0, 4],\n [-4, 2, 2, -4, -2, 4],\n [0, -2, -4, 4, 0, 4],\n [1, 0, -2, 0, 6, 2],\n [-3, 4, 4, 4, 2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554848", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, 6, 1, -2, -2, -1],\n [-6, 6, 4, 1, -5, -1],\n [2, 6, -4, -5, 3, -2],\n [4, 2, -1, 1, 1, 0],\n [-2, -5, 3, 3, -2, 5],\n [0, 5, 5, 0, 4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82954", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, -2, -2, -2, 4, 1],\n [-2, -6, -2, 3, 1, -5],\n [-2, -2, -2, -1, 0, 0],\n [-2, 3, -1, 2, -2, 2],\n [4, 1, 0, -2, 0, 2],\n [1, -5, 0, 2, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "721903", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 6) of the matrix A^4 where A is:\n[[-3, -5, -1, -5, -4, 1],\n [-4, -5, -1, -4, -6, 5],\n [-4, -1, -4, 2, 0, -2],\n [-5, 2, -2, 0, 2, -3],\n [2, -6, 5, -1, -5, 1],\n [-2, -4, -5, 1, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-847", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 4, -3, -5, 6, -5],\n [-5, 4, 5, -1, 0, 5],\n [-1, -5, -3, -4, 4, 6],\n [-3, -2, 0, 2, 4, -5],\n [1, -4, 2, 3, 5, -3],\n [-4, 3, -1, 3, 6, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-286420", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[0, -3, -4, 3, -3, -4],\n [5, -4, 5, 6, 2, -3],\n [2, 5, 3, -2, 0, -2],\n [-6, -5, 4, -2, -1, 0],\n [-5, 3, 2, -1, -5, -5],\n [-4, -6, 2, 3, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "923842", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 0, -4, 1, -4, 0],\n [0, -2, -2, 0, -2, -1],\n [-4, -2, 4, 2, -2, 2],\n [1, 0, 2, 5, 0, 2],\n [-4, -2, -2, 0, -2, -2],\n [0, -1, 2, 2, -2, -5]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9502", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, 2, -2, -2, 5, 0],\n [2, -4, 2, 0, -4, 0],\n [-2, 2, 4, 5, 0, -2],\n [-2, 0, 5, -1, -4, 2],\n [5, -4, 0, -4, -5, -2],\n [0, 0, -2, 2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22514", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 0, 2, 0, -1, 2],\n [0, -6, -1, 2, -1, -2],\n [2, -1, -3, 2, -1, -1],\n [0, 2, 2, -6, -2, -2],\n [-1, -1, -1, -2, -6, 4],\n [2, -2, -1, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10855", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 6, -2, 2, -3, 0],\n [6, 5, 0, 4, -2, -1],\n [-2, 0, -2, 0, -2, 0],\n [2, 4, 0, 4, 2, 1],\n [-3, -2, -2, 2, 1, 2],\n [0, -1, 0, 1, 2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "516909", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[2, -4, -1, -2, 1, -3],\n [-3, 6, 3, 4, 3, 6],\n [-2, 4, 6, 6, -1, 4],\n [-3, -5, 5, 5, -5, 5],\n [-4, -5, -6, 1, 5, -2],\n [3, -6, 6, 2, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1563", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 6, 5, 6, 3, 0],\n [4, 4, 0, -6, -1, 6],\n [-3, 3, 3, 3, 4, 5],\n [-5, 3, 0, 2, 6, -2],\n [1, -2, 0, 0, 2, -4],\n [-6, -5, 5, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "667732", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 5, 4, -2, 4, -6],\n [5, -6, -4, 1, -3, -4],\n [4, -4, -5, 0, 3, 0],\n [-2, 1, 0, 3, -2, -4],\n [4, -3, 3, -2, 4, 2],\n [-6, -4, 0, -4, 2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57535", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -2, 4, 2, 2, 0],\n [-2, -5, -2, 0, -2, -1],\n [4, -2, 6, 3, -2, 0],\n [2, 0, 3, 4, -4, -4],\n [2, -2, -2, -4, -2, 2],\n [0, -1, 0, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111532", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 2, 6, -4, -4, -6],\n [3, 6, -1, -3, 4, 1],\n [-5, 4, -5, 0, 6, -2],\n [6, -6, 0, 0, 3, -1],\n [-3, 5, 6, 1, 5, 4],\n [-5, -5, -5, -4, -1, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58024", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -5, 3, -5, 5, -6],\n [-4, 3, 0, 6, -6, 0],\n [-2, 2, -5, -6, 2, 1],\n [3, -1, -2, 1, 1, -2],\n [5, 0, 6, 6, -6, -3],\n [-5, 3, -4, 5, -6, 4]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -5, 6, -6, 1, -3],\n [-4, -6, -5, -4, -4, -1],\n [3, 1, -1, -5, -5, 0],\n [-6, -6, 0, 2, -2, 4],\n [-6, -2, 4, -6, 3, 5],\n [2, -3, 2, -5, 0, 5]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1752", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[6, -5, 5, -3, -1, -5],\n [-5, -5, -4, -2, 2, -1],\n [5, 2, 3, 6, -2, 4],\n [-1, 3, 5, 1, -4, -5],\n [-4, 2, -1, 3, 5, -3],\n [3, -4, 6, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46140", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[-3, 6, 1, -4, -2, -4],\n [6, 4, -5, -4, 3, -3],\n [1, -5, 0, 4, 2, -6],\n [-4, -4, 4, 0, 0, 1],\n [-2, 3, 2, 0, 5, 0],\n [-4, -3, -6, 1, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8750", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 2, 0, -4, -4, 2],\n [2, -2, 0, 2, 4, 3],\n [0, 0, 4, -1, -4, -2],\n [-4, 2, -1, -5, 2, 2],\n [-4, 4, -4, 2, 1, 4],\n [2, 3, -2, 2, 4, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "301726", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 3, 3, 4, 5, 4],\n [6, -1, 1, 6, -6, -1],\n [-1, 4, 6, -2, -3, -6],\n [4, 3, 4, 1, -1, -4],\n [5, -4, 5, -1, 5, 0],\n [1, -2, 3, -1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2775", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, 2, 3, -3, 3, 6],\n [-6, 4, 2, -3, -5, -6],\n [-4, 0, 4, 3, -5, 2],\n [5, 6, 4, -5, -2, 1],\n [6, 6, 5, 3, 1, -4],\n [-5, 2, -4, 1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "804094", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 4) of the 5th power of the matrix:\n[[-6, 4, -1, 6, 0, -3],\n [-6, -4, 2, -2, -1, -3],\n [-6, -2, -2, -2, -1, 4],\n [-5, -6, -5, 6, 3, -1],\n [-2, -2, 5, 5, -1, 3],\n [0, 2, 0, -5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-34323", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -5, -4, 1, 4, 2],\n [-3, 2, -5, 6, 4, -2],\n [4, -5, 4, -6, 6, -2],\n [-5, 6, 0, 1, -5, 0],\n [-3, -6, 4, -4, 4, 5],\n [-6, -2, 6, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1027", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, 0, 2, -2, -2, 0],\n [0, 0, 2, -5, 1, -2],\n [2, 2, -3, 2, -5, 2],\n [-2, -5, 2, 4, 1, -3],\n [-2, 1, -5, 1, -1, -1],\n [0, -2, 2, -3, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "465363", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -6, 6, 4, 3, -4],\n [1, -2, 1, -5, 0, 2],\n [0, -4, 0, 1, -6, 6],\n [6, -4, -2, 5, -1, -4],\n [-3, -2, -4, -3, -2, -5],\n [3, 2, 3, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61981", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 6) of the matrix A^5 where A is:\n[[3, 4, -4, 4, -5, 0],\n [1, 3, -6, -1, 0, 6],\n [2, 5, -4, -5, -2, 6],\n [3, -6, 6, -1, 2, 3],\n [2, 0, 4, 0, 1, 3],\n [-5, -1, -2, -2, 6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2154", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[-4, -1, 5, 3, 6, 3],\n [0, -6, -4, 5, -6, 3],\n [-4, -2, 2, -4, 3, 3],\n [2, -6, -1, 2, 5, -2],\n [4, 3, -5, -2, -6, 2],\n [3, 6, 3, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1738", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -4, -3, 6, -1, -3],\n [-6, 0, -2, 1, 2, -2],\n [1, 6, -6, -6, 0, -1],\n [-2, -2, 2, -6, 1, -5],\n [0, -1, 3, -5, 5, 6],\n [-4, -3, 0, 1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1162060", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 1) of the result:\nA =\n[[-5, 1, 4, 2, 0, -6],\n [-1, 1, -2, 5, -5, -2],\n [1, -5, -6, -3, -3, 2],\n [-4, -3, -4, -5, -3, 1],\n [-6, 1, 1, -4, 3, 3],\n [5, 5, -1, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64845", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, -6, -1, 2, 4, -2],\n [-6, -5, 2, -2, 0, -4],\n [-1, 2, 6, 4, -4, 2],\n [2, -2, 4, -5, -2, 4],\n [4, 0, -4, -2, 0, -3],\n [-2, -4, 2, 4, -3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-149724", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 2, 2, -4, -2, -2],\n [2, -1, -2, -4, -4, 2],\n [2, -2, 6, 4, 4, 2],\n [-4, -4, 4, -4, -1, -3],\n [-2, -4, 4, -1, 3, 0],\n [-2, 2, 2, -3, 0, -6]], determine the value at position (6, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6052", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[-1, -6, -6, 1, -5, 3],\n [6, -1, -1, -1, 1, -3],\n [-4, -1, -3, -5, -1, 3],\n [-2, 4, 2, 4, -1, -4],\n [4, -2, 3, 1, 2, 1],\n [-4, 2, -4, 1, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2957", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -3, 3, 2, -4, -4],\n [-5, 3, -4, -6, -3, 1],\n [-2, -5, -4, -6, -5, -6],\n [-5, -4, -6, 4, 2, 3],\n [-2, 1, -2, 1, 0, 5],\n [-3, 0, -1, -4, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53536", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 4, 0, -3, -2, -2],\n [4, 0, 0, -1, 4, 2],\n [0, 0, 3, 0, 0, -4],\n [-3, -1, 0, -3, 0, 0],\n [-2, 4, 0, 0, 3, 0],\n [-2, 2, -4, 0, 0, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "235056", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, -3, -6, 6, 6, 1],\n [-6, 5, -1, 0, 3, 5],\n [-5, -3, 4, -4, 6, 6],\n [2, 0, -5, 4, 5, -1],\n [2, 5, -4, 4, -1, -4],\n [-4, -3, 2, 4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101324", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 2) of the matrix A^4 where A is:\n[[-6, 1, 0, 2, -6, 2],\n [1, 4, 2, 3, -2, 0],\n [0, 2, -6, 0, 0, 0],\n [2, 3, 0, 2, 0, -2],\n [-6, -2, 0, 0, 3, 2],\n [2, 0, 0, -2, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2292", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -4, 0, -2, 0, 2],\n [-4, 1, 0, 0, 2, 0],\n [0, 0, 3, 2, 5, 2],\n [-2, 0, 2, 6, -1, 6],\n [0, 2, 5, -1, -1, 4],\n [2, 0, 2, 6, 4, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79047", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 0, 4, 3, -3, -6],\n [-4, 0, 4, 4, 0, 4],\n [6, -4, -6, 3, 2, 5],\n [-1, 6, 6, 5, 0, -6],\n [-6, -3, 0, 4, 4, 1],\n [3, 2, -6, -3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8579", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[0, -6, 2, 3, 0, 0],\n [-6, 1, 4, -2, 1, -2],\n [2, 4, -4, -3, -4, 0],\n [3, -2, -3, -4, -1, -2],\n [0, 1, -4, -1, 3, -2],\n [0, -2, 0, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77509", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, 2, 2, -1, 2, 4],\n [2, 3, 1, -5, 6, 0],\n [2, 1, -5, -1, 3, 2],\n [-1, -5, -1, -3, 0, 0],\n [2, 6, 3, 0, -2, -6],\n [4, 0, 2, 0, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14302", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 1, -1, 0, 3, 4],\n [-5, -2, 5, 0, 2, -6],\n [-4, -1, 0, -1, -6, -3],\n [-1, 1, 3, -3, 0, 4],\n [-4, 1, -6, -3, 1, 3],\n [-3, -5, -5, -3, 6, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9334", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-5, 0, 2, 4, -4, 2],\n [0, -6, -3, -4, -4, 3],\n [2, -3, 4, 0, 0, 0],\n [4, -4, 0, 3, -2, 1],\n [-4, -4, 0, -2, 0, -2],\n [2, 3, 0, 1, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-258333", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 1) of the matrix A^5 where A is:\n[[6, -5, -4, 4, 4, -3],\n [-2, 2, -1, -6, -4, 0],\n [1, 0, -2, 3, 1, 2],\n [0, 4, 2, -6, 2, -4],\n [-1, 1, -4, -3, 0, 5],\n [0, -3, 2, 6, -4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4084", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 3) of the result:\nA =\n[[1, 4, 2, -4, 1, -4],\n [4, 5, 0, -2, -4, -2],\n [2, 0, 3, 3, 2, 5],\n [-4, -2, 3, 0, 2, 4],\n [1, -4, 2, 2, -2, -2],\n [-4, -2, 5, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36374", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 3, 2, 4, 1, 5],\n [3, 3, 2, 0, 1, 0],\n [2, 2, -4, -3, 4, 2],\n [4, 0, -3, -1, -2, 4],\n [1, 1, 4, -2, 4, -4],\n [5, 0, 2, 4, -4, -5]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3708", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 6, -3, 3, 6, -1],\n [-2, -4, 3, 1, 1, 0],\n [-4, -6, -2, -6, -1, 4],\n [0, 5, -2, -3, -5, -2],\n [2, -3, -5, 6, -1, 1],\n [-5, 2, 0, 6, -5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8015", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, -2, 0, 6, -2, 4],\n [-1, 2, -4, -4, 1, 3],\n [5, -1, 5, 3, -4, -5],\n [6, -5, -5, -2, 5, -2],\n [-6, -5, -5, -3, 0, -4],\n [-2, 4, 2, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7182", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, -2, 1, -2, 5, -1],\n [1, -5, -4, 4, 2, -2],\n [-2, 2, 3, -4, -3, 0],\n [-5, 1, -2, -6, -4, 2],\n [-2, 1, -6, 0, 0, 1],\n [-4, -6, 4, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6229", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, -2, -4, 1, 0, 1],\n [-2, 5, -4, 4, -2, 0],\n [-4, -4, -2, 2, -2, 1],\n [1, 4, 2, -1, 4, 1],\n [0, -2, -2, 4, -4, 2],\n [1, 0, 1, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1017692", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 