| {"messages": [{"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, 0, -1, -4, 3],\n [-4, -3, 2, 4, 4],\n [3, -4, -5, 3, 2],\n [5, 5, 0, -1, 1],\n [0, 2, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-318", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[2, 2, 2, 3, 5],\n [0, -4, 1, 2, -5],\n [0, 0, -2, 4, 1],\n [0, 0, 0, 3, 5],\n [0, 0, 0, 0, -4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-4, 5, -3, 3, -3],\n [-2, 2, -3, -4, 5],\n [-1, -1, -1, -5, 3],\n [2, 2, -4, -4, 3],\n [4, -4, 5, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, 2, -5, 1, -4],\n [0, 3, 1, -5, -1],\n [0, 0, -4, 1, 5],\n [0, 0, 0, -2, -1],\n [0, 0, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the value at position (1, 3) of the result:\nA =\n[[5, 1, -2, 3, 0],\n [1, -1, -2, 4, 0],\n [-2, -2, 4, -1, -2],\n [3, 4, -1, 3, -2],\n [0, 0, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-236", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, -5, -2, 3, 3],\n [-2, -5, 2, 1, 0],\n [-3, 1, 5, 0, 2],\n [-1, -3, -5, -2, -2],\n [-5, -2, -5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2510", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[4, 3, 2, -5, 2],\n [2, 3, 2, 1, 2],\n [-1, -1, -2, -2, 2],\n [-2, 4, -1, -2, -2],\n [5, 2, -5, -1, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10389", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (4, 2) of the 3th power of the matrix:\n[[-1, 5, -4, 4, -1],\n [-2, 5, -5, -3, 1],\n [5, 1, -3, 1, -4],\n [-2, -2, 1, 3, 5],\n [5, 5, -1, 5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 2, -5, -3, 0],\n [0, -5, 4, 3, -1],\n [0, 0, 4, 0, -4],\n [0, 0, 0, 2, 5],\n [0, 0, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-64", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the value at position (5, 2) of the result:\nA =\n[[-3, 3, 3, -2, 5],\n [0, -1, -5, -1, -5],\n [0, 0, 5, 0, 5],\n [0, 0, 0, 4, -1],\n [0, 0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (4, 3) of the 3th power of the matrix:\n[[1, -3, 1, 0, -2],\n [2, 2, 0, -1, -2],\n [2, 4, 3, 2, 0],\n [-1, 2, 4, -4, -1],\n [5, 4, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[-5, 0, -1, 1, -2],\n [0, 2, 0, -2, 5],\n [0, 0, 2, 1, -4],\n [0, 0, 0, 1, -5],\n [0, 0, 0, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 2, -4, 2, 0],\n [2, 5, 2, -4, 2],\n [-4, 2, 1, -3, 4],\n [2, -4, -3, -5, 2],\n [0, 2, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4195", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, 0, 4, -3, 3],\n [0, 4, 1, -5, 2],\n [0, 0, -1, -5, 0],\n [0, 0, 0, 2, -5],\n [0, 0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "388", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[3, -4, 0, -2, 0],\n [-4, -5, 2, 0, -2],\n [0, 2, 2, -4, 4],\n [-2, 0, -4, 1, 2],\n [0, -2, 4, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2950", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 4, -4, 0, 3],\n [-4, 4, 2, -1, 2],\n [-2, -5, -5, -2, -1],\n [1, 4, 3, 2, -3],\n [5, 5, 1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2299", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[-5, 2, 3, 4, 4],\n [2, -4, -4, -2, -1],\n [3, -4, -5, 2, -2],\n [4, -2, 2, 2, -5],\n [4, -1, -2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5448", "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, -5, -5, 4],\n [0, 3, -3, 1, -3],\n [0, 0, -2, 3, 4],\n [0, 0, 0, -5, -2],\n [0, 0, 0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3696", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[4, 2, 0, 2, 4],\n [3, -5, 5, -4, 5],\n [2, -2, 1, 1, 0],\n [4, -3, -1, 5, -1],\n [-3, -5, -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": "462", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 2, 0, -4, -2],\n [-3, 1, 3, 2, 5],\n [3, 1, 2, 4, -1],\n [5, -3, 0, 4, -2],\n [-3, -4, 5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1104", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 1, -3, 2, -5],\n [3, 5, -5, -2, 1],\n [3, 4, 5, -3, 0],\n [2, 1, 2, 3, 0],\n [3, 1, 5, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, -2, -5, -4, 0],\n [-3, 4, 4, 1, 0],\n [5, -1, 0, 2, -3],\n [-3, 2, -4, 4, 2],\n [2, -3, -4, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2276", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (1, 1) of the 2th power of the matrix:\n[[-1, 4, 1, 1, 2],\n [-1, 4, 1, -2, -2],\n [5, 3, 3, -3, 3],\n [1, 2, 0, 5, 1],\n [-4, -3, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[5, -2, -2, 2, 5],\n [1, -1, -3, -5, 5],\n [-3, -4, -1, -2, 5],\n [0, 5, 2, -5, -5],\n [2, -1, -2, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (3, 2) of the 3th power of the matrix:\n[[-2, -4, -2, -1, 2],\n [-4, 0, 0, 0, 4],\n [-2, 0, 2, 3, -2],\n [-1, 0, 3, 4, 0],\n [2, 4, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-44", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (5, 1) of the result:\nA =\n[[1, -4, -2, 2, 2],\n [-4, -5, -1, 2, -4],\n [-2, -1, 5, 2, -2],\n [2, 2, 2, 2, 2],\n [2, -4, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1798", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-5, 4, 0, 1, 4],\n [4, 5, 0, -2, 0],\n [0, 0, 2, -4, 2],\n [1, -2, -4, -1, -2],\n [4, 0, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-5, 2, -4, 1, 4],\n [2, 0, 5, 2, 4],\n [-4, 5, -3, 1, 0],\n [1, 2, 1, 3, 4],\n [4, 4, 0, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5033", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (5, 4) of the matrix A^3 where A is:\n[[-3, 2, 4, 0, 0],\n [2, 1, 3, 0, 0],\n [4, 3, -2, 0, -2],\n [0, 0, 0, 2, -2],\n [0, 0, -2, -2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-54", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, -3, -5, 0, 0],\n [3, -4, -5, 1, 5],\n [-3, 1, 1, -2, -1],\n [4, 1, 0, -2, -2],\n [1, -5, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "523", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[1, -4, -5, -1, 3],\n [1, 4, 0, -3, 4],\n [3, -3, 4, 3, 3],\n [1, 0, 1, 5, 0],\n [0, -4, 5, -4, -5]], determine the value at position (3, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-60", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the value at position (5, 1) of the result:\nA =\n[[4, 4, 2, -4, -3],\n [0, -1, 1, -3, -1],\n [0, 0, 3, -5, -2],\n [0, 0, 0, 1, 4],\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": "For the matrix power A^2 where A =\n[[5, -2, -5, 3, -1],\n [3, 0, -2, -3, 1],\n [2, -2, -3, 0, -4],\n [3, 4, -1, 5, -2],\n [5, -2, 2, -3, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "417", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the value at position (3, 2) of the result:\nA =\n[[1, -1, -3, 2, -2],\n [1, 2, -5, -5, 3],\n [3, 5, 1, 1, -2],\n [4, -4, -2, 3, -5],\n [-3, -4, 4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (5, 2) of the matrix A^3 where A is:\n[[-2, 1, 0, 0, -2],\n [1, -4, 2, -2, 4],\n [0, 2, 5, 0, -2],\n [0, -2, 0, -1, -2],\n [-2, 4, -2, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "222", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -2, -1, -2, -1],\n [-2, -5, -2, -1, 4],\n [-1, -2, 1, 2, 0],\n [-2, -1, 2, 3, -3],\n [-1, 4, 0, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2039", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[0, 4, 4, 2, -2],\n [-1, 4, -1, -4, 5],\n [2, 3, -1, 4, -1],\n [-3, 5, 3, -5, 5],\n [4, -1, 3, -5, -5]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[4, -4, 0, 3, -4],\n [-3, 0, -3, 5, -5],\n [3, -2, 3, 0, -2],\n [1, 3, 3, 3, 2],\n [-3, -3, -5, -5, 5]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (4, 1) of the matrix A^4 where A is:\n[[-3, -4, 0, 2, -4],\n [-4, 5, -2, 0, -1],\n [0, -2, 5, -4, -2],\n [2, 0, -4, 2, 0],\n [-4, -1, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-362", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[-5, -1, -3, -4, -1],\n [-1, 3, 2, 3, 4],\n [-3, 2, -2, 2, 0],\n [-4, 3, 2, 4, 1],\n [-1, 4, 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": "5002", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (5, 2) of the matrix A^2 where A