{"messages": [{"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[1, -2, 5, 2, -1],\n [1, 4, -3, 1, 5],\n [5, 2, -1, -2, 2],\n [2, -3, 0, -1, -4],\n [2, 0, -4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-169", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 0, 3, -5, 5],\n [5, 4, -3, 1, -2],\n [3, -3, -1, -3, 1],\n [-1, 3, 1, -4, -2],\n [3, -4, 4, 3, 4]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-146", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, -4, -2, 1, 2],\n [-3, -5, -2, -4, 2],\n [-2, -4, 0, 0, 4],\n [-2, 0, -4, 4, -4],\n [4, -2, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17280", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -1, -4, -1, 2],\n [4, 3, 3, -5, 3],\n [1, 3, 2, -5, 2],\n [2, 5, -3, -5, 2],\n [-3, -3, -5, 5, -1]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-381", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[4, 1, 4, 3, 1],\n [3, 2, -4, -5, 1],\n [1, 2, -1, -3, 2],\n [0, 5, -3, -5, -3],\n [-1, -3, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1417", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 2, 2, 0, 0],\n [2, -3, 0, -2, 1],\n [2, 0, 1, 3, 4],\n [0, -2, 3, -3, 0],\n [0, 1, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40506", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 5, 4, 1, 3],\n [1, -5, -5, 3, 5],\n [3, -2, 3, -3, 1],\n [0, 2, 5, 3, -1],\n [-5, -3, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16426", "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, -4, -2],\n [-2, 4, -4, 3, -2],\n [0, -4, -1, -5, 0],\n [-4, 3, -5, -4, -4],\n [-2, -2, 0, -4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87766", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[-3, -2, 2, 1, -2],\n [-2, -2, -2, 0, 2],\n [2, -2, 0, 1, 2],\n [1, 0, 1, 0, 2],\n [-2, 2, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-328", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 5) of the matrix A^4 where A is:\n[[-2, 1, 0, 0, 0],\n [1, -3, -4, -2, 0],\n [0, -4, 2, 3, 0],\n [0, -2, 3, 3, 0],\n [0, 0, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 3, -2, -5, -4],\n [-5, -1, -1, 5, 1],\n [3, 3, -3, -3, -3],\n [-2, 2, 0, 2, -5],\n [2, -2, 5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-181", "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, -4, 0],\n [2, -3, 2, -3, -1],\n [-1, 2, -3, -1, 0],\n [-4, -3, -1, -1, -2],\n [0, -1, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11824", "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, 0, -2, -1],\n [2, 0, 2, -4, -2],\n [0, 2, 5, -2, -3],\n [-2, -4, -2, -3, -2],\n [-1, -2, -3, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "186277", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, 3, -1, 2, -5],\n [-1, -3, -5, -2, -1],\n [1, -5, -3, -4, 3],\n [4, 0, 4, -3, 2],\n [2, -4, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231834", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 5) of the 4th power of the matrix:\n[[5, 3, -2, 0, -1],\n [3, -5, 4, 4, -1],\n [-2, 4, 1, 3, -2],\n [0, 4, 3, 4, -2],\n [-1, -1, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1362", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-3, 1, -4, -4, 1],\n [0, -3, 3, 4, 0],\n [4, 4, 0, -5, -2],\n [4, 0, 0, 5, -1],\n [-5, 2, -1, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21726", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 0, -2, -3, 1],\n [2, -2, -4, 4, -3],\n [-5, 2, -3, 4, 1],\n [4, -1, 4, -1, 1],\n [3, -1, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15268", "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, 0, 3, 2],\n [-1, -5, 1, -1, 0],\n [1, -3, 4, -3, -1],\n [0, 3, -1, -5, -2],\n [-1, 4, 4, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104234", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -5, -1, 1, 4],\n [4, 0, -1, -2, -4],\n [-2, 4, 4, -3, 4],\n [-5, 2, -1, -2, 2],\n [1, -4, -5, 5, -2]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-118", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, -4, -4, -4, 0],\n [-4, 5, 0, -4, -2],\n [-4, 0, 4, 1, 0],\n [-4, -4, 1, 1, 0],\n [0, -2, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17198", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 5) of the matrix A^4 where A is:\n[[-4, -3, 3, 1, -2],\n [4, -1, -4, 5, 2],\n [-2, 3, -1, 3, -2],\n [4, -1, 3, 2, -3],\n [-5, -3, -2, -4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1310", "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, -4],\n [2, 1, -1, -3, 3],\n [-2, -1, -2, -1, 0],\n [2, -3, -1, -2, 0],\n [-4, 3, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129051", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, -1, -1, -3, 3],\n [-2, 5, -1, -2, -1],\n [1, 3, 1, -1, 4],\n [4, 1, 4, -1, -3],\n [1, 5, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27395", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (2, 4) of the result:\nA =\n[[4, 4, -5, 0, 1],\n [2, 4, 3, -4, 5],\n [4, -4, -1, -1, 0],\n [-3, 2, -5, 0, -2],\n [-5, 1, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 5) of the matrix A^5 where A is:\n[[0, 0, -2, 1, 4],\n [0, 4, 0, -2, 0],\n [-2, 0, -2, 0, -1],\n [1, -2, 0, 3, -2],\n [4, 0, -1, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1722", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^4 where A is:\n[[0, 4, -1, 0, -1],\n [5, -1, -2, -3, -3],\n [-2, 3, -4, 3, -5],\n [-5, -1, 0, 0, -3],\n [1, 3, 5, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 2, -1, 2, 4],\n [-2, 4, 2, 4, -4],\n [-1, 3, -2, 5, 0],\n [-5, 3, -5, -1, -2],\n [-3, 0, -4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162635", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the 4th power of the matrix:\n[[3, 0, 2, 0, 0],\n [0, -1, -2, 3, -5],\n [2, -2, -4, -1, 0],\n [0, 3, -1, 0, 0],\n [0, -5, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the 5th power of the matrix:\n[[-3, -5, -1, 1, 0],\n [-5, -1, -1, 0, -3],\n [-1, 1, -1, -1, -1],\n [4, 4, -3, -5, -1],\n [3, -5, -3, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12637", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, 2, -4, 2, 1],\n [4, 4, -4, 0, 0],\n [-3, 5, -4, -5, 0],\n [-1, 5, 3, -5, 1],\n [-1, -1, -4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33319", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[1, -2, -3, 0, -3],\n [-2, -4, 4, 0, 0],\n [-3, 4, 0, -4, 2],\n [0, 0, -4, -5, -3],\n [-3, 0, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39824", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, -1, 4, 2, -3],\n [-1, -1, -4, 2, 4],\n [4, -4, 3, 2, 2],\n [2, 2, 2, -2, 0],\n [-3, 4, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11634", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, -4, 4, -3, -3],\n [-1, -1, -4, 4, 0],\n [-1, 0, -5, -1, 3],\n [4, -4, -5, 4, 5],\n [3, 4, 3, 3, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3849", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 5, -5, 4, -2],\n [-5, 2, -5, -3, -2],\n [2, 0, 4, 1, 2],\n [-4, 4, 5, 2, -3],\n [1, -3, 1, 5, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3766", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 5th power of the matrix:\n[[4, 0, -3, -3, 3],\n [1, -1, 4, 1, 3],\n [-5, 1, 0, 4, 3],\n [-5, -2, 3, -2, 4],\n [-3, 3, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1028", "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, 2, -5, -3],\n [4, 3, -1, 0, -2],\n [4, -4, 5, 2, 5],\n [0, -1, 3, -5, -1],\n [0, -1, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176518", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 3, 0, 3, 2],\n [3, -3, 0, 0, 0],\n [0, 0, 0, -2, -2],\n [3, 0, -2, 0, -1],\n [2, 0, -2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23648", "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, -3, -1],\n [0, 4, 0, -2, -3],\n [-2, -5, -2, -5, -5],\n [4, 0, -1, 5, -2],\n [5, -3, -5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47886", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 4, -1, 1, 4],\n [-4, 2, -4, -2, -5],\n [-1, 3, -5, 3, 5],\n [2, 0, 1, -3, -5],\n [-1, -4, -1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1735", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, -4, -3, -3, -5],\n [2, 0, 2, 5, 3],\n [-1, -3, -1, -1, -1],\n [-3, 5, 4, -2, 3],\n [4, 3, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3467", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 2, -1, -2, -4],\n [2, -5, 0, -2, -2],\n [-1, 0, -1, 0, 0],\n [-2, -2, 0, 0, 1],\n [-4, -2, 0, 1, 4]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-102", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -5, -2, 1, 5],\n [-2, 0, 3, -5, -1],\n [5, 1, -5, -2, 0],\n [-4, 4, -1, 5, 4],\n [-5, 0, 0, -2, 2]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, 2, 2, -1, -2],\n [-4, 5, -3, -3, -2],\n [-2, 4, 5, 5, -1],\n [-2, 5, 4, 2, 0],\n [0, 2, 1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275262", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 2, -4, 3, -5],\n [2, 5, -2, -2, -1],\n [2, -1, 2, 4, -5],\n [4, 3, 0, -3, 2],\n [3, 0, 5, 1, -5]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-53", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 1) of the result:\nA =\n[[-1, 0, 0, 0, 2],\n [0, 3, -2, 2, 2],\n [0, -2, -1, 0, -2],\n [0, 2, 0, 3, -2],\n [2, 2, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "375", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 0, 2, -1, 0],\n [0, 5, 0, 4, -2],\n [2, 0, 5, -1, -2],\n [-1, 4, -1, -2, -2],\n [0, -2, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29756", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 4, -4, -1, -5],\n [1, -5, -2, 3, -5],\n [-2, 0, 0, 2, -5],\n [1, -5, 1, -3, 5],\n [2, -3, -5, 2, -3]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "722", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, -5, -3, -4, -4],\n [0, -5, -4, 0, -3],\n [-2, -5, 2, 1, 1],\n [-3, 4, 4, -3, -4],\n [-5, 1, 1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548900", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 1) of the result:\nA =\n[[2, -5, 3, 1, -3],\n [2, 1, 5, 2, 0],\n [3, -1, -3, -3, -5],\n [2, -4, -3, 2, 2],\n [5, -2, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4447", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, 1, -4, 1, 4],\n [1, -5, 1, -1, -3],\n [-3, -2, -4, -4, -5],\n [-1, -2, 5, 4, -4],\n [-3, 1, 1, -2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1708", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -2, -1, -4, 0],\n [-2, -2, 4, -2, -1],\n [-1, 4, 2, 1, 2],\n [-4, -2, 1, -5, 2],\n [0, -1, 2, 2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-103429", "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, 0, 5, -2, 4],\n [4, -4, 1, -1, 5],\n [0, -4, -1, 4, -2],\n [3, 0, -4, -5, -1],\n [3, 0, 4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12635", "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, -1, 2, -1],\n [0, 5, 2, 0, 0],\n [-1, 2, 4, -4, 2],\n [2, 0, -4, 0, 2],\n [-1, 0, 2, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165721", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, -2, 1, 1, 4],\n [-2, -5, 2, 0, 0],\n [1, 2, -4, 0, 0],\n [1, 0, 0, 2, -4],\n [4, 0, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1440", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 0, -1, 4, 3],\n [0, 3, 4, 0, -2],\n [-1, 4, 2, -2, -4],\n [4, 0, -2, 4, 0],\n [3, -2, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2574", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 2, 0, 0, 0],\n [2, 5, -2, -3, 2],\n [0, -2, -5, -2, 0],\n [0, -3, -2, 1, 1],\n [0, 2, 0, 1, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3904", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[3, 5, 4, 3, 4],\n [4, 1, -5, 1, 4],\n [-1, 0, 4, 1, -1],\n [1, 3, -3, 2, -4],\n [5, 1, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3154", "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, -4, 5, 4, 1],\n [-5, 2, -3, -4, -3],\n [-1, 5, 2, 4, 1],\n [1, 1, 2, -5, -2],\n [0, 3, -4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21109", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-4, 1, -3, 4, -4],\n [5, 1, -4, -3, 5],\n [1, -2, -5, -1, 3],\n [2, 3, 4, 3, 1],\n [-2, -1, -5, -5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[2, 0, 0, -2, 0],\n [0, -5, 0, 1, -2],\n [0, 0, -2, 5, 4],\n [-2, 1, 5, 0, -2],\n [0, -2, 4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-199", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 4) of the matrix A^4 where A is:\n[[1, -2, 2, 0, 0],\n [-2, 0, -2, 0, 2],\n [2, -2, 3, 0, 2],\n [0, 0, 0, 2, 0],\n [0, 2, 2, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "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, -3, -2, 4, -5],\n [5, 4, -3, -4, -4],\n [-5, 2, -3, -3, 0],\n [2, 3, 3, -2, -1],\n [-4, 5, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21955", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[5, 3, -3, 3, -4],\n [4, 3, 2, 3, -1],\n [5, 5, -4, 2, 0],\n [2, 5, -1, 4, -4],\n [0, -1, -1, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4089", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, -3, 4, -3, 2],\n [2, -4, 2, 5, -5],\n [0, 2, -3, 2, -5],\n [5, 5, 3, 5, 3],\n [-1, 4, -2, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19722", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 5) of the result:\nA =\n[[1, -1, 5, 4, 3],\n [-3, 1, 4, 4, 5],\n [-1, 1, -4, -2, -4],\n [1, -4, 5, -5, 3],\n [-5, 2, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2678", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -4, 0, 2, 2],\n [-4, -1, -2, -4, 1],\n [0, -2, -2, 4, -2],\n [2, -4, 4, 0, 0],\n [2, 1, -2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3957", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 2) of the matrix A^4 where A is:\n[[-4, -2, 5, -3, -2],\n [1, 5, -5, 0, -3],\n [5, 4, 1, 4, -4],\n [-4, -2, -5, -3, 3],\n [1, 1, 5, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-186", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[-2, -2, 2, 1, -4],\n [-2, 2, 0, 2, 1],\n [2, 0, -3, -1, -3],\n [1, 2, -1, 4, 2],\n [-4, 1, -3, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-498", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, 2, 2, 0, -4],\n [2, 2, 1, -3, -2],\n [2, 1, -1, 2, 4],\n [0, -3, 2, 1, -2],\n [-4, -2, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31389", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[0, 1, -1, 1, 0],\n [1, 2, 0, -5, 1],\n [-1, 0, -4, 0, 1],\n [1, -5, 0, 3, 2],\n [0, 1, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2895", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -1, -2, -1, -1],\n [-1, 4, -2, 0, -2],\n [-2, -2, -5, 2, 0],\n [-1, 0, 2, 1, 0],\n [-1, -2, 0, 0, -4]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "412", "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, 2],\n [4, -3, 4, 1, 4],\n [0, 4, 1, 0, -3],\n [-2, 1, 0, -2, 2],\n [2, 4, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4950", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 0, 4, -3, 3],\n [4, 5, -4, 0, 1],\n [3, -3, 4, -3, 1],\n [-2, 2, 1, -1, 1],\n [-3, -4, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20031", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -2, -2, 2, 4],\n [-2, 4, -1, -2, -2],\n [-2, -1, -5, -1, 0],\n [2, -2, -1, -2, -2],\n [4, -2, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4704", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 0, 2, -4, -2],\n [0, -4, -2, -2, 2],\n [2, -2, -3, 3, 1],\n [-4, -2, 3, -1, -4],\n [-2, 2, 1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38211", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -4, 1, -1, -1],\n [0, 3, 0, 2, 1],\n [3, -2, -4, 1, 0],\n [-5, 5, 3, 3, -4],\n [-3, -1, -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": "24451", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -2, 1, 5, 4],\n [-3, 0, 4, 4, 3],\n [-5, -1, -2, 2, 5],\n [-5, 3, 0, -2, 3],\n [5, -1, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 0, 0, 0, 0],\n [0, -4, 0, 1, -3],\n [0, 0, -5, 0, -3],\n [0, 1, 0, 5, 2],\n [0, -3, -3, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11873", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, -4, 2, 2, 3],\n [-4, 3, 0, 2, 2],\n [2, 0, -4, 0, -2],\n [2, 2, 0, -4, 2],\n [3, 2, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30377", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 2, 0, -1, 0],\n [-4, -5, 1, 1, 4],\n [5, 4, -4, -4, -5],\n [4, 2, 2, -5, 5],\n [2, 3, -2, -5, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13843", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -1, -1, 3, 4],\n [-4, -4, 0, 3, -5],\n [3, 3, 3, -1, 3],\n [5, -2, -4, 0, -2],\n [0, -3, 0, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26783", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, 2, -4, 4, -2],\n [2, 0, 2, -1, 2],\n [-4, 2, 1, -3, 1],\n [4, -1, -3, -5, -3],\n [-2, 2, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4187", "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, -3, -1],\n [4, 2, -4, 0, -1],\n [4, 3, -1, -4, -1],\n [-2, 5, 1, 0, -4],\n [5, 5, -1, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127712", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, -1, 3, -2, 5],\n [-3, -2, -1, 0, -3],\n [-4, -2, -1, -2, 5],\n [-3, 2, 4, -2, -4],\n [-4, -5, -2, 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": "60306", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 2, 1, 0, 1],\n [2, -5, 1, 0, 1],\n [1, 1, -2, 1, 0],\n [0, 0, 1, 4, 2],\n [1, 1, 0, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5110", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, 4, 3, 4, 2],\n [4, 3, 4, 2, 2],\n [-5, 4, 5, -1, -2],\n [-4, 2, -3, -2, 1],\n [4, 3, -4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88816", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[4, -5, 0, -2, 1],\n [-5, -3, -4, 0, -2],\n [0, -4, 0, 2, -3],\n [-2, 0, 2, 3, 2],\n [1, -2, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2608", "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, 0, 0],\n [0, -5, 2, 0, 0],\n [0, 2, 4, 1, 4],\n [0, 0, 1, -1, -2],\n [0, 0, 4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10903", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 2) of the matrix A^4 where A is:\n[[5, -2, 2, 0, -3],\n [-2, -4, 0, 4, 0],\n [2, 0, 2, -4, -4],\n [0, 4, -4, 0, 0],\n [-3, 0, -4, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 5) of the matrix A^4 where A is:\n[[-3, -2, 1, 0, 2],\n [-2, 4, 1, -2, 2],\n [1, 1, 3, -1, -3],\n [0, -2, -1, 1, -2],\n [2, 2, -3, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-333", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 4) of the matrix A^5 where A is:\n[[2, -5, 3, -1, -2],\n [0, 0, -4, 2, 1],\n [-5, -1, 0, -2, -4],\n [-2, -5, 1, -4, -4],\n [3, -1, -4, 5, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, -2, 2, -2, -1],\n [-2, 4, -2, -3, -2],\n [2, -2, 0, 4, -2],\n [-2, -3, 4, -5, 3],\n [-1, -2, -2, 3, 4]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16319", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -2, -1, 0, 0],\n [-2, -3, -4, 0, -4],\n [-1, -4, -2, 0, 2],\n [0, 0, 0, 0, -4],\n [0, -4, 2, -4, -3]], determine the value at position (5, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "608", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, 3, 0, 3, -1],\n [-4, 2, -1, -4, -2],\n [3, -2, -2, -4, 0],\n [5, -4, 1, -3, -3],\n [-1, -3, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107166", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 3, 0, 0, 2],\n [3, -3, 0, -1, -2],\n [0, 0, 1, -2, -2],\n [0, -1, -2, -5, -2],\n [2, -2, -2, -2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205156", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[1, -2, 0, -2, -1],\n [-2, 5, 0, 0, 2],\n [0, 0, 1, -2, 4],\n [-2, 0, -2, -1, 2],\n [-1, 2, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, -1, 0, -2, -2],\n [-1, -4, -3, -2, -4],\n [0, -3, 5, 2, 0],\n [-2, -2, 2, -2, -4],\n [-2, -4, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-343701", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, -2, 4, -2, 2],\n [-2, 3, -5, 3, 0],\n [4, -5, -4, -2, 3],\n [-2, 3, -2, -1, 5],\n [2, 0, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5414", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -5, -5, 1, 2],\n [-3, -1, -5, 1, -1],\n [2, 2, 3, 1, 5],\n [-5, -3, 2, -3, 2],\n [-5, -1, -2, -1, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2573", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, -2, 5, -2, -3],\n [1, -3, -3, 5, 4],\n [-1, -1, 0, 2, 4],\n [0, -5, 2, 2, 3],\n [3, -4, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "195664", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, 1, 0, 1, 2],\n [1, 1, 0, 0, -2],\n [0, 0, 2, 0, 0],\n [1, 0, 0, 4, -1],\n [2, -2, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10264", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 5, 4, 3, -4],\n [0, -2, -2, -1, -3],\n [-5, 2, -1, -3, 4],\n [1, 1, -5, 3, -4],\n [-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": "1406", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[1, 5, 0, 0, 5],\n [3, 0, -4, -4, -1],\n [-2, 5, -4, -3, 1],\n [2, 0, 5, -1, -5],\n [2, -3, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "902", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 3, -1, 2, 4],\n [4, 2, -5, -1, -3],\n [-5, -2, 2, -3, 4],\n [-4, 5, 3, 4, -1],\n [1, 5, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27947", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 1, -3, -2, 2],\n [1, 4, 0, -2, 4],\n [-3, 0, 3, -1, 2],\n [-2, -2, -1, 2, -2],\n [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": "194362", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 4) of the matrix A^4 where A is:\n[[4, 0, 0, 0, 1],\n [0, 0, -1, -1, 0],\n [0, -1, 4, -2, 0],\n [0, -1, -2, 1, 0],\n [1, 0, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 2) of the matrix A^5 where A is:\n[[1, -2, -2, 2, 2],\n [-4, -4, -3, -3, -5],\n [-3, 0, 2, 4, 0],\n [-1, -2, -3, -2, 1],\n [-5, 1, -5, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2685", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[-5, 2, 2, 4, 4],\n [2, -5, 0, 2, -3],\n [2, 0, 0, 2, -1],\n [4, 2, 2, 3, 2],\n [4, -3, -1, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1395", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the 5th power of the matrix:\n[[0, 0, -4, 2, 0],\n [0, -3, 2, 0, 1],\n [-4, 2, -1, -2, -2],\n [2, 0, -2, -2, 0],\n [0, 1, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1896", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 2) of the result:\nA =\n[[-3, -5, 2, 3, -2],\n [0, 3, 0, 3, -2],\n [2, 3, -2, -1, 2],\n [4, 0, 1, -3, 1],\n [2, 4, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-740", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 0, -2, 2, 2],\n [0, -4, 1, 2, 2],\n [-2, 1, -4, -4, 3],\n [2, 2, -4, 2, 2],\n [2, 2, 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": "137064", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 0, 4, -2, 0],\n [0, -4, -1, 0, -2],\n [4, -1, 2, -3, -2],\n [-2, 0, -3, 3, 0],\n [0, -2, -2, 0, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3457", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 4) of the result:\nA =\n[[3, -2, 2, -2, 0],\n [-2, 2, -2, 2, 2],\n [2, -2, 0, -2, -3],\n [-2, 2, -2, -4, -4],\n [0, 2, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2808", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, -2, 4, -2, -2],\n [-2, 0, 3, 0, 0],\n [4, 3, -3, -2, -2],\n [-2, 0, -2, 4, 0],\n [-2, 0, -2, 0, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140637", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, -2, 5, 3, 2],\n [4, 4, -5, -4, 3],\n [2, -3, 2, -5, 4],\n [-2, -3, 0, 1, -2],\n [1, 3, 5, -4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "254998", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 2, -2, 4, -1],\n [2, 2, 0, 0, 0],\n [-2, 0, 2, 2, 0],\n [4, 0, 2, -2, -2],\n [-1, 0, 0, -2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-368", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 4) of the 5th power of the matrix:\n[[-4, 0, 0, 2, -3],\n [0, 1, 0, 2, 2],\n [0, 0, 0, 0, -4],\n [2, 2, 0, -5, 0],\n [-3, 2, -4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1946", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 1) of the result:\nA =\n[[4, 5, 1, 5, -1],\n [3, -3, -5, -2, 3],\n [-2, -4, 4, -1, -3],\n [3, -2, 0, -4, 0],\n [-3, 3, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16799", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 3, -2, -2, -1],\n [3, -1, 0, 0, -2],\n [-2, 0, -2, 0, -1],\n [-2, 0, 0, 5, 1],\n [-1, -2, -1, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10726", "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, -5, -2, -4],\n [-4, -3, 2, 2, 1],\n [0, 3, -2, -5, 2],\n [1, 1, -3, -2, 4],\n [3, 0, -1, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56909", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, -1, -2, -2, -5],\n [1, 3, -3, -4, -3],\n [-5, 0, 5, 5, 1],\n [5, 5, -4, 2, 0],\n [-2, -1, 2, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142288", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, 0, -1, 0, 4],\n [0, 4, -2, 2, 0],\n [-1, -2, -3, -2, 4],\n [0, 2, -2, 1, 0],\n [4, 0, 4, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128669", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[2, 0, -1, -2, 2],\n [-5, 3, -5, 2, -2],\n [3, 5, -1, -3, 3],\n [5, 3, -2, 5, -2],\n [2, -4, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10110", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[2, -2, -3, 0, 4],\n [-2, -1, -2, -2, -4],\n [-3, -2, -5, -2, 2],\n [0, -2, -2, -5, -2],\n [4, -4, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2002", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 3, -3, 4, -2],\n [0, 2, -1, -3, 0],\n [-2, 3, -3, -2, 1],\n [1, -2, 0, -3, 0],\n [-4, 2, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-823", "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, 1, 