0, -6, -6, 4, 6],\n [-6, -5, 2, 6, -2, 2],\n [6, -2, 0, -1, -5, -4],\n [-2, -3, 4, -1, 1, 1],\n [-4, -3, -6, -5, 6, 2],\n [5, 3, 3, -5, 5, -1]], determine the value at position (6, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1072", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -1, 1, 2, 1, -2],\n [1, 3, 3, 2, 1, -5],\n [-5, 5, -4, 0, 2, 1],\n [2, -1, -6, 5, -3, 6],\n [-1, 5, -1, 1, -6, 6],\n [4, -5, -5, 6, -1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24518", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, -4, 0, 0, -4, -2],\n [-4, 3, 0, 6, 2, -4],\n [0, 0, 4, 5, 0, -2],\n [0, 6, 5, -4, -2, -3],\n [-4, 2, 0, -2, 6, 2],\n [-2, -4, -2, -3, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184155", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-6, 4, 0, -1, 0, 0],\n [1, 1, 3, 4, -5, 5],\n [5, 5, -3, -3, 6, 4],\n [3, 5, 6, 1, 6, 6],\n [-4, 5, 6, 6, 5, -4],\n [6, -5, -6, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71581", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 1, -2, -6, 2, -1],\n [5, 0, 1, 6, -2, -1],\n [5, 6, 0, 0, -5, 4],\n [5, -6, 1, -2, 3, -5],\n [-4, -1, 3, -1, 1, -2],\n [-2, 0, 3, 6, -2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "545", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 2, 4, 0, 2, 2],\n [2, -3, 0, 0, 2, 4],\n [4, 0, -4, 4, -4, 2],\n [0, 0, 4, 3, 0, 0],\n [2, 2, -4, 0, -5, -2],\n [2, 4, 2, 0, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "685165", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-5, 0, 3, -2, -1, 1],\n [0, 0, -3, 4, 0, 0],\n [3, -3, 4, 0, 2, -1],\n [-2, 4, 0, 5, -4, 2],\n [-1, 0, 2, -4, -4, 3],\n [1, 0, -1, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69365", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 2, -2, -2, 2, 0],\n [2, 2, -2, -2, 0, -1],\n [-2, -2, -6, 4, 3, 0],\n [-2, -2, 4, 6, 0, 2],\n [2, 0, 3, 0, 1, 3],\n [0, -1, 0, 2, 3, -2]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1338", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[6, 4, -4, 2, 0, -2],\n [4, -3, -2, -1, 0, -2],\n [-4, -2, -2, -2, -2, 6],\n [2, -1, -2, 0, -2, -2],\n [0, 0, -2, -2, -1, -1],\n [-2, -2, 6, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12283", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 5, 4, 1, -2, 0],\n [-4, 1, 1, -4, 2, 1],\n [-6, 1, 5, 4, -3, -1],\n [6, 3, 2, -2, 0, 6],\n [-6, 2, -1, 4, -3, -1],\n [-2, -4, 0, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29226", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 1) of the matrix A^5 where A is:\n[[-5, -3, 0, -2, 2, 3],\n [0, 5, 2, 2, 5, -5],\n [-6, 4, -3, -3, 6, -5],\n [-4, -4, -2, -6, 2, 1],\n [1, -4, -5, -6, 5, -1],\n [6, 3, -6, 4, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9685", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (6, 3) of the result:\nA =\n[[4, 2, 6, 5, -3, 0],\n [4, 0, -3, -2, 4, 2],\n [0, 0, 3, 0, 2, -2],\n [-1, -4, -6, 4, 5, -5],\n [1, 6, -6, 3, 0, -2],\n [6, -1, 1, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4552", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 0, -5, 5, 1, 6],\n [0, 5, 5, 1, -5, -4],\n [5, -3, 5, 2, 5, 5],\n [-2, -1, -6, -3, -3, 3],\n [1, 1, 3, -1, 1, 2],\n [-2, -6, -6, -5, -5, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74017", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 1) of the result:\nA =\n[[0, 0, -3, 6, -3, 4],\n [3, -4, 4, -5, -4, 1],\n [-6, -3, 0, -2, -5, -6],\n [-1, 6, 6, -2, -4, 4],\n [4, 4, 2, -4, -5, -2],\n [2, 1, -1, -4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-845", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[-6, -2, 0, 2, 5, -6],\n [-4, 1, -1, 6, -2, 6],\n [3, -5, -4, 5, -5, -6],\n [0, -4, 0, 5, 0, 1],\n [-6, -2, 3, 2, 5, 4],\n [0, -6, 1, -4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5844", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[-3, 3, 5, 1, -6, 1],\n [2, 2, -2, -3, -3, 2],\n [1, 3, 3, 5, 0, 5],\n [-4, -3, 2, 6, 1, 5],\n [5, -6, -4, 5, 3, -5],\n [-5, 6, 6, 1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3037", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 4, 2, 0, -3, -2],\n [4, 0, 0, -2, -6, 0],\n [2, 0, -2, -4, -2, 4],\n [0, -2, -4, 6, -3, -2],\n [-3, -6, -2, -3, -3, 2],\n [-2, 0, 4, -2, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31631", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-2, 3, 4, -2, -4, -2],\n [3, 3, 0, 0, 4, -2],\n [4, 0, 3, -3, -2, 0],\n [-2, 0, -3, -3, -3, -4],\n [-4, 4, -2, -3, 0, -4],\n [-2, -2, 0, -4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1099950", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, -2, 2, 5, 0, 0],\n [-2, 0, -3, 0, -2, -2],\n [2, -3, -1, 3, -4, 4],\n [5, 0, 3, -4, 2, 2],\n [0, -2, -4, 2, 0, -3],\n [0, -2, 4, 2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562141", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-6, 0, -6, 6, 1, 3],\n [5, -5, 3, 6, 5, -2],\n [6, -1, 2, 0, -1, -2],\n [-1, 4, -3, -6, 5, 2],\n [4, -2, 1, 0, 1, -6],\n [2, -6, -4, 1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1428", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, -6, -1, -2, 4, -1],\n [-4, 3, 5, 3, -1, -5],\n [1, 5, -1, 6, 6, -3],\n [-3, 4, 0, -4, 4, -4],\n [-1, 2, -6, -2, -6, -6],\n [-4, -4, -3, -4, -1, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5773", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 2, 0, -1, 4, -5],\n [2, -6, -3, -2, 0, 2],\n [0, -3, -5, -6, -2, -2],\n [-1, -2, -6, 3, -2, 3],\n [4, 0, -2, -2, 6, 2],\n [-5, 2, -2, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2034881", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, -4, 2, -4, -2, 0],\n [-4, 2, 0, -4, -2, -2],\n [2, 0, -6, 0, 2, -4],\n [-4, -4, 0, 2, 2, 0],\n [-2, -2, 2, 2, 0, -2],\n [0, -2, -4, 0, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35088", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, -4, 0, 0, 0, 0],\n [-4, 0, -4, -6, 2, 0],\n [0, -4, 0, 1, -4, -1],\n [0, -6, 1, 3, 0, -4],\n [0, 2, -4, 0, -6, 2],\n [0, 0, -1, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-198912", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (6, 5) of the result:\nA =\n[[3, 0, -3, -5, 1, -5],\n [2, -2, 2, 2, 1, 1],\n [-3, -3, -5, -3, -3, -1],\n [-4, -5, 1, -5, 1, 0],\n [-4, -1, -1, 3, -2, 6],\n [1, 4, 5, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2006", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, 0, 6, 2, -4, 3],\n [0, 6, 3, -4, 6, -5],\n [5, 0, -3, -6, -1, 4],\n [-1, -1, -5, -6, -4, 5],\n [-5, -1, 6, 5, -1, 6],\n [-2, 3, 3, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "147831", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[6, 3, -1, 4, -3, 3],\n [-6, -3, -5, 3, -4, 0],\n [0, -6, 1, 0, -6, 1],\n [-5, 1, -4, 3, 0, 6],\n [-1, -2, 4, 3, 4, -5],\n [-5, 6, 5, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "842025", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[1, -2, -6, -4, 2, -3],\n [-2, 3, 2, -4, 4, 0],\n [-6, 2, 3, -5, 3, 4],\n [-4, -4, -5, 0, 6, -3],\n [2, 4, 3, 6, -5, 6],\n [-3, 0, 4, -3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1327223", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 5) of the 5th power of the matrix:\n[[-3, -1, -1, 0, 0, -2],\n [-1, -3, -2, 1, 2, 3],\n [-1, -2, 3, 3, 0, -2],\n [0, 1, 3, 6, 4, -2],\n [0, 2, 0, 4, -6, -6],\n [-2, 3, -2, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-148796", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 5, 4, -1, 6, 2],\n [2, -4, 1, 6, -3, 0],\n [-1, 1, -1, -3, -5, 0],\n [4, 6, 4, -3, 6, 2],\n [2, 0, -2, -4, -4, 2],\n [2, 5, 6, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100619", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-6, 6, 3, -2, 1, 3],\n [-3, 3, 3, -3, 6, 5],\n [2, 2, 0, 3, 1, 5],\n [5, -3, 1, -1, 6, -4],\n [0, -4, 4, 0, -2, -3],\n [-4, 1, -3, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1793", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 6, 2, -1, -2, -2],\n [6, -4, -5, -1, 4, -6],\n [0, -2, -3, 2, 3, -6],\n [4, -3, -4, -1, -2, 0],\n [6, -6, 6, -2, -5, -5],\n [4, 4, -5, 2, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162592", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, -2, -3, -3, -2, 3],\n [2, 5, 2, -1, 4, 5],\n [-4, -1, 3, -3, -4, -1],\n [4, -1, -5, 2, 1, -1],\n [-6, 5, -5, -3, 0, 2],\n [3, -2, 3, -5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1867", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[4, 4, -6, 3, 6, -6],\n [-2, 0, 2, 2, 1, -6],\n [-2, -1, -1, -3, -6, -4],\n [3, -3, -3, 6, -3, -2],\n [6, 4, 2, -3, 2, 2],\n [-6, -2, 2, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2212", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[6, -6, -2, 0, -1, 2],\n [-6, -4, 0, 2, -6, 1],\n [-2, 0, -4, 4, -4, 0],\n [0, 2, 4, 0, -5, -2],\n [-1, -6, -4, -5, -5, -2],\n [2, 1, 0, -2, -2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117708", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -5, -5, 2, -6, -2],\n [-6, 0, 2, -1, -5, -1],\n [2, -4, 2, 1, 6, 5],\n [0, 1, 3, -1, -4, 0],\n [-3, 4, 3, -2, 1, 0],\n [0, 1, 3, -4, -4, -5]], determine the value at position (4, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, 4, 0, 0, 0, 2],\n [4, 1, 0, -2, -6, 6],\n [0, 0, 3, 2, 2, -2],\n [0, -2, 2, -6, 0, -4],\n [0, -6, 2, 0, -4, 2],\n [2, 6, -2, -4, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95882", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[2, -6, 3, -4, -2, -5],\n [-4, -3, -3, 4, 2, -6],\n [5, 2, 2, 4, -1, 4],\n [-6, 4, 6, 5, -1, 1],\n [-2, -2, -6, -6, 1, 6],\n [-2, 1, 3, -5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2547", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 4, 2, 3, -2, 0],\n [4, 0, -2, -2, -2, 0],\n [2, -2, 0, 4, -6, 0],\n [3, -2, 4, -1, 4, 0],\n [-2, -2, -6, 4, -2, -1],\n [0, 0, 0, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "642616", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 3, -5, -5, -1, -4],\n [-6, -5, 6, 0, -3, 5],\n [-5, 4, 5, 5, 1, -3],\n [-3, -5, -6, -6, -4, -1],\n [0, 6, 2, -2, 2, 1],\n [-6, 4, 5, -4, 1, 2]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-211", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 0, -2, -4, 0, 0],\n [0, -1, 0, 4, -1, 0],\n [-2, 0, 4, 0, 2, 3],\n [-4, 4, 0, -6, 0, 0],\n [0, -1, 2, 0, 3, 0],\n [0, 0, 3, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14226", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, 2, -2, 2, 2, 4],\n [2, -5, -4, -4, 2, -4],\n [-2, -4, 3, -2, 2, 3],\n [2, -4, -2, -5, 0, 0],\n [2, 2, 2, 0, 6, -2],\n [4, -4, 3, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81663", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 2, -1, -5, 1, 3],\n [2, 5, 1, -5, 1, -4],\n [-4, 2, 6, 2, 2, -3],\n [5, 0, 6, 1, 6, 6],\n [-2, 6, -6, 2, -1, -4],\n [-4, 3, -6, 6, 1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68224", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, -2, 2, 4, 2, -3],\n [-2, 1, 3, 1, 2, -1],\n [2, 3, -6, -2, 5, -2],\n [4, 1, -2, 6, -2, 0],\n [2, 2, 5, -2, -4, -2],\n [-3, -1, -2, 0, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "776266", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, 0, 2, -1, 0, 0],\n [0, 2, -3, 0, 0, -5],\n [2, -3, -2, 0, -4, 1],\n [-1, 0, 0, 6, 2, 4],\n [0, 0, -4, 2, 2, 0],\n [0, -5, 1, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73831", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[6, 0, 1, 0, 1, -3],\n [0, 5, 2, 2, 0, 0],\n [1, 2, 0, 0, 4, 2],\n [0, 2, 0, -2, -2, 0],\n [1, 0, 4, -2, -4, 1],\n [-3, 0, 2, 0, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8018", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[-2, -4, -4, 6, -5, 1],\n [-6, 5, 1, -4, 2, 5],\n [5, 4, -5, 3, 2, -1],\n [-6, -2, 3, 2, 6, -1],\n [0, -3, -6, -2, -5, 1],\n [-3, -6, 3, 0, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3009", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-5, -4, 2, 6, 2, -5],\n [-4, 4, 5, 2, -6, -5],\n [4, -5, 3, -4, 3, -4],\n [3, 6, -5, 1, 1, 1],\n [-5, 6, 2, 4, 0, 5],\n [-2, 0, 1, 2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13011", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 1, -2, -5, 0, 2],\n [1, 4, 0, -2, 4, 2],\n [-2, 0, 3, 2, 0, 4],\n [-5, -2, 2, -4, 2, 1],\n [0, 4, 0, 2, -4, 1],\n [2, 2, 4, 1, 1, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19319", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 2, -5, 2, 0, 4],\n [2, -3, 2, -3, -4, 0],\n [-5, 2, 0, 6, -2, -2],\n [2, -3, 6, -6, -4, -1],\n [0, -4, -2, -4, -2, 0],\n [4, 0, -2, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24413", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 