is:\n[[3, 4, -2, 4, 2],\n [-1, -1, 1, -4, 5],\n [5, -1, 2, -4, 4],\n [2, -4, 3, -2, -1],\n [4, 0, -3, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "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, -1, 2],\n [-2, 3, -4, 0, -3],\n [-2, -4, -5, -2, 2],\n [-1, 0, -2, 5, -2],\n [2, -3, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34269", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[2, -3, -5, 4, -2],\n [2, -3, 0, 4, 5],\n [-4, 1, 2, 2, 0],\n [1, 3, 4, 4, -3],\n [-3, -2, -2, -2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4025", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, 0, 0, -4, -1],\n [0, 0, -2, 0, -4],\n [0, -2, -4, 1, 2],\n [-4, 0, 1, 5, 2],\n [-1, -4, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-158", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, 4, 0, 4, 3],\n [1, 3, -4, -3, 1],\n [1, -3, -5, 1, 5],\n [5, 2, 4, 1, 3],\n [-2, 1, -5, 4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -5, 5, 4, -5],\n [-1, -5, 2, -4, 2],\n [0, 4, 2, 2, 1],\n [-4, -1, 2, -1, 4],\n [-4, -2, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "454", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[4, 0, -4, 1, -4],\n [2, -5, 1, 4, 3],\n [4, 1, 4, -1, -2],\n [-5, 3, -1, 2, 0],\n [2, -3, -4, -5, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-22", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 2, 5, 1, -4],\n [2, 2, -2, 0, -2],\n [5, -2, 0, 4, -2],\n [1, 0, 4, -3, 1],\n [-4, -2, -2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11963", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 4, 3, -3, -4],\n [-4, -3, -1, -2, -2],\n [-2, -1, 2, 1, -2],\n [-3, -4, -5, 2, -1],\n [2, -5, -2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "415", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (4, 3) of the 4th power of the matrix:\n[[1, 0, -2, 4, 1],\n [0, -2, -1, -3, 2],\n [-2, -1, 4, 0, -2],\n [4, -3, 0, 4, 0],\n [1, 2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-502", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, -3, -4, 0, 3],\n [2, -2, -2, -1, -2],\n [-1, 1, 2, 5, 3],\n [-5, 2, -2, 5, 0],\n [2, 0, -5, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1835", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, -4, 0, -2, 4],\n [-2, -5, 2, -2, -3],\n [-5, -4, -5, -2, -3],\n [3, -5, 0, 5, 0],\n [2, 4, -2, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-844", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[-4, 2, 1, -3, 2],\n [-4, -4, -3, -2, -2],\n [-3, 2, 2, -3, 4],\n [-3, 2, 3, 3, 3],\n [-4, 1, -4, -2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-122", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[2, 0, 2, -2, 3],\n [0, 2, 2, 4, 2],\n [2, 2, 5, 2, 2],\n [-2, 4, 2, 4, 0],\n [3, 2, 2, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "454", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the value at position (4, 1) of the result:\nA =\n[[-5, 2, -3, -2, 2],\n [2, 0, -1, 3, 0],\n [-3, -1, 4, 0, -2],\n [-2, 3, 0, 3, 0],\n [2, 0, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (1, 5) of the 3th power of the matrix:\n[[-4, -2, -1, -1, 1],\n [-3, 2, 1, -5, 0],\n [-3, 1, 0, 2, -5],\n [-4, -4, -2, -3, 4],\n [-4, -5, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -4, -1, -2, -2],\n [-4, -3, 0, 1, 4],\n [-1, 0, -3, 3, 4],\n [-2, 1, 3, 5, 0],\n [-2, 4, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40267", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[4, -3, -3, 0, 4],\n [4, -5, -4, 4, -5],\n [0, -5, 1, -1, -4],\n [5, -4, -4, 4, 1],\n [3, -2, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "218", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[-4, 1, 0, 0, -2],\n [4, -4, 2, 1, 2],\n [3, -3, -2, -1, 3],\n [-3, -2, 5, 2, 3],\n [-2, 5, 5, 4, 3]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[-2, 2, 0, 0, 2],\n [2, 3, 0, -2, 2],\n [0, 0, -5, 0, -2],\n [0, -2, 0, -4, 0],\n [2, 2, -2, 0, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-221", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[1, 