0],\n [0, 0, 3, -4, -5],\n [0, 4, 5, 2, -3],\n [4, -5, 3, -5, -3],\n [2, -3, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34433", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 3) of the 5th power of the matrix:\n[[0, -5, -5, 2, 5],\n [-2, -5, 4, 1, -1],\n [-1, -5, 4, 5, 0],\n [3, 3, 2, -1, -5],\n [3, -5, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2847", "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, 1, 3, 1],\n [5, -3, 5, -5, 2],\n [-3, 2, 2, -1, -5],\n [4, 1, 4, -1, 2],\n [3, 5, 1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41186", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-2, -4, -4, -4, -2],\n [-5, -2, -4, -1, -3],\n [2, -2, -5, -5, 4],\n [-3, 3, 1, -4, 3],\n [4, -4, -3, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5521", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -3, 0, 3, 3],\n [1, -3, -2, 0, 5],\n [-1, -4, 0, -3, 2],\n [-4, -5, 3, -3, 5],\n [-5, 1, 4, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3075", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 3, 1, 2, 3],\n [0, -1, 0, 5, -4],\n [-2, -3, 1, 3, -1],\n [0, 4, -4, -3, -3],\n [3, 1, 2, 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": "11252", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 2, 0, -4, -4],\n [2, 1, -3, 0, 2],\n [0, -3, -1, 0, 0],\n [-4, 0, 0, 4, 0],\n [-4, 2, 0, 0, -5]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-450", "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, -3, 4, 0],\n [-1, 2, -2, -4, -1],\n [-3, -2, -1, 4, 4],\n [4, -4, 4, -2, 4],\n [0, -1, 4, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73410", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 0, 0, 0, -3],\n [0, -1, 0, 1, 2],\n [0, 0, 1, -2, -2],\n [0, 1, -2, 5, -2],\n [-3, 2, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7481", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 0, -4, 0, -3],\n [0, 1, -3, 1, 3],\n [-4, -3, 4, -2, -2],\n [0, 1, -2, -2, -4],\n [-3, 3, -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": "306569", "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, -2, -4],\n [0, 0, 1, -2, 4],\n [-4, 1, 1, -1, 0],\n [-2, -2, -1, -2, -2],\n [-4, 4, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11592", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 0, 1, -2, 4],\n [0, -1, 0, 3, -2],\n [1, 0, 0, -4, -2],\n [-2, 3, -4, 0, 3],\n [4, -2, -2, 3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8358", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, -1, 5, 1, -1],\n [-1, -4, -4, 0, -3],\n [5, -4, -3, 0, -2],\n [1, 0, 0, -2, -2],\n [-1, -3, -2, -2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-248889", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -4, 2, 1, -1],\n [-4, 0, 2, 4, -3],\n [2, 2, 4, -2, -4],\n [1, 4, -2, 2, 2],\n [-1, -3, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34894", "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, 0, -2, -1],\n [-2, -2, 2, -2, -1],\n [0, 2, 2, -2, 0],\n [-2, -2, -2, -4, 0],\n [-1, -1, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117352", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[5, -3, -2, -4, -2],\n [-3, 5, 0, -4, 0],\n [-2, 0, -4, 4, 1],\n [-4, -4, 4, 2, -2],\n [-2, 0, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1104", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 3, 0, 2, 2],\n [3, -5, -4, 2, 2],\n [0, -4, -1, -4, 0],\n [2, 2, -4, 1, 2],\n [2, 2, 0, 2, 0]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2742", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -2, -2, -4, -4],\n [-2, 2, 1, 0, 4],\n [-2, 1, -4, -2, -4],\n [-4, 0, -2, 5, 4],\n [-4, 4, -4, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38803", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 3) of the matrix A^5 where A is:\n[[-4, 0, 0, -5, 1],\n [2, -4, 2, 3, 0],\n [-1, 3, 5, 3, -5],\n [5, -3, 3, 5, -4],\n [-2, -2, -4, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14120", "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, 4, -1, -3],\n [-2, 4, 2, 2, -2],\n [4, 2, 2, 0, 4],\n [-1, 2, 0, 5, -3],\n [-3, -2, 4, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "561000", "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, -2, -2],\n [0, -1, 2, -1, -2],\n [0, 2, 3, -1, -4],\n [-2, -1, -1, 3, 0],\n [-2, -2, -4, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212487", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 0, 1, 0, 0],\n [0, -2, 2, -2, -1],\n [1, 2, 1, -2, -3],\n [0, -2, -2, 2, 0],\n [0, -1, -3, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[-3, 4, -2, -1, 0],\n [4, -1, 0, 4, -3],\n [-2, 0, -4, -2, -2],\n [-1, 4, -2, 3, -2],\n [0, -3, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-833", "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, 4, 4],\n [0, -5, -2, 1, -5],\n [2, 4, 5, 0, -1],\n [4, 5, 3, -4, -1],\n [0, 1, -1, 3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153921", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 4, 1, -2, 3],\n [5, -1, -2, 1, -2],\n [-3, 3, 5, 2, -5],\n [1, 3, 2, 2, 0],\n [5, -2, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13991", "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, 2, 4, 1],\n [0, 2, 0, -2, 1],\n [2, 0, -4, 5, 2],\n [4, -2, 5, 4, 2],\n [1, 1, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35974", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, -3, 5, -1, 2],\n [2, -2, 5, 5, -5],\n [-5, -2, 0, 2, 0],\n [3, 3, -4, 4, -5],\n [-4, -1, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16650", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[5, 1, 0, 0, -4],\n [1, 5, -2, 0, -3],\n [0, -2, 0, 0, 0],\n [0, 0, 0, 2, 0],\n [-4, -3, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 4, 0, -2, 0],\n [4, 4, 0, 2, -2],\n [0, 0, -3, -2, 3],\n [-2, 2, -2, 4, -2],\n [0, -2, 3, -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": "128656", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 3, -3, -3, 0],\n [3, 2, 4, 2, -2],\n [-3, 4, 1, -4, 4],\n [-3, 2, -4, 0, -1],\n [0, -2, 4, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5969", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 4, 0, 3, 2],\n [4, -4, 0, 0, 5],\n [0, 0, 5, 3, -4],\n [3, 0, 3, 0, 0],\n [2, 5, -4, 0, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14622", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the 4th power of the matrix:\n[[3, 0, -2, -2, -2],\n [0, -1, 1, -2, -5],\n [-2, 1, 4, -3, -4],\n [-2, -2, -3, 5, -4],\n [-2, -5, -4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "584", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 2, 1, 2, 3],\n [2, 5, -1, 3, -2],\n [1, -1, -5, -1, -2],\n [2, 3, -1, -1, 1],\n [3, -2, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17779", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, 1, 2, 3],\n [0, 2, 2, 1, -2],\n [1, 2, -2, -4, 1],\n [2, 1, -4, 1, 0],\n [3, -2, 1, 0, -1]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "637", "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, 0, 3, 0],\n [-2, -4, 0, 0, 2],\n [0, 0, -4, 2, -1],\n [3, 0, 2, -2, 2],\n [0, 2, -1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116470", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[0, 0, -1, 3, 4],\n [2, 1, 1, 0, -1],\n [-2, -3, -3, 0, -2],\n [0, -3, -2, 3, -1],\n [1, 4, -4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[5, -3, 3, 5, 0],\n [-2, 1, 2, 0, -1],\n [0, -1, 2, -5, 5],\n [1, 4, 4, 5, -4],\n [3, -5, 5, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8028", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -5, -2, -2, 3],\n [5, -1, -1, 0, -5],\n [-5, 3, -3, -2, -5],\n [3, 2, -4, 2, 1],\n [5, 0, -5, 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": "55342", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 3, -4, -2, 2],\n [3, 3, 0, -2, -2],\n [-4, 0, -3, -5, -4],\n [-2, -2, -5, -3, 0],\n [2, -2, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-450851", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 1) of the 5th power of the matrix:\n[[5, -4, 1, -2, 2],\n [-4, -4, -1, 0, 4],\n [1, -1, 0, 0, -2],\n [-2, 0, 0, -1, -2],\n [2, 4, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2818", "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, 2, 2],\n [2, -2, -1, -1, 0],\n [2, -1, 3, 0, 0],\n [2, -1, 0, -3, -4],\n [2, 0, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23465", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, -5, -5, -1, 5],\n [-1, 5, -5, 0, -5],\n [-1, 3, -1, 0, 2],\n [5, -5, -4, 3, -3],\n [0, -1, 5, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52877", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -5, -2, 0, 1],\n [1, 1, -3, 0, 2],\n [-2, 2, -4, 4, 3],\n [3, 2, 4, 4, -5],\n [-4, 0, 4, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1165", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -4, 0, -3, 4],\n [-4, 5, 0, 2, 5],\n [0, 0, -4, 4, -1],\n [-3, 2, 4, 0, 0],\n [4, 5, -1, 0, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240812", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -2, 2, 4, 2],\n [-2, -3, -3, 0, 0],\n [2, -3, 0, 0, -1],\n [4, 0, 0, -5, 2],\n [2, 0, -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": "83381", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-2, 0, -2, 0, 2],\n [0, -1, 5, 2, -4],\n [-2, 5, 2, -2, 0],\n [0, 2, -2, -5, -2],\n [2, -4, 0, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-5, 2, 2, 4, 4],\n [2, 0, -2, 2, 0],\n [2, -2, -4, 0, 1],\n [4, 2, 0, -2, 1],\n [4, 0, 1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5041", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 5, 3, 3, 4],\n [-4, -2, 2, 1, -5],\n [-1, 1, -2, -5, 3],\n [-1, 5, -4, 2, 5],\n [-4, -3, 4, -5, 5]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1054", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -1, 4, 0, 2],\n [-1, -2, 2, 2, -2],\n [4, 2, -5, -1, 4],\n [0, 2, -1, 4, -1],\n [2, -2, 4, -1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3116", "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, 2, 0, 0],\n [-4, 2, 5, -2, -4],\n [2, 5, 5, -2, 2],\n [0, -2, -2, 5, 2],\n [0, -4, 2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68479", "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, -1, -2, 0, 4],\n [-1, 2, -1, -2, 0],\n [-2, -1, -4, 1, -4],\n [0, -2, 1, -1, -2],\n [4, 0, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101515", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -3, -3, -2, -1],\n [-5, -2, 5, 2, 4],\n [1, 3, -1, 4, -2],\n [2, 3, 1, 1, -1],\n [-2, 4, -5, 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": "135163", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 4) of the result:\nA =\n[[1, -2, -1, -3, 3],\n [-2, -3, -2, 1, 0],\n [-1, -2, -1, 0, 1],\n [-3, 1, 0, 3, -1],\n [3, 0, 1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5902", "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, -2, 2, 0],\n [0, 0, -4, 2, 2],\n [-2, -4, 5, 0, 1],\n [2, 2, 0, -2, -2],\n [0, 2, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120673", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 1, -2, -1, -1],\n [1, 3, 0, -4, -4],\n [-2, 0, 2, 0, -3],\n [-1, -4, 0, 0, -2],\n [-1, -4, -3, -2, 2]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -5, 1, -1, 4],\n [-5, -3, 1, 4, -5],\n [1, -1, -5, -5, -5],\n [5, 3, 5, -3, -1],\n [5, 4, 3, 0, 3]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2530", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 2, -2, 0, -2],\n [2, -3, -3, 2, 0],\n [-2, -3, -3, -2, 0],\n [0, 2, -2, 3, 2],\n [-2, 0, 0, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4109", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 3, 2, -2, -2],\n [3, -5, -4, -4, 0],\n [-2, 5, 4, -3, -3],\n [-3, 0, 2, 5, 1],\n [-2, 5, -2, 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": "175461", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[5, 5, 5, -4, -5],\n [3, -4, 2, 3, -2],\n [2, 3, 4, 4, -1],\n [1, 4, -2, -5, -3],\n [-1, -3, 5, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1299", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[0, 2, -3, 0, 0],\n [2, 4, -1, 3, 2],\n [-3, -1, 4, 3, 0],\n [0, 3, 3, 5, 4],\n [0, 2, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, 4, -4, -4, -3],\n [4, 1, -4, -5, 0],\n [3, -3, 0, -3, -5],\n [-1, 4, 5, -2, 1],\n [0, 4, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-119854", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 2, -2, 0, 0],\n [2, -1, -2, -3, 2],\n [-2, -2, 0, 1, 2],\n [0, -3, 1, -4, 1],\n [0, 2, 2, 1, 2]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-506", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 2, 2, -4, -3],\n [2, 5, -4, 2, 2],\n [2, -4, 5, 1, 4],\n [-4, 2, 1, -5, -2],\n [-3, 2, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75037", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 2) of the result:\nA =\n[[0, 2, 0, -2, -1],\n [2, 2, 0, -3, -2],\n [0, 0, 4, 0, 1],\n [-2, -3, 0, -3, 0],\n [-1, -2, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-722", "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, 0],\n [2, 5, -2, 0, 1],\n [2, -2, -3, -3, 0],\n [-2, 0, -3, 4, 2],\n [0, 1, 0, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127533", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 1, 0, -4, 2],\n [1, 5, -1, -1, 1],\n [3, 5, 3, 3, 0],\n [4, 0, -3, -5, 1],\n [-2, -5, 2, 0, 0]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1064", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 3) of the matrix A^5 where A is:\n[[-4, -5, -4, -2, -4],\n [-5, 1, 5, 5, 2],\n [0, -2, 0, -3, 2],\n [4, -4, -1, -5, 0],\n [-4, -2, 0, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1611", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, 2, 2, 1, 0],\n [2, 2, 2, 0, -2],\n [2, 2, 5, 0, 1],\n [1, 0, 0, 1, 0],\n [0, -2, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69781", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -5, 1, 3, 2],\n [-1, -2, 1, -1, 1],\n [-5, -5, 4, -3, 5],\n [-4, -4, 1, 4, -4],\n [5, -2, -4, 0, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17577", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -2, -1, -2, -3],\n [-1, 3, 2, 2, 2],\n [2, 1, 2, 5, 2],\n [2, 4, 1, -5, -2],\n [-2, -1, 4, 0, -2]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11001", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, 0, 2, 2, 1],\n [0, -4, 1, 5, -1],\n [0, 4, 2, 2, -3],\n [1, -5, -5, 1, 4],\n [3, 1, 4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4668", "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, -2],\n [0, 2, -5, 4, -1],\n [0, -5, 3, 0, 0],\n [4, 4, 0, -4, 3],\n [-2, -1, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61190", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 4) of the 4th power of the matrix:\n[[-4, 2, 0, -2, 2],\n [2, 2, -4, -2, 0],\n [0, -4, 3, 3, 1],\n [-2, -2, 3, 3, 2],\n [2, 0, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2232", "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, 0, 0],\n [2, 1, 2, 3, 0],\n [-3, 4, -3, 5, -5],\n [5, -1, -2, 3, 3],\n [-1, 4, -2, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278674", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 1, -4, -4, 2],\n [1, -5, -2, 2, 0],\n [-4, -2, 2, 2, 4],\n [-4, 2, 2, 2, 2],\n [2, 0, 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": "22594", "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, 3, -1, 2],\n [0, -5, 0, -4, -2],\n [3, 0, -1, 0, -2],\n [-1, -4, 0, 3, -2],\n [2, -2, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22418", "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, -5],\n [-3, 5, -4, 3, -5],\n [3, 3, 2, 2, 5],\n [-5, 5, 2, 4, -3],\n [5, 1, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-174166", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 4) of the 4th power of the matrix:\n[[4, 0, -1, -2, -2],\n [0, 0, -2, -4, 0],\n [-1, -2, 0, 0, 0],\n [-2, -4, 0, 5, -1],\n [-2, 0, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1346", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -1, 3, -2, 2],\n [-1, 2, 0, 0, -1],\n [3, 0, -3, -4, 1],\n [-2, 0, -4, 5, -4],\n [2, -1, 1, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1314", "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, -3, 4, -3],\n [2, 2, 5, -5, 4],\n [-4, 2, -5, 2, 2],\n [-4, -2, 0, 5, 3],\n [2, 2, 1, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168576", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 4, 0, 2, 2],\n [4, 4, -2, 4, 4],\n [0, -2, 2, -3, -4],\n [2, 4, -3, -3, 2],\n [2, 4, -4, 2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30098", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 1, -2, 1, 1],\n [-5, 0, 3, -4, -3],\n [4, -1, 3, -2, -5],\n [-2, 0, -1, -5, -2],\n [0, 4, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-532", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 1, 4, 3, 2],\n [1, -5, 0, 1, 0],\n [4, 0, -1, -3, -1],\n [3, 1, -3, 2, -4],\n [2, 0, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20265", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 4) of the matrix A^5 where A is:\n[[1, 5, -1, 4, -1],\n [1, -1, 2, 5, 0],\n [-1, 3, 5, -4, -5],\n [2, -3, 5, 1, 4],\n [5, 2, 0, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20967", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 4, -1, 2, -4],\n [1, -2, 3, -5, 1],\n [0, 2, -1, -5, -5],\n [3, 4, 0, 4, -1],\n [-5, 0, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97445", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, -5, 0, 4, -5],\n [0, -5, 0, -3, 2],\n [0, 5, -5, -1, 2],\n [-3, 0, -1, 0, 4],\n [-5, 1, 3, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154214", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, 4, 0, -2, -1],\n [4, -4, -2, -4, -4],\n [0, -2, 1, -3, 4],\n [-2, -4, -3, -3, 0],\n [-1, -4, 4, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "304923", "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, 1, 5, -4, -5],\n [-3, -2, 0, 4, -1],\n [-2, 2, 5, -2, 4],\n [-4, -3, 0, 2, 2],\n [5, 3, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67399", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 5) of the matrix A^5 where A is:\n[[1, 2, -3, 1, 4],\n [3, -3, 4, 0, -4],\n [-4, -1, -1, 1, -4],\n [5, 1, -1, 0, 2],\n [4, -2, 1, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11286", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[-4, 3, 0, 0, -1],\n [3, -2, 2, 0, 2],\n [0, 2, 5, 0, -2],\n [0, 0, 0, 3, -2],\n [-1, 2, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, -5, -2, 0, 1],\n [5, 5, 4, -3, 3],\n [1, -5, -4, -5, 5],\n [3, 3, 1, 4, -3],\n [-1, -2, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159018", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[2, 4, 1, 4, 2],\n [4, 1, 0, 1, -4],\n [1, 0, 4, -2, 0],\n [4, 1, -2, 0, 2],\n [2, -4, 0, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-604", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 0, 5, 5, -5],\n [-3, -4, -3, -1, 5],\n [4, 0, 3, 5, 4],\n [-2, 1, 0, -4, 4],\n [5, 5, 5, 2, 1]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-285", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 1) of the matrix A^5 where A is:\n[[1, 2, 5, -5, -5],\n [2, -2, -1, 2, -1],\n [4, -2, 0, -1, 1],\n [4, 1, -2, -1, -3],\n [-2, -2, -3, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-228", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-1, 4, -2, 0, -1],\n [4, 0, -2, -4, -1],\n [-2, -2, 0, 2, -2],\n [0, -4, 2, 0, -2],\n [-1, -1, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3413", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 3) of the 5th power of the matrix:\n[[1, -3, -3, 0, 0],\n [-2, 3, -2, 3, -2],\n [-4, -4, -1, -2, 1],\n [5, -1, 0, 4, -2],\n [-4, 4, 3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1992", "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, 1, -4, -1],\n [-2, -3, 2, -2, 5],\n [1, 2, -4, -2, 2],\n [-4, -2, -2, 5, 0],\n [-1, 5, 2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174515", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 4, -4, -5, -5],\n [5, -5, -1, 4, 1],\n [-4, 4, 2, -2, -3],\n [4, 5, 2, -4, 5],\n [5, -3, -3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4012", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 0, -4, -5, -4],\n [0, -2, 0, 3, 4],\n [4, 2, -5, 2, 3],\n [0, 4, -1, 0, 0],\n [3, -2, -4, 5, 5]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6907", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 4) of the matrix A^5 where A is:\n[[3, -4, 4, 3, -4],\n [2, 3, 4, 3, 4],\n [3, -4, -2, 1, -4],\n [-5, -3, -2, 2, 0],\n [5, -4, 3, -4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14799", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[-2, 0, 1, 0, 1],\n [0, -4, 2, -3, 1],\n [1, 2, 0, 0, -3],\n [0, -3, 0, 3, -2],\n [1, 1, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1517", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 3) of the 4th power of the matrix:\n[[1, 2, 0, 0, 0],\n [2, 2, -1, -2, 1],\n [0, -1, 1, -3, 4],\n [0, -2, -3, 5, 2],\n [0, 1, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1648", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[-1, -3, -5, -3, 0],\n [1, 2, 5, -2, -3],\n [-1, 3, 0, 3, 0],\n [-4, -1, 5, 3, 2],\n [1, -5, -2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6297", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 0, 2, 5, 0],\n [4, -3, -2, -3, -5],\n [4, -1, -5, -5, -4],\n [-2, 0, 2, -3, -5],\n [-3, -3, -1, 5, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15417", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, 2, 2, 2, 0],\n [2, -3, 0, 1, 4],\n [2, 0, -2, 0, -2],\n [2, 1, 0, -2, 3],\n [0, 4, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2520", "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, 2, -3],\n [1, -3, 1, 5, 4],\n [4, 5, 5, 0, -4],\n [5, -3, 0, -2, 0],\n [-5, 4, -5, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "392107", "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, 1, 0, 1],\n [3, 5, 0, -2, 2],\n [1, 0, 5, 0, 1],\n [0, -2, 0, 3, 0],\n [1, 2, 1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18603", "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, 0, 0],\n [5, 0, 4, -1, -1],\n [-4, 4, 3, 0, 0],\n [0, -1, 0, -2, 0],\n [0, -1, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183358", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, 4, 0, 1],\n [0, -2, 4, -2, 1],\n [4, 4, 1, 2, -4],\n [0, -2, 2, 4, 2],\n [1, 1, -4, 2, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27563", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, -5, -5, -1, -4],\n [-2, -5, -2, 5, 0],\n [4, -2, -5, 1, -4],\n [3, -3, 2, 2, -3],\n [-2, -4, -2, 5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-43778", "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, 0, 1, 2],\n [4, -2, 0, -4, 1],\n [0, 0, 3, -2, -2],\n [1, -4, -2, -4, 4],\n [2, 1, -2, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30972", "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, 4, 0, 0, 2],\n [2, 0, -3, -1, -4],\n [-1, 3, 4, -5, 4],\n [-1, 0, 5, 1, 3],\n [0, -1, 1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20085", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, -4, -2, 1, -1],\n [0, -4, -3, 1, 5],\n [-4, 0, -1, 4, -5],\n [5, 4, 5, -2, 5],\n [-4, -2, -5, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9018", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[0, -4, 0, 4, 3],\n [1, 3, -1, 1, 5],\n [1, -3, 1, -5, 3],\n [4, 0, -1, 1, -1],\n [4, -1, 5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2029", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 4, 1, 5, -3],\n [-3, 4, -3, 0, 0],\n [-3, -3, 2, 2, 1],\n [4, -2, -2, -3, -1],\n [-3, 2, 1, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14233", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-1, 3, 1, 1, 0],\n [-4, 3, 0, 2, -5],\n [-1, -5, 4, 5, 2],\n [2, -5, 3, -4, 3],\n [-5, 4, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22909", "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, 0, 0],\n [4, -4, 1, -3, 1],\n [2, 1, 2, 0, 4],\n [0, -3, 0, -2, 2],\n [0, 1, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8541", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 1, -1, 3, -2],\n [0, -4, -4, -4, 4],\n [1, -4, -4, 3, 1],\n [5, -3, -3, 1, -1],\n [4, 0, 2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38804", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 4, 3, -2, -1],\n [4, 0, -4, -2, 2],\n [3, -4, -3, 4, -1],\n [-2, -2, 4, -3, -2],\n [-1, 2, -1, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[0, -3, 2, 1, 1],\n [0, -1, 4, 2, -1],\n [3, 3, -5, 0, 1],\n [-3, 1, 5, 5, 1],\n [5, -4, 1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "348", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 1, 1, 5, -4],\n [2, -3, 2, -3, 4],\n [1, -4, -2, 5, 0],\n [5, 3, -1, 3, -1],\n [4, 2, -5, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138489", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 5) of the result:\nA =\n[[-1, 0, -1, -5, 3],\n [-4, 3, 4, -4, 3],\n [0, 5, 3, 0, 0],\n [5, -4, 2, -3, 1],\n [-1, -3, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3245", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -5, -3, 0, -4],\n [-5, -2, 3, -1, 4],\n [-3, 3, -4, -2, -1],\n [0, -1, -2, -3, -1],\n [-4, 4, -1, -1, -4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-36873", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 0, 0, -3, 0],\n [0, -1, 2, -2, 2],\n [0, 2, 4, 3, 3],\n [-3, -2, 3, -2, 3],\n [0, 2, 3, 3, 4]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5553", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -5, -3, 3, -2],\n [-1, 1, -1, -2, -4],\n [-4, -2, 4, 4, 3],\n [2, -3, 3, -1, 5],\n [-3, -1, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31986", "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, 2, 3, -2],\n [1, -4, 0, 2, 1],\n [1, 2, 1, -1, 1],\n [4, -3, -1, 1, 3],\n [-4, -2, 1, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4834", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 2, 3, 