6) of the matrix A^5 where A is:\n[[0, 2, 0, 0, 2, 1],\n [2, -3, 0, 4, -3, 2],\n [0, 0, -4, -2, 2, 0],\n [0, 4, -2, -3, -1, -6],\n [2, -3, 2, -1, -4, 0],\n [1, 2, 0, -6, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3939", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, 1, 0, 4, 1, 2],\n [-5, 3, -2, 1, -4, 4],\n [4, -1, -1, 0, 6, 4],\n [-4, 1, 1, 2, 1, -4],\n [-1, 2, -6, -4, -5, 5],\n [1, -1, 3, 4, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16768", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, 4, -1, 0, 1, 2],\n [-2, 4, -4, -5, 1, -6],\n [3, -1, -5, -4, 1, -6],\n [-1, -4, -1, -4, 4, 4],\n [1, -2, -3, 2, -2, 5],\n [-3, 1, 1, 1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54147", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, -5, -3, 3, -5, 4],\n [3, -4, 2, 2, 4, 2],\n [0, -3, -6, -4, 1, -3],\n [3, 3, -5, 1, 0, 4],\n [3, 2, -5, -2, -1, 6],\n [-5, -5, 6, 3, -3, 1]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2764", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 2) of the matrix A^5 where A is:\n[[6, 4, -2, 2, -3, -4],\n [3, 1, -6, 2, -3, 4],\n [2, 1, -4, -4, 2, -4],\n [-3, 2, 5, -3, 4, -4],\n [0, -1, -6, 3, 1, -6],\n [-3, -1, -1, 0, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4160", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, -2, -3, -1, 0, 3],\n [3, -6, 2, 1, 0, 2],\n [-4, 3, -3, 0, -1, 6],\n [-5, -5, 3, 0, 2, 4],\n [5, 2, 0, 4, 1, 3],\n [-4, -6, 0, 1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42238", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 3, 4, 2, 6, -4],\n [1, 4, -5, -4, -6, -2],\n [-3, 6, -6, 3, 2, -1],\n [-1, 4, -5, 0, 5, 5],\n [2, -1, 4, 1, 5, -2],\n [-5, 6, -3, 5, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10984", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (6, 4) of the result:\nA =\n[[-1, -5, -1, -6, 4, 3],\n [-4, 2, -5, 1, -1, 5],\n [-1, 0, -2, 5, 4, -3],\n [-1, 1, -3, -2, 0, -1],\n [6, -3, 6, -3, 3, -3],\n [-6, -2, 1, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27982", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, -5, 6, 2, 0, 0],\n [-5, -3, -1, 0, 0, -2],\n [6, -1, 2, -1, -4, 0],\n [2, 0, -1, 5, 2, 4],\n [0, 0, -4, 2, 2, 0],\n [0, -2, 0, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884510", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 6) of the matrix A^5 where A is:\n[[1, 6, 5, -4, 2, 3],\n [-4, 3, 5, 1, -6, -3],\n [-3, -1, 5, 5, -5, 0],\n [-2, 3, -1, 4, -1, 5],\n [4, -1, 3, 5, 1, 3],\n [-3, 3, 1, 2, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18023", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-3, -6, -4, -6, 0, 5],\n [-6, 4, -3, 6, -6, 6],\n [6, -5, 4, -6, 6, -2],\n [0, -4, 1, -2, -2, 6],\n [-2, 1, -5, -5, 5, 1],\n [2, 4, 5, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-231661", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 3) of the 5th power of the matrix:\n[[-3, 4, -6, -3, 1, 2],\n [4, -6, -5, -2, 0, 0],\n [-6, -5, -3, 1, -2, -2],\n [-3, -2, 1, -1, 2, -2],\n [1, 0, -2, 2, 1, 2],\n [2, 0, -2, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39572", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[-4, -3, 1, -1, 6, 6],\n [-2, 6, 2, 3, -4, 0],\n [2, 4, 6, 4, 5, -3],\n [3, 3, -4, -6, 2, 6],\n [-6, -5, 2, -2, -3, 2],\n [2, -5, -4, 5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6623", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 6) of the result:\nA =\n[[6, -4, 3, -1, -5, -1],\n [-1, -5, -1, -1, -1, 5],\n [6, -2, 0, 6, 5, -2],\n [4, -6, 5, 2, -4, -5],\n [3, -1, 1, -5, -3, -5],\n [5, 5, 2, 3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1171", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 0, 5, 2, 2, -4],\n [0, 0, -4, 5, -4, 2],\n [5, -4, -5, -2, 0, -4],\n [2, 5, -2, 3, -2, 0],\n [2, -4, 0, -2, -1, 0],\n [-4, 2, -4, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75718", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[6, -6, 6, 6, -1, 0],\n [-1, -2, -1, 6, -4, 2],\n [-2, -5, 5, 3, 3, 0],\n [-4, -6, -4, 2, -2, 0],\n [-4, -3, -6, -4, 0, -3],\n [-5, -2, -2, -5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475358", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -3, -6, -4, 2, 3],\n [0, 6, -1, -6, 2, 6],\n [2, -6, 6, 6, -1, 0],\n [-5, 3, 1, 1, -1, 2],\n [-4, -5, -5, -1, 0, -1],\n [4, -4, -2, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563089", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -1, -2, 2, -1, -1],\n [-1, 0, -5, 0, 0, 2],\n [-2, -5, -4, 1, 2, 0],\n [2, 0, 1, 1, 2, -4],\n [-1, 0, 2, 2, -3, -6],\n [-1, 2, 0, -4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8015", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-6, -2, -5, -4, 0, 5],\n [-2, 4, -2, 0, 2, 0],\n [-5, -2, 1, 2, 2, 4],\n [-4, 0, 2, 2, 0, -4],\n [0, 2, 2, 0, -1, -4],\n [5, 0, 4, -4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-168335", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, -2, 4, 4, 1, -1],\n [2, 4, -2, 3, -3, 2],\n [5, 3, 4, -2, -6, -2],\n [-2, -2, 6, -5, 6, -1],\n [-2, -5, 5, 3, 1, -1],\n [4, 3, 5, 4, -4, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "375450", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, 4, 4, -3, -4, 0],\n [5, 6, 1, 0, -6, -6],\n [6, -2, 1, 3, 4, -4],\n [1, -4, -3, 3, 0, -4],\n [-3, 1, -3, 2, -3, 6],\n [-3, 6, -2, -6, 0, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1249309", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 2, -6, 0, 0, -1],\n [2, -3, 4, -4, 3, -4],\n [-6, 4, 3, -6, 2, 0],\n [0, -4, -6, 1, 4, 6],\n [0, 3, 2, 4, 0, -1],\n [-1, -4, 0, 6, -1, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18164", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -4, 3, 1, -1, 3],\n [2, 2, 4, -1, -5, 2],\n [-5, -4, -1, -5, -2, -5],\n [5, -3, 4, 4, -4, -2],\n [-1, 6, 0, 3, 1, 2],\n [-3, -3, 0, 5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66313", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[4, 2, 4, -5, 6, 4],\n [-1, 3, 3, 1, 6, -2],\n [-2, 1, -6, -1, 3, 6],\n [2, 5, -1, 0, -3, 5],\n [3, -6, 2, 5, -1, -4],\n [-3, 3, 5, -1, -1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33642", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, -1, 0, -3, -5, -2],\n [-1, 3, 0, -2, 4, 2],\n [0, 0, 4, 0, 0, -4],\n [-3, -2, 0, -6, 6, 3],\n [-5, 4, 0, 6, 0, -1],\n [-2, 2, -4, 3, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9366", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[6, 3, -4, -4, -3, 2],\n [2, -2, 5, 2, -1, 1],\n [4, 1, 5, 3, 0, -3],\n [-3, -1, 2, 0, -2, -2],\n [1, -1, -6, -6, 2, 1],\n [-1, 6, -6, -5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40389", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 4) of the result:\nA =\n[[3, 5, -4, -5, 5, -5],\n [-1, 0, -3, -6, -1, 0],\n [-3, -1, 2, -3, 5, 3],\n [-3, 3, 5, -2, -4, 3],\n [-5, 2, 6, -6, -2, -2],\n [1, -1, -1, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10765", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[-4, 2, 0, 2, 4, 2],\n [2, -2, 0, -2, -1, -4],\n [0, 0, -1, 2, 0, -2],\n [2, -2, 2, 2, -5, -4],\n [4, -1, 0, -5, 0, 2],\n [2, -4, -2, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3050", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, 3, -1, -5, 1, 2],\n [-4, 6, -1, -1, -5, 3],\n [1, -2, 4, 4, 1, 6],\n [1, 5, -4, -2, 0, -2],\n [-1, -5, 1, -2, -1, -6],\n [3, -5, 4, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7700", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 3) of the 5th power of the matrix:\n[[-1, 3, 0, -1, 2, 2],\n [3, 6, -1, 2, 4, -3],\n [0, -1, 2, -4, -2, 0],\n [-1, 2, -4, 0, 0, 0],\n [2, 4, -2, 0, -1, 2],\n [2, -3, 0, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10909", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 5, -4, -6, -2, 1],\n [-2, 3, -4, 2, -5, -4],\n [5, -3, 3, -6, 4, -3],\n [-3, 2, 1, -5, 6, 0],\n [-1, 0, 4, -3, -2, -1],\n [2, -5, 4, 2, 3, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58504", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 5, -2, 2, -1, -3],\n [-5, -2, 1, 1, -1, 4],\n [-6, 1, -3, -5, -6, 0],\n [-5, 6, -3, -3, 6, 3],\n [-6, -5, -6, -1, 6, -4],\n [-6, 5, 1, 5, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111441", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 4, -5, -2, -2, -3],\n [4, -6, 2, -4, -1, 4],\n [-5, 2, -6, -1, -6, -2],\n [-2, -4, -1, -2, 2, 2],\n [-2, -1, -6, 2, 3, -2],\n [-3, 4, -2, 2, -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": "333674", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[6, -5, 3, 2, 5, -2],\n [4, 1, 3, -3, -5, -3],\n [5, 4, -3, 4, 2, 3],\n [4, -1, 3, -1, -2, -1],\n [-6, 6, -2, 5, -1, 1],\n [-3, -2, -3, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13090", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, -1, 6, -3, 5, 1],\n [4, -4, 1, 6, -5, -1],\n [1, -6, -1, 2, 6, 3],\n [3, -5, 4, 6, -6, -5],\n [-2, -1, -6, 0, 4, -3],\n [2, -1, 2, -6, -3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14369", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -3, 2, -4, -6, 4],\n [6, 4, -6, 5, 2, 2],\n [-2, -5, 2, 6, 5, 6],\n [1, 6, 4, 3, 3, -1],\n [0, 5, -1, -2, -3, 0],\n [-3, 3, 3, 3, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "834352", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 1, 0, 0, 0, -2],\n [1, 5, -2, 0, -2, 0],\n [0, -2, -3, -2, 4, 4],\n [0, 0, -2, 1, 0, -2],\n [0, -2, 4, 0, -4, 2],\n [-2, 0, 4, -2, 2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2759", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-2, 1, 5, -4, 5, 0],\n [1, 0, -5, 1, -1, 3],\n [-4, -3, 0, -4, -6, -1],\n [-4, 4, 3, -1, 3, 5],\n [-4, -1, 4, -3, 6, -3],\n [3, 3, 4, -5, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276292", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[5, -3, 4, 0, -2, 1],\n [0, 3, 2, 1, 2, -6],\n [3, 6, 5, -4, -2, 2],\n [1, 3, 0, -5, 4, -1],\n [-3, -2, -2, 6, -3, -3],\n [-3, 4, -5, -6, 5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "193117", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 0, -4, -2, 1, -4],\n [0, 0, -4, 2, 2, 2],\n [-4, -4, 3, 5, 3, 2],\n [-2, 2, 5, -3, 0, 1],\n [1, 2, 3, 0, 5, -2],\n [-4, 2, 2, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "585299", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 0, 0, 2, -2, -2],\n [0, 5, 2, 0, -2, -1],\n [0, 2, -1, 2, 0, 4],\n [2, 0, 2, 5, -2, 4],\n [-2, -2, 0, -2, -5, 2],\n [-2, -1, 4, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18417", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 5) of the 5th power of the matrix:\n[[0, -2, -4, 3, 1, 1],\n [2, 4, 5, -1, -5, -4],\n [6, 4, 5, 3, 4, -1],\n [-6, -5, 1, 4, 1, -1],\n [-4, -5, 6, -1, -6, 3],\n [-1, 2, 0, 2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8480", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 2, 0, 2, 4, -1],\n [0, 3, -2, -1, -6, -6],\n [-5, 4, -3, 4, 2, 0],\n [-1, -6, -2, 4, 5, 6],\n [-3, -2, 4, 2, 5, -4],\n [-3, 1, -4, 6, -4, 6]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44738", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -2, 3, -6, 0, 0],\n [-1, -1, -4, -4, 3, 4],\n [2, -6, 0, 6, 5, 4],\n [3, 0, 1, -1, 1, -6],\n [-6, 2, 5, -3, -4, -1],\n [3, 5, 6, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1310567", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the 4th power of the matrix:\n[[4, -4, 2, -2, 4, -3],\n [-4, -4, 4, -4, -2, -4],\n [2, 4, 1, 0, 2, -4],\n [-2, -4, 0, 2, -4, -4],\n [4, -2, 2, -4, -3, 0],\n [-3, -4, -4, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3509", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 2, 0, 5, -2, -1],\n [3, 2, -6, 4, 2, -1],\n [5, -3, 5, -2, 6, -6],\n [0, 6, 6, 1, 4, -2],\n [-5, 1, 3, 0, 3, 2],\n [-3, 4, 2, -3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "131522", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 3, -5, 3, -4, 1],\n [4, 1, -5, 4, -5, -5],\n [3, 0, -1, 5, 4, -6],\n [-5, -6, 5, 4, 0, -1],\n [-5, -5, -5, 1, 0, -6],\n [-3, 4, -3, 0, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3895", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[-6, 5, 6, 3, 3, -4],\n [5, -6, -4, -2, 1, 1],\n [6, -4, 1, 0, -2, -2],\n [3, -2, 0, -1, -2, 0],\n [3, 1, -2, -2, -4, 0],\n [-4, 1, -2, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8029", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 4, -4, 2, 6, 3],\n [4, -5, -2, -2, 4, 0],\n [-4, -2, -3, -2, 1, -6],\n [2, -2, -2, -5, -1, 4],\n [6, 4, 1, -1, -1, -1],\n [3, 0, -6, 4, -1, 2]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200871", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 0, 6, 0, 2, 6],\n [0, -1, 3, -3, -1, 