0, 0, 0, 2],\n [0, 5, -2, 1, -1],\n [0, -2, -4, -2, 2],\n [0, 1, -2, 5, -2],\n [2, -1, 2, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "294", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, -1, -5, -1, 1],\n [3, -3, 2, -4, 4],\n [-5, -4, 3, 2, -5],\n [-3, -4, 3, -2, -4],\n [-3, 1, 0, 3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, -2, 3, -3, -5],\n [-1, 5, -1, -4, -1],\n [3, -1, -4, 1, -5],\n [4, -4, 3, -1, 0],\n [5, -4, -1, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21868", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-3, 2, 2, 0, -2],\n [2, 2, 2, 0, 4],\n [2, 2, 2, 0, -2],\n [0, 0, 0, -1, -1],\n [-2, 4, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "257", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (3, 1) of the 3th power of the matrix:\n[[5, -1, 5, -2, -4],\n [2, 0, 5, -5, 3],\n [3, 2, 5, -3, 1],\n [2, 4, 3, -1, 2],\n [5, -2, -3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-2, -4, 0, -4, 0],\n [5, 0, 4, 5, -4],\n [-2, 5, -2, 5, -4],\n [4, -2, -5, -4, -5],\n [-3, -3, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[4, 1, -4, -3, 4],\n [3, 5, 5, 4, -2],\n [1, 1, 1, 3, 4],\n [-5, -4, 2, 5, -5],\n [2, 4, 0, -3, 5]], determine the value at position (5, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -2, 0, 0, 0],\n [-2, 0, 0, 2, -2],\n [0, 0, -2, 0, 0],\n [0, 2, 0, 2, -3],\n [0, -2, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (3, 1) of the 4th power of the matrix:\n[[2, -2, -3, 0, 2],\n [-2, -3, -3, 0, -4],\n [-3, -3, 2, -2, 0],\n [0, 0, -2, 3, -4],\n [2, -4, 0, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-123", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 3th power of the matrix:\n[[5, -4, 2, 2, 5],\n [-4, 0, -1, -1, 0],\n [2, -1, 5, -3, 0],\n [2, -1, -3, 0, 2],\n [5, 0, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2481", "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, 1, -3, -2, -2],\n [1, 5, -2, 2, -3],\n [-3, -2, 1, -4, -1],\n [-2, 2, -4, -2, 2],\n [-2, -3, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21117", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[-4, 2, -2, -1, -1],\n [2, 4, -2, 2, 2],\n [-2, -2, 2, 0, -1],\n [-1, 2, 0, 3, 2],\n [-1, 2, -1, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12182", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 3th power of the matrix:\n[[5, 3, -3, 5, 4],\n [4, 4, -2, 0, 3],\n [-4, -5, 3, 3, -4],\n [-4, 1, 4, 4, -3],\n [-1, -5, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-552", "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, 0, 2, -2],\n [4, -2, 2, 3, 4],\n [0, 2, -4, -2, 4],\n [2, 3, -2, -5, -4],\n [-2, 4, 4, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57755", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[5, -2, 2, -2, -4],\n [-2, 5, 2, -3, 0],\n [2, 2, -4, 2, 0],\n [-2, -3, 2, 2, 2],\n [-4, 0, 0, 2, -3]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1170", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the value at position (5, 3) of the result:\nA =\n[[-4, -4, 0, -3, -3],\n [4, -3, 5, -1, 0],\n [-3, -5, 4, -3, -3],\n [-5, -3, -4, -2, -2],\n [-5, -4, 4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "264", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the value at position (3, 2) of the result:\nA =\n[[0, -3, 5, -1, 5],\n [-3, 2, -1, 0, 4],\n [-1, 0, -3, 1, -1],\n [3, 0, 4, -5, 2],\n [4, -2, 4, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[0, -1, 1, -3, -2],\n [-1, 3, -2, 0, 0],\n [1, -2, 4, 0, -3],\n [-3, 0, 0, 3, 0],\n [-2, 0, -3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[2, 4, 2, 3, 5],\n [-4, 2, -2, 2, 5],\n [-2, -4, -2, 1, 3],\n [-4, 3, 3, -1, 4],\n [-1, -4, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-200", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (1, 5) of the matrix A^2 where A is:\n[[-1, 0, -2, -5, -4],\n [0, -5, 0, -2, 3],\n [-2, 0, -1, 4, -2],\n [-5, -2, 4, -4, 1],\n [-4, 3, -2, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the value at