| {"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 0, 0],\n [0, 3, 0],\n [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": "162", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[2, 3, -3],\n [0, 3, 3],\n [3, 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": "263", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -3, 2],\n [0, -3, -1],\n [0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "408", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 1, -1],\n [1, -2, 0],\n [-1, 0, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[1, 2, -2],\n [-1, 3, 0],\n [-3, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -3, 2],\n [0, 1, -2],\n [0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 2, -1],\n [0, -3, -3],\n [0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "282", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[3, 1, 1],\n [0, -2, 2],\n [0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[3, 0, 0],\n [0, 1, 0],\n [0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 0, -1],\n [0, 3, -3],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "308", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[3, 0, -2],\n [0, 0, -2],\n [0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (2, 3) of the matrix A^2 where A is:\n[[-1, -2, 2],\n [-2, -2, -2],\n [2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (1, 3) of the 2th power of the matrix:\n[[1, -3, -1],\n [3, 3, -3],\n [-3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, -1, 3],\n [3, -3, -1],\n [0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1703", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -3, 3],\n [0, 3, 0],\n [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": "160", "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, -2],\n [1, -3, 0],\n [-2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1624", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[2, 0, -2],\n [0, 3, 1],\n [-2, 1, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-2, -2, 1],\n [0, -2, 1],\n [0, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-17", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (1, 3) of the 2th power of the matrix:\n[[-1, 2, 0],\n [2, 1, -2],\n [0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, -1, 3],\n [-1, 1, 1],\n [-3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-3, -1, 0],\n [0, 3, 0],\n [0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-2, 0, 0],\n [0, 2, -2],\n [0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[-3, 2, -1],\n [2, -2, 2],\n [-1, 2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -2, 2],\n [-2, 1, 2],\n [2, 2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "963", "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[[-2, 1, 0],\n [-1, 2, 3],\n [-1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 0, -2],\n [0, 1, -2],\n [-2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (1, 2) of the matrix A^4 where A is:\n[[-1, 2, 0],\n [0, 0, -2],\n [1, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-18", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^2 where A is:\n[[2, -2, -2],\n [0, 2, 3],\n [0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the value at position (2, 3) of the 4th power of the matrix:\n[[-1, 2, 2],\n [0, 2, -1],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-15", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (3, 2) of the matrix A^3 where A is:\n[[3, -2, 0],\n [-2, 2, 0],\n [0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, 2, -1],\n [-3, -2, 0],\n [1, -1, -3]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[1, -2, -3],\n [0, 2, -1],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the value at position (3, 1) of the result:\nA =\n[[3, -1, 3],\n [0, -3, 2],\n [0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, 2, 2],\n [3, 3, -2],\n [-1, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[1, 0, -2],\n [0, -2, 0],\n [-2, 0, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[2, 2, 0],\n [0, -2, -3],\n [0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, -2, 3],\n [0, 2, -3],\n [0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[3, -1, 2],\n [-3, 2, -2],\n [1, -3, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the value at position (3, 2) of the result:\nA =\n[[0, 0, 0],\n [1, 0, 1],\n [1, 0, -3]]\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 2th power of the matrix:\n[[-2, 3, -3],\n [0, 1, -1],\n [0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-4, 4, 1, 0],\n [-2, -4, -4, 1],\n [-2, 2, 4, 2],\n [-1, -3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "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, -4, 0],\n [-1, 