2],\n [6, 3, 6, 4, -2, -2],\n [0, -3, 4, 6, 4, 0],\n [2, -1, -2, 4, -5, 0],\n [6, 2, -2, 0, 0, 6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2253293", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -1, 4, -4, 4, 4],\n [3, 0, 6, 0, 1, -2],\n [-5, 6, -4, 2, -1, 1],\n [1, -2, -6, -1, 0, 2],\n [-5, 5, 6, -5, 3, -6],\n [-2, -5, -4, -5, 4, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-71090", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 5) of the result:\nA =\n[[4, -4, 2, 3, 5, -5],\n [0, 4, -4, 3, 1, -3],\n [-3, 2, 4, -4, 0, -6],\n [0, 3, 4, -5, 5, -1],\n [6, 2, -1, -4, -6, 5],\n [5, -3, -3, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4265", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 6, 0, 3, 0, 0],\n [5, -5, 2, -1, -5, -6],\n [4, -6, -6, -3, -3, 5],\n [2, 6, 5, 5, -6, -4],\n [-4, 1, -5, -1, 4, -3],\n [6, 3, -1, 6, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123805", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 4, 0, -2, -4, -2],\n [4, -4, -2, 2, 1, 2],\n [0, -2, -5, 2, 2, 2],\n [-2, 2, 2, -3, -3, 0],\n [-4, 1, 2, -3, 2, 4],\n [-2, 2, 2, 0, 4, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "934925", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 0, -2, 0, 4, -2],\n [0, 5, -3, 0, -2, 0],\n [-2, -3, -4, -2, -6, 2],\n [0, 0, -2, -5, -2, 0],\n [4, -2, -6, -2, 4, 0],\n [-2, 0, 2, 0, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26416", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 2, -3, -2, 4, 4],\n [2, 0, 0, -2, -2, -3],\n [-3, 0, 5, 4, -2, -4],\n [-2, -2, 4, 2, 4, -4],\n [4, -2, -2, 4, -3, 6],\n [4, -3, -4, -4, 6, -5]], determine the value at position (5, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6862", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 3, 3, 0, 5, 3],\n [-2, 5, 3, -1, -6, -3],\n [-3, 4, 1, -5, -6, 0],\n [-1, -2, 5, 6, 6, 6],\n [1, 4, 6, -5, -5, 2],\n [-6, -1, 6, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1512348", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-2, 1, 0, 6, 5, -3],\n [1, 4, 4, 3, 4, -5],\n [0, -2, 4, -1, -4, 4],\n [3, 0, 0, -5, -6, 3],\n [-5, 5, 1, 4, 3, -4],\n [4, -3, 1, -4, -1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268965", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, -6, 2, -3, -1, 0],\n [-5, 1, 5, 2, 3, 4],\n [-5, -2, -5, 4, -2, 0],\n [-1, -3, -5, 0, 5, 3],\n [2, -6, -4, 0, 2, 6],\n [-2, 0, 3, 0, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255236", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 1) of the 5th power of the matrix:\n[[-5, -2, 1, -6, 0, 0],\n [-2, 0, 0, 2, 0, 0],\n [1, 0, -4, 6, 0, 3],\n [-6, 2, 6, 1, 2, 2],\n [0, 0, 0, 2, -4, 2],\n [0, 0, 3, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17420", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 3) of the matrix A^5 where A is:\n[[2, 6, 0, -4, 4, 3],\n [-3, 5, 3, -5, 2, -2],\n [5, -5, 3, -1, 0, 6],\n [-5, -6, 6, 0, -6, -4],\n [-3, -5, 0, -2, -6, 5],\n [5, 1, 3, 0, -3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10512", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 2, -5, -2, -2, -2],\n [2, 5, 0, 0, 1, 1],\n [-5, 0, 3, -4, 0, 0],\n [-2, 0, -4, 0, -3, 0],\n [-2, 1, 0, -3, 1, -3],\n [-2, 1, 0, 0, -3, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18587", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 5) of the matrix A^5 where A is:\n[[-5, -3, -1, -1, -6, 1],\n [-5, 6, -2, -3, -2, -2],\n [3, 1, 3, 0, 5, 2],\n [5, 4, 6, -6, -1, -1],\n [-5, 4, 1, -1, 4, 6],\n [3, 2, 3, -2, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12939", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[4, -2, -1, -3, -4, 6],\n [-6, -6, -1, 2, 1, 5],\n [-5, 2, 1, 5, 2, -3],\n [2, -5, 6, -6, 6, 2],\n [3, 1, 0, 6, 1, 5],\n [-6, 2, 5, 3, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42156", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 1) of the 4th power of the matrix:\n[[5, 5, 2, 2, 2, 2],\n [5, -5, 0, 1, -3, -4],\n [2, 0, 6, 6, 0, 6],\n [2, 1, 6, -4, 0, 0],\n [2, -3, 0, 0, 6, 0],\n [2, -4, 6, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "764", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, -2, 6, 2, -4, -2],\n [-4, 5, -4, -6, -5, -5],\n [2, 0, 1, -5, 2, 6],\n [-4, 3, 6, -5, 5, -6],\n [2, 1, 6, 5, 4, -3],\n [0, 5, -4, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13658", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[3, -3, 3, -4, 1, 4],\n [-5, 4, 2, -4, -3, 6],\n [3, 3, -4, -4, 1, 1],\n [6, 6, -1, -3, -6, -3],\n [1, -1, -5, -4, 5, 0],\n [4, 4, -3, -3, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42354", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 2, -2, -6, -3, -1],\n [-1, 2, 3, 6, -2, -2],\n [-1, 4, -1, -4, -1, 1],\n [5, -1, 5, 4, -2, -4],\n [-6, -2, -1, -1, -1, -4],\n [-3, -4, -5, 1, 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": "248751", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 2) of the matrix A^4 where A is:\n[[1, 0, -3, 0, 4, 0],\n [0, 3, 0, -4, -2, 1],\n [-3, 0, 1, 0, 0, 2],\n [0, -4, 0, 0, 0, 0],\n [4, -2, 0, 0, 0, -2],\n [0, 1, 2, 0, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-534", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, -4, -3, 0, -2, -1],\n [-4, 3, 2, -4, -3, 2],\n [-3, 2, -4, -1, 2, 0],\n [0, -4, -1, -4, -4, 2],\n [-2, -3, 2, -4, 0, -2],\n [-1, 2, 0, 2, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-147337", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, -6, -2, 4, 2, -4],\n [-6, 6, 0, 0, -4, 1],\n [-2, 0, -2, 2, -3, -4],\n [4, 0, 2, -6, 0, 2],\n [2, -4, -3, 0, -5, 2],\n [-4, 1, -4, 2, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-94680", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, -6, -1, -5, 1, -2],\n [-4, 3, 0, 4, -5, -2],\n [4, 1, 6, 4, -6, -6],\n [-4, -4, 6, 0, -1, 0],\n [-3, 4, -5, -5, 3, -6],\n [6, 2, 0, 3, -4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105423", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[-4, 0, -2, 5, -4, 2],\n [-5, 0, 3, -1, -1, 0],\n [-1, -5, 4, -2, -4, 2],\n [1, 3, 4, -5, -6, -3],\n [-3, 5, 3, 4, -5, 0],\n [6, -4, 0, 0, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "746", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[-3, 4, 1, 1, -4, -3],\n [-6, 3, -5, 0, 4, 5],\n [0, 6, 2, 3, 2, 2],\n [-1, 1, 2, 5, 0, -3],\n [-3, -1, 4, -3, 4, 0],\n [1, 1, 1, -5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11579", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, -5, -3, -2, -3, -2],\n [-3, 0, 3, -6, 6, -6],\n [-5, 6, -6, 5, 3, 5],\n [5, 3, 6, 4, -4, -1],\n [3, 4, -1, -6, -1, -2],\n [0, -1, 5, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-137309", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, -6, 0, 2, -5, 5],\n [0, -4, -1, -4, 6, 3],\n [6, 4, 4, 4, -2, -5],\n [1, 1, 0, -1, -6, 1],\n [-6, 1, 4, -5, 1, 3],\n [5, -3, 0, -2, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122215", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, 0, -6, -1, 0, 4],\n [0, -2, 0, -2, 0, -4],\n [-6, 0, -2, -2, 2, 0],\n [-1, -2, -2, -1, 0, -1],\n [0, 0, 2, 0, -4, -1],\n [4, -4, 0, -1, -1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "743432", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 1, -1, 0, -2, -2],\n [1, -6, 5, -5, 1, 2],\n [-1, 5, -6, 1, -2, 2],\n [0, -5, 1, 3, -6, 2],\n [-2, 1, -2, -6, -5, -6],\n [-2, 2, 2, 2, -6, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-311633", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 1) of the matrix A^5 where A is:\n[[5, 2, -2, 3, 2, -2],\n [2, -5, 2, 0, -5, -4],\n [-2, 2, -5, 2, -4, -2],\n [3, 0, 2, -5, -2, -1],\n [2, -5, -4, -2, -6, -4],\n [-2, -4, -2, -1, -4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9851", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 4) of the result:\nA =\n[[5, -1, 1, -4, 3, -2],\n [-1, 1, 4, 3, 6, 1],\n [1, 4, 5, 3, 2, 3],\n [-4, 3, 3, -4, 0, -2],\n [3, 6, 2, 0, -2, -2],\n [-2, 1, 3, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12768", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 3) of the matrix A^5 where A is:\n[[-5, 2, -4, 2, -2, -3],\n [2, -5, -1, 5, 0, 0],\n [-4, -1, 0, 2, 0, -2],\n [2, 5, 2, 5, -1, -3],\n [-2, 0, 0, -1, 1, 3],\n [-3, 0, -2, -3, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9004", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 0, -4, 0, 2, -2],\n [0, -6, -2, 0, 2, 2],\n [-4, -2, 1, 0, -2, 2],\n [0, 0, 0, 2, 0, 4],\n [2, 2, -2, 0, 6, 1],\n [-2, 2, 2, 4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17367", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 6) of the 5th power of the matrix:\n[[-2, -1, -4, -1, 6, 1],\n [3, 6, 4, 2, -4, 1],\n [5, -4, -5, -2, -3, 6],\n [-2, -1, -4, -6, -3, -1],\n [-5, -5, -6, 2, -4, -5],\n [-3, -1, -6, 2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63892", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, -3, -5, 1, 0, 5],\n [-3, -4, -1, -6, -5, 0],\n [4, -4, 6, -6, -5, 3],\n [3, 2, 0, 0, 3, 1],\n [5, 5, 1, 2, -5, 1],\n [1, 6, -2, -2, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138447", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -6, -2, 4, 2, -5],\n [-6, 2, -5, 0, 2, -4],\n [-2, -5, 0, 4, 4, -2],\n [4, 0, 4, -2, 0, 2],\n [2, 2, 4, 0, -6, -3],\n [-5, -4, -2, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7892166", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 2, 2, -2, 5, 6],\n [-1, 4, 6, -1, 3, -3],\n [-6, -2, 6, -6, -6, 4],\n [-2, -2, 0, -5, -1, -5],\n [6, 3, -2, -3, 4, 3],\n [-2, -5, 1, 1, -1, -4]], determine the value at position (6, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15297", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-3, -5, -1, 2, -3, 2],\n [-5, -3, -2, -1, 0, -2],\n [-1, -2, 2, -2, 0, -2],\n [2, -1, -2, -6, 0, -4],\n [-3, 0, 0, 0, -5, 2],\n [2, -2, -2, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-272507", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -3, 0, 0, 2, 2],\n [-3, -3, 3, 1, 4, 2],\n [0, 3, -6, 0, 1, 3],\n [0, 1, 0, 0, -4, -4],\n [2, 4, 1, -4, -1, 0],\n [2, 2, 3, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71823", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 6) of the result:\nA =\n[[-6, 6, 0, -4, 0, 0],\n [6, 2, 4, -6, 3, 0],\n [0, 4, -4, 3, 0, 4],\n [-4, -6, 3, 6, 1, -2],\n [0, 3, 0, 1, 4, 1],\n [0, 0, 4, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1355", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, 6, -1, 0, 4, 2],\n [5, 5, 0, -3, 3, -2],\n [6, -1, 6, 2, -2, -2],\n [0, -5, -4, 5, -5, 3],\n [3, 5, -5, -4, -1, -2],\n [4, 6, -2, -5, -5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "241704", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-6, 0, 0, 1, 2, 1],\n [0, -2, -3, 4, -1, -4],\n [0, -3, 3, -2, 0, -2],\n [1, 4, -2, 3, -1, -5],\n [2, -1, 0, -1, -6, -2],\n [1, -4, -2, -5, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "822800", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, -2, 0, -1, -1, 0],\n [-2, -2, -5, 0, 0, 2],\n [0, -5, -5, -4, 0, 4],\n [-1, 0, -4, 4, 2, 2],\n [-1, 0, 0, 2, -3, 3],\n [0, 2, 4, 2, 3, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-277071", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 3, 6, -1, -3, -1],\n [3, 0, -1, 4, -6, -2],\n [1, 1, 5, 3, 2, -3],\n [3, -1, 0, -2, 4, 1],\n [-4, 1, -2, -6, 6, -1],\n [-5, 0, 2, -4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56700", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[-3, -3, -4, -2, 2, 4],\n [1, 3, -5, 5, 2, 5],\n [3, -5, 0, -2, 6, 0],\n [-2, 5, -1, 1, -6, 6],\n [4, 6, 5, -6, -2, -6],\n [-4, 3, 2, 6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-125261", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 1, 1, -1, -3, -3],\n [-3, -1, -6, 5, -5, -1],\n [4, -6, 2, 5, -1, 0],\n [5, -6, 1, 5, 5, 5],\n [5, 5, -2, -2, -1, 0],\n [0, -2, -6, 4, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6870", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[6, 4, 2, 0, -4, 4],\n [4, -4, 0, 2, 3, 2],\n [2, 0, 1, -2, -3, 1],\n [0, 2, -2, -2, 0, 1],\n [-4, 3, -3, 0, -6, -2],\n [4, 2, 1, 1, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188409", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[6, 2, 4, -6, -6, 3],\n [-4, 3, -4, -2, -3, -1],\n [5, 1, 1, 4, -3, -6],\n [6, 0, -1, -2, -3, -1],\n [1, -1, -4, 2, -4, -3],\n [6, -2, 4, -5, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44904", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 3, -5, -1, -5, 3],\n [-6, 1, 3, 3, 6, -6],\n [3, -1, 5, -6, 1, -2],\n [-4, -2, 6, -6, -6, 5],\n [-3, 2, 2, -6, -4, 6],\n [5, -3, -5, 0, -4, -6]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31721", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-6, -4, 