position (2, 2) of the result:\nA =\n[[5, 0, -2, -2, 0],\n [0, -3, 0, 1, -2],\n [-2, 0, 4, -2, 1],\n [-2, 1, -2, 0, 2],\n [0, -2, 1, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 1, -2, -2, 0],\n [1, -5, 2, 3, 1],\n [-2, 2, 5, 2, 2],\n [-2, 3, 2, 3, 0],\n [0, 1, 2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14801", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (4, 5) of the matrix A^3 where A is:\n[[-3, 1, 2, 4, -4],\n [1, 4, 2, -4, 3],\n [2, 2, -2, 2, 0],\n [4, -4, 2, 1, 0],\n [-4, 3, 0, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[5, -4, 0, 2, 1],\n [5, 1, 3, -5, 4],\n [-2, 1, -1, -1, 3],\n [2, 2, -5, 5, -1],\n [5, -1, 0, -4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1871", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, -4, 2, 0, -4],\n [4, -4, 1, 0, -3],\n [-1, -2, -4, 5, 0],\n [-4, -2, 1, -3, -1],\n [-1, 2, 4, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-92", "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, 5, -3],\n [1, -5, -3, -2, -3],\n [5, 2, 4, 4, -2],\n [-2, -5, -4, -2, 2],\n [3, 3, 2, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12808", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 2th power of the matrix:\n[[2, -4, -3, 4, 0],\n [0, -2, 1, -2, -3],\n [4, -5, 2, -2, 0],\n [-4, 5, -4, -5, -3],\n [-3, -1, 1, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "167", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[3, 1, 2, 2, 0],\n [1, -3, 0, -2, 4],\n [2, 0, 1, 4, 2],\n [2, -2, 4, -3, -4],\n [0, 4, 2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[-1, -3, 0, 4, -1],\n [5, -1, 3, 1, -3],\n [2, -4, 2, 4, 0],\n [-4, -1, 0, 0, -1],\n [4, -3, 2, -3, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-332", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the value at position (3, 3) of the result:\nA =\n[[2, 0, -3, 2, 0],\n [0, 2, 2, -1, 4],\n [-3, 2, -5, 0, -2],\n [2, -1, 0, 3, 2],\n [0, 4, -2, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-281", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[1, 1, 2, 4, -4],\n [1, 5, 0, 1, -4],\n [2, 0, -2, 0, 1],\n [4, 1, 0, 2, -2],\n [-4, -4, 1, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "247", "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, 1, 4, 0, 2],\n [-2, 4, -2, 0, 0],\n [-2, 0, 0, -5, -4],\n [-2, 2, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31728", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, -3, -2, -4, 2],\n [3, 3, -1, 3, 2],\n [3, 1, -1, -2, -4],\n [-1, 5, -5, 1, 4],\n [-4, 0, 0, -1, 3]]\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, 3) of the 3th power of the matrix:\n[[0, 0, 4, -1, 0],\n [0, -5, 2, 1, 2],\n [4, 2, 5, -2, -3],\n [-1, 1, -2, 3, -1],\n [0, 2, -3, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-197", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 0, -2, 1, 1],\n [5, 3, 0, 5, 2],\n [-2, 1, -5, 3, 0],\n [-3, 4, -4, 2, -3],\n [5, 3, 5, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4169", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[-4, 0, 1, 4, -3],\n [2, 0, -3, 0, -4],\n [-3, -3, 2, -4, -4],\n [-5, 0, -5, 0, 0],\n [2, -2, 1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "376", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[-5, 4, 2, 0, 0],\n [4, 3, -2, 2, 4],\n [2, -2, 1, 0, 2],\n [0, 2, 0, 1, 0],\n [0, 4, 2, 0, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26632", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 0, 4, 0, 2],\n [0, 3, 1, 3, 2],\n [4, 1, 2, 0, 2],\n [0, 3, 0, 1, 0],\n [2, 2, 2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9890", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, 0, 3, 2, -1],\n [2, 5, -2, -3, -4],\n [2, -3, 2, -2, -4],\n [-5, -1, 2, -2, -3],\n [-2, 5, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-97", "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, -3, 4, -5],\n [2, 3, 5, 3, 5],\n [4, -4, 0, -1, -4],\n [-1, 0, -4, -4, -2],\n [2, 4, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36617", "dataset": "MATH"} | |