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[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, 0, 2, -1, 0, 0],\n [0, 2, -3, 0, 0, -5],\n [2, -3, -2, 0, -4, 1],\n [-1, 0, 0, 6, 2, 4],\n [0, 0, -4, 2, 2, 0],\n [0, -5, 1, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
73831
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[6, 0, 1, 0, 1, -3],\n [0, 5, 2, 2, 0, 0],\n [1, 2, 0, 0, 4, 2],\n [0, 2, 0, -2, -2, 0],\n [1, 0, 4, -2, -4, 1],\n [-3, 0, 2, 0, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8018
MATH
[ { "content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[-2, -4, -4, 6, -5, 1],\n [-6, 5, 1, -4, 2, 5],\n [5, 4, -5, 3, 2, -1],\n [-6, -2, 3, 2, 6, -1],\n [0, -3, -6, -2, -5, 1],\n [-3, -6, 3, 0, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
3009
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[-5, -4, 2, 6, 2, -5],\n [-4, 4, 5, 2, -6, -5],\n [4, -5, 3, -4, 3, -4],\n [3, 6, -5, 1, 1, 1],\n [-5, 6, 2, 4, 0, 5],\n [-2, 0, 1, 2, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13011
MATH
[ { "content": "For the matrix power A^4 where A =\n[[2, 1, -2, -5, 0, 2],\n [1, 4, 0, -2, 4, 2],\n [-2, 0, 3, 2, 0, 4],\n [-5, -2, 2, -4, 2, 1],\n [0, 4, 0, 2, -4, 1],\n [2, 2, 4, 1, 1, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19319
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 2, -5, 2, 0, 4],\n [2, -3, 2, -3, -4, 0],\n [-5, 2, 0, 6, -2, -2],\n [2, -3, 6, -6, -4, -1],\n [0, -4, -2, -4, -2, 0],\n [4, 0, -2, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
24413
MATH
[ { "content": "What is the value at position (1, 6) of the matrix A^5 where A is:\n[[0, 2, 0, 0, 2, 1],\n [2, -3, 0, 4, -3, 2],\n [0, 0, -4, -2, 2, 0],\n [0, 4, -2, -3, -1, -6],\n [2, -3, 2, -1, -4, 0],\n [1, 2, 0, -6, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3939
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, 1, 0, 4, 1, 2],\n [-5, 3, -2, 1, -4, 4],\n [4, -1, -1, 0, 6, 4],\n [-4, 1, 1, 2, 1, -4],\n [-1, 2, -6, -4, -5, 5],\n [1, -1, 3, 4, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
16768
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, 4, -1, 0, 1, 2],\n [-2, 4, -4, -5, 1, -6],\n [3, -1, -5, -4, 1, -6],\n [-1, -4, -1, -4, 4, 4],\n [1, -2, -3, 2, -2, 5],\n [-3, 1, 1, 1, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-54147
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-6, -5, -3, 3, -5, 4],\n [3, -4, 2, 2, 4, 2],\n [0, -3, -6, -4, 1, -3],\n [3, 3, -5, 1, 0, 4],\n [3, 2, -5, -2, -1, 6],\n [-5, -5, 6, 3, -3, 1]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
2764
MATH
[ { "content": "What is the value at position (2, 2) of the matrix A^5 where A is:\n[[6, 4, -2, 2, -3, -4],\n [3, 1, -6, 2, -3, 4],\n [2, 1, -4, -4, 2, -4],\n [-3, 2, 5, -3, 4, -4],\n [0, -1, -6, 3, 1, -6],\n [-3, -1, -1, 0, 4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-4160
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, -2, -3, -1, 0, 3],\n [3, -6, 2, 1, 0, 2],\n [-4, 3, -3, 0, -1, 6],\n [-5, -5, 3, 0, 2, 4],\n [5, 2, 0, 4, 1, 3],\n [-4, -6, 0, 1, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
42238
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 3, 4, 2, 6, -4],\n [1, 4, -5, -4, -6, -2],\n [-3, 6, -6, 3, 2, -1],\n [-1, 4, -5, 0, 5, 5],\n [2, -1, 4, 1, 5, -2],\n [-5, 6, -3, 5, -6, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10984
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (6, 4) of the result:\nA =\n[[-1, -5, -1, -6, 4, 3],\n [-4, 2, -5, 1, -1, 5],\n [-1, 0, -2, 5, 4, -3],\n [-1, 1, -3, -2, 0, -1],\n [6, -3, 6, -3, 3, -3],\n [-6, -2, 1, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answ...