2, -2, -6, -2],\n [-4, 5, 0, 2, 3, 5],\n [2, 0, 6, 1, 0, 0],\n [-2, 2, 1, 2, 0, 3],\n [-6, 3, 0, 0, -1, 0],\n [-2, 5, 0, 3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99349", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, -1, -6, 3, 0],\n [0, 3, 0, 0, 0, 2],\n [-1, 0, 1, 2, -2, -4],\n [-6, 0, 2, -4, 0, 4],\n [3, 0, -2, 0, -5, 2],\n [0, 2, -4, 4, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14529", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, 0, 4, -2, 2, 2],\n [0, 5, 0, 2, 0, 2],\n [4, 0, -3, 0, -2, 2],\n [-2, 2, 0, -1, 0, 2],\n [2, 0, -2, 0, 4, 4],\n [2, 2, 2, 2, 4, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "743854", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 3, -3, -4, -2, -2],\n [3, -5, 4, -4, 1, -3],\n [-3, 4, 5, 2, 2, 2],\n [-4, -4, 2, 4, 2, 0],\n [-2, 1, 2, 2, -6, 4],\n [-2, -3, 2, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29583", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 0, 1, 0, -2, 4],\n [0, 2, -2, 0, 0, -1],\n [1, -2, 1, -1, -2, -2],\n [0, 0, -1, -4, -2, 0],\n [-2, 0, -2, -2, 6, 3],\n [4, -1, -2, 0, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31877", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 2) of the 4th power of the matrix:\n[[-4, 1, -4, -6, 2, 1],\n [-3, 1, -2, -4, -6, 6],\n [3, -2, 4, -1, -3, 0],\n [-4, 0, -6, 0, -6, 6],\n [4, -6, -5, -5, -3, 6],\n [-6, -3, -5, -3, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1783", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[2, -4, -1, -2, 1, 0],\n [-4, -5, -4, 0, 4, 2],\n [-1, -4, 5, -3, -4, -4],\n [-2, 0, -3, 2, 2, 2],\n [1, 4, -4, 2, 4, -4],\n [0, 2, -4, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16061", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[0, 0, -1, -4, -5, 3],\n [0, -5, 0, 2, -4, 2],\n [-1, 0, 6, 3, 0, 0],\n [-4, 2, 3, 4, 0, 1],\n [-5, -4, 0, 0, -4, 1],\n [3, 2, 0, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-199095", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 2, 6, 1, 6, -5],\n [5, 1, 1, -2, 6, -4],\n [2, 5, 0, -6, 1, 3],\n [6, -2, -1, 2, 3, 1],\n [4, -4, 6, -2, -3, -6],\n [-2, 3, 0, -6, -3, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361511", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 4, 1, 2, 3, 0],\n [4, -4, 0, 2, 0, 0],\n [1, 0, 5, 2, 0, 1],\n [2, 2, 2, 4, 0, -2],\n [3, 0, 0, 0, 2, 0],\n [0, 0, 1, -2, 0, 1]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6232", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[6, 4, 0, -3, 1, 4],\n [4, -4, -2, 4, -1, 2],\n [0, -2, -3, 2, -1, 2],\n [-3, 4, 2, 3, 4, 0],\n [1, -1, -1, 4, -1, 0],\n [4, 2, 2, 0, 0, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19345", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -3, -6, 3, -4, -5],\n [1, 1, 5, -2, -2, 4],\n [-3, -6, -6, 6, -1, -3],\n [-3, -4, 2, -4, 1, -5],\n [-3, -6, 4, -2, -5, 4],\n [6, -6, -6, -5, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7929", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 2) of the result:\nA =\n[[2, -1, 5, -3, -4, 1],\n [-4, -6, -3, 4, 6, -2],\n [-2, -2, 1, 1, 5, 6],\n [-3, 2, -6, -2, -2, -2],\n [1, 2, -4, 2, 6, 4],\n [1, -4, -5, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-496", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, -4, 1, 0, 4, 3],\n [-4, -4, -2, 1, -2, 0],\n [1, -2, -4, -2, -2, 2],\n [0, 1, -2, -1, 2, -1],\n [4, -2, -2, 2, -2, 1],\n [3, 0, 2, -1, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34779", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 6) of the result:\nA =\n[[-3, 2, 0, -5, 6, -3],\n [-2, -5, 3, 1, -6, -4],\n [-6, -2, 1, 0, 2, -5],\n [5, 1, 1, -1, -4, -5],\n [1, -1, -3, -2, -2, 6],\n [2, 6, 6, 2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5039", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, -5, -4, 1, 6, -2],\n [0, 1, -1, -2, 1, -6],\n [-6, -6, -4, 3, 6, 5],\n [-1, -1, -2, 6, 6, 0],\n [-2, -5, -3, -6, 0, -3],\n [6, -3, 6, -3, -4, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39908", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 4) of the 4th power of the matrix:\n[[-3, 1, 2, 0, -4, 0],\n [1, -1, 2, -1, 4, -2],\n [2, 2, 4, 2, -5, 0],\n [0, -1, 2, -6, 4, 0],\n [-4, 4, -5, 4, 5, 0],\n [0, -2, 0, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2892", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 4, 6, 2, 0, 6],\n [-4, 5, -1, -4, 3, -3],\n [5, -3, -4, 3, -1, -2],\n [4, 2, 2, -4, 6, 2],\n [6, 5, -4, -3, -6, -2],\n [5, 2, -5, -3, 3, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158546", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 6) of the 5th power of the matrix:\n[[1, 2, -4, 6, 2, -1],\n [-1, 0, 5, -2, -1, 4],\n [-6, -4, 5, 2, 5, -2],\n [-2, 1, 4, 4, 6, -5],\n [6, 0, 2, 0, 5, -2],\n [6, -1, -3, 5, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15194", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 5) of the result:\nA =\n[[-3, 1, 3, -2, -1, 2],\n [1, -5, 6, 0, 5, -2],\n [3, 6, -1, -4, -1, 0],\n [-2, 0, -4, 1, 1, 4],\n [-1, 5, -1, 1, 5, -4],\n [2, -2, 0, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3266", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 2, 4, 4, 0, 0],\n [2, -2, 2, 0, 2, -5],\n [4, 2, 6, -2, 2, 5],\n [4, 0, -2, -5, 1, 2],\n [0, 2, 2, 1, -2, -2],\n [0, -5, 5, 2, -2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29770", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -4, 4, -5, 0, 3],\n [3, -3, -6, -1, -2, 4],\n [-5, -1, -6, -4, -3, 6],\n [-4, 6, -1, 4, -3, -6],\n [-2, -2, 2, 1, 1, -2],\n [1, 3, 0, -6, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72958", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 0, 1, 0, -2, 0],\n [0, -3, -1, 2, -4, 4],\n [1, -1, -5, 0, 4, 4],\n [0, 2, 0, 0, -4, 0],\n [-2, -4, 4, -4, -5, -2],\n [0, 4, 4, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1066535", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, -2, 5, 4, 3, 6],\n [-1, -4, -2, 5, 6, 6],\n [6, -6, 1, 4, -1, 5],\n [-5, -3, -3, 2, 2, -2],\n [5, -4, -6, -1, 1, -6],\n [4, -6, 4, 0, 0, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-220764", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, -2, 0, 2, 1, -2],\n [-2, -6, 5, -1, 5, 0],\n [0, 5, 6, -2, 2, 5],\n [2, -1, -2, 4, 4, 0],\n [1, 5, 2, 4, 3, 2],\n [-2, 0, 5, 0, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114547", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 4) of the 4th power of the matrix:\n[[2, 6, -6, 6, 1, -2],\n [-3, -6, 2, 6, 2, 6],\n [-2, 4, 2, 3, 2, 0],\n [1, -6, -3, 3, 3, -3],\n [5, 2, -4, 5, 3, 3],\n [-6, 4, -2, 0, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3776", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 1) of the matrix A^4 where A is:\n[[2, -1, -1, -4, 3, 3],\n [-2, 3, -1, -3, 6, -4],\n [-2, 0, 4, -1, -5, -6],\n [-2, -2, 5, 5, -1, -4],\n [-6, -3, -3, 3, -5, 1],\n [-1, 5, -4, -6, 5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2730", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, 1, -3, -4, 6, 4],\n [-3, 4, -3, -5, -3, 4],\n [5, 2, -3, 5, -6, -6],\n [-6, -2, -1, 5, -1, -1],\n [2, -6, 3, -1, 6, 1],\n [1, 5, -4, 6, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "813441", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, 5, -4, 4, 0, -4],\n [5, -5, 0, -2, -4, -3],\n [-4, 0, 0, 3, 6, -4],\n [4, -2, 3, -1, 2, 3],\n [0, -4, 6, 2, -3, 1],\n [-4, -3, -4, 3, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8459", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[6, -5, -1, -1, 5, -3],\n [-2, 0, 1, -1, -2, 5],\n [-4, 0, 1, -4, -2, 4],\n [-5, 3, 3, 5, -3, 5],\n [-3, 5, 6, 1, -4, -2],\n [4, -2, -5, 2, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "661851", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 0, 2, 0, -1, 0],\n [0, -1, 0, -4, -4, -1],\n [2, 0, 4, 2, 1, 0],\n [0, -4, 2, 4, 1, 5],\n [-1, -4, 1, 1, -5, 4],\n [0, -1, 0, 5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35035", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 2) of the matrix A^4 where A is:\n[[5, -2, 6, -5, 6, -3],\n [0, -1, 3, 0, -2, -5],\n [1, 5, -5, 5, 1, 0],\n [-4, 6, -3, 6, 0, -3],\n [2, 0, -6, -6, -3, 6],\n [2, 6, -3, 6, -2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1269", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 6) of the result:\nA =\n[[-5, 4, 2, 4, -4, -1],\n [4, -1, 4, -2, 0, 4],\n [2, 4, -6, -6, 1, -2],\n [4, -2, -6, 2, 0, -1],\n [-4, 0, 1, 0, 1, -4],\n [-1, 4, -2, -1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37702", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 0, 0, 2, -3, 0],\n [0, 1, 0, 0, -2, -3],\n [0, 0, -6, -3, 2, -5],\n [2, 0, -3, -1, -2, -2],\n [-3, -2, 2, -2, 2, -2],\n [0, -3, -5, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-693675", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-3, 0, 2, 2, 4, 4],\n [0, -4, 2, -4, 2, 0],\n [2, 2, 0, 3, 2, 1],\n [2, -4, 3, 4, -4, 2],\n [4, 2, 2, -4, 5, 2],\n [4, 0, 1, 2, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850930", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, -2, -4, 4, 0, 0],\n [-2, -3, 0, 0, 0, 4],\n [-4, 0, -3, 0, -4, 0],\n [4, 0, 0, 5, 0, 0],\n [0, 0, -4, 0, 1, 4],\n [0, 4, 0, 0, 4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "407046", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 1) of the 4th power of the matrix:\n[[0, -2, 3, 0, -5, -3],\n [-6, -2, 1, -6, 0, 0],\n [0, -6, 5, 4, -4, 4],\n [-5, -2, -5, 6, -2, -2],\n [-3, 4, 0, 3, -1, -5],\n [-3, 6, 4, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2597", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, -4, -6, 2, 1, 0],\n [-1, 3, 0, 4, 2, -1],\n [3, -4, 6, -4, -3, 3],\n [6, 3, 1, 3, 2, 1],\n [4, 3, -5, -3, -3, 5],\n [-5, 6, 1, -4, -5, 0]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23925", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, -1, 6, 6, -4, 6],\n [-4, -2, -4, 5, -3, 6],\n [6, -4, 0, -4, 3, -3],\n [-5, -5, 2, 4, -6, -6],\n [3, -6, -4, -5, -4, -2],\n [2, -5, 5, 4, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "780541", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -4, 6, 0, -1, 4],\n [0, 6, 6, -2, -6, -4],\n [-4, 0, 6, -4, 4, -2],\n [-3, -3, 6, 0, -6, 0],\n [1, -4, -4, -3, 6, -1],\n [0, -6, 6, -3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1801694", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, 0, -3, -5, 0, -2],\n [0, -2, 0, -2, -2, 2],\n [-3, 0, 2, 1, 0, -2],\n [-5, -2, 1, 3, -6, 4],\n [0, -2, 0, -6, -4, 2],\n [-2, 2, -2, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-179917", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[6, 2, -2, 2, 6, -1],\n [2, -5, -4, -3, 5, -2],\n [-2, -4, 2, -2, 0, -4],\n [2, -3, -2, -3, -4, -3],\n [6, 5, 0, -4, 0, -2],\n [-1, -2, -4, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-453657", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-6, -4, 4, -2, -2, -2],\n [-4, -2, 2, -2, -2, 0],\n [4, 2, 5, -4, 0, 1],\n [-2, -2, -4, 2, -2, 0],\n [-2, -2, 0, -2, 2, -3],\n [-2, 0, 1, 0, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79774", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -4, 0, 2, 2, 2],\n [-4, -2, -4, -1, 0, -1],\n [0, -4, -2, -1, 2, 5],\n [2, -1, -1, 4, 0, 0],\n [2, 0, 2, 0, -4, 3],\n [2, -1, 5, 0, 3, 1]], determine the value at position (6, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8052", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-6, 5, -4, -5, -3, -5],\n [5, 4, 1, -6, -3, -2],\n [3, -3, 1, -5, 2, -5],\n [-5, 6, -5, 5, 3, 1],\n [-4, 3, 4, 3, 1, 0],\n [3, -3, 0, 4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30215", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-1, -3, 0, 2, -4, 4],\n [-3, -2, -2, 0, 0, 1],\n [0, -2, 4, 2, 2, 0],\n [2, 0, 2, -6, 0, -2],\n [-4, 0, 2, 0, 6, -2],\n [4, 1, 0, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6934", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 2, 3, -2, 6, 0],\n [2, 5, 1, 0, -5, 2],\n [3, 1, 1, 4, 4, 4],\n [-2, 0, 4, 2, 0, -2],\n [6, -5, 4, 0, 6, 1],\n [0, 2, 4, -2, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "668885", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-6, 0, 2, -2, 4, -1],\n [0, -4, -3, -2, -3, 0],\n [2, -3, -2, 3, -2, -4],\n [-2, -2, 3, -5, -4, 0],\n [4, -3, -2, -4, 1, 2],\n [-1, 0, -4, 0, 2, -4]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2414", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, 1, -2, -1, -1],\n [0, -1, 0, 0, 0, 0],\n [1, 0, -5, -1, 3, -2],\n [-2, 0, -1, -1, 2, -4],\n [-1, 0, 3, 2, -1, 0],\n [-1, 0, -2, -4, 0, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4236", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, -4, 