2, 0],\n [2, -3, 2, 1, 0],\n [3, 2, -2, -2, -1],\n [2, 1, -2, 2, 0],\n [0, 0, -1, 0, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29895", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -3, 0, -2, 1],\n [-3, -5, 3, 0, 2],\n [-3, 2, -4, -2, -3],\n [4, -5, 1, 5, 4],\n [-4, -2, 3, 0, 2]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "774", "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, -2, 4, 3],\n [-2, 2, 1, 2, 0],\n [-2, 1, 5, 0, -3],\n [4, 2, 0, 2, 0],\n [3, 0, -3, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20657", "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, 0, -5, 2],\n [2, 0, -1, 1, 5],\n [0, -1, 2, 0, 5],\n [-5, 1, 0, 1, 2],\n [2, 5, 5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "249673", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, 0, -2, -2, 0],\n [0, -5, -3, 0, -2],\n [-2, -3, -2, -4, 4],\n [-2, 0, -4, -4, -2],\n [0, -2, 4, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "357270", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[1, 2, -4, 2, 0],\n [2, 2, 0, -2, -2],\n [-4, 0, -4, 0, -2],\n [2, -2, 0, 0, -2],\n [0, -2, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-114", "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, -1, -1],\n [0, -3, -1, -4, 4],\n [-5, 5, -5, 4, 1],\n [-4, -2, -1, 1, -4],\n [0, -5, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12193", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 5) of the matrix A^4 where A is:\n[[-1, 0, -4, 2, 2],\n [0, 3, 1, 2, -1],\n [-4, 1, 5, -3, -2],\n [2, 2, -3, 1, 0],\n [2, -1, -2, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, -5, 2, -2, -2],\n [-4, 5, 5, 5, -5],\n [4, 3, 1, -2, 0],\n [-4, 1, -4, 4, 2],\n [2, -5, 2, -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": "573870", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 3) of the result:\nA =\n[[-5, -1, 5, 1, 4],\n [-5, -4, 1, 0, -3],\n [4, -4, 4, -2, -3],\n [1, 2, -4, 4, 1],\n [2, 0, 0, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16878", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[-2, -5, -2, -4, 5],\n [-1, 4, 3, 5, 4],\n [-3, 2, -3, 0, -2],\n [2, 5, 0, 2, -5],\n [0, -5, -5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2827", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 0, 4, 2, 0],\n [0, 5, -3, -4, 2],\n [4, -3, -5, -2, -1],\n [2, -4, -2, 1, 2],\n [0, 2, -1, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-46233", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 5) of the result:\nA =\n[[-3, 3, -4, -3, -4],\n [-5, -2, -1, 0, -1],\n [-5, -3, -5, 5, -1],\n [-1, 5, 0, 2, 4],\n [-5, -2, 4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16775", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 3, -2, 0, 0],\n [3, -4, 1, 0, -2],\n [-2, 1, -4, -1, 2],\n [0, 0, -1, -2, -2],\n [0, -2, 2, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1890", "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, -4, -2, 0],\n [2, 1, 3, 2, -2],\n [-4, 3, 5, 4, 2],\n [-2, 2, 4, -5, -1],\n [0, -2, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "250728", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[1, -4, -5, 3, 3],\n [1, 1, -3, 4, -4],\n [5, 1, 3, -5, -2],\n [0, 1, 4, 1, 4],\n [-4, -2, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-372", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -3, 4, -3, 2],\n [3, 5, -5, 5, -4],\n [4, -4, -2, -4, 1],\n [3, 1, 0, 4, -5],\n [5, 4, 3, -1, 5]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1780", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, 1, 3, 0, 2],\n [1, -5, -4, -2, 2],\n [3, -4, 3, -2, 4],\n [0, -2, -2, -1, -2],\n [2, 2, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244019", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 5) of the result:\nA =\n[[-4, -2, -2, 4, -1],\n [-2, 4, 0, -2, 0],\n [-2, 0, -5, 0, -2],\n [4, -2, 0, 2, 3],\n [-1, 0, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14470", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -2, 4, 3, 4],\n [4, -5, -4, -1, -3],\n [-4, -5, 4, -3, -5],\n [-5, -5, 2, -3, 5],\n [-5, 1, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16974", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -2, -1, 0, 1],\n [-2, 2, 0, -5, -5],\n [3, 4, 0, 4, 2],\n [1, 0, -2, 1, 3],\n [5, 4, 4, 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": "35818", "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, 1, -2, 0],\n [0, 4, 0, -3, -2],\n [1, 0, 2, -1, 2],\n [-2, -3, -1, -4, 0],\n [0, -2, 2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37372", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -2, 5, -3, 1],\n [2, -4, -2, -3, -4],\n [0, -2, 0, -4, -2],\n [5, 0, -1, -3, 2],\n [1, -3, 0, -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": "11376", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 4) of the matrix A^5 where A is:\n[[-1, 5, -1, 1, 5],\n [-1, 5, -3, 4, -1],\n [1, -1, -1, 3, -3],\n [0, -5, 4, -1, 2],\n [-1, 3, 5, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-114", "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, -3, 1, 1],\n [4, 0, 1, -4, 3],\n [4, 4, -5, -5, -3],\n [-3, -5, 1, -2, 4],\n [-4, 4, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15713", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -4, -1, -3, -4],\n [-5, 4, -4, 0, 2],\n [-3, 5, 3, 3, -4],\n [2, 4, 5, -1, -2],\n [4, -1, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20716", "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, -4, -1, 0],\n [-1, -4, 1, -2, 2],\n [1, 1, 3, -5, 4],\n [0, 0, 0, 0, 4],\n [1, 4, 0, -5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33388", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 0, 2, -3, 4],\n [2, 2, -1, 2, 0],\n [-1, 3, 1, 2, -5],\n [5, -4, 2, 3, -2],\n [4, 5, 4, 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": "6082", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 4, 4, 3, 5],\n [1, -4, 3, -2, 2],\n [1, 1, 2, -5, -1],\n [-4, -4, -5, -1, -4],\n [-2, -3, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21384", "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, 3, 1, 2],\n [2, -2, 0, 2, -4],\n [3, 0, -2, 0, 3],\n [1, 2, 0, -3, -2],\n [2, -4, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20328", "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, -1, 3, -1, 2],\n [-1, 2, -2, 4, -2],\n [3, -2, -3, 0, 2],\n [-1, 4, 0, 4, -2],\n [2, -2, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24467", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 4) of the matrix A^5 where A is:\n[[-1, 1, 4, 0, 0],\n [1, 2, 4, 2, -2],\n [4, 4, -2, 2, -1],\n [0, 2, 2, 1, 1],\n [0, -2, -1, 1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1918", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, 5, 4, -1, 1],\n [-1, -5, 5, 1, 2],\n [1, 5, -2, 2, -1],\n [4, 3, 4, -1, -5],\n [3, -1, 0, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6623", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, -3, -1, -4, -4],\n [1, 4, 4, 5, 4],\n [0, -2, -1, -5, 1],\n [2, 3, 2, -1, -3],\n [4, 5, 3, 0, -1]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, -3, 4, 0],\n [-2, -4, 2, -2, 3],\n [1, -4, -2, -1, -3],\n [3, -1, -4, 5, -3],\n [3, 1, -4, 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": "8851", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, -4, 4, -2, -1],\n [-4, 4, -5, 1, 4],\n [-5, 5, 5, 2, -3],\n [4, 0, 1, 4, -5],\n [0, 1, 0, -2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "343132", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, 3, -2, 1, 1],\n [-4, -5, 2, 2, 1],\n [2, -3, 5, -4, 1],\n [2, -5, 4, 3, 5],\n [-2, -2, -3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3724", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -4, 3, -4, 1],\n [-5, 1, -1, 2, -2],\n [4, 1, 0, -1, -2],\n [1, -1, -1, -5, -4],\n [-1, -3, -4, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15245", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, -2, -3, 1, 3],\n [-1, -2, 5, -4, -4],\n [-1, 1, 4, 4, 3],\n [1, -1, 4, 4, 4],\n [0, 5, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4157", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-5, -5, 2, -2, -3],\n [-5, 3, -4, -2, 4],\n [2, -4, 2, -2, 0],\n [-2, -2, -2, -5, 0],\n [-3, 4, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28915", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 0, 3, -5, 1],\n [4, 5, -1, 2, 1],\n [-2, -2, 0, 0, 3],\n [-1, 2, -1, -4, 0],\n [3, -3, -5, -5, -3]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -2, -2, 2, 2],\n [-2, 3, -2, 0, 0],\n [-2, -2, -1, 0, -2],\n [2, 0, 0, -1, -4],\n [2, 0, -2, -4, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-27210", "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, 0, 4],\n [4, 5, -2, 3, -5],\n [5, -4, -2, -3, -5],\n [-1, 1, -4, -1, 0],\n [5, 1, -5, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "827886", "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, -2, 1, 0, -2],\n [-2, 2, 1, -3, -1],\n [1, 1, -4, 0, -1],\n [0, -3, 0, 2, 0],\n [-2, -1, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4717", "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, -4],\n [-2, -5, 2, 0, -4],\n [2, 2, 5, -2, 1],\n [0, 0, -2, 5, 0],\n [-4, -4, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "473817", "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, 5],\n [3, 5, 3, 2, -3],\n [-3, -4, -1, -2, 1],\n [-2, 3, -4, 5, 0],\n [1, -2, 0, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109113", "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, -5, 1, 3],\n [4, -1, -4, 4, 0],\n [1, -4, -4, 4, 4],\n [-5, -2, 1, 3, -3],\n [5, 1, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178780", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -4, -2, 0, -4],\n [-4, 0, -4, -2, -3],\n [-2, -4, 0, -2, 4],\n [0, -2, -2, 1, 2],\n [-4, -3, 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": "24735", "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, 0, -3, -1],\n [4, 3, 5, -3, -1],\n [2, 0, -2, 2, 5],\n [-3, -3, -2, 3, -1],\n [2, 0, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5655", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[2, -2, 4, -1, 0],\n [-2, 2, -4, 1, -2],\n [4, -4, 3, 2, -4],\n [-1, 1, 2, 4, -2],\n [0, -2, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1838", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the 5th power of the matrix:\n[[2, 1, -4, -1, 1],\n [1, 3, 1, 2, 2],\n [-4, 1, 2, 0, 0],\n [-1, 2, 0, 4, 4],\n [1, 2, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29159", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -2, 0, 2, 5],\n [-2, -4, -2, -1, -1],\n [0, -2, -4, 4, 0],\n [2, -1, 4, 0, -2],\n [5, -1, 0, -2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199626", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[-2, -1, -3, 0, 2],\n [-1, -2, -2, 0, -4],\n [-3, -2, -4, -2, 0],\n [0, 0, -2, 4, 0],\n [2, -4, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-112", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -3, -4, -4, 3],\n [5, -1, 1, -1, 1],\n [-2, 2, 5, 4, 5],\n [4, 1, 4, -1, 5],\n [0, -1, 1, -4, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45496", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 2) of the matrix A^5 where A is:\n[[4, -3, 0, 2, 2],\n [-3, 1, 2, 1, -1],\n [0, 2, -5, -2, 4],\n [2, 1, -2, -1, 0],\n [2, -1, 4, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8908", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 5, -5, -3, -3],\n [1, -5, 3, 5, 0],\n [-2, -3, -3, -4, -4],\n [4, -1, 3, -4, -4],\n [0, 4, -4, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43504", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, 0, 0, -5, -1],\n [0, -1, 4, -1, 4],\n [0, 4, 2, -2, 2],\n [-5, -1, -2, -2, -1],\n [-1, 4, 2, -1, 0]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 0, 0, 3, 2],\n [0, 3, 2, 0, 2],\n [0, 2, 1, 0, 2],\n [3, 0, 0, -1, -1],\n [2, 2, 2, -1, 3]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "932", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 1, 2, 0, 2],\n [1, 0, 1, -2, 2],\n [2, 1, 2, 2, 2],\n [0, -2, 2, 3, 0],\n [2, 2, 2, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7127", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 2, 1, -1, 4],\n [1, 4, -2, 3, 5],\n [4, -4, 3, 3, -1],\n [5, -5, 1, 4, 4],\n [-2, 3, 0, -3, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17423", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 0, -1, -4, 4],\n [4, -4, 1, -4, 0],\n [-1, -2, 1, 2, -2],\n [-5, -5, -5, 5, -5],\n [-1, -2, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3971", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, 2, 0, 4, -5],\n [2, 4, -3, 2, -2],\n [2, 5, -5, -3, 0],\n [3, -4, 5, -5, 4],\n [-3, -2, 5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38102", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[4, 4, 0, 0, 1],\n [4, 4, -2, -2, 0],\n [0, -2, -3, 0, -4],\n [0, -2, 0, -4, 0],\n [1, 0, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-264", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -5, 2, -3, 0],\n [-2, 3, 1, 3, 4],\n [-3, -5, -1, -3, 0],\n [2, 5, -2, -1, -1],\n [-2, -2, -2, -2, -2]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "273", "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, -2, 0, -3],\n [-2, -4, 0, 0, 3],\n [-2, 0, 4, -3, -5],\n [0, 0, -3, -1, -4],\n [-3, 3, -5, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32220", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 0, -4, -2, 0],\n [0, 3, -2, 0, -3],\n [-4, -2, 1, 2, -2],\n [-2, 0, 2, 4, 4],\n [0, -3, -2, 4, 3]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-442", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, -5, -2, -2, -4],\n [3, 3, -4, 3, 0],\n [2, 4, -2, -4, -4],\n [3, -5, 1, 5, -3],\n [-3, -4, 4, 0, 4]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7080", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 5th power of the matrix:\n[[-4, 4, -2, 2, 0],\n [4, 0, -2, 0, -4],\n [-2, -2, 2, 0, -2],\n [2, 0, 0, 4, 0],\n [0, -4, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1672", "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, 4, -4, -3, -2],\n [3, -3, 1, -3, 1],\n [1, 3, -4, 0, 3],\n [-4, -4, -1, 4, 4],\n [4, 2, 5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37471", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 5) of the result:\nA =\n[[-1, -1, 0, 2, 1],\n [-1, -3, 2, -1, -1],\n [0, 2, 5, 1, 0],\n [2, -1, 1, -4, 0],\n [1, -1, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 4, 0, 2, -2],\n [4, -4, 4, 0, -2],\n [0, 4, -3, -2, 4],\n [2, 0, -2, 5, 2],\n [-2, -2, 4, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3906", "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, 0, -4, 2, 2],\n [0, -5, -1, 2, -2],\n [-4, -1, 1, 2, 1],\n [2, 2, 2, -1, -5],\n [2, -2, 1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26867", "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, -5, 5, -4, -4],\n [-1, 4, 1, -5, 4],\n [-5, -5, 0, -4, -5],\n [0, -4, 0, 4, 2],\n [-4, 5, 3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579983", "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, 2, -2, 0],\n [0, 0, 0, 2, -1],\n [2, 0, 1, 0, 4],\n [-2, 2, 0, 3, 4],\n [0, -1, 4, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9093", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 3, -4, -3, 4],\n [-4, -3, 0, -3, 4],\n [2, 5, 0, 1, -5],\n [-3, -3, -4, 1, 3],\n [-2, -1, -3, 5, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44361", "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, -1, -5, 5, -4],\n [3, -4, -1, 2, -3],\n [0, -2, 5, 1, 4],\n [-3, 0, 4, 3, 5],\n [4, -5, -3, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20649", "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, 0, -2],\n [0, -3, 0, 2, -3],\n [0, 0, 0, 2, 0],\n [0, 2, 2, -1, 4],\n [-2, -3, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4342", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 2, -3, -1, 5],\n [2, 4, 0, -2, -2],\n [-3, 0, 0, 3, -2],\n [-1, -2, 3, -1, 0],\n [5, -2, -2, 0, -5]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2988", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, -1, -3, 5, 1],\n [3, -4, 2, 3, 5],\n [-3, -4, 1, -1, -1],\n [4, -1, -2, -1, -2],\n [0, -2, -4, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5284", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 4, 0, 3, 3],\n [-3, -5, -5, -3, -1],\n [-3, 3, 3, -3, -3],\n [-1, -4, 0, 1, 3],\n [0, -3, -1, -2, -1]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-115", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, 2, 0, -5, 2],\n [2, -4, -2, -4, -2],\n [4, 1, 3, 2, 3],\n [2, -4, 1, -4, 5],\n [-4, -2, -5, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8820", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 4, 2, -4, -5],\n [-4, 1, -2, 4, -1],\n [1, -3, 4, -4, 1],\n [-1, -5, -5, 3, -1],\n [-5, 1, 3, 5, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1863", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 0, 0, -3, 2],\n [0, -4, -2, -4, 0],\n [0, -2, 3, 0, -2],\n [-3, -4, 0, 0, -2],\n [2, 0, -2, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9672", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 4, 4, 2, -1],\n [5, 5, 4, -5, 1],\n [-3, 4, 2, -3, -5],\n [-1, -4, 5, -2, -5],\n [3, 0, 2, 5, -2]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2335", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, -4, 3, -1, 0],\n [-3, -2, 0, 1, -5],\n [1, -5, -1, 0, -4],\n [4, 3, 4, 0, 1],\n [4, 2, 5, 4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23438", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 1) of the result:\nA =\n[[2, -2, 4, 2, 0],\n [5, 3, 5, -2, -4],\n [-4, -1, 4, 3, -3],\n [2, -2, 0, 4, 0],\n [-3, -1, -3, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 3, 1, 0, 0],\n [3, -1, -2, -4, 1],\n [1, -2, -2, -1, 2],\n [0, -4, -1, 1, 4],\n [0, 1, 2, 4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9893", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 3) of the result:\nA =\n[[5, 2, 4, 0, -2],\n [2, -4, -2, 3, 0],\n [4, -2, 5, 1, 2],\n [0, 3, 1, 1, 0],\n [-2, 0, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31104", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 5) of the matrix A^4 where A is:\n[[-1, -2, -4, -2, 2],\n [-2, 2, 1, 2, -4],\n [-4, 1, -1, 0, -2],\n [-2, 2, 0, -5, -2],\n [2, -4, -2, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, -4, -4, 1, -5],\n [1, -5, 0, -3, 2],\n [0, 5, -4, 2, -1],\n [2, 2, 0, -4, 2],\n [5, 0, 0, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19064", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 2) of the 5th power of the matrix:\n[[-4, 3, 5, 2, 1],\n [1, -1, -4, 5, 0],\n [4, -3, -2, 4, 5],\n [-4, -4, 2, 2, 4],\n [0, -1, 2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3214", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, -1, -5, -5, -4],\n [2, 1, 4, 3, -1],\n [-4, 1, 2, 1, 1],\n [-1, -4, 0, -2, 4],\n [-4, 3, 1, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13113", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, 4, 4, -2, -3],\n [5, 2, -3, 1, 1],\n [1, 1, -4, 4, -3],\n [4, 3, -3, -4, 3],\n [4, 3, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 0, 0, 0, 2],\n [0, -3, 0, 1, 2],\n [0, 0, -3, -2, 1],\n [0, 1, -2, 5, 0],\n [2, 2, 1, 0, 2]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[5, 0, 2, 0, -2],\n [0, -4, -2, -2, -1],\n [2, -2, 0, 4, -4],\n [0, -2, 4, -2, -2],\n [-2, -1, -4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-38", "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, 3, 2, 1],\n [-3, -4, 1, -1, 0],\n [-2, -4, 3, -3, 1],\n [2, -4, 0, 5, 2],\n [1, 5, -3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74356", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, -2, 1, 2, 0],\n [-2, -5, -5, -2, 2],\n [1, -5, -5, 2, 0],\n [2, -2, 2, 0, 0],\n [0, 2, 0, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285004", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 0, -1, -2, 2],\n [0, 5, 4, 1, -5],\n [-1, 4, 5, 2, 0],\n [-2, 1, 2, 1, 1],\n [2, -5, 0, 1, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "147605", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, -1, 2, 0, 4],\n [-1, -2, 0, 1, 2],\n [2, 0, -5, 4, 4],\n [0, 1, 4, 1, 2],\n [4, 2, 4, 2, 3]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13116", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 5) of the matrix A^5 where A is:\n[[-4, 1, 1, -2, 3],\n [2, -5, -4, -4, 5],\n [2, -5, -2, 4, -1],\n [3, 1, 2, 5, 3],\n [1, -1, -1, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4234", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -2, 3, 2, -4],\n [-2, 1, 0, -2, 0],\n [3, 0, 1, -3, 2],\n [2, -2, -3, 5, -2],\n [-4, 0, 2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -5, 2, 0, 1],\n [-5, -3, 1, 2, 2],\n [2, 1, -1, -1, 0],\n [0, 2, -1, 3, -2],\n [1, 2, 0, -2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120567", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 5, -2, -3, -4],\n [0, 2, 0, 3, -1],\n [-4, 2, 3, 4, -2],\n [0, 5, 4, 2, 3],\n [-1, 0, 5, -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": "349484", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 3) of the result:\nA =\n[[1, 3, 4, 5, 0],\n [0, 2, 5, -2, -3],\n [1, -1, -4, -4, 5],\n [0, 2, -5, 5, 0],\n [-4, -4, 1, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18645", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 1, 2, 1, 0],\n [3, -3, 5, 0, -2],\n [-4, -5, -5, 5, 4],\n [-3, -2, -4, 5, 5],\n [5, -5, -2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54150", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[5, 0, 0, 5, 3],\n [-4, -2, -1, -5, 2],\n [2, 0, -1, 2, -3],\n [-3, -4, -1, -3, -3],\n [0, 2, -4, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "478", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -5, -5, 4, 1],\n [1, -5, -5, -2, -1],\n [-1, -2, 2, 1, 3],\n [1, 4, -5, 1, -5],\n [1, 4, 2, 5, 3]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-446", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 3) of the matrix A^4 where A is:\n[[-3, -2, -2, 3, 1],\n [-3, 4, -1, 1, 2],\n [-5, -4, 1, 5, -4],\n [1, 3, 5, -4, 1],\n [-2, 5, -4, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3265", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[-5, 0, 0, 1, 0],\n [0, -1, -2, 0, 0],\n [0, -2, 4, 0, 0],\n [1, 0, 0, 5, 2],\n [0, 0, 0, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 2) of the result:\nA =\n[[0, -1, 2, -3, -1],\n [-1, 3, -4, -3, -4],\n [2, -4, 4, 2, -1],\n [-3, -3, 2, -5, 2],\n [-1, -4, -1, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28305", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -2, -1, 4, -1],\n [-5, 0, 3, -4, 1],\n [0, -1, -2, -2, 0],\n [-2, -1, 0, -1, 1],\n [3, 4, 1, 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": "2211", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 2, -2, -5, -1],\n [2, -2, 2, 2, -3],\n [3, -3, -5, -4, 0],\n [4, -4, 0, -5, 5],\n [-5, -1, 4, 5, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "576104", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 2) of the result:\nA =\n[[2, -3, -3, -5, -3],\n [5, -5, 2, -5, -1],\n [3, 1, -2, 5, 3],\n [3, -4, 4, 4, 5],\n [0, -2, 2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24698", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 5, 4, 3, -1],\n [0, -5, 0, -4, 0],\n [3, 2, 3, 4, 2],\n [-3, 2, 0, 0, 0],\n [-3, 4, -5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7606", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[0, 3, 0, 0, 0],\n [3, 5, 0, 0, -4],\n [0, 0, 4, 2, 4],\n [0, 0, 2, 4, -2],\n [0, -4, 4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1616", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[2, 4, -3, 3, 0],\n [4, -4, -3, 0, -2],\n [-3, -3, 3, -1, 0],\n [3, 0, -1, 5, 2],\n [0, -2, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85962", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-5, -4, 2, -5, 1],\n [-4, -1, -2, -2, 0],\n [2, -2, 0, 0, -2],\n [-5, -2, 0, -2, 0],\n [1, 0, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31656", "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, -4, 0, -5],\n [-5, 5, -3, -3, 5],\n [-1, -5, 4, 0, 1],\n [4, 5, -3, -2, 4],\n [5, 4, 4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37888", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, -4, 0, 0, 0],\n [-4, -5, 4, -2, 0],\n [0, 4, 3, 2, -1],\n [0, -2, 2, -2, -2],\n [0, 0, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290176", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 0, -4, 4, 5],\n [1, 3, 0, -3, 1],\n [-1, -5, -3, -1, 1],\n [-3, 0, -1, -5, 4],\n [0, 2, -5, -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": "15340", "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, 0, 4, 2],\n [4, -2, 2, -2, 4],\n [0, 2, 2, 0, -5],\n [4, -2, 0, -3, 4],\n [2, 4, -5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "971952", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, -3, 3, -1, 3],\n [4, 0, 3, 1, 1],\n [2, 1, 3, 5, 3],\n [0, 1, -4, 3, -5],\n [-5, -3, 0, -1, -4]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1950", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[3, 3, -1, -2, -2],\n [3, 4, -2, -2, -4],\n [-1, -2, 2, 2, 2],\n [-2, -2, 2, 4, 0],\n [-2, -4, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1462", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, -3, 2, -2, 0],\n [-3, -5, -3, 1, 4],\n [2, -3, -5, 0, 2],\n [-2, 1, 0, -5, -4],\n [0, 4, 2, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11514", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 4, 4, -2, 1],\n [4, -4, -2, -1, -4],\n [4, -2, 3, -3, 1],\n [-2, -1, -3, 0, 2],\n [1, -4, 1, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3817", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 1) of the matrix A^5 where A is:\n[[4, -4, 5, 4, 0],\n [0, -4, -4, -4, 4],\n [-5, -1, 2, -4, -1],\n [2, 4, -1, -4, -3],\n [0, 5, 5, -1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8495", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, -2, -1, -4, 