2, 2, 0],\n [-4, 2, -3, -1],\n [0, 0, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3525", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the value at position (3, 3) of the result:\nA =\n[[0, 4, -2, -4],\n [4, 0, 2, 2],\n [-2, 2, 2, 0],\n [-4, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[-3, 0, -2, 3],\n [0, -1, 2, 2],\n [-2, 2, -4, -2],\n [3, 2, -2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-285", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-3, -1, -1, 2],\n [1, -4, 1, -4],\n [-4, 1, 1, -1],\n [4, 1, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "697", "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, 3, 4],\n [-3, 4, 0, 2],\n [-1, 2, 3, -1],\n [0, -4, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2306", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[3, 2, -4, 2],\n [0, 3, 0, -2],\n [-1, -4, 2, 0],\n [-3, 3, -1, -4]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-66", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (2, 2) of the matrix A^4 where A is:\n[[1, 0, 0, 0],\n [0, 2, -3, 4],\n [0, -3, 1, -2],\n [0, 4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1806", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, -1, -1, 2],\n [-4, -4, 1, 3],\n [-3, -1, 1, 2],\n [-4, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[4, 2, 2, 2],\n [3, -3, 4, 0],\n [0, 4, 1, 0],\n [1, 1, 0, 3]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (3, 4) of the matrix A^4 where A is:\n[[0, -2, 0, -2],\n [-2, 4, -2, -2],\n [0, -2, -2, 2],\n [-2, -2, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (1, 3) of the matrix A^2 where A is:\n[[-1, 0, 1, 0],\n [3, 4, 3, 2],\n [-2, 4, 0, -4],\n [-4, -1, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-2, 0, 4, -1],\n [4, 1, -4, -3],\n [-3, 2, 4, -4],\n [2, 1, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "280", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 0, -2, 4],\n [0, 3, 2, -4],\n [-2, 2, 2, -2],\n [4, -4, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14967", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[4, 2, 1, 3],\n [2, 2, 0, 2],\n [1, 0, 3, 0],\n [3, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[4, 2, 2, -2],\n [2, 1, -4, 0],\n [2, -4, 4, 0],\n [-2, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "952", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[-2, -2, -4, -3],\n [-1, 3, 3, 3],\n [-2, 1, 1, 0],\n [-1, -2, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1295", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[0, 3, -3, 4],\n [1, 3, 2, -4],\n [-2, -1, 0, -3],\n [4, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "162", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[-1, 0, 0, 4],\n [0, 1, -2, 2],\n [0, -2, 4, -1],\n [4, 2, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "303", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[3, 0, 2, 0],\n [0, 3, 0, 0],\n [2, 0, 1, 0],\n [0, 0, 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": "44", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[2, 1, 0, 1],\n [1, -4, 1, 1],\n [0, 1, -4, 2],\n [1, 1, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-35", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the value at position (1, 2) of the result:\nA =\n[[1, 0, -3, 0],\n [2, -2, -4, 3],\n [-1, -2, 1, -3],\n [4, -1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 2, -4, 4],\n [0, 3, 4, 1],\n [-3, 1, 4, 2],\n [-2, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1600", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[0, -1, 4, -3],\n [1, 1, 4, -4],\n [-4, -4, 4, 3],\n [4, -1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-307", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, -2, 3, 0],\n [0, 2, -1, 2],\n [-1, 1, 1, 3],\n [-2, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-490", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, -1, -1, 2],\n [2, -2, -2, 1],\n [-2, 4, -2, 3],\n [-2, 2, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (1, 3) of the matrix A^2 where A is:\n[[-3, 1, 1, 2],\n [-4, 3, -2, 0],\n [2, -4, 2, 4],\n [3, 1, -4, 0]]?