4, 0, 0, 0],\n [-4, 6, -1, 6, 5, -1],\n [4, -1, -4, 1, -2, 3],\n [0, 6, 1, 3, -2, 0],\n [0, 5, -2, -2, -4, 2],\n [0, -1, 3, 0, 2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304953", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 0, 2, 2, 5, 0],\n [0, 2, -4, 6, -2, 0],\n [2, -4, 0, -4, 2, -4],\n [2, 6, -4, 0, -2, 2],\n [5, -2, 2, -2, 0, -2],\n [0, 0, -4, 2, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46327", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, -1, 2, -3, -1, -6],\n [5, -1, 5, -4, 2, -3],\n [0, -3, 4, -1, 0, -5],\n [3, -1, 1, 6, 6, 5],\n [-1, -5, -3, -6, 0, 1],\n [3, -5, 3, -2, 4, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85212", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[4, 1, -2, 1, -1, -2],\n [6, 4, -3, -2, 5, -3],\n [-6, -4, 1, 0, 5, 0],\n [4, -4, 2, -1, 1, 1],\n [-4, -3, -1, -5, 5, 5],\n [4, 5, 0, -5, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3154", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, -3, 2, 6, 6, -5],\n [0, 6, 0, 0, -6, 1],\n [-5, -2, -5, 6, -2, 0],\n [-1, 6, 5, -2, -3, 1],\n [4, 1, -6, 3, -5, -4],\n [6, -6, 4, -4, 3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1409885", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, -3, 6, 6, 0, 0],\n [4, -2, 5, -6, 3, -3],\n [0, -2, -5, 1, -5, 4],\n [1, 6, 4, -5, 4, -2],\n [-3, -6, 5, 1, 3, 5],\n [-4, 6, -3, -3, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154624", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 1) of the result:\nA =\n[[2, -2, 0, 2, 0, 2],\n [-2, 1, 4, 2, 1, -2],\n [0, 4, -2, 6, -3, 2],\n [2, 2, 6, -2, -3, -2],\n [0, 1, -3, -3, -6, 2],\n [2, -2, 2, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6998", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[6, 4, -5, -5, 6, -3],\n [-6, 0, 6, -6, -4, 3],\n [0, 4, 5, 5, -1, 0],\n [-2, 1, -1, 5, -3, 4],\n [-6, -5, 5, -1, -3, -4],\n [0, 0, -5, 1, 4, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45159", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[4, 4, 2, -1, 4, -4],\n [4, 5, 1, -4, 0, 0],\n [2, 1, -2, 1, 0, -2],\n [-1, -4, 1, 0, -6, 6],\n [4, 0, 0, -6, 2, 0],\n [-4, 0, -2, 6, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170442", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, -2, 2, 2, 0, -5],\n [-2, 5, 0, 1, -1, 4],\n [2, 0, -5, 6, 2, 2],\n [2, 1, 6, 4, -2, 4],\n [0, -1, 2, -2, -5, 2],\n [-5, 4, 2, 4, 2, -1]], determine the value at position (6, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6028", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 2) of the result:\nA =\n[[1, -1, -3, -4, -5, 6],\n [-6, -5, -5, -2, 2, -6],\n [-3, 3, 0, 4, 3, -4],\n [1, -4, 1, 6, -5, -2],\n [-3, 4, 2, -4, 5, 4],\n [-2, 3, 2, 6, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17338", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-6, 0, 4, -1, 3, 0],\n [0, 0, -4, -4, -1, 0],\n [4, -4, -2, 4, -2, 2],\n [-1, -4, 4, 4, 4, 2],\n [3, -1, -2, 4, -1, 2],\n [0, 0, 2, 2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108665", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -4, -2, 0, 2, 0],\n [-4, -5, 0, -3, 4, -1],\n [-2, 0, -1, 6, 4, 0],\n [0, -3, 6, 6, -2, 0],\n [2, 4, 4, -2, -1, 0],\n [0, -1, 0, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66208", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, -2, -1, -6, 1, -4],\n [-2, 0, -4, 3, 6, -1],\n [-2, 0, 3, 4, -4, 6],\n [-5, -3, -4, -3, 0, -2],\n [-3, -1, 0, 5, 4, -2],\n [5, 0, -4, 0, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143049", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, -2, 4, 2, 0, 0],\n [-2, 5, -4, 2, -2, 2],\n [4, -4, 6, 2, -1, -1],\n [2, 2, 2, 2, 0, -4],\n [0, -2, -1, 0, -3, 4],\n [0, 2, -1, -4, 4, 5]], determine the value at position (6, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2700", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[-5, -2, 2, 3, 2, 0],\n [-2, 0, -4, 4, -2, 2],\n [2, -4, -6, 2, 4, -1],\n [3, 4, 2, -3, 2, 5],\n [2, -2, 4, 2, 6, 2],\n [0, 2, -1, 5, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1396", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 5) of the matrix A^5 where A is:\n[[-1, 3, 2, 6, 0, -6],\n [2, -4, 2, -3, 2, 6],\n [1, 0, -3, 2, -3, -6],\n [-1, -3, 3, -4, 5, -2],\n [-4, 4, 2, 5, -1, -4],\n [-2, 1, 1, -1, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-82782", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 2) of the matrix A^5 where A is:\n[[-6, 0, 4, 5, -2, 1],\n [0, 0, -4, 2, 6, -2],\n [4, -4, 5, -2, 2, -4],\n [5, 2, -2, 4, -3, 1],\n [-2, 6, 2, -3, 4, 2],\n [1, -2, -4, 1, 2, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-51170", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -4, 2, 2, 0, 1],\n [-4, 0, 1, 0, -1, 4],\n [2, 1, 1, 1, -2, -4],\n [2, 0, 1, 3, 4, 2],\n [0, -1, -2, 4, 3, 0],\n [1, 4, -4, 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": "408456", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 6, -5, 0, -6, 6],\n [3, -2, 2, 6, 6, -6],\n [1, 2, 2, 1, -3, 0],\n [-6, 0, -1, -2, -6, 1],\n [3, -6, -6, -4, 6, 1],\n [1, 0, -2, 1, -5, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50466", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, 5, -6, 4, -2, 4],\n [5, -3, 0, -3, 0, 2],\n [-6, 0, 5, -2, 0, -4],\n [4, -3, -2, 0, -2, 1],\n [-2, 0, 0, -2, -5, 3],\n [4, 2, -4, 1, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70460", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 6) of the 5th power of the matrix:\n[[-2, 0, 0, 1, 0, 1],\n [0, -6, -4, 2, -2, 5],\n [0, -4, 2, 0, 2, -6],\n [1, 2, 0, -1, 0, -4],\n [0, -2, 2, 0, 2, 0],\n [1, 5, -6, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102142", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 2, -2, 2, -2, -1],\n [2, 1, 0, 6, 0, 0],\n [-2, 0, 4, -1, 4, 0],\n [2, 6, -1, -3, -5, 0],\n [-2, 0, 4, -5, 4, 4],\n [-1, 0, 0, 0, 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": "130838", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[6, 4, 0, 1, -6, -4],\n [4, -1, 2, 0, -2, 0],\n [0, 2, 5, -4, -2, 0],\n [1, 0, -4, 3, 0, 4],\n [-6, -2, -2, 0, -3, -2],\n [-4, 0, 0, 4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1366740", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[5, 3, 2, 0, -6, 0],\n [-2, 3, 6, 6, 0, 5],\n [2, 1, -1, -5, 1, 5],\n [-3, 1, 0, -3, 1, 4],\n [4, 5, 4, -5, 2, -1],\n [0, 3, -6, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50715", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 0, -6, 2, -2, 6],\n [5, -4, 0, 3, 1, 3],\n [3, -4, 0, 0, -3, 3],\n [2, -6, -6, -2, 6, -4],\n [3, 6, 2, -2, 0, -6],\n [-5, 4, 5, -3, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1225", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 2) of the result:\nA =\n[[-2, 2, 1, -5, 0, -6],\n [3, 4, 4, 2, -4, 6],\n [-5, -3, -3, -4, -5, -2],\n [-3, -2, 6, 5, 5, 1],\n [4, -5, 2, 3, -6, 1],\n [5, -2, -5, 1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-205", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 5, -5, 1, -4, 4],\n [5, 3, 0, -3, 2, -2],\n [-5, 0, 6, 1, 1, 4],\n [1, -3, 1, -1, -4, -3],\n [-4, 2, 1, -4, -3, 2],\n [4, -2, 4, -3, 2, 3]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5634", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 2, -1, -3, -4, 5],\n [6, -3, 1, 5, -2, 6],\n [4, -6, -2, 1, 4, 5],\n [-3, -5, 6, -4, 4, 2],\n [0, -4, -2, -4, 3, -3],\n [5, 1, -4, -4, 4, 4]], determine the value at position (6, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1300", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 3, 6, 3, 0, 0],\n [3, -5, 5, 0, 3, 4],\n [3, -4, 0, 6, -3, 6],\n [1, 1, -1, 6, 5, -4],\n [-1, -1, -4, 4, -3, -5],\n [-6, -5, 0, 3, -2, 2]], determine the value at position (6, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-52", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 5) of the result:\nA =\n[[-4, -1, 2, -4, 3, -2],\n [-1, -1, -1, 2, 2, -3],\n [2, -1, -6, 0, 0, 0],\n [-4, 2, 0, 3, 2, -2],\n [3, 2, 0, 2, 1, -1],\n [-2, -3, 0, -2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6600", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, -3, -1, -2, 5, -5],\n [1, -4, -2, 1, 4, 2],\n [6, 2, -2, -5, 0, 4],\n [4, 0, 5, 6, 1, 1],\n [-2, -6, 6, 4, 6, -3],\n [-3, 4, -4, 1, -4, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46391", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 6) of the 5th power of the matrix:\n[[-2, -5, -1, -1, 1, 1],\n [-6, -2, -5, 3, 5, -2],\n [3, 5, 2, -3, 1, -6],\n [1, -1, 1, -1, 4, -4],\n [5, 4, 1, -2, 5, 3],\n [-2, 5, 0, -1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12701", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, 4, 4, 5, -2, 2],\n [4, 6, 3, -5, -6, 4],\n [1, 1, -5, 6, 1, -2],\n [-5, 0, 0, -4, -6, 4],\n [-3, -5, -3, 1, -5, -6],\n [4, -4, 3, 0, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "596257", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, -1, 0, 1, -4, -4],\n [3, 6, 1, 5, 6, 6],\n [0, 3, -2, -3, -1, 2],\n [-1, 1, -6, 5, -1, -5],\n [-4, -1, -5, -3, -1, -2],\n [-1, -1, 1, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8449", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -4, -3, 0, -4, 6],\n [-4, -6, 0, -4, -2, -2],\n [-3, 0, 5, 5, -1, 0],\n [0, -4, 5, 0, 0, -6],\n [-4, -2, -1, 0, 5, 2],\n [6, -2, 0, -6, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144569", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 0, -1, 1, 0, -2],\n [0, -5, 0, 3, 3, 0],\n [-1, 0, 5, 0, 2, -5],\n [1, 3, 0, 5, 3, -2],\n [0, 3, 2, 3, 0, 0],\n [-2, 0, -5, -2, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19043", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, -1, -2, -3, 3, 2],\n [4, 1, 5, 0, 4, -6],\n [2, 2, -1, 0, 6, -4],\n [-2, 0, -6, 5, -6, -2],\n [2, 0, -6, 6, 6, 5],\n [-2, 1, 1, 5, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1456642", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -2, 2, -4, -6, 6],\n [-3, 0, -6, -5, -2, 2],\n [-6, 5, -3, 5, -4, -2],\n [-2, 3, -5, -2, 2, -2],\n [4, 3, -5, 0, -1, 0],\n [1, 3, -2, -5, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46318", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 3) of the result:\nA =\n[[1, 0, 4, -3, 5, 2],\n [0, -5, -1, 0, 2, 2],\n [4, -1, -4, -4, 4, -4],\n [-3, 0, -4, -6, -4, -2],\n [5, 2, 4, -4, 3, 2],\n [2, 2, -4, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65014", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[6, -3, 1, -1, -3, 1],\n [-3, -2, 4, 0, -2, -2],\n [1, 4, -2, 0, -2, 3],\n [-1, 0, 0, -2, 2, -2],\n [-3, -2, -2, 2, -5, 3],\n [1, -2, 3, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4899", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 4) of the result:\nA =\n[[-1, -5, -1, -1, 1, -2],\n [-6, 1, 5, 2, -6, -2],\n [5, -1, -3, 4, -5, -2],\n [-3, 6, 0, -1, -4, 2],\n [-3, 4, -2, -4, 1, 4],\n [0, 4, 4, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8351", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, 0, -4, 6, -6, 2],\n [0, -3, 6, 2, -2, -2],\n [-4, 6, -1, 5, 0, 3],\n [6, 2, 5, 0, 1, -4],\n [-6, -2, 0, 1, -5, 2],\n [2, -2, 3, -4, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39088", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[5, 2, 2, -2, 1, -4],\n [2, 1, 0, -1, -2, 0],\n [2, 0, 3, -3, 0, -2],\n [-2, -1, -3, 1, -4, 0],\n [1, -2, 0, -4, 4, 0],\n [-4, 0, -2, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535003", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -3, -4, -2, 2, -2],\n [-3, -4, 4, 5, -4, -4],\n [-4, 4, 5, 0, -2, 2],\n [-2, 5, 0, -2, 4, -2],\n [2, -4, -2, 4, -5, 2],\n [-2, -4, 2, -2, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34807", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the 4th power of the matrix:\n[[0, 1, 4, 1, -2, -2],\n [1, 1, 0, 5, -1, 4],\n [4, 0, -6, 0, -1, -1],\n [1, 5, 0, -3, 0, -2],\n [-2, -1, -1, 0, 0, -4],\n [-2, 4, -1, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1028", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -2, 6, 4, -2, 0],\n [-6, -4, -5, 4, 3, -1],\n [4, 5, -1, 3, -6, -1],\n [3, -5, 4, -3, -1, -4],\n [-4, 5, -4, -3, 2, -3],\n [6, -3, -3, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1871310", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (6, 3) of the result:\nA =\n[[-5, -1, 0, 5, -4, 0],\n [-1, 3, -2, 2, -2, -2],\n [0, -2, 6, 2, 0, 2],\n [5, 2, 2, -1, -2, 1],\n [-4, -2, 0, -2, 3, -2],\n [0, -2, 2, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5940", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 0, 1, 1, 2, -2],\n [0, -6, 0, 1, 0, 6],\n [1, 0, -3, 4, -4, 2],\n [1, 1, 4, -3, 0, 0],\n [2, 