3],\n [-4, 4, -4, 4, 3],\n [-3, 4, 1, -2, 0],\n [-2, 4, 1, -5, -3],\n [-3, -5, 0, 5, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15783", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[2, 5, 1, 4, 2],\n [0, 3, -3, 4, 4],\n [3, -2, 1, 3, -4],\n [-4, 3, -3, 3, -1],\n [0, -4, 2, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 0, 0, 1, 4],\n [0, 3, -4, -1, 0],\n [0, -4, -3, 0, 0],\n [1, -1, 0, -4, 2],\n [4, 0, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1710", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 0, 4, 2, 4],\n [4, -4, 3, -3, 2],\n [2, -3, -3, 0, -5],\n [-2, -5, -3, 3, -1],\n [-1, 5, -2, -3, -1]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11033", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^5 where A is:\n[[5, -2, 2, -2, 5],\n [2, 0, 5, -1, -2],\n [-2, -2, 5, 3, -2],\n [3, 4, 0, 4, 1],\n [4, -3, 2, -3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-597", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 2, -4, 4, 2],\n [2, 3, -2, 0, -3],\n [-4, -2, 5, -3, -5],\n [4, 0, -3, -3, 2],\n [2, -3, -5, 2, -5]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5112", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, -5, 5, -4],\n [1, -5, 1, -2, 4],\n [0, 2, 3, 0, 5],\n [3, -2, 0, 2, 3],\n [-3, -4, 0, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5216", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, 2, 2, -2, 0],\n [2, -1, 0, 2, 0],\n [2, 0, -5, -1, 0],\n [-2, 2, -1, -4, -1],\n [0, 0, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34337", "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, 2, 2, 3],\n [0, -1, -1, -3, 4],\n [2, -1, -1, 2, -3],\n [2, -3, 2, 4, 2],\n [3, 4, -3, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19732", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[5, -2, 0, 5, -3],\n [-2, -5, -2, -2, -1],\n [0, -2, 3, -2, 2],\n [5, -2, -2, 2, -2],\n [-3, -1, 2, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24015", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 5, -4, -1, -2],\n [3, -1, 3, 5, 3],\n [-4, 3, -3, -2, -5],\n [-5, -5, 3, 5, 2],\n [-1, -1, 3, -3, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14202", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 3, 0, -4, -5],\n [-4, -5, 4, 4, 3],\n [4, 2, 1, -3, 2],\n [-4, -4, 5, 4, -3],\n [1, -5, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35315", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 4, -5, -2, -5],\n [-5, 4, -5, 1, 1],\n [-2, -4, -3, 2, 2],\n [5, 5, 0, 4, 3],\n [5, 3, -2, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6399", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, -3, 0, 2, 1],\n [-3, 0, 1, 2, -1],\n [0, 1, -2, 2, 0],\n [2, 2, 2, 1, 2],\n [1, -1, 0, 2, -1]]\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[[-2, 0, 2, -1, 0],\n [0, 4, -1, -2, 0],\n [2, -1, 4, 4, -4],\n [-1, -2, 4, -4, 4],\n [0, 0, -4, 4, 2]]\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[[0, 3, 2, -1, 2],\n [3, 3, 0, -2, 1],\n [2, 0, -3, -1, -3],\n [-1, -2, -1, -3, 0],\n [2, 1, -3, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75582", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 2, -1, -2, 0],\n [2, 0, -3, 0, 2],\n [-1, -3, 0, 4, -2],\n [-2, 0, 4, 5, 2],\n [0, 2, -2, 2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5494", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 0, -4, 2, 0],\n [0, -3, 0, 1, 2],\n [-4, 0, 4, 0, 0],\n [2, 1, 0, 3, -4],\n [0, 2, 0, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "973", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 2, -3, 5, 3],\n [-4, 0, -5, 1, -3],\n [1, -2, 3, -1, -3],\n [2, 0, -4, -3, 2],\n [4, 1, 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": "10921", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, -3, -2, 0, 0],\n [-3, -2, 4, 2, 2],\n [-2, 4, 1, 0, -2],\n [0, 2, 0, 5, 2],\n [0, 2, -2, 2, 1]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7006", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 4) of the matrix A^5 where A is:\n[[5, 3, 5, 4, 0],\n [2, 3, 4, -2, -5],\n [2, -4, 5, -5, 1],\n [4, 3, 5, 3, -3],\n [0, 1, 4, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5270", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[2, 1, -2, -4, 2],\n [5, -1, 0, 5, 1],\n [4, -5, 2, -2, 3],\n [-5, 5, -4, 0, 5],\n [4, 5, -5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31990", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 0, 2, 2, 0],\n [0, -5, 0, 2, 0],\n [2, 0, -1, 2, 0],\n [2, 2, 2, 4, 1],\n [0, 0, 0, 1, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58328", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 1) of the 5th power of the matrix:\n[[-5, 0, -3, -5, -2],\n [0, 3, 4, 4, -1],\n [-3, 4, 3, -5, -2],\n [-5, 4, -5, -1, 2],\n [-2, -1, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17060", "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, -5, -3],\n [5, -4, -4, 3, 2],\n [-5, -2, -5, -5, -2],\n [-4, -3, 5, 3, -4],\n [-2, -5, -4, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329217", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 4, 2, -2, 2],\n [4, 0, 0, 0, 2],\n [2, 0, 0, -2, 4],\n [-2, 0, -2, 4, 0],\n [2, 2, 4, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3534", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 4, 1, -2, 5],\n [-2, 1, 3, 5, -2],\n [-2, 0, 0, 1, -5],\n [5, -3, 3, 0, 0],\n [-1, 5, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2806", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 2) of the 5th power of the matrix:\n[[-5, 0, 1, -3, 0],\n [0, -2, -2, 1, -2],\n [1, -2, 1, 4, 1],\n [-3, 1, 4, -1, -2],\n [0, -2, 1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3735", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 5, -1, 4, -1],\n [5, 4, 0, -4, 1],\n [-1, 0, -2, -2, -2],\n [4, -4, -2, 2, -2],\n [-1, 1, -2, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135753", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, -3, 4, -4, 0],\n [-3, 5, -2, -5, 5],\n [4, -2, 5, -2, 0],\n [-4, -5, -2, 0, 2],\n [0, 5, 0, 2, -2]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2570", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 0, -2, -2, 4],\n [0, 1, 2, 2, 2],\n [-2, 2, -3, -2, -2],\n [-2, 2, -2, -3, -4],\n [4, 2, -2, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54404", "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, -1, 2, -2],\n [-4, -3, 0, 4, 0],\n [-1, 0, -5, -4, 1],\n [2, 4, -4, -3, -4],\n [-2, 0, 1, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51596", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 4, -2, -5, -4],\n [5, -5, 0, -3, 1],\n [-1, 3, 1, -2, -1],\n [-1, 5, -1, 4, 3],\n [4, -3, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161384", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 1, -3, -5, -2],\n [0, -3, -5, 0, -5],\n [3, 5, -5, 0, -5],\n [1, -3, 0, 1, -5],\n [-5, -1, 0, 3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2203", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 4, 2, 4, 3],\n [-3, 5, -4, -2, -4],\n [-5, -3, 1, -5, -4],\n [-5, 2, -1, 2, -3],\n [1, 2, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7270", "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, 1, -5, -1],\n [-5, 2, -2, -2, -4],\n [-1, -5, 3, -1, 0],\n [-4, 4, 4, -5, -2],\n [1, 0, 4, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26701", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 1, -3, 2, -1],\n [1, 1, 0, 0, 0],\n [-3, 0, 3, 0, -4],\n [2, 0, 0, -3, -2],\n [-1, 0, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9293", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the 5th power of the matrix:\n[[2, 0, -2, 0, -2],\n [0, 3, 0, 4, -4],\n [-2, 0, -2, 2, 1],\n [0, 4, 2, 3, 0],\n [-2, -4, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5192", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 3) of the 5th power of the matrix:\n[[4, -1, -4, -1, -1],\n [-1, -2, 0, 0, -2],\n [-4, 0, 2, 0, 3],\n [-1, 0, 0, -5, 4],\n [-1, -2, 3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4389", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 2, -4, -2, 5],\n [2, 2, 0, 2, -1],\n [-4, 0, -2, -2, -2],\n [-2, 2, -2, 5, 1],\n [5, -1, -2, 1, -1]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2732", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 3, 3, 3, 5],\n [-5, 3, 2, -4, 5],\n [-5, -5, 0, 3, 1],\n [-1, 5, -4, -5, -4],\n [-5, -3, 0, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48385", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 3, 4, -1, 1],\n [2, -3, -4, -4, -1],\n [-5, -4, 3, 1, 0],\n [3, 1, 5, -1, 3],\n [0, 0, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48316", "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, 3, 2, 0],\n [2, 3, -2, -4, -5],\n [3, -2, -4, -1, 2],\n [2, -4, -1, 1, 0],\n [0, -5, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "191086", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -1, 2, -2, 0],\n [-1, 5, -2, 2, 0],\n [2, -2, 1, 0, -2],\n [-2, 2, 0, -2, -2],\n [0, 0, -2, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13471", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-1, 5, 2, 2, 2],\n [5, -5, 0, -2, -2],\n [2, 0, 1, -2, 0],\n [2, -2, -2, 3, -2],\n [2, -2, 0, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-62548", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 2, 5, -4, 2],\n [-2, 4, 4, -5, -1],\n [-5, 1, 2, -3, -3],\n [1, -2, -3, 2, -3],\n [1, -4, 5, 5, -5]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3651", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 0, -1, 0, 4],\n [0, -3, 2, 2, -2],\n [-1, 2, -3, 0, 0],\n [0, 2, 0, -1, -2],\n [4, -2, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1590", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 0, 0, -3, 0],\n [0, -1, 1, -2, 2],\n [0, 1, 5, -2, 0],\n [-3, -2, -2, -3, -2],\n [0, 2, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-24111", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 5, -5, 1, -3],\n [5, 2, 0, -2, 5],\n [2, 3, 4, -4, 0],\n [-1, -1, 4, 5, -3],\n [2, 2, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4970", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -3, -4, 3, -4],\n [3, -2, -4, 4, -5],\n [-2, 3, 3, -2, 3],\n [0, -5, 4, 0, 3],\n [-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": "-1625", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 0, 2, 2, -3],\n [0, 0, 0, -3, 2],\n [2, 0, 0, -2, -2],\n [2, -3, -2, 4, 0],\n [-3, 2, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3981", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 2, -2, 3, 2],\n [1, 1, -3, 0, -1],\n [-5, 5, -3, -5, -2],\n [4, -3, 5, -2, 3],\n [-3, 0, 0, 1, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5585", "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, -2, 1],\n [0, -1, 2, -4, 5],\n [0, 2, 3, -2, -4],\n [-2, -4, -2, 3, -2],\n [1, 5, -4, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25189", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, 3, -4, -1, -2],\n [3, 1, 0, -1, -1],\n [-4, 0, 5, 0, -4],\n [-1, -1, 0, -2, -2],\n [-2, -1, -4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5024", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -5, 3, -3, 4],\n [-3, 5, -4, 2, -3],\n [0, -4, 1, -2, 3],\n [4, 3, 1, 2, -3],\n [5, -1, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45187", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, 3, 5, 5, 1],\n [4, 4, 2, 3, 0],\n [4, -4, -4, -2, 3],\n [1, -4, 2, 5, 1],\n [3, 2, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118984", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -2, 2, -2, 3],\n [-2, 0, -2, 4, 5],\n [2, -2, 2, -4, 0],\n [-2, 4, -4, -1, -4],\n [3, 5, 0, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3141", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -3, 1, 0, 3],\n [-1, -2, -3, 4, -5],\n [-3, -3, 1, 1, -5],\n [-3, 2, 3, 1, 1],\n [5, 2, 0, 5, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142487", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 3) of the 4th power of the matrix:\n[[-5, 2, -5, -4, 0],\n [2, 1, 3, -4, 2],\n [-5, 3, 0, -2, 0],\n [-4, -4, -2, -3, -2],\n [0, 2, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2614", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -2, -1, 1, 2],\n [0, -5, 1, -3, 0],\n [2, 1, 4, 0, 3],\n [3, -5, -5, -5, 2],\n [4, 1, -3, -4, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-72836", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -1, 4, 2, -2],\n [-1, 0, -2, 0, 4],\n [4, -2, -2, 0, -2],\n [2, 0, 0, 1, 4],\n [-2, 4, -2, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1283", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, -1, 4, 4, 1],\n [-1, -5, 4, 4, 0],\n [4, 4, 0, 0, 0],\n [4, 4, 0, -2, 4],\n [1, 0, 0, 4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12450", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 0, -2, -4, 2],\n [0, -4, 0, 0, 0],\n [-2, 0, -4, 2, 2],\n [-4, 0, 2, -5, 3],\n [2, 0, 2, 3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-51382", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -4, 2, 5, -4],\n [3, -2, -5, -2, -3],\n [0, 1, 2, -4, 0],\n [0, 4, -1, 4, 4],\n [1, -3, -2, 4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1599", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 0, -4, -2, 2],\n [0, 1, 2, 0, -2],\n [-4, 2, 3, 2, -3],\n [-2, 0, 2, 0, 0],\n [2, -2, -3, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "970", "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, 0, -4, 1],\n [0, -5, 0, 2, 0],\n [0, 0, 3, 2, -2],\n [-4, 2, 2, -2, 0],\n [1, 0, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15972", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[-2, 0, 0, -2, -2],\n [0, 3, -4, 5, 1],\n [0, -4, -2, 0, 2],\n [-2, 5, 0, -5, 2],\n [-2, 1, 2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2252", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 4, 4, 2, 0],\n [4, -5, 0, 0, -1],\n [4, 0, -3, -4, 2],\n [2, 0, -4, 0, 2],\n [0, -1, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4282", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 2, 4, -1, -2],\n [2, 4, 1, 4, -1],\n [4, 1, 1, 1, 0],\n [-1, 4, 1, -4, 2],\n [-2, -1, 0, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30509", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 3) of the 4th power of the matrix:\n[[4, -4, 2, 2, 1],\n [-4, 1, 0, -1, 2],\n [2, 0, 1, 1, 1],\n [2, -1, 1, -2, 0],\n [1, 2, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 3, -4, 0, -1],\n [-1, -2, 0, -1, 5],\n [-2, 3, 0, 5, 4],\n [4, 4, -3, 4, 0],\n [-5, -1, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21086", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 0, 0, 2, -3],\n [0, -2, 0, 2, -1],\n [0, 0, -3, 4, 0],\n [2, 2, 4, 5, -3],\n [-3, -1, 0, -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": "367049", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 1, 0, 1, -3],\n [-3, 5, -5, -2, -4],\n [4, 2, -3, 1, 1],\n [3, 0, -5, 2, -5],\n [-3, 5, -1, 2, 3]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[1, 4, 0, -4, 0],\n [4, 2, 0, 0, 2],\n [0, 0, 4, -2, -2],\n [-4, 0, -2, 4, -2],\n [0, 2, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1953", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 5, -3, -5, -4],\n [-1, 4, -1, 4, -5],\n [-5, 3, -4, 1, 4],\n [-2, 1, 2, -1, -5],\n [-2, 4, -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": "13459", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[4, 4, 0, -4, 1],\n [-3, -5, 4, -3, 3],\n [4, 5, 5, 0, 5],\n [0, -2, 2, -1, 1],\n [3, -1, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -4, -2, -4, 0],\n [-4, 2, 0, -4, -1],\n [-2, 0, -1, -2, -2],\n [-4, -4, -2, 1, -4],\n [0, -1, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31496", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, -2, 0, 2, 4],\n [-2, -1, 3, 3, 2],\n [0, 3, 1, -2, 2],\n [2, 3, -2, 0, 4],\n [4, 2, 2, 4, -2]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8296", "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, 0, 0, 0],\n [-4, -4, 2, 4, -2],\n [0, 2, 0, 0, -2],\n [0, 4, 0, -1, 3],\n [0, -2, -2, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26144", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, 4, -3, 2, 0],\n [-4, -4, 3, 1, 4],\n [3, 0, -1, -5, 0],\n [0, -3, -3, -3, -3],\n [1, 4, 5, -4, 4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-334", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -4, 1, 3, 0],\n [-4, 1, 0, 4, 3],\n [1, 0, 1, 1, 0],\n [3, 4, 1, -1, -2],\n [0, 3, 0, -2, 2]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2252", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 0, -1, -1, 4],\n [-4, -2, 2, 2, 5],\n [-5, -4, -1, 3, 4],\n [5, 5, 1, 4, -1],\n [-5, 0, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61622", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 5, -2, 3, 4],\n [-5, 0, -3, 5, 3],\n [-1, 0, 5, 3, 3],\n [2, 3, -2, 0, -1],\n [-1, -2, -4, 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": "28525", "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, -2, -3, -2],\n [0, 3, 0, -1, -4],\n [-2, 0, 5, 4, 2],\n [-3, -1, 4, -3, -4],\n [-2, -4, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "407992", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, -3, 1, 0, 2],\n [-3, -3, -2, -3, 3],\n [5, -2, 0, 2, 5],\n [2, -1, -1, 0, 4],\n [1, 4, 1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7328", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[1, 0, -2, -1, 0],\n [0, 5, -2, 2, 0],\n [-2, -2, 5, 4, -1],\n [-1, 2, 4, -3, 2],\n [0, 0, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -2, 0, 5, 1],\n [-2, 0, 4, -2, 3],\n [0, 4, 2, 1, -4],\n [5, -2, 1, -1, 2],\n [1, 3, -4, 2, -5]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21542", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 1, 2, -5, -3],\n [1, 3, 2, 2, 3],\n [4, -3, 2, -5, 2],\n [1, 2, -5, 0, 1],\n [5, -1, -1, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14344", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 0, 1, -5, -4],\n [-2, 2, 5, 4, 0],\n [-5, 4, -1, 1, 0],\n [3, 2, -2, 5, -1],\n [1, 2, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22933", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the 5th power of the matrix:\n[[-2, -2, 2, -5, 2],\n [-1, 5, -5, -2, -4],\n [-2, 2, -1, -5, 1],\n [-5, 3, -3, -3, 0],\n [4, 0, 5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3036", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 4) of the result:\nA =\n[[-5, -1, 0, 2, -5],\n [-1, -3, -4, 5, 2],\n [1, 4, 1, -1, 3],\n [-1, -4, -3, -2, -1],\n [-3, 1, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-123", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 4, 4, 2, 3],\n [5, -2, -1, -1, 2],\n [3, 1, -1, -3, -5],\n [5, 3, -1, 3, 4],\n [-2, -1, -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": "16799", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -2, -1, 0, 2],\n [5, 2, 1, -2, 0],\n [-2, 1, 5, -5, -1],\n [4, 4, -2, 5, 1],\n [3, -1, -2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "723", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^4 where A is:\n[[3, 2, -2, 2, 2],\n [2, -1, 4, -3, 2],\n [-2, 4, 3, 0, 0],\n [2, -3, 0, -4, -2],\n [2, 2, 0, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, -2, 4, -4, -3],\n [-3, 3, -2, -5, -5],\n [1, 1, -4, 3, 3],\n [-1, -3, -3, -3, 0],\n [-2, 2, 5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10400", "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, -5, 2, 0, -1],\n [-5, -3, 4, 1, 4],\n [2, 4, 2, 2, 0],\n [0, 1, 2, 3, 2],\n [-1, 4, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "326312", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 1) of the matrix A^5 where A is:\n[[-5, -4, 4, -3, 2],\n [0, 4, 5, -1, -5],\n [5, 3, -3, -3, -4],\n [-2, -4, 3, 4, 1],\n [2, -3, 0, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25959", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-5, -2, 1, 4, -1],\n [-2, 4, 4, 0, 0],\n [1, 4, -1, -3, 4],\n [4, 0, -3, 2, -1],\n [-1, 0, 4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2968", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 1, -4, 0, 4],\n [1, -2, -1, 2, 0],\n [-4, -1, -3, -1, -2],\n [0, 2, -1, -3, 2],\n [4, 0, -2, 2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-26031", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -3, 4, 4, -2],\n [1, -4, -3, 1, 1],\n [4, -3, -5, -3, -1],\n [1, -2, 5, 5, -5],\n [0, -4, -3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26584", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[0, -2, 2, -1, -4],\n [-2, 4, 3, -2, 0],\n [2, 3, 0, -2, 4],\n [-1, -2, -2, -2, -2],\n [-4, 0, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "597", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, -2, -2, -2, 4],\n [-2, 5, 3, 0, -3],\n [-2, 3, -1, -1, 0],\n [-2, 0, -1, -5, 0],\n [4, -3, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35627", "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, 1, 2, 0],\n [-4, 2, 2, 4, 4],\n [1, 2, 4, 2, -2],\n [2, 4, 2, -4, 0],\n [0, 4, -2, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32351", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -3, 3, -2, -2],\n [-3, -1, -3, 3, -3],\n [-4, -1, 0, -5, 5],\n [0, 4, -3, -2, 0],\n [2, 3, 0, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-344", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, -2, 0, 2, 0],\n [-2, -5, -1, 0, 3],\n [0, -1, 1, 2, 1],\n [2, 0, 2, -1, 4],\n [0, 3, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3886", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, 4, -1, -3, 2],\n [1, -1, 4, -3, -1],\n [-3, 4, -1, -5, 0],\n [4, -2, -2, 2, -4],\n [-2, -4, -5, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12278", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 1, 2, 0, -1],\n [1, 2, 0, -2, 0],\n [2, 0, -4, -2, -1],\n [0, -2, -2, -2, 0],\n [-1, 0, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2326", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 0, 2, 2, 1],\n [0, 0, 4, 5, 0],\n [2, -5, -1, -3, 2],\n [5, 0, -4, 1, 1],\n [-1, 2, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11023", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -3, -3, -1, -1],\n [-3, -4, 1, -2, 3],\n [-3, 1, -1, 2, 0],\n [-1, -2, 2, -5, 1],\n [-1, 3, 0, 1, -3]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "426", "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, 4],\n [2, 0, 3, 0, 4],\n [1, 3, -4, 1, 0],\n [2, 0, 1, 4, 0],\n [4, 4, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "417721", "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, -4, 1, 2],\n [-2, 0, 0, 0, 0],\n [-4, 0, 5, 2, 1],\n [1, 0, 2, 2, -1],\n [2, 0, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "134300", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[5, 2, -3, -2, -4],\n [2, 2, 0, 2, 0],\n [-3, 0, 1, 2, 2],\n [-2, 2, 2, -5, 4],\n [-4, 0, 2, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5766", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, 4, 2, 2, -2],\n [4, 1, -1, 0, 2],\n [2, -1, 1, -3, -2],\n [2, 0, -3, 2, -1],\n [-2, 2, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31951", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -3, 0, 1, 2],\n [1, -3, 0, -1, 4],\n [-2, -5, 1, 2, -4],\n [1, 0, -1, -2, -4],\n [4, 0, -1, -4, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14237", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 2, 2, 4, 2],\n [2, -1, 3, 2, -4],\n [2, 3, 1, -2, -2],\n [4, 2, -2, -2, -1],\n [2, -4, -2, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7911", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 4) of the matrix A^5 where A is:\n[[0, 1, 2, 5, 3],\n [3, 2, 4, 5, -3],\n [-4, -1, -5, -3, -5],\n [-3, -2, 1, -1, -1],\n [-5, 2, -2, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8416", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-4, -5, 4, -1, -2],\n [-5, -5, 1, -4, 4],\n [4, 1, 1, -1, 0],\n [-1, -4, -1, -3, 0],\n [-2, 4, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-32001", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -3, -1, 1, -4],\n [-3, -3, 2, 0, -2],\n [-1, 2, 5, 2, 0],\n [1, 0, 2, 1, 2],\n [-4, -2, 0, 2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22440", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[-3, 3, -2, 4, -4],\n [0, -5, 0, 4, -5],\n [2, -1, 0, -4, -4],\n [3, -3, 0, 4, -1],\n [-2, 4, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-555", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 5, -4, 0, 2],\n [1, -5, -1, -4, 0],\n [1, 1, -3, 1, -1],\n [2, 2, 1, 0, -4],\n [0, 5, 3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54517", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, -1, 5, 0, -3],\n [2, 1, -4, 1, -5],\n [3, 1, 0, -4, -3],\n [-5, 4, -1, 3, 0],\n [-1, -3, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7080", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 0, 2, 1, 1],\n [0, 3, -1, 0, 0],\n [2, -1, -2, -2, 2],\n [1, 0, -2, 4, -2],\n [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": "-2314", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 0, 0, -2, 0],\n [0, -3, 0, 3, 4],\n [0, 0, 2, -2, 0],\n [-2, 3, -2, 0, 4],\n [0, 4, 0, 4, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5234", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 5) of the matrix A^4 where A is:\n[[-2, -5, -5, -2, -1],\n [1, -2, 4, -5, 5],\n [4, 1, -4, 5, -4],\n [2, 4, 4, 4, -1],\n [4, -4, -1, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-125", "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, -1, -4],\n [-4, 1, -5, 4, -4],\n [4, -2, -5, -2, 5],\n [4, -1, 3, -5, -1],\n [-4, 3, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11515", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -5, -3, 4, -5],\n [5, 5, 2, -5, -1],\n [-2, 1, -1, 2, 5],\n [-5, -1, -2, -3, -1],\n [4, -3, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4507", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 2, 0, 1, 0],\n [2, -4, 3, 0, 0],\n [0, 