\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 3th power of the matrix:\n[[-1, 0, 2, 0],\n [0, -1, 0, 0],\n [2, 0, 0, 1],\n [0, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "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, -4, -2, 3],\n [0, 2, 3, 2],\n [0, -1, 0, 1],\n [1, -3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "339", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[4, 2, -4, -3],\n [4, 2, 1, -4],\n [-3, 1, -2, 3],\n [-2, -4, 3, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[1, 2, -2, 0],\n [2, 1, 1, 0],\n [-2, 1, -2, -2],\n [0, 0, -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": "385", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (3, 3) of the matrix A^2 where A is:\n[[-1, -4, -1, -2],\n [-4, 4, 0, 2],\n [-1, 0, 0, 0],\n [-2, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (4, 3) of the matrix A^4 where A is:\n[[-1, 0, -1, 0],\n [0, -4, 2, 1],\n [-1, 2, 2, 0],\n [0, 1, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-3, 0, 4, 2],\n [0, 4, 3, 2],\n [4, 3, 3, 4],\n [2, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "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[[2, -2, -1, 0],\n [-2, -2, 0, 0],\n [-1, 0, 4, -2],\n [0, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[1, 0, 0, 1],\n [0, -2, 3, 0],\n [0, 3, -2, 0],\n [1, 0, 0, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[1, 1, 2, 0],\n [3, 3, 4, -3],\n [3, 0, 3, -2],\n [-3, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "192", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[0, -1, 0, 3],\n [2, -4, 0, 0],\n [3, 1, 4, 4],\n [4, -4, -2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-109", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^2 where A =\n[[-2, -1, 2, 2],\n [-1, 0, -1, -4],\n [2, -1, 2, -2],\n [2, -4, -2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[0, 0, 2, -1],\n [0, -1, 0, -1],\n [2, 0, 0, 0],\n [-1, -1, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of all entries of the 2th power of the matrix:\n[[-3, -1, -1, 1],\n [0, -3, 4, 1],\n [4, 0, 3, 0],\n [-3, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-4, -4, 4, -2],\n [-1, -2, -1, -2],\n [3, 1, -2, -3],\n [-3, -3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[-3, -1, 2, -2],\n [-1, -2, 4, 0],\n [2, 4, 0, 0],\n [-2, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the value at position (4, 1) of the matrix A^4 where A is:\n[[0, 0, 0, -1],\n [0, 3, 2, -2],\n [0, 2, -4, 3],\n [-1, -2, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-63", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, 0, -4, 0],\n [0, -1, -1, 0],\n [-4, -1, -4, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1260", "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[[-4, 2, -2, -1],\n [2, 3, 0, 1],\n [-2, 0, -2, -4],\n [-1, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1306", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[1, -4, -4, 2],\n [-4, 0, 0, -2],\n [0, -3, 4, -1],\n [-3, 3, -3, 4]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^2 and find the value at position (4, 2) of the result:\nA =\n[[-1, 1, -3, -4],\n [0, 0, 0, -3],\n [-4, 3, 2, -2],\n [3, 0, -1, 4]]\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 (3, 3) of the matrix A^2 where A is:\n[[0, 3, 0, 2],\n [3, 3, 0, 1],\n [0, 0, 3, -2],\n [2, 1, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[3, -2, -2, -1],\n [-2, -4, 1, -1],\n [-2, 1, 2, 2],\n [-1, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[-3, 0, 0, 0],\n [-4, 3, -4, -3],\n [-4, -1, -4, -1],\n [-2, 2, 0, 4]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-184", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, 2, -1, -3],\n [4, 3, -3, -4],\n [3, 4, -4, 1],\n [3, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-982", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^4 where A =\n[[3, 4, -3, 3],\n [3, 4, 0, 2],\n [0, -2, -4, 3],\n [2, 0, 1, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7774", "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, -2, -2],\n [-2, -4, -2, 0],\n [-2, -2, 3, -2],\n [-2, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4254", "dataset": "MATH"} | |
| {"messages": [{"content": "For the matrix power A^3 where A =\n[[2, 0, -2, -2],\n [0, 4, 1, 0],\n [-2, 1, -1, 1],\n [-2, 0, 1, -3]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-28", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of absolute values of all entries of the matrix A^2 where A is:\n[[4, 0, 1, 1],\n [0, -3, -1, 1],\n [1, -1, -1, 0],\n [1, 1, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 1, -1, 1],\n [1, 0, 0, -2],\n [-1, 0, 4, 1],\n [1, -2, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133", "dataset": "MATH"} | |
| {"messages": [{"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, 4, 1, 2],\n [4, -1, 2, 0],\n [1, 2, 3, 2],\n [2, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1188", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 0, 2, -2],\n [0, 3, 0, -2],\n [2, 0, 4, -2],\n [-2, -2, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2894", "dataset": "MATH"} | |
| {"messages": [{"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 0, -1, 2],\n [0, -1, -2, 0],\n [-1, -2, 2, -3],\n [2, 0, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "453", "dataset": "MATH"} | |