0, -4, 0, -1, 4],\n [-2, 6, 2, 0, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1587376", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, -5, 4, 3, -1, 0],\n [-5, -1, 0, 1, 2, 5],\n [4, 0, -3, 0, -6, -4],\n [3, 1, 0, 4, -1, 2],\n [-1, 2, -6, -1, 4, -4],\n [0, 5, -4, 2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "219512", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 1) of the result:\nA =\n[[-4, 0, 6, 1, 2, 0],\n [1, 4, -1, -5, -6, -4],\n [2, 6, 0, -5, -6, -5],\n [-4, -1, 5, 2, 1, 3],\n [2, 4, 4, 1, 0, -1],\n [1, -1, -5, 6, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[-4, 2, -5, 5, -4, -1],\n [-3, 1, -6, 6, -1, -5],\n [-1, -6, -5, 2, -1, 1],\n [0, 2, 2, 4, -3, 0],\n [-2, 0, -3, 5, 3, 4],\n [4, -6, -3, 6, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-416", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (6, 2) of the result:\nA =\n[[2, -4, -1, 2, -3, 1],\n [-4, 1, 2, -5, 3, 2],\n [-1, 2, -6, 2, 4, 4],\n [2, -5, 2, -4, 0, 0],\n [-3, 3, 4, 0, 1, -2],\n [1, 2, 4, 0, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-704", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, -4, -2, 2, -4, -2],\n [-4, 6, 6, 2, 0, 0],\n [-2, 6, 3, -3, 0, -4],\n [2, 2, -3, 0, -5, 2],\n [-4, 0, 0, -5, 6, -2],\n [-2, 0, -4, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "167853", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 2, -1, -3, -5, 3],\n [2, -3, 2, -5, 0, 4],\n [4, -2, 1, 4, 1, -3],\n [6, -3, 1, -4, 0, 1],\n [1, 4, 3, -3, 2, 3],\n [-3, 1, -1, -2, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[6, 4, -6, 0, 1, 5],\n [2, 6, -4, 2, 3, -2],\n [3, -1, -6, 2, 2, -1],\n [1, -3, -2, -2, 0, 0],\n [0, -2, -3, 1, -6, -6],\n [-1, -5, 5, -4, -3, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42706", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 4) of the matrix A^5 where A is:\n[[3, 3, 4, -4, -2, 0],\n [3, 2, 4, -3, -3, 0],\n [4, 4, 5, 4, 6, 0],\n [-4, -3, 4, -5, 4, 4],\n [-2, -3, 6, 4, -6, -4],\n [0, 0, 0, 4, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-97361", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 5) of the result:\nA =\n[[4, 6, 3, 0, -1, 6],\n [-6, 3, -5, 4, 0, -4],\n [-5, -1, 1, 1, 4, -5],\n [-1, 5, -2, 0, -3, 5],\n [6, -5, 3, -4, 2, 3],\n [1, 6, 2, -2, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-601", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 3) of the result:\nA =\n[[0, 0, -6, 5, -2, 1],\n [0, 4, -5, 1, -5, 3],\n [-6, 4, 4, 4, -4, -4],\n [-1, 5, -4, 0, 1, -4],\n [2, -6, -4, 5, -4, 0],\n [4, 4, -2, -3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2205", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -2, 0, 2, 0, 3],\n [-2, 0, 2, 1, 1, 4],\n [0, 2, 1, -1, -5, 0],\n [2, 1, -1, 1, -2, 2],\n [0, 1, -5, -2, -1, -5],\n [3, 4, 0, 2, -5, 0]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17099", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 4) of the 5th power of the matrix:\n[[3, -2, 2, -1, 0, 1],\n [-2, 1, 4, -2, 2, 4],\n [2, 4, 3, 2, -1, 0],\n [-1, -2, 2, 0, 1, -2],\n [0, 2, -1, 1, 2, 0],\n [1, 4, 0, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1265", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 5) of the matrix A^4 where A is:\n[[-3, 1, 2, -2, 6, -1],\n [-4, 5, -2, -2, -5, 3],\n [-1, 2, 4, 0, 1, -5],\n [4, 6, 2, -4, 3, -2],\n [0, -3, 0, 1, 6, 3],\n [3, -3, -2, 4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-864", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 6) of the matrix A^5 where A is:\n[[1, -4, 6, -2, 3, -6],\n [-5, -4, -6, 6, 4, 5],\n [4, 2, 2, -2, -3, -2],\n [-3, 5, -2, 0, 4, 1],\n [-5, -3, 1, 0, 2, -2],\n [-1, 4, 1, 5, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36710", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, -3, 1, 5, -4, -2],\n [1, 3, 5, 0, -6, 5],\n [-3, -5, -5, 6, 0, 5],\n [5, -4, -4, -1, -1, -6],\n [-6, 4, -1, 0, 2, -3],\n [3, -1, 5, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14816", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[4, -3, 2, -6, -2, 4],\n [0, -4, -5, 6, 4, -5],\n [-6, -2, 6, -4, 4, 5],\n [0, -6, 2, -5, 1, 3],\n [-3, -1, 2, 0, 1, 0],\n [-5, 2, -6, -5, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9011", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, -3, -2, -1, -6, 6],\n [1, -1, 3, 2, -2, 0],\n [4, -3, -1, -1, 6, -3],\n [-1, 1, 4, -2, -5, 2],\n [4, -3, -3, 4, 0, 3],\n [3, -1, -3, -1, -4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46851", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, -4, -6, 5, 3, -2],\n [3, -5, 0, 6, 0, -3],\n [-1, -6, -5, -1, -5, 5],\n [5, 4, -3, -3, 3, 2],\n [3, 0, 0, 5, 4, -6],\n [4, -2, -4, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25276", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, -4, 2, 1, 2, -2],\n [-4, -2, 0, 6, 0, 2],\n [2, 0, 1, 2, 3, 0],\n [1, 6, 2, 3, 1, 2],\n [2, 0, 3, 1, -3, -1],\n [-2, 2, 0, 2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18923", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[0, 0, -2, -5, 5, -5],\n [6, 5, 3, 5, 1, 4],\n [-1, 1, -4, -6, 6, -1],\n [-5, 5, 2, -2, -2, 6],\n [3, 1, -1, -4, 2, 3],\n [-3, 3, -3, 5, 6, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15616", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, -3, 0, 6, -4, 1],\n [1, 3, 4, -5, -3, 1],\n [-6, -6, -3, 4, -5, -6],\n [1, -5, -3, -4, -5, 1],\n [-4, 2, 3, -2, 2, -4],\n [5, -2, 3, -1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-157102", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-5, -4, 2, -4, -4, 0],\n [-4, 1, -1, 2, -1, 2],\n [2, -1, -3, -2, -2, -2],\n [-4, 2, -2, -3, -2, 3],\n [-4, -1, -2, -2, 3, 0],\n [0, 2, -2, 3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "582224", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -3, -1, 5, 5, 5],\n [5, 5, 5, -2, -1, 5],\n [-5, 0, 1, 6, 4, 2],\n [-1, 0, 6, 5, 6, -6],\n [2, -1, 5, -3, 3, 2],\n [5, -6, -5, -4, -6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93234", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 0, 3, 6, -1, 5],\n [2, -2, 2, 6, 5, 3],\n [2, -5, 5, 2, -4, 4],\n [-4, 5, 4, 2, 0, 4],\n [1, 0, 2, 1, -3, -5],\n [6, 4, -2, -5, -3, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "489516", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 2) of the matrix A^5 where A is:\n[[-5, 0, -2, 4, -1, 5],\n [0, -5, -2, 4, 1, -4],\n [-2, -2, -6, -1, -2, -2],\n [4, 4, -1, 4, 0, 4],\n [-1, 1, -2, 0, 0, -4],\n [5, -4, -2, 4, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20696", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 3, 0, 1, -2, 2],\n [3, 0, 0, 0, -2, 4],\n [0, 0, 5, 3, 6, 3],\n [1, 0, 3, 4, -4, -3],\n [-2, -2, 6, -4, 5, 0],\n [2, 4, 3, -3, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304880", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, -1, 0, 2, 1, 6],\n [-1, -5, 2, -2, 0, 0],\n [0, 2, 2, -2, 0, -1],\n [2, -2, -2, 0, 2, -2],\n [1, 0, 0, 2, 2, -2],\n [6, 0, -1, -2, -2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3383", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 2, -5, -6, 2, 3],\n [2, -5, 2, -2, -2, -1],\n [-5, 2, -1, -4, 0, -3],\n [-6, -2, -4, -4, 0, 0],\n [2, -2, 0, 0, -3, 1],\n [3, -1, -3, 0, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-755243", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[2, 6, 0, 0, 4, 6],\n [6, -6, 3, 0, 1, 1],\n [0, 3, 2, 4, 2, -2],\n [0, 0, 4, -4, 0, 0],\n [4, 1, 2, 0, 2, 4],\n [6, 1, -2, 0, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1817784", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 2) of the result:\nA =\n[[3, 4, 1, 0, -2, 3],\n [4, -4, 2, 1, 1, 1],\n [1, 2, 6, 0, -4, -3],\n [0, 1, 0, -2, 3, -2],\n [-2, 1, -4, 3, 2, 2],\n [3, 1, -3, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8990", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[-1, -2, -3, -3, 0, -4],\n [-2, -2, -3, 3, 2, 4],\n [-3, -3, 3, -1, 1, 0],\n [-3, 3, -1, -6, 2, 4],\n [0, 2, 1, 2, -5, 0],\n [-4, 4, 0, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -2, -3, 6, -1, -6],\n [-5, -3, -3, 1, 2, 5],\n [-3, -1, -3, -3, 5, 4],\n [5, 2, -3, 6, -1, 6],\n [2, -4, 0, 0, -6, 4],\n [-5, -2, 1, -1, 6, 6]], determine the value at position (6, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7328", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -4, -1, 2, -4, 6],\n [6, 6, -1, 0, -2, 3],\n [6, 1, 1, -1, 0, -4],\n [6, 0, 0, -3, 3, 6],\n [-3, -4, 3, 0, -2, -4],\n [-1, 5, -1, -1, -5, 6]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-106", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 3, 5, 0, 6, 0],\n [3, 5, -3, 4, -1, -3],\n [-3, -1, 2, 5, 6, 0],\n [-5, -1, -2, -1, 6, 1],\n [1, -4, 2, -1, 0, 2],\n [6, 0, 3, 2, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "313683", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, -3, 2, 4, -6, 0],\n [-3, 1, -4, 0, -1, -2],\n [2, -4, 2, 0, -2, -2],\n [4, 0, 0, 3, 1, -2],\n [-6, -1, -2, 1, -6, 5],\n [0, -2, -2, -2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154349", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 6) of the 5th power of the matrix:\n[[5, -4, 0, 0, 3, -3],\n [-4, 5, 0, 6, 0, 0],\n [0, 0, 3, 3, -5, -2],\n [0, 6, 3, 2, -2, 3],\n [3, 0, -5, -2, -1, 1],\n [-3, 0, -2, 3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39771", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, -1, -5, -4, 2, -1],\n [1, 4, -2, -5, 0, -1],\n [4, -5, -1, 6, 1, 6],\n [-6, -3, -6, -5, -6, -1],\n [4, -1, -6, -3, -3, 1],\n [-1, -5, -2, -3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84632", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (6, 4) of the matrix A^4 where A is:\n[[5, 1, -2, -4, 3, 5],\n [-3, -6, -1, 4, 6, 3],\n [-3, -1, -5, -2, 4, 2],\n [1, -4, -6, 3, -4, 1],\n [4, -4, -2, -5, -6, 4],\n [3, -2, -2, -1, -5, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2044", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-5, -5, 5, -2, 2, -3],\n [-1, -5, 6, -3, 5, 2],\n [-5, -6, -3, -3, -6, -3],\n [-4, 6, -5, 6, 3, -3],\n [1, 0, 2, 1, -6, 5],\n [-5, 5, -5, 5, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "113479", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, 2, -5, -3, 6, 6],\n [-6, -4, -1, 2, 4, -6],\n [-2, 5, -5, 0, -3, -2],\n [1, -5, -4, 4, -2, 3],\n [-3, -2, -4, 6, 5, 2],\n [1, -1, -6, -3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439214", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -3, 2, 1, -4, -1],\n [5, 5, -3, 0, -6, -6],\n [5, 5, -1, 3, 4, 6],\n [6, 0, 6, 2, 0, 2],\n [3, 2, 1, 0, 5, -4],\n [4, -4, 4, -2, 0, 6]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-316", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 4, -2, -4, 0, -6],\n [4, 4, 1, -5, 0, -2],\n [-2, 1, 6, -3, 0, 0],\n [-4, -5, -3, 0, 0, 0],\n [0, 0, 0, 0, 2, -2],\n [-6, -2, 0, 0, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13625", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[5, -6, -4, 0, 0, -2],\n [-4, 6, 0, -2, -1, -4],\n [-1, 0, 1, -5, -5, -1],\n [1, -2, -6, 4, -6, 3],\n [2, -3, 5, 3, -6, 4],\n [1, -5, 5, -5, -6, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54620", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 2, -4, 0, 0, 2],\n [2, -2, 0, -2, 0, -2],\n [-4, 0, 3, 2, 3, -2],\n [0, -2, 2, 1, 0, 4],\n [0, 0, 3, 0, -1, 4],\n [2, -2, -2, 4, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204306", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 2, -2, -2, 6, 2],\n [2, 2, 2, 0, -2, -2],\n [-2, 2, -5, -2, -3, 0],\n [-2, 0, -2, -5, 4, -2],\n [6, -2, -3, 4, -6, 4],\n [2, -2, 0, -2, 4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-59798", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 0, -1, 2, -3, 0],\n [0, -4, 2, 0, -2, 3],\n [-1, 2, -2, 0, 5, -3],\n [2, 0, 0, -6, 2, 2],\n [-3, -2, 5, 2, 5, 0],\n [0, 3, -3, 2, 0, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "753088", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -4, 0, 5, 2, 6],\n [4, -1, -2, 0, 4, 2],\n [-2, -2, 3, -3, -2, 0],\n [-4, -3, 2, 5, -5, 1],\n [2, -2, 0, -1, -6, 1],\n [2, 3, 4, -6, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16112", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (6, 3) of the 4th power of the matrix:\n[[5, -1, 3, 1, -2, 1],\n [0, 0, 0, 2, -1, -1],\n [4, 2, -1, 0, 0, -5],\n [6, 5, 1, 5, 4, -1],\n [-3, 4, 6, 0, 1, -6],\n [3, 6, 6, -3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1533", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 6, -1, -3, 6, -6],\n [1, 4, 2, -2, -2, 3],\n [1, 1, -2, -3, -1, 3],\n [-2, 1, 2, 6, -6, 2],\n [6, 2, -1, 4, 3, -2],\n [0, 4, 1, 2, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9608", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, -4, 