3, -5, 4, -2],\n [1, 0, 4, 3, -2],\n [0, 0, -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": "202730", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 1, -2, 2, -3],\n [-5, -1, -4, -3, 0],\n [-3, -3, 0, -1, 4],\n [3, -5, -3, -3, 5],\n [0, 2, -3, -3, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72819", "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, 0, 4, -3, -2],\n [-5, 2, -2, 0, 5],\n [-3, 5, 5, 0, 5],\n [3, 3, 4, -3, -3],\n [-2, 1, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29109", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 2, 0, -2, 5],\n [5, -1, -4, 0, -3],\n [0, -1, -4, -1, -1],\n [3, 5, 2, 1, -3],\n [4, -2, 0, -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": "32496", "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, -3, 1],\n [4, -3, 4, 3, -3],\n [-2, 4, -1, 0, 3],\n [-3, 3, 0, -1, 2],\n [1, -3, 3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2446", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 2, -5, -2, 0],\n [-2, 0, -1, 3, 4],\n [3, -2, -2, 2, 4],\n [-2, -4, -4, -5, -1],\n [0, 3, -1, 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": "12271", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the 4th power of the matrix:\n[[-3, -2, -3, 0, 0],\n [-2, 5, 4, 4, -2],\n [-3, 4, -4, -1, -1],\n [0, 4, -1, -1, 2],\n [0, -2, -1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1342", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[2, 0, 5, 0, -4],\n [0, 5, 2, 2, -2],\n [5, 2, -4, 0, -4],\n [0, 2, 0, -5, 0],\n [-4, -2, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67152", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 2, 5, 3, 2],\n [2, -1, -1, -1, -1],\n [5, -1, 2, 1, -1],\n [3, -1, 1, 4, 4],\n [2, -1, -1, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13991", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (2, 4) of the result:\nA =\n[[0, -3, 5, 4, 2],\n [1, -5, 4, -1, 4],\n [3, 5, 0, 2, 4],\n [-5, 4, 5, 1, -3],\n [3, 0, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, -2, 0, -2, 2],\n [-2, 2, 4, -2, 2],\n [0, 4, -3, 1, -4],\n [-2, -2, 1, 5, 2],\n [2, 2, -4, 2, 4]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1068", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 1) of the matrix A^5 where A is:\n[[1, 1, 0, 1, -4],\n [1, -4, 1, 0, -2],\n [0, 1, 3, 4, 2],\n [1, 0, 4, 5, 0],\n [-4, -2, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1617", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -3, 5, -3, -5],\n [4, -5, 0, -5, -1],\n [-2, -1, 1, 0, 3],\n [0, 3, -2, -5, -5],\n [4, 1, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14776", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 1, -1, 2, 1],\n [-4, -5, 3, -1, 5],\n [-1, 4, -2, -4, -1],\n [-4, 1, 5, 3, 3],\n [5, 0, -5, 0, -1]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5601", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 0, 0, 1, 0],\n [0, -2, 0, 2, 0],\n [0, 0, 3, -1, 0],\n [1, 2, -1, 5, 4],\n [0, 0, 0, 4, -5]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-471", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-5, -4, 4, 4, -1],\n [-2, -5, -2, -2, 4],\n [-2, -5, 3, -3, -2],\n [-1, 1, 0, -1, 2],\n [-5, 1, 0, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "438", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[1, 0, -4, 0, -1],\n [0, -3, 1, 2, 1],\n [-4, 1, 1, -2, 0],\n [0, 2, -2, -2, 2],\n [-1, 1, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-222", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 1, 0, -4, 5],\n [1, 0, -1, 2, -1],\n [5, -4, 0, -5, -1],\n [0, 1, -4, -5, 0],\n [-3, -1, 5, -4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57409", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, 5, -2, 4, -4],\n [-5, 0, -2, 4, 1],\n [5, 0, -1, 4, -4],\n [-1, 3, 3, -4, 1],\n [4, -2, -3, 5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359785", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 5, 3, 3, 1],\n [-3, -3, -2, 1, 1],\n [-4, -1, 1, 1, 0],\n [4, 4, 2, -3, -5],\n [-3, 5, -4, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1654", "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, 3, -4, 0],\n [-3, -4, -3, 4, 2],\n [3, -3, -1, 4, 0],\n [-4, 4, 4, -2, -2],\n [0, 2, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "581797", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -4, -5, 0, 0],\n [4, -4, -5, 4, -3],\n [4, -1, 0, -3, 3],\n [5, -1, -4, 4, 0],\n [2, 5, 0, -2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3080", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[2, 1, 4, 0, -1],\n [1, -4, -3, -1, 1],\n [4, -3, 4, 2, 4],\n [0, -1, 2, 2, 0],\n [-1, 1, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109328", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 5) of the matrix A^5 where A is:\n[[-2, -3, -2, 4, 1],\n [4, 2, -5, 2, -1],\n [1, 5, 5, -5, -4],\n [-5, -1, 0, 4, 3],\n [2, 1, -1, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7180", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, -4, -2, 0, 2],\n [-4, 5, -3, 0, -3],\n [-2, -3, -4, 2, 2],\n [0, 0, 2, -3, -2],\n [2, -3, 2, -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": "30552", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[2, -1, -2, 0, 4],\n [-1, 1, 1, -2, -1],\n [-2, 1, -3, -2, 2],\n [0, -2, -2, -5, 3],\n [4, -1, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-932", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 0, 4, -4, -4],\n [0, -1, 0, 4, -2],\n [4, 0, 3, 4, 0],\n [-4, 4, 4, -5, -2],\n [-4, -2, 0, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13381", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, -2, 0, -2, -2],\n [-2, 5, -2, 1, 0],\n [0, -2, -2, 4, 0],\n [-2, 1, 4, -4, -4],\n [-2, 0, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "324742", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -4, -1, 4, -3],\n [-3, 2, -2, -2, -3],\n [5, -5, 2, -5, 1],\n [-1, -2, -2, 2, 5],\n [5, 0, -5, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32055", "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, 1, 1, -1, 1],\n [1, 4, -4, 2, 0],\n [1, -4, -2, 2, 1],\n [-1, 2, 2, -4, 0],\n [1, 0, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101840", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 0, 0, 0, 4],\n [0, -1, 2, -2, -2],\n [0, 2, -1, 0, 0],\n [0, -2, 0, 3, 0],\n [4, -2, 0, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7383", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, -2, -4, -3, 4],\n [-3, -2, 0, -3, 4],\n [-5, -5, 3, 3, -1],\n [3, 5, 1, 3, 1],\n [3, -4, 5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-19196", "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, -2, -2, 0],\n [-2, 2, 0, -2, 5],\n [-2, 0, -1, 0, 0],\n [-2, -2, 0, 2, -2],\n [0, 5, 0, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9447", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 1, 0, 0, -4],\n [1, 3, -4, -2, 4],\n [0, -4, -5, 3, 1],\n [0, -2, 3, -2, -2],\n [-4, 4, 1, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "279773", "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, 2, 2, -1],\n [3, -2, 2, 4, 1],\n [2, 2, 4, -2, 0],\n [2, 4, -2, 2, -2],\n [-1, 1, 0, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9932", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 3, -3, 4, -2],\n [4, -2, 4, -1, 0],\n [-3, -2, -3, -4, 4],\n [3, -5, -4, 2, 1],\n [-5, -1, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "243451", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -4, -2, 0, 0],\n [-4, 4, -2, 4, 2],\n [-2, -2, -5, 0, 0],\n [0, 4, 0, 1, 2],\n [0, 2, 0, 2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225814", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, -4, 2, 1, 0],\n [-1, -1, 3, -5, 3],\n [0, -2, 4, 1, 3],\n [-1, -1, 2, 1, 2],\n [5, 4, -4, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84918", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 2, -4, 0, 2],\n [2, 5, -2, 2, -2],\n [-4, -2, -4, -2, 1],\n [0, 2, -2, 4, -3],\n [2, -2, 1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3754", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, -2, 4, 3, 4],\n [3, -2, 3, -3, -1],\n [4, 3, 0, -3, 4],\n [3, 0, -2, -2, 2],\n [1, -5, 0, 2, -3]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1548", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 4, -4, -2, -5],\n [4, -4, 1, -5, 2],\n [-4, 1, 4, 4, -4],\n [-2, -5, 4, -2, -2],\n [-5, 2, -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": "71780", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[4, 3, 1, -5, 2],\n [2, -2, 2, -2, 2],\n [-1, -2, 0, -4, -4],\n [-4, 3, 4, -3, 4],\n [-2, 4, 2, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5515", "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, -1, 3],\n [-2, -3, -4, -5, 5],\n [0, 4, -4, 2, 0],\n [-1, -4, 1, -4, -1],\n [-4, 5, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225420", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 0, 2, -2, -1],\n [0, -4, -1, -2, 0],\n [2, -1, -3, -1, 0],\n [-2, -2, -1, 1, -2],\n [-1, 0, 0, -2, 3]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1182", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 5) of the result:\nA =\n[[-3, -5, 4, 0, -5],\n [-5, 2, 3, -4, 3],\n [-1, 2, 1, 1, -2],\n [-4, -1, 5, 5, -3],\n [3, 0, -5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2836", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[3, 5, 0, -2, -5],\n [2, 5, -4, 5, 5],\n [2, 0, 2, 0, -1],\n [-1, 4, 4, 5, 2],\n [1, 2, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451", "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, 3, 2, 2, -2],\n [3, -5, 1, -1, 0],\n [2, 1, 5, 0, -2],\n [2, -1, 0, -5, 0],\n [-2, 0, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320609", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, -3, 1, -3, -2],\n [3, -2, -3, -1, 1],\n [-1, -2, 2, -2, -4],\n [4, 0, -4, -3, -5],\n [-1, 3, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5309", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 2, 5, 0, -2],\n [-2, -4, -3, 1, -3],\n [-1, 4, 0, 0, -2],\n [0, -3, 1, 1, -2],\n [-4, 5, 1, -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": "87515", "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, 4, -2],\n [2, -5, -1, -2, -4],\n [-1, -1, 1, -4, 0],\n [4, -2, -4, 4, -5],\n [-2, -4, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68876", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 2, -2, -2, 2],\n [2, 0, 0, -2, -3],\n [-2, 0, -3, -3, -2],\n [-2, -2, -3, 1, 0],\n [2, -3, -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": "13762", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[0, 5, -1, 2, 5],\n [-4, -5, 1, 0, 2],\n [5, 2, -4, 2, 0],\n [3, 1, -4, 2, 3],\n [1, -2, 3, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 2, -2, 2, 2],\n [2, 4, -1, 0, 0],\n [-2, -1, -4, 2, 1],\n [2, 0, 2, -1, -3],\n [2, 0, 1, -3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20875", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 1, -2, -4, -2],\n [1, 3, -3, -2, 2],\n [-2, -3, 0, 0, -1],\n [-4, -2, 0, -4, 0],\n [-2, 2, -1, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-30266", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[3, 0, 0, -3, -3],\n [0, 4, 0, 2, -2],\n [0, 0, -3, 0, 0],\n [-3, 2, 0, 2, 0],\n [-3, -2, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5214", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, -4, -1, -5, -2],\n [-4, 2, -2, -1, 5],\n [-2, -1, -1, -1, 5],\n [-3, 1, -3, -4, -3],\n [5, -3, 2, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8459", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 5) of the 4th power of the matrix:\n[[4, -1, -2, 3, 2],\n [5, 1, 2, -1, -2],\n [1, -5, 0, 2, 1],\n [-4, 1, 0, -1, -2],\n [-5, -4, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-362", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-1, 2, 2, 0, -1],\n [-4, 3, -5, 5, -4],\n [-5, -2, -2, -1, -1],\n [2, 5, 5, -3, 0],\n [-3, -4, 2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12255", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, -1, 4, 0, 1],\n [-1, 0, 1, 1, -3],\n [4, 1, 5, -1, 0],\n [0, 1, -1, 2, -2],\n [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": "12891", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -2, 5, 2, 1],\n [-2, -2, 0, 0, -3],\n [5, 0, -2, 0, 2],\n [2, 0, 0, 5, 2],\n [1, -3, 2, 2, 3]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-587", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[5, 4, 4, 0, -2],\n [4, -1, -2, -2, 2],\n [4, -2, -5, 4, -2],\n [0, -2, 4, 2, 0],\n [-2, 2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38136", "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, 5, 0, -4],\n [-1, -3, 1, -2, -5],\n [0, 0, 1, 5, 2],\n [-3, 0, 4, -4, 3],\n [-4, -3, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1929", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-5, -1, -5, -1, 2],\n [2, 5, 2, -4, 2],\n [-1, -5, 1, 0, -1],\n [-5, -5, 0, 4, 1],\n [4, 4, -5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "378030", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, -4, 2, 3, 0],\n [-4, 3, -2, -1, 0],\n [2, -2, 4, -1, 0],\n [3, -1, -1, -4, 0],\n [0, 0, 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": "15357", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[1, 0, 4, 2, 2],\n [0, -3, 0, 1, -2],\n [4, 0, 0, -2, -4],\n [2, 1, -2, 1, -2],\n [2, -2, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5128", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, -1, -2, -3, 0],\n [-1, 3, -2, 1, -2],\n [-2, -2, 4, 0, -4],\n [-3, 1, 0, 0, 1],\n [0, -2, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68551", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[-1, 0, -2, 2, -1],\n [0, -4, 2, 2, -1],\n [-2, 2, -3, 2, 3],\n [2, 2, 2, 2, 2],\n [-1, -1, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-952", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[5, -5, -4, 5, -4],\n [1, 0, 5, -4, 2],\n [3, 1, -2, -5, -2],\n [-2, 2, -2, -2, -4],\n [4, 1, -2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29396", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-3, 2, 2, -2, 2],\n [2, -1, 4, -1, -3],\n [2, 4, 1, -3, -1],\n [-2, -1, -3, 5, 2],\n [2, -3, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3629", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 1, 0, 5, -1],\n [1, 4, 1, 4, -2],\n [0, 1, 2, 4, 1],\n [5, 4, 4, 3, 0],\n [-1, -2, 1, 0, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "796152", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 4, 4, -4, 0],\n [0, 3, 3, -1, -1],\n [3, 2, 1, 2, 0],\n [-3, 1, 2, 2, -5],\n [1, -3, -4, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27201", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -3, -3, 0, 5],\n [4, -5, 0, -3, 5],\n [-2, 3, -3, -5, -3],\n [1, 1, 5, -1, -5],\n [5, 2, 4, 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": "26754", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 4, -4, 4, -3],\n [-2, -5, -2, -1, -3],\n [5, 4, -4, 0, 2],\n [1, 5, -5, -2, -3],\n [0, 3, 3, 1, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41009", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -1, 3, 1, -1],\n [2, 1, 3, 4, -5],\n [3, 1, -5, -5, -1],\n [2, 3, 0, 4, 2],\n [0, 5, 0, -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": "14433", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -2, 0, -4, 3],\n [-2, -1, -2, 1, 0],\n [0, -2, -2, -2, 0],\n [-4, 1, -2, -4, 4],\n [3, 0, 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": "412614", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, -2, 0, 0, 4],\n [-2, -1, 1, 4, -2],\n [0, 1, -2, -1, -2],\n [0, 4, -1, -2, -2],\n [4, -2, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "558", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, -3, 4, 0, 0],\n [3, 3, -2, 3, 0],\n [-4, 4, 5, 0, -4],\n [2, -2, -1, 2, 5],\n [2, 0, -2, -5, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18782", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 3, -4, -5, -2],\n [-1, 4, -5, -1, 0],\n [-3, 1, 0, -2, -3],\n [-1, -3, 4, 3, 3],\n [0, 5, 0, -2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6947", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[-4, 0, 2, 2, 4],\n [0, 3, -2, -2, -1],\n [2, -2, 1, -2, 2],\n [2, -2, -2, 5, -2],\n [4, -1, 2, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-218", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 4) of the result:\nA =\n[[3, -3, -2, 1, 4],\n [2, 2, -2, 1, 4],\n [-5, 0, 0, 0, -4],\n [2, -1, -1, -4, -2],\n [3, 3, 0, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8723", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 5, -5, -4, -5],\n [2, 3, 4, 0, -4],\n [0, 3, -3, 3, -4],\n [5, -1, 5, -4, 1],\n [5, 4, 3, 1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28893", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 1, 2, 3, 2],\n [1, 4, 0, 3, -2],\n [2, 0, 5, 2, 2],\n [3, 3, 2, 3, 2],\n [2, -2, 2, 2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "318400", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, -2, 1, 5, 2],\n [1, -3, -2, 1, 2],\n [1, 0, 3, 3, 5],\n [1, 2, 0, -5, -5],\n [0, -4, 2, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1602", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[2, 2, 2, -4, -2],\n [2, 1, 1, -2, 0],\n [2, 1, -2, 0, 0],\n [-4, -2, 0, -5, -2],\n [-2, 0, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[-5, 2, -4, 1, 5],\n [3, 0, -4, -4, 3],\n [4, 2, 3, -2, -2],\n [-4, 4, -5, 4, -2],\n [4, 4, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "190", "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, 0, -2, -2],\n [2, 3, -2, 0, 3],\n [0, -2, 3, 0, -2],\n [-2, 0, 0, -3, -5],\n [-2, 3, -2, -5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "265062", "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, 2, 2, -3, 0],\n [1, 3, -1, 3, 0],\n [4, 4, 4, -2, -5],\n [-5, 4, -1, -3, -1],\n [-1, -5, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15199", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[3, -2, 0, -2, 2],\n [-2, -5, -2, 1, -2],\n [0, -2, 5, 0, -2],\n [-2, 1, 0, 0, 0],\n [2, -2, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1465", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[5, 3, 0, 0, 2],\n [3, -2, 4, -1, 2],\n [0, 4, -1, 3, 2],\n [0, -1, 3, -5, 0],\n [2, 2, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2095", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 0, -2, 4, 2],\n [0, 1, -4, 0, 0],\n [-2, -4, -2, -2, 3],\n [4, 0, -2, -3, 2],\n [2, 0, 3, 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": "170589", "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, -2, 4, -4],\n [-2, -4, -3, -2, -2],\n [4, 3, 4, 0, 3],\n [-2, 3, 5, 3, 0],\n [-1, -3, -1, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3288", "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, -1, 0, -2],\n [-2, -2, 3, -3, -1],\n [-1, 3, -5, -1, -2],\n [0, -3, -1, 1, 0],\n [-2, -1, -2, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58997", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[5, 2, -1, 5, -1],\n [-5, 0, -2, -3, 0],\n [-4, 2, -5, 3, 2],\n [-5, 4, 3, -4, -3],\n [-4, 2, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1113", "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, -2],\n [0, -3, -3, -2, 1],\n [-3, -3, -4, 0, -2],\n [2, -2, 0, -3, -4],\n [-2, 1, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38875", "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, 2, 0],\n [-4, 3, -2, 4, -2],\n [-3, -2, 3, -1, 0],\n [2, 4, -1, -2, -2],\n [0, -2, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182287", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[1, 2, -2, -2, 1],\n [2, 5, -1, 0, -2],\n [-2, -1, 4, 0, 0],\n [-2, 0, 0, -5, -4],\n [1, -2, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164", "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, -2, -2, 1],\n [-3, 2, 2, 5, 1],\n [-4, -1, 0, 4, -2],\n [4, -1, 3, 5, 1],\n [-4, 5, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-370", "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, -4, 5, -3, 4],\n [5, 5, 3, -2, 3],\n [5, -3, -5, 5, -1],\n [4, 4, -4, -2, -4],\n [-4, -3, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210941", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 3) of the 4th power of the matrix:\n[[5, 4, 0, 2, 0],\n [4, 0, -1, -2, 2],\n [0, -1, -5, 3, -2],\n [2, -2, 3, 5, -1],\n [0, 2, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-326", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[-1, 4, 1, 2, 0],\n [4, 4, 1, 0, -2],\n [1, 1, -3, 4, 0],\n [2, 0, 4, 3, -1],\n [0, -2, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "858", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 4, -1, 4, -1],\n [4, -3, 1, 1, 3],\n [-1, 1, -3, 0, 4],\n [4, 1, 0, 0, -2],\n [-1, 3, 4, -2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2439", "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, 1, 0, -4, 1],\n [1, -2, -4, -2, -2],\n [0, -4, -2, -2, 4],\n [-4, -2, -2, -3, -2],\n [1, -2, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19929", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 5, 0, 5, 4],\n [-2, 2, 3, -4, 1],\n [3, 3, -1, -5, 0],\n [2, -5, -4, -5, -1],\n [-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": "10030", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 2, -1, -4, 2],\n [-5, 1, -5, 0, 0],\n [-1, -4, -4, 3, -1],\n [-1, 1, 0, -4, 5],\n [-5, -1, -2, -3, -4]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -4, -2, -4, -2],\n [-3, 3, 1, 5, -3],\n [2, 3, 1, 0, -2],\n [-1, 2, -3, -4, -3],\n [1, 2, -5, 1, 3]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-3, -3, 2, -2, 2],\n [-1, -3, -2, -2, 2],\n [0, 1, 3, 0, -3],\n [-3, 5, -3, 4, -4],\n [-5, 5, 4, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6887", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[-3, -1, 1, 1, -1],\n [-1, 2, -2, 1, -2],\n [1, -2, -1, 0, -2],\n [1, 1, 0, 4, 1],\n [-1, -2, -2, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 2, 2, -2, 0],\n [2, -4, 2, 2, 0],\n [2, 2, 4, 0, 0],\n [-2, 2, 0, -5, -2],\n [0, 0, 0, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13389", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, -2, 5, -4, -3],\n [-1, 5, -4, -2, -5],\n [-2, 1, -3, 4, 2],\n [0, 0, -5, -1, -3],\n [4, -5, 2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2506", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 4, 4, -2, 5],\n [0, 3, -3, 3, -2],\n [-1, 1, 0, 4, 2],\n [2, 2, -3, 4, 0],\n [1, 3, 4, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75280", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 2) of the result:\nA =\n[[-1, 2, -5, 0, -2],\n [-1, 5, -1, -4, 2],\n [-4, -2, -1, -5, 0],\n [-4, -1, 0, 5, 2],\n [3, 0, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9153", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 1, -1, 1, 5],\n [-5, -5, -1, -4, 2],\n [-3, -5, -4, 4, 4],\n [1, 0, 2, 1, 4],\n [2, -3, 0, 1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8429", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[5, -4, -4, 2, 2],\n [-4, -3, -2, 1, 0],\n [-4, -2, 0, 1, 2],\n [2, 1, 1, 0, 2],\n [2, 0, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153471", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 2) of the matrix A^5 where A is:\n[[-5, 5, 3, -1, -5],\n [2, 1, 1, -1, -5],\n [3, 5, 3, 2, -1],\n [-3, 2, -5, -3, 5],\n [1, -2, 1, 5, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6941", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 1, 4, 1, 1],\n [1, 5, 1, -3, -3],\n [1, -4, -4, -3, -2],\n [0, 2, 4, 4, 1],\n [-2, -4, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1163", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 1, 1, 0, -4],\n [1, -1, 4, -4, 2],\n [1, 4, -5, -2, 0],\n [0, -4, -2, -2, -2],\n [-4, 2, 0, -2, -2]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3717", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 2, 0, -2, 0],\n [2, 2, 0, 0, 0],\n [0, 0, 3, -2, -4],\n [-2, 0, -2, 5, -4],\n [0, 0, -4, -4, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3344", "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, -4, -4, -3],\n [1, 5, -3, -5, 0],\n [-3, -5, -2, -5, -5],\n [-4, 4, 2, -4, 5],\n [-4, 5, 5, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31759", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 3) of the 5th power of the matrix:\n[[2, 0, 5, -2, -3],\n [-5, 5, -3, 3, -1],\n [0, -1, -5, 4, -5],\n [-2, -3, 5, 2, 1],\n [5, 1, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16910", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -4, -2, 2, -1],\n [-4, -3, -2, 0, -5],\n [-2, -2, 4, 3, -4],\n [2, 0, 3, -1, 1],\n [-1, -5, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45300", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, -4, 5, -5, 4],\n [-4, 0, -3, 4, -1],\n [-5, 2, -2, 3, -2],\n [-4, -3, -1, 4, 0],\n [1, -2, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29925", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, -2, 2, 3, 1],\n [2, 2, -4, 3, 0],\n [5, -2, -1, 4, -1],\n [1, 3, 1, 3, -2],\n [4, 4, -2, 0, 2]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2582", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, -2, -3, 4, 4],\n [-2, 3, 1, -2, 0],\n [-3, 1, -1, 2, -4],\n [4, -2, 2, -4, 3],\n [4, 0, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39825", "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, -4, 0, -1, -4],\n [-4, 3, -2, 0, -1],\n [0, -2, -1, 0, 1],\n [-1, 0, 0, 1, -3],\n [-4, -1, 1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8363", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 4) of the result:\nA =\n[[3, 2, -3, -4, 4],\n [1, 1, 3, -1, -2],\n [2, -2, -2, -4, -5],\n [-2, 1, 3, 3, 4],\n [-5, -1, 1, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-565", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 1) of the 5th power of the matrix:\n[[0, 4, 2, 2, -2],\n [4, 4, -1, 2, 0],\n [2, -1, -5, -2, 2],\n [2, 2, -2, -3, -3],\n [-2, 0, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13806", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 1, 3, -4, -1],\n [5, 4, 3, -3, -5],\n [-4, 0, -1, -5, -5],\n [5, -2, -2, 0, 0],\n [4, 0, -5, 4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-57043", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 1) of the result:\nA =\n[[5, 1, 1, 5, 1],\n [-4, -4, 0, 1, -3],\n [-2, -3, 1, 1, -2],\n [1, -1, -5, 4, -2],\n [1, -4, -4, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7035", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 2, 5, 2, 2],\n [-5, -5, 4, -2, 0],\n [2, -4, -3, 0, 4],\n [-2, -4, 1, -2, 2],\n [2, 1, 4, 3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, 0, 2, -2, 0],\n [0, 3, 2, -1, -2],\n [2, 2, -5, 2, -1],\n [-2, -1, 2, -2, 0],\n [0, -2, -1, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "839", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 1) of the matrix A^5 where A is:\n[[2, -1, 3, 3, -3],\n [4, 0, 0, -2, 5],\n [4, -3, -5, 1, -1],\n [4, 1, -5, 2, -3],\n [1, -3, -3, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3632", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 3) of the result:\nA =\n[[-4, 1, -2, 0, 2],\n [1, 1, 0, -1, -2],\n [-2, 0, -2, 2, 0],\n [0, -1, 2, 2, 0],\n [2, -2, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3792", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -2, 2, -1, 0],\n [-2, 3, 2, 2, 0],\n [2, 2, 5, 0, -1],\n [-1, 2, 0, -1, 0],\n [0, 0, -1, 0, -3]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4626", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, 2, 1, 0, -4],\n [1, 2, -5, 3, -2],\n [2, 4, 1, 4, 1],\n [-4, -5, -2, -4, 2],\n [4, 1, 2, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8062", "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, 4, -5],\n [-5, 2, 0, 2, 2],\n [5, 2, 4, 1, 1],\n [4, -2, 3, -4, 5],\n [3, 4, -3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1082", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, -4, -5, 4, 5],\n [-1, 3, -1, 5, 4],\n [3, 4, 0, -3, -2],\n [-2, -5, -3, -3, -5],\n [3, 5, -5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11204", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, -4, -2, 0, 4],\n [-4, -3, -4, 4, 3],\n [-2, -4, 4, 3, 0],\n [0, 4, 3, 0, 4],\n [4, 3, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690990", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 2) of the matrix A^4 where A is:\n[[-1, -1, 2, 4, -2],\n [3, 1, 1, -3, -2],\n [1, 5, 5, -1, -3],\n [-5, 1, 0, 4, 1],\n [-4, -2, -4, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-972", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 3) of the result:\nA =\n[[-5, -4, -4, -2, -3],\n [-5, -4, 5, 3, -5],\n [3, 1, -4, -4, -1],\n [-1, -2, 4, 4, -3],\n [-2, 4, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6222", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the 4th power of the matrix:\n[[-1, -3, 2, 2, 4],\n [-3, 0, 2, -4, 2],\n [2, 2, -1, -2, 0],\n [2, -4, -2, -4, -2],\n [4, 2, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "925", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 0, -3, -2, -5],\n [2, -5, -1, 0, -4],\n [1, 1, -5, -2, -2],\n [-1, -5, -5, 1, 3],\n [-5, -4, 0, 0, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-544680", "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],\n [2, -3, -2, 0, 4],\n [-1, -2, -4, 4, -3],\n [2, 0, 4, -4, -2],\n [4, 4, -3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258539", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -1, 0, 0, 0],\n [-1, 3, 1, 2, 0],\n [0, 1, -5, 0, -3],\n [0, 2, 0, -3, 0],\n [0, 0, -3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6645", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, -4, 0, 1, -1],\n [-4, 0, -3, 3, 2],\n [0, -3, -2, -1, 4],\n [1, 3, -1, 2, 0],\n [-1, 2, 4, 0, -2]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9119", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 0, 1, 3, 1],\n [0, 1, 0, 2, 2],\n [1, 0, 1, -2, 2],\n [3, 2, -2, 4, -2],\n [1, 2, 2, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8091", "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, 3, 2],\n [2, 4, -5, 0, 3],\n [2, -3, -2, -3, 0],\n [3, 2, 4, -2, -4],\n [2, 2, 5, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20647", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 3) of the result:\nA =\n[[3, -5, 3, -4, -5],\n [2, 2, 5, -2, 2],\n [1, -4, -1, 4, -2],\n [-3, -5, -1, 4, 2],\n [3, 1, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10019", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, 0, -1, -2, 4],\n [0, -2, 0, -2, 2],\n [-1, 0, -5, -2, 0],\n [-2, -2, -2, 4, -4],\n [4, 2, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17029", "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, -5, -1, -3],\n [-2, -2, 5, 1, 4],\n [5, 2, 5, 4, -1],\n [4, 1, -3, -3, -3],\n [-2, 0, -1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43873", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, -1, 4, -4, 5],\n [5, -1, 1, -4, 0],\n [1, -1, 3, -2, 4],\n [-5, 2, 2, 1, 2],\n [-4, -3, 3, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15694", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[2, 1, 5, -1, -2],\n [4, 4, 4, 4, 0],\n [5, -5, -1, -2, -2],\n [1, 3, 2, 5, 2],\n [-1, 0, -4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9546", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[-1, -4, -3, -2, 0],\n [-1, 4, -2, -4, 5],\n [-1, -1, 5, 1, -5],\n [-2, 5, -1, 2, 2],\n [-5, -1, 4, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, 0, 1, 0, -2],\n [0, -5, -3, -1, 2],\n [1, -3, -1, 4, 0],\n [0, -1, 4, 2, -2],\n [-2, 2, 0, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2565", "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, -1, 2, -1],\n [3, -4, 1, 0, -2],\n [-1, 1, 1, -3, 2],\n [2, 0, -3, 1, -3],\n [-1, -2, 2, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171542", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, 1, 4, 0, -1],\n [1, -3, 0, -2, 1],\n [4, 0, 3, 0, 0],\n [0, -2, 0, 4, -2],\n [-1, 1, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99992", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -3, -4, 5, 0],\n [-3, -4, -5, 2, -5],\n [-1, 5, 0, 5, -3],\n [1, -4, 1, -4, -1],\n [1, 5, 5, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1063", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -5, -3, 3, 4],\n [-1, 2, -4, -3, 1],\n [4, -2, 3, 1, 5],\n [-5, -2, 4, 5, 0],\n [0, 4, 0, -1, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1637", "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, 2, -4, 0],\n [-4, -4, 2, -2, -4],\n [2, 2, 1, -4, 0],\n [-4, -2, -4, 1, -2],\n [0, -4, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554432", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 3, 0, -2, 2],\n [3, -5, 2, -3, 0],\n [0, 2, -4, -2, -2],\n [-2, -3, -2, 4, -2],\n [2, 0, -2, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19924", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, -1, -4, -4, -2],\n [-1, -1, 0, 0, 1],\n [-4, 0, 4, 0, -4],\n [-4, 0, 0, -4, -3],\n [-2, 1, -4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-168564", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 1) of the 5th power of the matrix:\n[[4, -5, -2, 0, -2],\n [1, 1, 0, 3, -4],\n [4, 2, 2, 5, 4],\n [5, -2, 0, 5, 0],\n [-1, -5, -3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12388", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, -3, -1, 4, 2],\n [-3, -1, 0, -2, 0],\n [-1, 0, 3, 4, -4],\n [4, -2, 4, 0, 0],\n [2, 0, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4301", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 3) of the matrix A^5 where A is:\n[[3, 2, 2, 0, -2],\n [2, -1, 1, -1, -1],\n [2, 1, 4, -2, 2],\n [0, -1, -2, -5, 2],\n [-2, -1, 2, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5038", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, 2, 3, -4, 1],\n [-4, 0, -4, 4, 0],\n [-4, -5, 1, -3, -2],\n [0, -1, -2, 3, 0],\n [0, -4, 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": "10422", "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, 4, 5, -3],\n [4, 1, 1, -5, 2],\n [-2, -1, 0, -3, -1],\n [4, -1, -5, -3, -3],\n [-5, 1, -5, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30087", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, 1, -1, 1, 3],\n [4, 0, -5, 0, -5],\n [-2, 2, -1, -1, 4],\n [5, 2, 2, -5, -1],\n [-1, 2, -5, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3888", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[3, -4, -3, -2, -5],\n [1, 4, -3, -3, -3],\n [2, 3, 4, -4, 4],\n [4, -5, 3, 0, 3],\n [0, -4, -5, 2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1916", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 3) of the result:\nA =\n[[-5, 2, -3, 1, 0],\n [2, 3, 2, -4, 0],\n [-3, 2, 3, 0, -2],\n [1, -4, 0, 2, 0],\n [0, 0, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-432", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 2, 0, -5, 1],\n [-5, -3, 2, 3, -3],\n [-5, -5, 1, -1, -5],\n [0, 0, -2, 1, 1],\n [3, -5, -1, 4, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1250", "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, -5, -5],\n [4, -4, -4, -5, 2],\n [0, 0, 4, 4, 3],\n [-1, -2, 5, 0, 2],\n [-5, 1, 2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87667", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[2, 1, -3, -4, -3],\n [-2, -2, 0, 1, -2],\n [4, 0, 3, 0, -3],\n [-5, 5, 4, 4, -1],\n [4, 4, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2078", "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, 4, -2, -2, -2],\n [4, -1, -1, 2, 4],\n [-2, -1, 5, -2, 2],\n [-2, 2, -2, 4, 1],\n [-2, 4, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "327556", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-1, -1, -2, 1, 0],\n [-1, -4, 2, 0, -3],\n [-2, 2, 2, 1, 0],\n [1, 0, 1, -4, -2],\n [0, -3, 0, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23029", "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, -3, -5, 2],\n [1, -4, 1, -3, 3],\n [2, -1, 1, -3, -5],\n [-5, 5, -4, 2, -5],\n [5, -1, 3, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37245", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 4, -4, 0, -1],\n [4, 4, -4, 2, 0],\n [-4, -4, 0, 4, 2],\n [0, 2, 4, 3, -3],\n [-1, 0, 2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3928", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 1, -1, 1, 4],\n [1, -1, 0, -3, 0],\n [-1, 0, 4, -2, -2],\n [1, -3, -2, 1, -4],\n [4, 0, -2, -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": "146475", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -5, -5, -5, -2],\n [-2, 2, -5, 4, -3],\n [5, -5, 3, 4, 3],\n [1, 2, -5, -1, -4],\n [-5, -3, 1, -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": "79369", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, -4, -2, -3, -3],\n [4, -1, -3, 5, 1],\n [-1, -2, -3, -2, -4],\n [-5, -3, 5, -4, -5],\n [-5, -4, 3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43036", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 5, 0, -5, 4],\n [-1, -5, 1, 4, 5],\n [2, 2, 1, -4, -1],\n [-2, -1, 4, 3, -2],\n [2, 2, -4, 0, -1]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3412", "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, 0, 0, -4],\n [4, 4, -4, 0, -2],\n [0, -4, -2, -4, -3],\n [0, 0, -4, 5, -2],\n [-4, -2, -3, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382396", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 5, 2, 0, -3],\n [0, 1, 0, 4, 0],\n [-5, -3, 1, -2, -2],\n [1, 3, 5, -4, 3],\n [-3, 0, -2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12198", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 0, 2, -4, 1],\n [0, -4, -4, -2, -2],\n [-3, 2, 1, -4, -3],\n [4, 3, -1, -4, -3],\n [2, -2, -4, -4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7994", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 0, 0, 0, 0],\n [0, 3, -1, 2, 2],\n [0, -1, -4, -2, 2],\n [0, 2, -2, 4, 4],\n [0, 2, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10422", "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, 1, -1, -4],\n [-1, 1, 1, -2, -5],\n [0, -3, 5, -1, -2],\n [-4, 1, -1, 1, 3],\n [-2, -1, 3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42641", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, -1, -1, 2, -2],\n [-2, 1, 5, -1, 0],\n [0, 0, 4, -1, -1],\n [3, 2, -2, 1, 2],\n [3, -1, -3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35852", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[0, 4, 5, -1, 3],\n [5, 5, -3, -4, 0],\n [1, -1, -5, -3, -3],\n [-2, 4, 0, -1, -5],\n [0, 3, 5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2353", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[2, 0, 1, 1, 4],\n [0, -3, 4, -1, 1],\n [1, 4, -2, 1, 0],\n [1, -1, 1, 2, -3],\n [4, 1, 0, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, -4, 4, -4, 3],\n [1, 0, 1, 2, -5],\n [2, -3, -3, 0, -2],\n [-2, -2, 4, 3, 2],\n [-3, -5, -5, -5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40162", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -2, 5, 5, -3],\n [2, 2, 0, 3, 4],\n [-5, 2, 0, -5, -2],\n [-1, 1, 2, 3, 0],\n [4, 3, -2, 2, -3]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-902", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 2) of the matrix A^5 where A is:\n[[-2, 4, -2, 0, 3],\n [0, -5, -1, 3, -1],\n [0, -3, 2, 4, 5],\n [-2, -2, 5, -1, 4],\n [3, 2, 1, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5189", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, 4, 4, -4, -2],\n [2, -5, -1, 2, -4],\n [-4, 2, 4, 3, 1],\n [2, -1, -5, -2, -4],\n [-3, -3, 3, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3402", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -3, -3, 1, 2],\n [5, 0, -2, 0, 5],\n [-5, 4, 2, -5, -1],\n [-4, 0, 3, -1, -2],\n [-4, -3, 0, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2223", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[-1, -1, 4, -3, 1],\n [0, -5, -2, 0, 5],\n [0, 5, -3, 0, 4],\n [0, 3, 3, -4, -2],\n [3, -2, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15416", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, -1, 0, 2, -2],\n [-1, 4, -4, -1, 5],\n [0, -4, 2, 4, 1],\n [2, -1, 4, 4, -2],\n [-2, 5, 1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "988637", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 3) of the 5th power of the matrix:\n[[3, 3, -1, -2, 3],\n [3, -3, -1, -3, 4],\n [-4, -5, 4, -4, 2],\n [5, 2, -3, 1, 1],\n [-4, 3, -3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5306", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 4, -3, 0, -3],\n [4, 5, 3, 2, 2],\n [-3, 3, -5, -2, 0],\n [0, 2, -2, 0, -2],\n [-3, 2, 0, -2, -3]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1631", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, -1, 0, -2, -4],\n [-1, -2, 0, 0, -4],\n [0, 0, -2, -2, 0],\n [-2, 0, -2, 2, -4],\n [-4, -4, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-378847", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 2) of the matrix A^5 where A is:\n[[5, 1, -5, 5, -3],\n [0, 0, 0, 5, -4],\n [-4, 0, 4, -1, 1],\n [1, -1, 2, 4, 0],\n [-1, -2, 1, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2219", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, -5, -5, -3, 5],\n [-3, -4, -4, 0, -5],\n [0, -1, 0, -1, 1],\n [-5, -3, 0, -5, 5],\n [5, 1, -2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47855", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 0, 2, -2, -2],\n [0, 2, 0, 0, 0],\n [2, 0, 5, 1, 2],\n [-2, 0, 1, -4, -1],\n [-2, 0, 2, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5422", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 2, -2, -4, -2],\n [2, 4, 2, 0, -2],\n [-2, 2, 4, -1, -3],\n [-4, 0, -1, 4, -1],\n [-2, -2, -3, -1, -3]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, 5, -3, 4, -5],\n [-3, 3, -2, -3, 2],\n [-5, -1, -5, 1, -1],\n [-4, -5, 5, 1, -5],\n [-3, 5, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-39909", "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, -5, 1, -4],\n [0, 2, -1, 4, -3],\n [5, 2, 2, -2, 2],\n [-1, 5, -1, -3, 1],\n [5, 5, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "260352", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 4, 5, -1, -5],\n [-2, -5, -4, -4, -2],\n [2, -4, 3, 3, -4],\n [-5, 4, 4, 3, -4],\n [2, -3, -5, 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": "52002", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -4, 0, 2, 4],\n [-4, -2, 0, -2, 0],\n [0, 0, -1, 1, 2],\n [2, -2, 1, 1, 1],\n [4, 0, 2, 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": "36930", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 2, 2, 2, 0],\n [2, 4, 0, 2, -3],\n [2, 0, 5, 0, 1],\n [2, 2, 0, -4, 0],\n [0, -3, 1, 0, 5]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2684", "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, 2, -5, 3, 1],\n [-4, 5, 0, 2, 5],\n [-1, 0, 4, 2, 0],\n [3, 3, 3, 0, 3],\n [-3, -1, -4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14981", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, 0, 0, -1, -5],\n [5, 1, 4, 2, -5],\n [4, 1, -2, 0, 3],\n [-1, 2, -1, -4, -2],\n [-4, 1, 1, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29508", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, -2, 0, -1, 1],\n [-2, 0, -4, 0, 2],\n [0, -4, -5, -2, -1],\n [-1, 0, -2, 5, 0],\n [1, 2, -1, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12067", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, 3, -2, -3, 4],\n [5, 0, -3, -5, -2],\n [-5, -4, -3, 2, 4],\n [-2, -2, 4, 3, 1],\n [-4, -3, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "877", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 4) of the result:\nA =\n[[2, 4, 4, 0, -3],\n [5, 3, 4, 2, 3],\n [-1, -3, -2, -1, 3],\n [3, -3, 1, 0, -2],\n [-1, 4, -4, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "422", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[-2, -4, 3, 0, 1],\n [-4, 4, 0, -2, -3],\n [3, 0, -1, -1, -1],\n [0, -2, -1, 1, -4],\n [1, -3, -1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 1, 5, -2, 3],\n [2, 2, -1, -5, 3],\n [-4, 0, 4, -1, 4],\n [2, 5, -3, 0, 0],\n [4, -3, 1, 5, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3402", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 3) of the 5th power of the matrix:\n[[-1, 2, 0, 3, -3],\n [2, 3, 4, 1, -3],\n [0, 4, 2, -3, -4],\n [3, 1, -3, 2, 0],\n [-3, -3, -4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46248", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 2, -2, 1, 4],\n [-3, 4, 5, -3, -4],\n [0, 0, -5, 1, -2],\n [5, -3, 2, -4, 3],\n [2, 2, -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": "23973", "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, 0, -1, -5],\n [4, -5, 0, -3, -3],\n [1, -5, -5, 4, -3],\n [2, -5, 4, -2, 3],\n [-2, 4, 2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34233", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 2, 0, 0, -4],\n [2, -5, 2, 0, -2],\n [0, 2, 1, -2, -2],\n [0, 0, -2, -4, 0],\n [-4, -2, -2, 0, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9120", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, 5, 2, 1, -5],\n [0, 1, 5, -2, -4],\n [4, 3, 1, -5, 2],\n [-3, -2, -1, -5, 0],\n [4, 0, -4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5662", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 2, 0, -2, -2],\n [3, 0, 2, 2, 1],\n [-3, 4, -5, -1, 4],\n [4, -4, 4, -4, 1],\n [5, -3, 2, 3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8406", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -1, -3, -3, 1],\n [-1, 0, 0, 3, -5],\n [2, 4, -1, 0, 0],\n [-5, -3, 0, 5, 5],\n [3, 0, 0, -5, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129478", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -2, -2, -3, -2],\n [-2, -5, -2, -4, 1],\n [-2, -2, 1, 2, 3],\n [-3, -4, 2, 5, 2],\n [-2, 1, 3, 2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7684", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 4, 0, -4, -4],\n [5, -2, 3, -3, 0],\n [-4, -5, -1, 2, 4],\n [4, -4, 4, 3, 2],\n [-3, -5, -2, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157609", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[4, -4, 1, -2, 0],\n [-1, -4, 4, -4, 3],\n [5, 4, -4, 2, 2],\n [-5, -5, -2, -4, -5],\n [3, -3, -5, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-192734", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, 2, 2, 0, -4],\n [2, 5, 1, 0, 2],\n [2, 1, 5, -2, 1],\n [0, 0, -2, -4, 0],\n [-4, 2, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112038", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, -4, 0, -2, -1],\n [-4, -3, 0, 3, 2],\n [0, 0, 3, 4, 4],\n [-2, 3, 4, 4, -2],\n [-1, 2, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17687", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 5) of the 5th power of the matrix:\n[[4, -2, -1, -2, 2],\n [2, -3, -5, 0, -4],\n [-4, -3, 2, -3, 1],\n [4, 4, 3, 2, -5],\n [1, 1, 2, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7191", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 3, 3, 2, 0],\n [0, -5, 0, -2, -2],\n [-4, 5, -2, -1, -1],\n [-1, -2, -5, 4, 2],\n [-3, -4, 3, 1, 3]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8456", "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, 3, 4, 3, 5],\n [3, 4, 4, -2, 4],\n [-3, 0, -3, 5, 3],\n [-3, -4, 2, 0, 2],\n [1, -3, 2, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166210", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the 4th power of the matrix:\n[[-5, 2, 1, 4, 0],\n [2, -1, -1, 4, 0],\n [1, -1, 3, 0, -1],\n [4, 4, 0, -3, -4],\n [0, 0, -1, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2406", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[5, -1, -2, -5, 3],\n [-2, -1, 1, -4, 2],\n [5, -4, 5, 4, -1],\n [-4, -4, -2, -2, 2],\n [0, 4, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7492", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, -4, 3, -4, -5],\n [2, 4, 3, -5, 1],\n [-4, 0, 5, -1, -5],\n [-4, -4, 4, 4, 0],\n [5, -5, 5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12898", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[5, 0, 0, 0, -2],\n [0, 0, -5, 0, 4],\n [0, -5, -4, 0, 2],\n [0, 0, 0, -2, -2],\n [-2, 4, 2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-956", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, 2, -2, -3, 1],\n [2, -2, 0, 0, -4],\n [-2, 0, -1, 0, 1],\n [-3, 0, 0, -1, 2],\n [1, -4, 1, 2, -4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3744", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, -2, 4, 2, -1],\n [-2, 4, -2, 2, 0],\n [4, -2, 2, 2, 1],\n [2, 2, 2, -5, 4],\n [-1, 0, 1, 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": "374926", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 4, -1, 5, 3],\n [0, 2, 2, 1, -1],\n [-4, 4, 4, -1, 1],\n [1, 5, -4, 1, 0],\n [1, 5, 2, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7922", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 5) of the result:\nA =\n[[2, 2, -3, -3, -1],\n [-3, -1, 2, -5, -4],\n [-4, -2, 3, -4, 5],\n [3, 1, 4, 2, -5],\n [-1, 3, -2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-706", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, -3, 2, -3, -4],\n [0, -3, -5, -3, 0],\n [-3, 3, 1, -1, -4],\n [3, -1, 1, 3, -2],\n [3, -5, 0, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10321", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, 0, -4, 1, 0],\n [0, 2, 0, -3, -2],\n [-4, 0, 5, -1, 1],\n [1, -3, -1, -3, 4],\n [0, -2, 1, 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": "153536", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, 0, 0, 0, 4],\n [0, -3, 2, -2, 4],\n [0, 2, -2, -3, 2],\n [0, -2, -3, 3, 0],\n [4, 4, 2, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3379", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[-5, -2, 0, 2, -2],\n [-2, -4, 0, 4, -2],\n [0, 0, -3, -4, 0],\n [2, 4, -4, -1, -2],\n [-2, -2, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-766", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-1, -1, -1, -2, 0],\n [-1, 5, 2, -1, -4],\n [-1, 2, -2, 4, -2],\n [-2, -1, 4, 5, 1],\n [0, -4, -2, 1, 2]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3384", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, 0, 5, 2, -4],\n [0, 5, 1, 2, -2],\n [5, 1, 2, 0, -4],\n [2, 2, 0, -4, -4],\n [-4, -2, -4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68630", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 2, 3, 1, 2],\n [2, 0, -2, 0, -5],\n [3, -2, 0, 2, 4],\n [1, 0, 2, 4, 0],\n [2, -5, 4, 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": "316187", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -5, -3, -5, -1],\n [-3, -4, -3, 3, 5],\n [2, -3, 5, -4, -1],\n [-5, -2, 2, -5, -1],\n [-2, 0, 1, 3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10563", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 2, 0, -2, 1],\n [2, 1, 2, 2, 3],\n [0, 2, 2, 0, 4],\n [-2, 2, 0, 2, 1],\n [1, 3, 4, 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": "132599", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[5, 0, 5, -2, -4],\n [-4, -3, -4, -5, 2],\n [-1, 4, -5, 3, 2],\n [-2, 2, 4, 1, 5],\n [5, 1, -5, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23389", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[4, 4, 2, 0, 0],\n [4, 1, 2, -2, 0],\n [2, 2, 1, 2, 0],\n [0, -2, 2, 4, 0],\n [0, 0, 0, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8186", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 5th power of the matrix:\n[[-5, -4, -3, 1, -4],\n [-1, -4, 1, 4, 2],\n [2, 2, 4, 3, -5],\n [-5, 4, -4, 5, 0],\n [-5, -1, -1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2402", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, -5, 5, 5, 0],\n [1, 2, -4, 1, 0],\n [3, 2, 5, -2, 3],\n [-5, 5, 0, 2, 5],\n [5, -2, -4, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3682", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, -5, -1, 0, -2],\n [-2, -1, -1, 3, 2],\n [3, -3, -3, -5, 4],\n [0, -2, 5, 2, -4],\n [5, -4, 1, -1, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 3) of the matrix A^5 where A is:\n[[1, 1, 4, 0, -2],\n [2, 5, -4, -4, -4],\n [-3, 0, -5, 5, -4],\n [4, -4, -5, -3, 4],\n [1, -5, 1, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3316", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[-4, -2, 2, 0, 0],\n [-2, -1, -2, -2, 0],\n [2, -2, -2, 0, 1],\n [0, -2, 0, 5, -4],\n [0, 0, 1, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3752", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 0, -4, 2, 4],\n [0, 0, -4, -4, 2],\n [-4, -4, 1, 1, -2],\n [2, -4, 1, 5, -1],\n [4, 2, -2, -1, -4]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20548", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, -4, -1, 0, -4],\n [-4, -4, 0, 2, 3],\n [-1, 0, 4, 0, 2],\n [0, 2, 0, -3, 0],\n [-4, 3, 2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3582", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -3, -4, -2, 3],\n [-2, -1, 2, -4, 5],\n [-3, 0, 1, -2, -5],\n [1, 3, -5, -5, -5],\n [4, 1, 5, 3, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138891", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[2, 3, -3, -3, -5],\n [-4, 1, -3, 1, -1],\n [4, 2, -1, -3, 3],\n [1, -1, 1, 5, 4],\n [3, -1, 1, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[-5, -2, -5, 2, -3],\n [-4, -2, 5, -3, 5],\n [-1, 2, 4, 2, 5],\n [1, 2, -1, 4, 4],\n [5, 5, 0, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5794", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 0, 5, -1, -2],\n [-5, 5, 4, 5, 2],\n [0, -3, -3, 0, 1],\n [2, -1, 4, 0, -5],\n [0, 3, 4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1919", "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, 3, -2, -4],\n [-5, -3, 1, 5, 4],\n [-4, 3, 5, -4, -1],\n [2, 4, 2, -3, -4],\n [3, -3, 2, -4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36928", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, 0, -1, 0, 1],\n [0, -3, -1, 2, 0],\n [-1, -1, -1, -2, -1],\n [0, 2, -2, -5, -2],\n [1, 0, -1, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63085", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 0, 2, -2, 0],\n [0, 3, 3, 0, -4],\n [2, 3, 3, -2, 1],\n [-2, 0, -2, 5, -4],\n [0, -4, 1, -4, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35804", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 1) of the matrix A^5 where A is:\n[[2, 0, 2, 0, -2],\n [0, -3, 0, -3, 2],\n [2, 0, 3, 0, -3],\n [0, -3, 0, 4, 0],\n [-2, 2, -3, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5104", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 4) of the result:\nA =\n[[4, 0, -2, -4, 4],\n [0, -3, -2, 2, 2],\n [-2, -2, -3, 0, 0],\n [-4, 2, 0, 3, -4],\n [4, 2, 0, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-79700", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 3) of the matrix A^5 where A is:\n[[4, -4, 2, 0, 0],\n [-4, 1, 2, -1, -2],\n [2, 2, -5, -2, -2],\n [0, -1, -2, -1, 0],\n [0, -2, -2, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13525", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 0, 2, 0, 2],\n [0, 5, -4, -2, 2],\n [2, -4, 0, 0, 4],\n [0, -2, 0, 4, -1],\n [2, 2, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5886", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (3, 2) of the result:\nA =\n[[5, 1, 2, 4, -4],\n [0, -1, -1, -3, -3],\n [0, 4, 4, 1, -5],\n [-3, -5, 4, -3, -1],\n [3, -3, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12108", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, 2, 4, 1, 0],\n [2, -4, 2, -4, 2],\n [4, 2, 3, -1, 2],\n [1, -4, -1, 0, 0],\n [0, 2, 2, 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": "203405", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 5) of the 5th power of the matrix:\n[[-1, 1, -2, -4, 3],\n [1, -1, -2, 0, -4],\n [-2, -2, 1, -1, 3],\n [-4, 0, -1, 1, 4],\n [3, -4, 3, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10798", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 4) of the matrix A^4 where A is:\n[[1, -4, -1, 0, 0],\n [-4, -1, 0, -4, -2],\n [-1, 0, 3, -2, -2],\n [0, -4, -2, 2, 0],\n [0, -2, -2, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 2) of the matrix A^4 where A is:\n[[0, 0, -4, -4, -2],\n [0, -5, 0, -2, 1],\n [-4, 0, 2, -4, 2],\n [-4, -2, -4, 4, -2],\n [-2, 1, 2, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-127", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 4, 5, -3, -1],\n [5, -1, -2, 2, 0],\n [0, -5, 0, -3, 0],\n [4, 5, 0, -4, -5],\n [5, -3, -1, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-20424", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 2) of the matrix A^5 where A is:\n[[-2, 2, 1, 4, 3],\n [-5, -1, -2, 0, -5],\n [0, -5, -5, 2, -4],\n [4, 0, 0, 0, 2],\n [-2, -3, 0, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7390", "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, -1, 5, 3],\n [5, 0, -3, 5, -1],\n [4, 2, 3, 2, -3],\n [3, -3, 2, 4, 3],\n [1, -2, 4, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "228149", "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, 0, -4, -2],\n [-3, 2, -2, 0, -2],\n [0, -2, -5, 0, 0],\n [-4, 0, 0, 4, 0],\n [-2, -2, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1712", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 5) of the result:\nA =\n[[1, 2, -1, 2, 1],\n [2, -1, 0, 2, 0],\n [-1, 0, -2, 4, 2],\n [2, 2, 4, 1, 1],\n [1, 0, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-2, 0, 5, 2, -4],\n [0, 4, -2, 0, -2],\n [5, -2, -5, -1, 0],\n [2, 0, -1, 1, 0],\n [-4, -2, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-875", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, -4, 2, 2, 2],\n [-4, 5, 2, -4, 0],\n [2, 2, 5, 2, -4],\n [2, -4, 2, -3, 1],\n [2, 0, -4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3740", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -5, 3, 0, 0],\n [2, 5, -1, 3, 5],\n [-1, -4, 0, 3, -3],\n [4, -2, 4, 5, 2],\n [0, 1, 1, -2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "196356", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, -3, 2, 1, -2],\n [4, -3, 1, 4, 3],\n [4, -3, 4, 3, 2],\n [-3, 2, -2, 0, 4],\n [-4, 2, 3, 1, 2]], determine the value at position (2, 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^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 1, 4, -1, -2],\n [1, 1, 1, 3, 3],\n [4, 1, -5, 0, 4],\n [-1, 3, 0, -5, 0],\n [-2, 3, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26972", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, -5, -2, -2, -3],\n [1, -5, 3, 2, -4],\n [-4, 2, 5, -5, 1],\n [3, -3, 1, 0, 1],\n [1, 4, -5, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "131424", "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, -3, -5, -4],\n [4, -1, 5, -3, 0],\n [3, 0, -4, -4, 2],\n [5, 2, 0, 4, 1],\n [-5, 3, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29386", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, 1, 5, -2, -3],\n [-2, -2, 4, 4, 2],\n [-2, -1, -4, -2, 1],\n [-3, -5, 2, 2, 0],\n [1, 4, 5, -4, -1]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2174", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[1, 2, -2, -3, 2],\n [2, 0, 0, 0, -1],\n [-2, 0, -2, -2, 0],\n [-3, 0, -2, -2, -1],\n [2, -1, 0, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-14678", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, -4, 1, 0, 5],\n [-3, 2, 2, -5, -3],\n [-1, -4, -1, 5, 4],\n [-3, 3, 5, -5, -2],\n [4, 0, 3, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6684", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 2) of the 4th power of the matrix:\n[[-1, 1, -1, 5, 2],\n [-1, 1, 0, 4, -4],\n [-3, 5, 5, -2, -1],\n [3, 0, -5, -3, 1],\n [2, 1, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-734", "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, -4],\n [2, -3, 0, 2, -4],\n [2, 0, 1, 0, -1],\n [0, 2, 0, -2, -2],\n [-4, -4, -1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-63171", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[0, 0, 2, 1, 4],\n [0, 2, 2, 2, 2],\n [2, 2, -1, -1, 0],\n [1, 2, -1, 0, 0],\n [4, 2, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91012", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -1, 1, -3, 0],\n [2, 2, -4, 0, 1],\n [1, -3, 3, -4, 5],\n [-3, 5, -4, 5, 3],\n [-2, -4, -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": "546201", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 0, -4, 1, -1],\n [0, 1, -2, -4, 0],\n [-4, -2, 5, 0, 0],\n [1, -4, 0, 3, -3],\n [-1, 0, 0, -3, 3]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7354", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -2, 1, 2, -1],\n [-2, -1, 1, -2, 1],\n [1, 1, 2, 0, -2],\n [2, -2, 0, -4, -4],\n [-1, 1, -2, -4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11070", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, 1, -3, -1, 5],\n [3, -1, 3, -5, 3],\n [-1, 2, -1, 0, 2],\n [-4, -3, 5, 3, -1],\n [-1, 3, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 2) of the result:\nA =\n[[1, -4, 2, -1, -5],\n [-3, 3, -1, 2, -5],\n [1, 1, 2, -3, -5],\n [5, 3, -5, 5, 0],\n [3, -4, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1612", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, -3, 2, -2, 4],\n [-3, -2, 2, -1, 0],\n [2, 2, 0, 0, -2],\n [-2, -1, 0, 0, 2],\n [4, 0, -2, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35969", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[-5, -5, 5, -5, -4],\n [3, -1, 3, -1, 1],\n [0, -4, -3, -1, -2],\n [5, 0, 2, 2, -3],\n [-2, -5, -4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-83", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, -4, 0, 1, 0],\n [2, 3, 2, -1, 2],\n [4, 4, 3, 2, -4],\n [-4, -3, 1, 3, 2],\n [3, 0, -5, -2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68911", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 2, -5, 5, -4],\n [-4, 0, 5, 1, -4],\n [-1, 0, -2, -5, -3],\n [4, 3, 0, -4, 3],\n [-2, 5, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "242362", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, -3, 2, -2, -4],\n [5, -1, -5, 2, 2],\n [-3, -5, -2, 3, 3],\n [-5, 5, 1, 0, 1],\n [1, 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": "37618", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, -2, -2, 5, 4],\n [2, -3, -3, -4, -5],\n [2, 3, 3, 5, 2],\n [-1, -5, 3, 0, 1],\n [2, -1, 0, 1, 1]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4627", "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, -5, 2, -1],\n [4, -4, -3, 0, 4],\n [0, 2, -1, -1, 1],\n [4, -1, 3, 0, 1],\n [2, -1, 5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21850", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 3, -5, -3, -2],\n [1, 0, 4, 4, 5],\n [-5, -2, 0, -3, -4],\n [-4, 4, -2, -5, 4],\n [-4, 4, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-363504", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 2, 2, 1, 1],\n [2, 4, -2, 5, 0],\n [2, -2, 1, 4, 0],\n [1, 5, 4, -4, -1],\n [1, 0, 0, -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": "22761", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 0, 0, -2, 0],\n [0, 4, 0, 4, 2],\n [0, 0, -5, 4, 0],\n [-2, 4, 4, -3, 2],\n [0, 2, 0, 2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5666", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, -5, 5, -4, 2],\n [1, -1, 4, -4, 3],\n [-1, 2, -2, 3, 4],\n [1, -4, -3, -4, -1],\n [-4, -1, 3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69231", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 1, -1, 2, 1],\n [0, -4, 0, -4, -5],\n [3, -1, 4, 4, -2],\n [5, 2, -1, 1, -3],\n [2, 2, -3, 3, 2]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-403", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[-5, 2, 5, -2, 0],\n [4, 3, -1, 1, -5],\n [3, 0, 5, -2, 0],\n [-1, -3, 1, -3, -4],\n [-2, 1, -1, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2544", "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, 3, -4, -5],\n [5, -2, -2, -4, -3],\n [-3, -1, -5, 3, 2],\n [2, -3, -4, -5, 0],\n [4, -5, 5, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145508", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, 2, 0, 0, 0],\n [2, -2, 0, 2, 2],\n [0, 0, 4, -1, -1],\n [0, 2, -1, -5, 4],\n [0, 2, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3221", "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, 2, -2, 0],\n [5, -3, 1, -4, 2],\n [1, 2, -4, -3, -2],\n [3, -1, 0, -5, -2],\n [-2, 4, 2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42209", "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],\n [-2, -4, -3, 2, 0],\n [2, -3, -2, 0, 2],\n [-2, 2, 0, -3, 0],\n [-5, 0, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8157", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[-5, 0, -1, -3, 5],\n [5, 5, 3, -3, -4],\n [-1, 3, 2, 0, -3],\n [0, -1, -5, -1, 1],\n [3, -5, -3, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4018", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 3) of the matrix A^5 where A is:\n[[-1, 0, -1, 1, -3],\n [0, 1, -4, 1, 0],\n [-1, -4, -1, 0, 4],\n [1, 1, 0, 2, 0],\n [-3, 0, 4, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4557", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 3, 3, -1, -2],\n [-2, 3, 2, 4, 4],\n [1, -3, -2, 3, 2],\n [-5, -3, 4, -4, -4],\n [2, 0, 0, -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": "31854", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, -2, 0, -2, -4],\n [-2, -2, 2, -2, -2],\n [0, 2, 1, 0, 0],\n [-2, -2, 0, -5, 0],\n [-4, -2, 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": "123173", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -2, 0, 0, 0],\n [-2, -1, 4, -2, 1],\n [0, 4, 4, -2, -1],\n [0, -2, -2, -2, -2],\n [0, 1, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2758", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 0, -2, -5, -5],\n [-1, -1, 4, 1, -2],\n [3, -2, 1, -1, -1],\n [0, 2, -1, -3, 0],\n [-4, 2, 2, -3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7184", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, -2, -1, 1, 0],\n [-2, -1, -4, 4, 4],\n [-1, -4, -5, -2, -2],\n [1, 4, -2, 4, 0],\n [0, 4, -2, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "401", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 5, -4, 0, 4],\n [5, -1, 2, -2, 1],\n [-4, 2, -5, -4, 0],\n [0, -2, -4, 0, 2],\n [4, 1, 0, 2, 4]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-632", "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, -4, 2, 0, -2],\n [-2, 5, 1, -3, 5],\n [-3, 0, 3, -5, -1],\n [-5, -5, -3, -3, -2],\n [-3, 0, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122700", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[2, 5, -5, 5, -5],\n [1, -5, 3, 2, -5],\n [-4, -4, -4, 0, -2],\n [2, -5, 4, -2, 4],\n [5, -1, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4256", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 0, 0, 0, -2],\n [0, 5, 0, -1, 0],\n [0, 0, -5, 2, 1],\n [0, -1, 2, 5, -2],\n [-2, 0, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8869", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 2) of the result:\nA =\n[[-1, 2, 1, -4, 0],\n [2, -2, 2, 0, -2],\n [1, 2, -3, 0, -1],\n [-4, 0, 0, -4, -3],\n [0, -2, -1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1774", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[4, -5, 0, -3, 1],\n [2, -1, -1, -4, 2],\n [4, -5, 4, 3, -5],\n [-5, -5, 1, -2, 1],\n [-1, 1, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1705", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, 2, -4, 3, -1],\n [3, 3, 2, 2, -2],\n [-2, -4, -2, -2, 0],\n [-3, -4, 2, -4, 2],\n [1, -3, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31405", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-1, 1, 4, 0, 0],\n [1, 5, 1, 0, -2],\n [4, 1, 4, -4, -4],\n [0, 0, -4, 0, 0],\n [0, -2, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37616", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, 2, 0, -2, 2],\n [2, -1, 4, -2, 0],\n [0, 4, -2, 4, -2],\n [-2, -2, 4, -3, 1],\n [2, 0, -2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1237", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[2, -2, 4, 1, 2],\n [-2, 0, -2, 4, 0],\n [4, -2, -4, -2, 4],\n [1, 4, -2, -5, -1],\n [2, 0, 4, -1, 0]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6595", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 4, -3, 0, -4],\n [4, -5, -2, -4, 2],\n [-3, -2, 2, -4, -2],\n [0, -4, -4, -2, -3],\n [-4, 2, -2, -3, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-179919", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -2, 2, 1, 1],\n [4, 1, 4, 5, -1],\n [1, -2, 2, 3, -3],\n [1, 4, 3, -5, -4],\n [1, -4, 1, -5, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27604", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 5, 0, 3, 3],\n [-3, 2, -2, 1, 0],\n [2, 0, -2, -4, 1],\n [5, 5, -2, 3, 3],\n [1, -1, -3, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1390", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 5, -2, 5, -5],\n [4, -1, 2, 4, -2],\n [4, 4, -2, 3, 3],\n [1, 4, 2, -2, 2],\n [0, -3, 1, -3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "420213", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, -1, -2, -3, 2],\n [-2, 2, 4, -3, 4],\n [3, 0, -1, -1, -3],\n [-4, 0, 5, -5, 1],\n [-1, -2, 3, 4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22340", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (4, 1) of the result:\nA =\n[[5, 0, 1, -2, -1],\n [0, -5, 2, -3, 0],\n [1, 2, -4, 1, 4],\n [-2, -3, 1, -2, 0],\n [-1, 0, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4186", "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, 4, -2],\n [-3, 0, 5, 0, -4],\n [3, 2, 0, -5, -4],\n [-2, 1, 3, 4, -1],\n [4, -4, 5, 5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23323", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[-5, 4, -2, 2, 3],\n [4, 3, 1, -4, 1],\n [-2, 1, -2, -4, -2],\n [2, -4, -4, -2, 1],\n [3, 1, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-29883", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 1) of the matrix A^4 where A is:\n[[-5, -2, -1, -2, -3],\n [-2, -4, 0, -4, -1],\n [-1, 0, 5, 1, 0],\n [-2, -4, 1, -3, 3],\n [-3, -1, 0, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2013", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -2, 4, -5, -2],\n [-3, -4, -5, 0, 1],\n [0, 3, 3, -4, -4],\n [3, -5, -1, -5, 1],\n [3, 0, -4, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12550", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 3, 2, 1, 2],\n [4, 0, -3, 1, -2],\n [5, 4, -1, 2, 1],\n [1, 2, 4, -3, -3],\n [-4, -5, 4, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-516", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, 2, 0, 0, -5],\n [1, 1, 4, 3, 1],\n [2, -2, 3, -5, 2],\n [-3, -5, -4, 0, -1],\n [-3, 3, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15803", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the 5th power of the matrix:\n[[2, -2, 0, -1, 4],\n [-2, -1, 0, 1, -1],\n [0, 0, 3, -2, 2],\n [-1, 1, -2, 5, -3],\n [4, -1, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11481", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 0, 2, -2, 2],\n [0, -4, -2, 0, 2],\n [2, -2, 0, 0, -2],\n [-2, 0, 0, 5, 4],\n [2, 2, -2, 4, 1]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1132", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[4, 3, 1, 2, -2],\n [3, 1, -2, 2, 0],\n [1, -2, -3, 0, -1],\n [2, 2, 0, 4, -4],\n [-2, 0, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-842", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 5) of the matrix A^5 where A is:\n[[1, -2, -4, 5, 2],\n [-2, -2, -4, -5, -5],\n [-3, 0, 1, 3, -1],\n [3, 2, -5, 5, -3],\n [2, 3, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2197", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[3, 0, 2, 0, 0],\n [0, -2, -1, 2, 2],\n [2, -1, -5, 2, 2],\n [0, 2, 2, -4, 0],\n [0, 2, 2, 0, -2]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10207", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, -1, -2, 2, -2],\n [-1, 4, 1, 0, -4],\n [-2, 1, -1, -1, -2],\n [2, 0, -1, 4, -1],\n [-2, -4, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70755", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^5 where A is:\n[[5, 3, -4, 2, 3],\n [-4, 3, 1, 3, 0],\n [-4, 2, 4, 3, 2],\n [-4, 2, -3, -3, 3],\n [3, 3, -2, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6457", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, -5, 3, 0, -3],\n [-3, 4, -5, 2, -4],\n [-5, 1, 5, 3, 0],\n [2, 2, 3, 1, 3],\n [3, 5, -5, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2392", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[4, 3, -3, -4, 4],\n [3, 3, 0, -3, -2],\n [-3, 0, -5, -1, -1],\n [-4, -3, -1, 0, 3],\n [4, -2, -1, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "601", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, -2, -1, 1, 0],\n [2, 0, 4, 2, -2],\n [1, -3, -5, 3, 3],\n [0, -4, 2, 4, 0],\n [1, -5, -3, -5, 4]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1176", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, 3, -2, -2, 1],\n [3, -1, 2, 0, 0],\n [-2, 2, 0, 2, -2],\n [-2, 0, 2, 5, -2],\n [1, 0, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6040", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, 2, -5, 2, -3],\n [3, 5, -4, 4, 3],\n [0, -5, -1, 4, 3],\n [0, 1, -2, -5, -1],\n [-4, 2, -2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99251", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 5, -4, -3, 3],\n [3, -4, -3, 5, 3],\n [-5, -4, 5, -4, 4],\n [-3, 4, -3, 4, -4],\n [2, 2, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90772", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, 2, -2, 1, 3],\n [2, -4, -2, 4, -1],\n [-2, -2, -3, 4, 2],\n [1, 4, 4, -3, 0],\n [3, -1, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4173", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, 0, 1, -2, 0],\n [0, -3, 0, 0, 0],\n [1, 0, -1, -2, 0],\n [-2, 0, -2, -3, 1],\n [0, 0, 0, 1, 3]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 4th power of the matrix:\n[[-4, -5, -3, 1, 3],\n [-4, 0, -3, -1, 3],\n [-3, -5, -1, -5, 2],\n [1, 5, -4, 5, 3],\n [-1, 1, -2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-735", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, -4, -2, 0, -2],\n [-4, 3, 1, -2, 0],\n [-2, 1, 1, 5, 4],\n [0, -2, 5, 3, 0],\n [-2, 0, 4, 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": "24320", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 1) of the matrix A^5 where A is:\n[[1, 4, 4, 0, -4],\n [4, -1, 1, 0, 2],\n [4, 1, 0, 2, 4],\n [0, 0, 2, 3, -2],\n [-4, 2, 4, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22223", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 2, 0, 4, 5],\n [5, 2, -4, 5, 0],\n [1, 2, 3, -1, 5],\n [-3, -4, 2, -5, 4],\n [0, -4, -3, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37473", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, -3, 0, -3, 5],\n [5, 2, -1, -2, 3],\n [-1, -2, 2, 2, 2],\n [-2, -5, -4, -2, 4],\n [-4, 5, 4, -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": "21983", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, 5, 3, 1, -2],\n [-5, -3, 2, -2, 4],\n [4, -4, 2, 1, 5],\n [4, 3, -4, -1, 0],\n [-4, -4, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5512", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, -1, 3, -2, -3],\n [4, 2, -5, 3, -2],\n [5, 3, 2, -3, -3],\n [3, -3, -2, 3, -2],\n [5, -3, 1, 0, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14450", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 1, -4, -4, -2],\n [1, 1, 2, 1, 2],\n [-4, 2, 1, 3, 1],\n [-4, 1, 3, 1, 2],\n [-2, 2, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78171", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 0, 4, -2, 3],\n [0, 3, -1, 4, 0],\n [4, -1, -5, 0, 2],\n [-2, 4, 0, 4, 5],\n [3, 0, 2, 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": "44076", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -5, -1, -2, -5],\n [4, 3, 0, 0, 5],\n [-4, 1, 3, 0, 5],\n [2, -1, -4, -2, -5],\n [-5, 0, -4, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7141", "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, -3, 3, -4],\n [2, 0, 0, 1, -1],\n [5, -2, 0, 2, -2],\n [-1, 1, 0, -2, -2],\n [4, -2, -5, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29848", "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, 5, -5],\n [1, 5, -3, -2, -1],\n [2, 1, 3, 5, -3],\n [5, 4, -5, -5, 4],\n [-5, -4, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5159", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (5, 4) of the result:\nA =\n[[2, -2, -4, -3, 4],\n [-1, 3, 2, -3, 3],\n [4, -3, 4, 2, -5],\n [-2, -2, 0, -4, 1],\n [-1, 4, 0, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13000", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, -1, 0, 4, 0],\n [-1, 4, 0, 0, -2],\n [0, 0, -5, -2, -2],\n [4, 0, -2, -4, 1],\n [0, -2, -2, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6608", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, -2, 2, 0, -4],\n [-2, 2, 0, 4, 0],\n [2, 0, -2, -2, -4],\n [0, 4, -2, -4, 0],\n [-4, 0, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108128", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 0, 0, -2, 1],\n [0, -3, -1, -1, 2],\n [0, -1, -5, -1, 3],\n [-2, -1, -1, 2, -2],\n [1, 2, 3, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2943", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 5) of the 4th power of the matrix:\n[[3, 4, 0, 0, 0],\n [4, -3, -1, 0, 0],\n [0, -1, -1, -2, 2],\n [0, 0, -2, -3, -2],\n [0, 0, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "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, -4, 0, 0, 0],\n [-1, 1, -1, 5, -5],\n [3, -3, -4, 4, 0],\n [2, -4, -2, -4, 3],\n [4, -4, 4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79302", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 1) of the matrix A^5 where A is:\n[[-1, 3, -2, -2, 2],\n [3, 0, -2, -2, 0],\n [-2, -2, 4, -2, 1],\n [-2, -2, -2, 0, -2],\n [2, 0, 1, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2782", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, -2, -3, -2, 1],\n [-2, -1, -2, -4, 