6, 1, -6, 0],\n [5, -2, 6, 6, -5, -5],\n [1, -2, 5, 4, -4, -6],\n [4, 0, 4, 5, -4, 0],\n [5, -5, -3, -5, -3, -2],\n [1, -5, 3, -4, 3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "245553", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[6, -2, 4, 5, 5, 2],\n [3, 4, -2, 2, -3, 3],\n [-2, 2, -3, -2, -2, -3],\n [-3, 4, -2, 5, -1, 0],\n [-1, -6, -5, 0, -4, 5],\n [3, 4, 6, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15200", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-3, 5, 4, -2, -1, -4],\n [-6, -4, -4, -1, -3, 0],\n [6, 4, -5, 5, -3, 1],\n [4, -1, 3, -4, 3, 5],\n [-5, -4, -6, -6, -5, -4],\n [6, 2, 1, 5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-89882", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[2, 0, 0, -2, 0, -3],\n [-2, 5, -6, 4, -3, -4],\n [-5, -5, 1, -6, 1, 2],\n [-1, -6, 3, 5, 0, -2],\n [2, 0, -2, 6, -5, -3],\n [-5, 2, -5, -5, -5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2698", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 1, -5, -5, -2, 5],\n [6, 5, -3, -5, 1, 1],\n [6, -3, -3, 2, -3, 3],\n [4, 2, -4, -5, 4, 1],\n [5, -4, 6, -5, 6, 4],\n [1, 1, -2, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3366", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[-2, 4, 1, 3, -2, -2],\n [4, 0, 4, 1, 2, -1],\n [1, 4, -6, -2, 0, -2],\n [3, 1, -2, 2, 0, 3],\n [-2, 2, 0, 0, 4, -1],\n [-2, -1, -2, 3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-349", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -2, -3, 1, -1, -2],\n [-2, 1, 4, 2, 0, 0],\n [-3, 4, 1, -2, 1, 6],\n [1, 2, -2, 3, 4, 0],\n [-1, 0, 1, 4, 3, -5],\n [-2, 0, 6, 0, -5, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11619", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, -2, 2, 2, 2, -2],\n [-2, 0, 0, -4, 2, 1],\n [2, 0, -1, -4, -2, 0],\n [2, -4, -4, -1, 4, 0],\n [2, 2, -2, 4, 0, 4],\n [-2, 1, 0, 0, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20399", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[-3, 6, 4, 2, 0, 0],\n [6, 3, 0, 2, 4, -1],\n [4, 0, 6, 4, -3, 2],\n [2, 2, 4, -5, 0, 1],\n [0, 4, -3, 0, 5, -2],\n [0, -1, 2, 1, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3784", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 4, 6, -5, -4, 3],\n [-2, 6, -4, -2, -2, 1],\n [3, 2, 1, 5, -4, -6],\n [-4, -6, 6, 4, 2, 5],\n [6, -4, 1, -1, -4, 2],\n [1, -4, 0, -2, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799771", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-6, -3, 4, 6, 4, 5],\n [6, -3, 6, 3, -2, -3],\n [-6, 0, 3, 4, -5, 3],\n [-4, -2, 1, 3, 1, -5],\n [2, -1, 2, -3, -4, -2],\n [-2, -3, 6, 0, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525866", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 0, 6, 6, 0, 1],\n [5, -3, 3, 6, 6, -1],\n [-2, -6, 6, 2, -5, -1],\n [1, -4, -2, 0, -3, 5],\n [-2, -6, -3, 0, 5, 3],\n [0, 3, 3, -3, 5, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14687", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[6, -2, -6, 1, 5, 0],\n [-2, 6, 3, 3, 0, 3],\n [-4, 1, -2, -5, -5, -3],\n [0, 3, -3, 2, -5, -1],\n [-3, -1, 3, 2, 3, 5],\n [2, 2, 2, -4, 5, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8630", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -4, 3, -4, -2, -1],\n [2, -6, 1, -3, 3, 0],\n [-1, -1, 0, -3, -1, -4],\n [-2, 6, 6, 6, -5, -4],\n [6, 2, -1, -4, -5, -2],\n [3, -2, -6, -4, 0, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3543", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -3, -4, 3, 6, 2],\n [0, 5, 0, 6, 1, 3],\n [-6, 4, -3, 6, 6, -2],\n [-2, -6, -4, -5, 5, 0],\n [6, -2, -4, 4, 1, -6],\n [-6, -1, -6, -3, -1, -6]], determine the value at position (6, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4213", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 4th power of the matrix:\n[[6, 0, -4, 4, 3, 5],\n [0, 6, 2, 6, -4, 2],\n [-4, 2, 3, 4, -3, -3],\n [4, 6, 4, 0, -4, 6],\n [3, -4, -3, -4, 4, 2],\n [5, 2, -3, 6, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9262", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 5, 2, -6, -3, 2],\n [5, -5, -2, 2, 0, 1],\n [2, -2, -4, 0, 3, -2],\n [-6, 2, 0, 4, -4, -6],\n [-3, 0, 3, -4, -6, -3],\n [2, 1, -2, -6, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3496349", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 3, 1, -2, 0, 4],\n [3, 5, 4, -4, -1, 2],\n [1, 4, 1, -3, -2, 2],\n [-2, -4, -3, 4, 1, -2],\n [0, -1, -2, 1, -6, -1],\n [4, 2, 2, -2, -1, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172375", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -3, 3, -2, 1, 2],\n [4, 5, -5, -1, -4, -5],\n [5, 6, -6, -3, 1, -4],\n [-2, 3, -2, -2, 4, 2],\n [1, 1, 6, 6, -6, -6],\n [-5, 1, 3, -6, -3, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105438", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, 0, 1, 2, 2, 2],\n [0, -4, -2, 2, 0, 4],\n [1, -2, 2, 0, 2, 2],\n [2, 2, 0, -2, 0, -2],\n [2, 0, 2, 0, -5, 4],\n [2, 4, 2, -2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4043", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -6, 0, 3, -2, 5],\n [5, 3, -2, 4, 1, 5],\n [-2, -2, -6, -5, -2, 0],\n [-4, 5, -6, 4, 5, -5],\n [-4, 5, 2, 1, -3, 1],\n [6, 2, -4, -1, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87635", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 0, -2, -6, -1, 2],\n [0, -1, -4, -1, 2, -4],\n [-2, -4, 0, 2, 4, 2],\n [-6, -1, 2, 6, 2, 0],\n [-1, 2, 4, 2, 1, 3],\n [2, -4, 2, 0, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1128382", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^5 where A is:\n[[-1, -5, -4, -6, -4, 0],\n [-2, -3, 6, 5, 1, 1],\n [-6, 2, 2, -5, -5, 1],\n [5, 4, -1, -4, 5, -5],\n [-2, 1, -1, 5, -4, 5],\n [5, 2, 1, 3, -1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6293", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, -2, 0, -4, 3, 1],\n [-2, -3, 2, -1, 1, 2],\n [0, 2, 3, 0, -1, 3],\n [-4, -1, 0, 5, -2, -4],\n [3, 1, -1, -2, 6, 0],\n [1, 2, 3, -4, 0, -6]], determine the value at position (3, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8985", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 5th power of the matrix:\n[[6, 5, -4, 0, -3, -5],\n [5, -4, 0, 1, 4, 2],\n [-1, 3, 2, -3, 5, -2],\n [-6, 2, 2, 2, -4, 6],\n [3, 3, 3, 1, -4, 6],\n [-1, -2, 1, -4, -6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15309", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[2, 2, 4, -4, -5, -1],\n [2, -1, 1, -4, -1, -4],\n [4, 1, -2, 4, 2, -4],\n [-4, -4, 4, 4, -6, -4],\n [-5, -1, 2, -6, -3, 0],\n [-1, -4, -4, -4, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2039299", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 6) of the result:\nA =\n[[4, 4, 3, 2, 4, 0],\n [4, 3, -2, -4, -4, 5],\n [3, -2, -6, -5, 2, -2],\n [2, -4, -5, -6, -1, 0],\n [4, -4, 2, -1, 6, 2],\n [0, 5, -2, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44316", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 1) of the 5th power of the matrix:\n[[1, -6, 0, 2, -3, 6],\n [6, 2, -6, 2, -1, -3],\n [5, 5, -2, 0, 3, 6],\n [-3, 1, -4, -5, -6, 6],\n [-1, -5, 1, 4, 3, 6],\n [-3, 2, -3, -3, 6, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43588", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 6) of the result:\nA =\n[[1, 5, 4, 2, 2, 1],\n [5, -5, 1, 0, 0, 4],\n [4, 1, -4, 0, -2, 2],\n [2, 0, 0, 0, 2, 0],\n [2, 0, -2, 2, 0, 2],\n [1, 4, 2, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15196", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[2, 5, -1, -1, -4, 6],\n [-4, -3, -6, -1, -6, 4],\n [-3, 6, 0, 5, -1, 1],\n [-3, 2, 3, 1, -2, -1],\n [-2, -1, -6, -3, 2, -3],\n [-5, -1, -5, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16550", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-6, 2, -2, 3, -2, 2],\n [2, -1, -6, -2, 4, -4],\n [-2, -6, -2, -4, 0, 2],\n [3, -2, -4, 2, -6, 2],\n [-2, 4, 0, -6, -6, -2],\n [2, -4, 2, 2, -2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-276811", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, 1, 2, 3, -4, -2],\n [1, 6, 6, -2, 3, -2],\n [2, 6, -6, 1, 0, -2],\n [3, -2, 1, -3, 0, 0],\n [-4, 3, 0, 0, -3, -4],\n [-2, -2, -2, 0, -4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120522", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, -3, -4, -6, -4, -3],\n [-2, -1, -5, -5, -1, -2],\n [-6, -4, 4, -2, 6, 5],\n [5, -5, -6, 2, -2, -5],\n [3, -3, -4, 0, -6, 3],\n [5, 5, -3, 0, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1039905", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 4) of the result:\nA =\n[[6, -2, -3, -3, 4, 5],\n [-5, 1, 5, -3, -5, 2],\n [6, 5, 3, 6, 0, -4],\n [0, -6, 5, -6, -3, -3],\n [-3, 2, -1, -4, -1, -5],\n [-5, 0, -4, 0, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13791", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, -5, -3, -3, -4, 2],\n [-1, -2, 6, 5, 5, -1],\n [6, 4, 1, -2, 6, 6],\n [-3, 0, 5, -2, -3, -2],\n [4, -3, 1, 1, -6, 5],\n [-4, 4, -3, -5, 6, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-82199", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 3) of the 4th power of the matrix:\n[[4, 1, 5, -5, 2, 6],\n [0, -1, 1, -5, -2, -3],\n [1, 6, -6, 5, -4, 3],\n [1, -2, -3, -1, 5, -2],\n [-4, 6, 4, -2, -3, -6],\n [-6, 0, -3, -6, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-425", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 4, 5, 4, 4, -6],\n [1, 5, 6, 2, 4, -4],\n [0, 6, -2, -4, -2, 3],\n [0, 0, 2, 1, -3, -2],\n [-2, 3, 5, -5, 5, 0],\n [0, 2, 6, 2, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39327", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[0, 2, -2, 5, -2, 2],\n [2, 1, -6, 0, 4, 1],\n [-2, -6, -6, 1, -2, -1],\n [5, 0, 1, 0, -6, 5],\n [-2, 4, -2, -6, 2, 2],\n [2, 1, -1, 5, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28131", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-6, -6, 4, -4, 3, -5],\n [0, -4, 0, 2, 5, 4],\n [-6, -4, 6, 4, -1, 6],\n [2, -2, -4, 1, 6, 5],\n [-2, -1, 6, -5, -3, -6],\n [6, -3, -6, -3, -5, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16866", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, -2, 2, -2, -6, 2],\n [-2, -1, -6, 2, 0, 0],\n [2, -6, -1, -1, 0, -2],\n [-2, 2, -1, -3, -2, -2],\n [-6, 0, 0, -2, 6, -5],\n [2, 0, -2, -2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "988142", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 2, 1, -6, 4, 0],\n [6, 3, -4, 3, 6, 3],\n [2, -2, 4, -4, 1, 5],\n [-4, 0, 0, 0, 5, -6],\n [4, -2, 5, 4, -6, 0],\n [6, 6, 1, 0, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2151222", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -2, 2, 0, 5, -2],\n [-2, 5, 1, -2, 0, -2],\n [2, 1, -4, 5, 0, 1],\n [0, -2, 5, -5, 2, -2],\n [5, 0, 0, 2, -3, 0],\n [-2, -2, 1, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97868", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -3, 2, -2, 3, -5],\n [3, -6, 0, 4, -6, 1],\n [2, 0, 2, 3, -1, 0],\n [-4, 2, -4, -1, -3, 2],\n [-6, 2, 5, -3, 3, -2],\n [4, 6, -6, -6, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "252060", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[6, -3, 4, -6, 5, 0],\n [-3, -5, 0, 2, 5, 6],\n [4, 0, 5, 2, 4, -2],\n [-6, 2, 2, 5, -2, 2],\n [5, 5, 4, -2, 5, -2],\n [0, 6, -2, 2, -2, -6]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "198317", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 6, -1, -1, 5, -6],\n [0, 1, 5, -2, -5, -5],\n [4, -2, 0, 0, 6, -3],\n [4, -4, 2, 5, 0, -5],\n [-6, 4, -5, 6, 5, -4],\n [-2, -4, 3, 2, 3, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "793122", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, -3, -4, 3, -6, 5],\n [2, 6, 4, -6, 4, 6],\n [-6, -6, -2, 0, 0, 3],\n [-6, -1, 2, -1, -3, 3],\n [2, 6, -4, 6, 3, -3],\n [-3, -3, -1, 6, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174830", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 6) of the 5th power of the matrix:\n[[0, 2, 4, -4, 1, 1],\n [-6, -2, 6, 3, -2, 5],\n [1, 1, 5, -5, -4, -5],\n [-6, -5, 3, -1, 5, -6],\n [-1, -6, -5, 1, -1, 2],\n [-6, -2, 0, 2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16823", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 2, -2, 0, 1, 2],\n [2, 0, 0, 2, -2, -2],\n [-2, 0, -5, -2, 0, -2],\n [0, 2, -2, 3, 0, -2],\n [1, -2, 0, 0, 0, -2],\n [2, -2, -2, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116135", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 2, -1, 0, 4, 2],\n [2, -2, -1, -2, 1, 1],\n [-1, -1, 5, -3, -3, 1],\n [0, -2, -3, 0, 0, 3],\n [4, 1, -3, 0, -1, 4],\n [2, 1, 1, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34579", "dataset": "MATH"}