0],\n [-3, -2, 4, 0, 0],\n [-2, -4, 0, 3, -3],\n [1, 0, 0, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-33671", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[1, -2, -4, -1, -1],\n [-4, 5, 0, 4, -2],\n [-5, -3, 3, 4, 1],\n [0, -5, 3, 3, -5],\n [0, 1, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1603", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 0, 3, -3, -4],\n [-4, 0, 1, 0, 5],\n [-3, -1, 2, 0, -4],\n [1, 2, -2, -5, -4],\n [-2, 1, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14645", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -2, -3, 0, -3],\n [-2, 3, 3, -1, 0],\n [-3, 3, 5, 1, 2],\n [0, -1, 1, 0, -1],\n [-3, 0, 2, -1, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11058", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, -1, 3, 5, 4],\n [-4, -5, -5, 2, 4],\n [4, 4, -4, 3, 3],\n [-4, -3, -4, 0, 1],\n [0, -3, -3, -4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1400", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[5, 0, 2, 0, 1],\n [0, 3, 4, -1, 2],\n [2, 4, 4, 2, -2],\n [0, -1, 2, -1, 0],\n [1, 2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15837", "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, 5, 4, 5, -3],\n [3, 5, 5, -2, -3],\n [1, 2, 1, -5, -5],\n [-1, 2, 4, 5, -3],\n [2, -3, -2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48925", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, -2, 2, -2, 3],\n [-2, -2, -1, -5, 1],\n [3, 3, -5, 0, -3],\n [-2, 2, -2, 2, -2],\n [3, 0, -5, 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": "497997", "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, 1, -4, -2],\n [3, 4, 4, 0, 2],\n [1, 4, 2, -3, 0],\n [-4, 0, -3, -3, 4],\n [-2, 2, 0, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332559", "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, -4, 3, -4],\n [-3, 0, -4, -1, -4],\n [-2, 5, 5, -3, -1],\n [0, 1, 4, 2, 3],\n [-2, -2, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4476", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 3) of the result:\nA =\n[[5, 3, 5, -4, 5],\n [0, 4, 4, 2, -1],\n [-1, 2, -5, 0, 4],\n [3, 0, 1, -2, 4],\n [-5, 3, 0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-440", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[4, 0, 2, 1, -2],\n [0, -1, 0, 0, -2],\n [2, 0, 4, 4, 1],\n [1, 0, 4, -2, -4],\n [-2, -2, 1, -4, 5]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13036", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 4) of the 5th power of the matrix:\n[[-5, 4, 4, 2, -1],\n [4, 0, 1, 3, 4],\n [4, 1, -3, -2, 0],\n [2, 3, -2, 3, 2],\n [-1, 4, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15632", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (4, 5) of the matrix A^4 where A is:\n[[-2, -2, 0, 3, 1],\n [-1, -1, 2, 0, -5],\n [-5, 3, 2, 0, -5],\n [-4, 4, -3, 4, -3],\n [-4, -4, 0, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-23", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[-5, 0, 1, -2, 0],\n [3, -2, 4, -2, 4],\n [-1, -3, 4, -4, 3],\n [-5, -1, -1, 2, 0],\n [0, 0, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3257", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 5, 0, -1, 4],\n [-5, -1, -4, -5, -2],\n [0, 1, 3, -1, 2],\n [2, 5, 3, -3, -3],\n [3, 1, -2, -5, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9788", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[4, 0, -3, -1, -3],\n [2, -1, 4, 4, 0],\n [-4, 2, 3, -3, 0],\n [0, -4, 4, 2, -1],\n [5, 5, 2, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18749", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 5th power of the matrix:\n[[-1, 1, -1, 0, -4],\n [2, -1, 0, -5, 4],\n [-4, 5, -2, 5, 3],\n [0, 2, -4, 4, -1],\n [-5, -2, 4, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4236", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[5, 3, -4, 1, -3],\n [-4, -2, 1, 1, 3],\n [-3, 1, 0, 4, 1],\n [1, 4, -1, 3, 1],\n [1, -3, -5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-349", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[-1, 4, -3, 3, -4],\n [-3, -2, 4, -5, 5],\n [-2, -2, 3, 2, -4],\n [1, 0, 1, 5, -2],\n [-1, 0, 3, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1644", "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, 4, -2, 0, -2],\n [4, 0, 0, -3, -2],\n [-2, 0, 0, 0, -4],\n [0, -3, 0, -5, 2],\n [-2, -2, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25791", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, -5, 0, -3, -5],\n [2, -2, 4, 1, 4],\n [-4, 0, 0, 1, -5],\n [-5, -4, 5, -4, -1],\n [-5, 5, -4, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "744215", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -5, -1, -2, 2],\n [-3, 4, -5, 4, -1],\n [-5, 5, -1, 3, -1],\n [-4, -4, 4, 3, -1],\n [5, 2, 4, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "697", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 5, -2, 5, 3],\n [4, 5, 0, 4, 0],\n [-1, 0, -5, -1, 0],\n [2, -2, -1, -2, 1],\n [4, 0, -2, 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": "16098", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[2, 2, 0, -1, 0],\n [2, 2, 0, 0, 0],\n [0, 0, -4, 2, -1],\n [-1, 0, 2, -5, 0],\n [0, 0, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-569", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-5, 0, -4, 2, -1],\n [0, -3, -1, 4, 3],\n [-4, -1, 3, 2, -2],\n [2, 4, 2, 4, 2],\n [-1, 3, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168978", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, -2, 4, 4, 4],\n [3, -1, 2, 0, -2],\n [-3, 5, 0, -5, -4],\n [1, -2, -1, 5, 4],\n [-5, -4, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, 0, -2, 0, -3],\n [0, -1, 2, 0, 0],\n [-2, 2, -3, 2, 2],\n [0, 0, 2, 0, 0],\n [-3, 0, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59509", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[0, 0, 2, 1, 0],\n [0, -3, 2, 5, 0],\n [2, 2, 4, 2, -2],\n [1, 5, 2, 5, 2],\n [0, 0, -2, 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": "245704", "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, 1, -4, 2, -4],\n [1, 3, 4, 1, -2],\n [-4, 4, 0, -2, -2],\n [2, 1, -2, -2, 3],\n [-4, -2, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "275520", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -2, -4, -3, 1],\n [0, 0, 2, 2, 0],\n [-5, 4, 1, 2, -1],\n [5, -2, 1, 5, 0],\n [0, -3, 5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8737", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (1, 1) of the result:\nA =\n[[-1, 3, 2, -3, 0],\n [4, -5, -3, 4, 1],\n [1, -4, -3, 1, 0],\n [1, 4, 3, 2, 0],\n [-2, 4, 3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21536", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 1) of the matrix A^5 where A is:\n[[-4, 3, 1, 3, 5],\n [3, 4, -1, 1, -1],\n [-3, 4, 2, 2, 3],\n [5, 0, -4, -3, 5],\n [4, 5, 0, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9184", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 0, 2, 0, -2],\n [0, 0, -2, 4, 0],\n [2, -2, 3, -2, 4],\n [0, 4, -2, 3, 2],\n [-2, 0, 4, 2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14774", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-5, -5, -4, 5, -2],\n [5, 3, 1, 0, -5],\n [-1, 5, -2, -1, 5],\n [3, -3, -2, 2, -3],\n [-3, 3, -1, 4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18541", "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, 1, 0, 0, -3],\n [-3, 4, 5, 3, -5],\n [1, 5, 4, 1, 2],\n [0, 2, -5, -5, 3],\n [-2, -3, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393682", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 4) of the 4th power of the matrix:\n[[4, 5, -2, 3, -1],\n [1, -3, -3, -3, 2],\n [0, 3, 3, 2, -5],\n [0, -2, -2, -3, 3],\n [-4, -5, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[-2, 0, -5, -5, -4],\n [-2, 1, 0, 5, 3],\n [1, -1, 0, 4, 3],\n [-5, 5, 3, 0, -2],\n [-1, -5, 1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2399", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-1, -4, 2, 4, 1],\n [4, 3, -2, 5, 3],\n [-2, -3, 5, -3, 4],\n [-4, 4, -3, 2, 5],\n [2, -4, 5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-78190", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, -2, -2, 0, -4],\n [-2, -5, 0, 0, -1],\n [-2, 0, -4, 4, -2],\n [0, 0, 4, -2, 3],\n [-4, -1, -2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-37191", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, 5, -5, -4, -4],\n [4, -3, 2, 5, 0],\n [0, 3, 2, -4, 0],\n [-5, 3, -2, -2, 3],\n [-3, -1, -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": "1327171", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 3, 2, 2, -3],\n [3, 5, -4, -2, -4],\n [2, -4, -3, -2, 0],\n [2, -2, -2, 5, 2],\n [-3, -4, 0, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2869", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[0, 0, 3, -4, 0],\n [3, -2, 5, 0, 1],\n [-5, -1, -2, 4, -4],\n [-4, -4, 1, 5, 5],\n [-2, 0, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11546", "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, 4, 2, 0],\n [2, 0, 4, -4, 4],\n [4, 4, 1, -1, 0],\n [2, -4, -1, 3, -2],\n [0, 4, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "310104", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[1, -1, 0, 0, 4],\n [-1, -1, -3, -4, -1],\n [0, -3, 5, -1, 0],\n [0, -4, -1, 5, -2],\n [4, -1, 0, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16453", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, 0, 0, -2, 1],\n [0, 5, -4, 2, 2],\n [0, -4, -5, 1, -3],\n [-2, 2, 1, 1, 4],\n [1, 2, -3, 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": "254609", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -5, 5, -5, -5],\n [-2, -2, 3, -5, -3],\n [-3, 2, -4, 0, 5],\n [-2, 4, 0, -1, 3],\n [3, -5, -3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19594", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[-3, -5, 0, -1, 2],\n [-4, 2, -1, 2, 4],\n [-2, -2, 4, -2, 5],\n [0, -2, 3, 3, -3],\n [1, -1, 3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "390", "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, -1, 4, 1],\n [2, 2, -5, -5, -3],\n [-5, -5, 4, 2, -5],\n [3, -4, 3, 1, 3],\n [-3, -5, -5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80090", "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, 1, 3, 0, -1],\n [-4, -4, 2, -5, 2],\n [5, 4, 5, 1, 1],\n [-1, -3, 1, 1, 1],\n [5, -4, -3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100913", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, 4, -3, 1, -2],\n [4, -2, 0, 0, -2],\n [-3, 0, 1, 2, 1],\n [1, 0, 2, 4, 2],\n [-2, -2, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166444", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, -5, 1, 0, -1],\n [2, 5, -4, -4, 3],\n [-5, 0, -3, -1, 2],\n [1, -2, 2, 5, 5],\n [4, 5, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13418", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[5, 0, -3, 5, 4],\n [1, 1, -4, -5, 4],\n [-4, 2, 5, 4, -3],\n [5, -2, 2, -3, 0],\n [-4, -3, -5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-451", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 1, -4, 2, 3],\n [4, 5, -4, -1, -4],\n [5, -1, 1, 0, -2],\n [-4, 1, 4, 3, -5],\n [-3, 1, 3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1405", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[4, 2, -1, 0, -1],\n [2, -5, -2, -3, 0],\n [-1, -2, 5, 2, -2],\n [0, -3, 2, 1, -4],\n [-1, 0, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-482", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 2, 0, 0, 0],\n [2, 3, 0, -4, 0],\n [0, 0, 4, 0, 2],\n [0, -4, 0, 0, -2],\n [0, 0, 2, -2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2067", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, -1, 1, 0, -3],\n [-1, 4, 3, 0, -4],\n [1, 3, -4, -1, -1],\n [0, 0, -1, -2, 4],\n [-3, -4, -1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13334", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[5, 2, -2, 4, -4],\n [2, -2, 0, 2, 0],\n [-2, 0, 2, 0, -1],\n [4, 2, 0, -5, -4],\n [-4, 0, -1, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1364", "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, -1, -2, -1, -1],\n [4, 2, 4, 1, 3],\n [5, -5, 0, 0, -4],\n [5, 2, 0, 5, 4],\n [3, 4, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43780", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[5, -1, 0, -2, -3],\n [-5, -5, 0, 3, 2],\n [-4, 3, 2, 3, -2],\n [3, -4, -5, 3, 4],\n [2, 1, 2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "264840", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 5, 3, 5, 3],\n [0, -2, -4, 5, -2],\n [1, -5, 3, -3, -2],\n [-1, -3, -2, -1, -5],\n [3, 4, 4, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-808", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -5, -1, 3, -3],\n [-1, -3, -3, -5, -4],\n [-4, 3, 1, 2, -4],\n [3, -3, 4, -4, -5],\n [3, 2, 5, -2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, -3, -2, -4, 4],\n [-2, 4, -3, 2, 5],\n [-4, 5, 3, -3, -2],\n [4, 4, -3, -3, 2],\n [2, 0, -2, -5, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3079", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[2, 0, -4, -3, 1],\n [5, 5, -2, -2, -1],\n [2, 1, 3, -1, -5],\n [-2, 0, 0, 3, 4],\n [-1, -1, 0, 5, 0]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (5, 4) of the 4th power of the matrix:\n[[-3, 0, 1, -2, 2],\n [0, -3, -2, 0, 2],\n [1, -2, -3, 0, -1],\n [-2, 0, 0, 5, -2],\n [2, 2, -1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1420", "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, 0, 1, -2],\n [0, 2, 0, 0, 0],\n [0, 0, -1, -2, 0],\n [1, 0, -2, 5, -2],\n [-2, 0, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26286", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, -4, -2, 2, -2],\n [-4, -3, 2, 2, -2],\n [-2, 2, 0, -2, 4],\n [2, 2, -2, -4, -3],\n [-2, -2, 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": "43039", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[5, -2, 1, -1, 4],\n [0, 4, -2, -4, 3],\n [-4, -4, -4, -5, -3],\n [0, 1, -5, -1, -1],\n [-5, -2, 4, -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": "24848", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, -2, -1, 0, -4],\n [-2, 4, -4, 0, -2],\n [-1, -4, 0, 0, 4],\n [0, 0, 0, 1, 4],\n [-4, -2, 4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11299", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-5, -5, -3, -3, 1],\n [0, 1, -2, 5, -4],\n [-4, 4, -5, 3, 1],\n [4, -3, -4, -3, 1],\n [-1, -3, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25749", "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, 0, 0],\n [-2, 5, 2, -2, 0],\n [1, 2, 5, 0, -2],\n [0, -2, 0, 5, -2],\n [0, 0, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "137840", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 3) of the matrix A^5 where A is:\n[[0, -2, 5, 2, 2],\n [-3, -2, -5, 4, -4],\n [1, 5, 1, 3, 4],\n [3, 3, 0, 2, 3],\n [1, -2, -2, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-609", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 4) of the 5th power of the matrix:\n[[-2, 4, -2, 0, -1],\n [4, -4, 1, -2, -4],\n [-2, 1, -1, 1, 2],\n [0, -2, 1, -5, 0],\n [-1, -4, 2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8411", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, -2, 2, 0, 2],\n [-2, 0, -2, 1, 2],\n [2, -2, -5, -1, 4],\n [0, 1, -1, 0, 1],\n [2, 2, 4, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22119", "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, -1, 0, -2],\n [-2, 2, -2, 2, 4],\n [-1, -2, 4, -1, 2],\n [0, 2, -1, -1, -1],\n [-2, 4, 2, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40156", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, -3, 0, -2],\n [0, 3, -1, 1, 0],\n [-3, -1, 4, 0, -2],\n [0, 1, 0, -3, 0],\n [-2, 0, -2, 0, -5]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, 0, 4, -1, -5],\n [-1, 4, -5, 5, -3],\n [-4, -5, -2, -4, -1],\n [4, -5, 4, -5, 5],\n [4, -2, 1, -4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1765", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 0, 2, -2, -4],\n [0, 0, -1, -1, 3],\n [2, -1, 1, -2, 0],\n [-2, -1, -2, 1, -4],\n [-4, 3, 0, -4, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14352", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -3, -1, 0, -5],\n [-4, -5, -3, 2, 2],\n [-2, 0, 3, 1, -4],\n [5, -4, -3, 2, 4],\n [3, -3, 3, 4, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4685", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 3, 2, -4, 2],\n [3, 3, 1, -3, -2],\n [2, 1, -2, -1, 4],\n [-4, -3, -1, -5, 0],\n [2, -2, 4, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9707", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 1, 1, 4, -5],\n [4, 5, 5, -2, 0],\n [2, -3, -3, 2, 2],\n [2, -5, 2, 2, -4],\n [3, 1, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-45144", "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, 1, -1, 2],\n [0, -2, -2, 0, 1],\n [1, -2, 4, 0, -2],\n [-1, 0, 0, -3, 4],\n [2, 1, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5018", "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, 5, -1, 0, -3],\n [0, 2, 4, 5, 3],\n [-3, 2, -3, -4, -1],\n [-2, -1, 0, -3, -5],\n [-2, 0, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1016317", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, -3, -4, -2, 0],\n [-5, 3, 3, 2, 0],\n [-2, -4, 2, 1, -2],\n [-3, 0, -5, -4, 1],\n [5, -3, -5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6755", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 3) of the 4th power of the matrix:\n[[4, 3, 1, 1, 4],\n [2, 2, 3, -4, 2],\n [2, -1, -1, -2, -1],\n [-4, -4, -1, 5, -3],\n [-5, 3, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-53", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -4, 1, 4, -5],\n [5, -4, 5, -1, -4],\n [3, -2, 3, 5, -5],\n [-5, -5, -2, 3, 2],\n [1, -5, -3, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2295", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-1, -1, 5, 0, 4],\n [-1, -5, -1, -4, 0],\n [5, -1, -1, 2, -2],\n [0, -4, 2, -1, -3],\n [4, 0, -2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6738", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 0, -3, -2, -5],\n [3, 4, -1, 2, -3],\n [-2, -2, 2, 3, -3],\n [1, 3, -4, -2, -3],\n [2, -2, 3, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5531", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, 0, 0, 2, -2],\n [0, 4, 0, 0, 0],\n [0, 0, -3, -2, 3],\n [2, 0, -2, -2, 0],\n [-2, 0, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124936", "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, 4, 3, -1, 1],\n [-5, -2, 4, -2, -1],\n [0, -2, 0, 4, 1],\n [-3, 3, 2, -5, -4],\n [-4, 4, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81125", "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, 1, 2],\n [2, 2, -4, 0, 4],\n [4, -4, -3, -1, 0],\n [1, 0, -1, -4, 2],\n [2, 4, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38577", "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, 3, 1, -2, 4],\n [-1, 0, 3, -1, -1],\n [1, -4, -3, -4, 4],\n [4, -4, -3, 0, -1],\n [5, -1, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124401", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 3, -2, 2, 0],\n [3, 3, 2, -4, -2],\n [-2, 2, 3, 2, 0],\n [2, -4, 2, -3, 0],\n [0, -2, 0, 0, -5]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-16951", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-4, 3, -1, -2, -5],\n [3, 5, 3, -2, 3],\n [4, -5, -1, -5, -2],\n [-1, 5, -3, -4, 0],\n [5, -3, 4, -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": "299571", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-1, -4, -4, -2, -2],\n [-2, 1, -5, 2, 4],\n [3, 4, 0, -2, 0],\n [4, 1, 0, 5, -5],\n [-1, 2, 2, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-64781", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 2) of the matrix A^5 where A is:\n[[-2, 4, 0, 1, -1],\n [5, 2, -3, 2, -1],\n [-5, 0, -4, 1, 3],\n [-3, 4, -2, -2, -2],\n [-3, -1, 3, 5, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8068", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[4, -2, 2, 0, -2],\n [-2, -1, -2, -2, 1],\n [2, -2, 5, 0, 0],\n [0, -2, 0, 3, 0],\n [-2, 1, 0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2970", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-2, -2, 0, -5, -4],\n [0, 5, -5, 3, 0],\n [1, -5, 2, -1, -1],\n [0, 1, 1, -1, -5],\n [5, 3, 0, 3, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2055", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[-2, -1, -1, -2, 2],\n [-1, -3, 4, 2, 0],\n [-1, 4, -1, -2, 2],\n [-2, 2, -2, -1, -1],\n [2, 0, 2, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-872", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[-4, -3, 1, 5, -3],\n [-3, 4, -2, 1, -2],\n [1, -2, 0, -2, 1],\n [5, 1, -2, 1, 1],\n [-3, -2, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-775", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, 4, 0, -4, 2],\n [4, -4, 0, 3, 2],\n [0, 0, 0, 0, 0],\n [-4, 3, 0, 4, -2],\n [2, 2, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1268", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, 1, -4, -4, -3],\n [1, 3, -2, -2, -2],\n [-4, -2, -3, -4, -2],\n [-4, -2, -4, -5, 1],\n [-3, -2, -2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88439", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[2, 4, 5, 0, 1],\n [3, 0, 3, -4, -4],\n [-4, 0, -4, -3, 2],\n [2, 5, -2, 3, 2],\n [-5, 2, -5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "879", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[0, 1, 4, -2, 2],\n [2, 3, 0, -2, -4],\n [1, 4, -3, 5, -3],\n [-3, -2, -4, -1, -3],\n [4, -1, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-40", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 4, 0, 0, 5],\n [-3, 4, 3, -2, -1],\n [-3, -1, 2, 2, 2],\n [0, -5, 5, 4, 0],\n [5, 4, 1, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201465", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[5, -1, 2, -2, -1],\n [-1, 0, -4, 0, -1],\n [2, -4, 0, 0, 4],\n [-2, 0, 0, 5, 0],\n [-1, -1, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158985", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, -2, 0, 2, -2],\n [-2, 1, 1, 1, 0],\n [0, 1, -4, 4, -4],\n [2, 1, 4, 3, -3],\n [-2, 0, -4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-848", "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, 1, -4, 1],\n [-5, 4, 4, 2, 4],\n [4, -4, -3, 2, -3],\n [-5, 3, 2, -2, 2],\n [-1, -3, -5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488339", "dataset": "MATH"}
{"messages": [{"content": "Calculate the matrix power A^5 and find the value at position (2, 4) of the result:\nA =\n[[5, 0, -4, 0, 0],\n [0, -5, -2, -4, 0],\n [-4, -2, -4, -2, -3],\n [0, -4, -2, -2, 2],\n [0, 0, -3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-25828", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[-1, -2, -2, 2, 0],\n [-2, -2, -2, -3, -1],\n [-2, -2, 1, 4, -1],\n [2, -3, 4, 5, -1],\n [0, -1, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-257", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -1, 2, 3, 0],\n [-1, 3, -1, -3, 4],\n [2, -1, 2, 1, 0],\n [3, -3, 1, 0, -1],\n [0, 4, 0, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15835", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[5, 4, -1, 4, 0],\n [4, -4, 0, -1, 2],\n [-1, 0, 2, -4, 3],\n [4, -1, -4, 3, 0],\n [0, 2, 3, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, 2, 2, 4, -3],\n [2, -2, -5, 2, 4],\n [2, -5, -2, 1, 2],\n [4, 2, 1, -4, 5],\n [-3, 4, 2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "654532", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[-3, 0, 1, 2, 1],\n [0, 5, 0, 0, -2],\n [1, 0, 3, 2, 0],\n [2, 0, 2, 2, 4],\n [1, -2, 0, 4, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21994", "dataset": "MATH"}
{"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, 1, 0, 2, 0],\n [1, -2, 1, 1, 2],\n [0, 1, 2, 0, 0],\n [2, 1, 0, -3, 4],\n [0, 2, 0, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55710", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 5) of the 4th power of the matrix:\n[[-5, 3, -4, -4, 0],\n [3, -1, -3, 4, -4],\n [-4, -3, 0, -2, 2],\n [-4, 4, -2, 2, -2],\n [0, -4, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "514", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^5 where A =\n[[5, -5, -5, -4, -1],\n [3, 0, -2, -3, 2],\n [-3, -5, -2, 5, -1],\n [-1, -1, 2, 2, -2],\n [3, -5, -1, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7833", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 2, -2, 0, 0],\n [2, -3, -2, 0, -4],\n [-2, -2, -4, 3, -4],\n [0, 0, 3, -5, 0],\n [0, -4, -4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8483", "dataset": "MATH"}
{"messages": [{"content": "For the matrix power A^4 where A =\n[[0, 2, 2, 2, 0],\n [2, 2, -1, 2, -2],\n [2, -1, 1, 0, 2],\n [2, 2, 0, -4, 0],\n [0, -2, 2, 0, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1834", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (5, 5) of the matrix A^4 where A is:\n[[-3, -1, -2, 0, 2],\n [-1, -4, -1, 0, -2],\n [-2, -1, 2, 2, -2],\n [0, 0, 2, 3, 2],\n [2, -2, -2, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393", "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, 0, -2, 0],\n [-2, -5, -2, -2, 1],\n [0, -2, -1, -2, -2],\n [-2, -2, -2, 1, 0],\n [0, 1, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75016", "dataset": "MATH"}
{"messages": [{"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[2, 2, -1, -3, 0],\n [2, 0, 0, 2, -4],\n [-1, 0, 5, 2, -4],\n [-3, 2, 2, -5, 3],\n [0, -4, -4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-756", "dataset": "MATH"}
{"messages": [{"content": "What is the value at position (1, 4) of the matrix A^5 where A is:\n[[4, -1, 0, 1, 1],\n [-1, 1, -2, 0, 0],\n [0, -2, -2, 1, 0],\n [1, 0, 1, 3, 0],\n [1, 0, 0, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1207", "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, -2, 2, 2],\n [0, 2, 2, -4, 2],\n [-2, 2, 1, -2, 2],\n [2, -4, -2, 3, 2],\n [2, 2, 2, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169287", "dataset": "MATH"}