27982
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, -5, 6, 2, 0, 0],\n [-5, -3, -1, 0, 0, -2],\n [6, -1, 2, -1, -4, 0],\n [2, 0, -1, 5, 2, 4],\n [0, 0, -4, 2, 2, 0],\n [0, -2, 0, 4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
884510
MATH
[ { "content": "What is the value at position (4, 6) of the matrix A^5 where A is:\n[[1, 6, 5, -4, 2, 3],\n [-4, 3, 5, 1, -6, -3],\n [-3, -1, 5, 5, -5, 0],\n [-2, 3, -1, 4, -1, 5],\n [4, -1, 3, 5, 1, 3],\n [-3, 3, 1, 2, 6, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18023
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[-3, -6, -4, -6, 0, 5],\n [-6, 4, -3, 6, -6, 6],\n [6, -5, 4, -6, 6, -2],\n [0, -4, 1, -2, -2, 6],\n [-2, 1, -5, -5, 5, 1],\n [2, 4, 5, 3, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-231661
MATH
[ { "content": "Find the value at position (6, 3) of the 5th power of the matrix:\n[[-3, 4, -6, -3, 1, 2],\n [4, -6, -5, -2, 0, 0],\n [-6, -5, -3, 1, -2, -2],\n [-3, -2, 1, -1, 2, -2],\n [1, 0, -2, 2, 1, 2],\n [2, 0, -2, -2, 2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-39572
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[-4, -3, 1, -1, 6, 6],\n [-2, 6, 2, 3, -4, 0],\n [2, 4, 6, 4, 5, -3],\n [3, 3, -4, -6, 2, 6],\n [-6, -5, 2, -2, -3, 2],\n [2, -5, -4, 5, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
6623
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (2, 6) of the result:\nA =\n[[6, -4, 3, -1, -5, -1],\n [-1, -5, -1, -1, -1, 5],\n [6, -2, 0, 6, 5, -2],\n [4, -6, 5, 2, -4, -5],\n [3, -1, 1, -5, -3, -5],\n [5, 5, 2, 3, 6, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer...
-1171
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 0, 5, 2, 2, -4],\n [0, 0, -4, 5, -4, 2],\n [5, -4, -5, -2, 0, -4],\n [2, 5, -2, 3, -2, 0],\n [2, -4, 0, -2, -1, 0],\n [-4, 2, -4, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
75718
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[6, -6, 6, 6, -1, 0],\n [-1, -2, -1, 6, -4, 2],\n [-2, -5, 5, 3, 3, 0],\n [-4, -6, -4, 2, -2, 0],\n [-4, -3, -6, -4, 0, -3],\n [-5, -2, -2, -5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
475358
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -3, -6, -4, 2, 3],\n [0, 6, -1, -6, 2, 6],\n [2, -6, 6, 6, -1, 0],\n [-5, 3, 1, 1, -1, 2],\n [-4, -5, -5, -1, 0, -1],\n [4, -4, -2, 1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed...
563089
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -1, -2, 2, -1, -1],\n [-1, 0, -5, 0, 0, 2],\n [-2, -5, -4, 1, 2, 0],\n [2, 0, 1, 1, 2, -4],\n [-1, 0, 2, 2, -3, -6],\n [-1, 2, 0, -4, -6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
8015
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-6, -2, -5, -4, 0, 5],\n [-2, 4, -2, 0, 2, 0],\n [-5, -2, 1, 2, 2, 4],\n [-4, 0, 2, 2, 0, -4],\n [0, 2, 2, 0, -1, -4],\n [5, 0, 4, -4, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
-168335
MATH
[ { "content": "For the matrix power A^5 where A =\n[[5, -2, 4, 4, 1, -1],\n [2, 4, -2, 3, -3, 2],\n [5, 3, 4, -2, -6, -2],\n [-2, -2, 6, -5, 6, -1],\n [-2, -5, 5, 3, 1, -1],\n [4, 3, 5, 4, -4, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
375450
MATH
[ { "content": "For the matrix power A^5 where A =\n[[6, 4, 4, -3, -4, 0],\n [5, 6, 1, 0, -6, -6],\n [6, -2, 1, 3, 4, -4],\n [1, -4, -3, 3, 0, -4],\n [-3, 1, -3, 2, -3, 6],\n [-3, 6, -2, -6, 0, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
1249309
MATH
[ { "content": "For the matrix power A^5 where A =\n[[5, 2, -6, 0, 0, -1],\n [2, -3, 4, -4, 3, -4],\n [-6, 4, 3, -6, 2, 0],\n [0, -4, -6, 1, 4, 6],\n [0, 3, 2, 4, 0, -1],\n [-1, -4, 0, 6, -1, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-18164
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -4, 3, 1, -1, 3],\n [2, 2, 4, -1, -5, 2],\n [-5, -4, -1, -5, -2, -5],\n [5, -3, 4, 4, -4, -2],\n [-1, 6, 0, 3, 1, 2],\n [-3, -3, 0, 5, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{...
66313
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[4, 2, 4, -5, 6, 4],\n [-1, 3, 3, 1, 6, -2],\n [-2, 1, -6, -1, 3, 6],\n [2, 5, -1, 0, -3, 5],\n [3, -6, 2, 5, -1, -4],\n [-3, 3, 5, -1, -1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33642
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, -1, 0, -3, -5, -2],\n [-1, 3, 0, -2, 4, 2],\n [0, 0, 4, 0, 0, -4],\n [-3, -2, 0, -6, 6, 3],\n [-5, 4, 0, 6, 0, -1],\n [-2, 2, -4, 3, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9366
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[6, 3, -4, -4, -3, 2],\n [2, -2, 5, 2, -1, 1],\n [4, 1, 5, 3, 0, -3],\n [-3, -1, 2, 0, -2, -2],\n [1, -1, -6, -6, 2, 1],\n [-1, 6, -6, -5, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-40389
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (5, 4) of the result:\nA =\n[[3, 5, -4, -5, 5, -5],\n [-1, 0, -3, -6, -1, 0],\n [-3, -1, 2, -3, 5, 3],\n [-3, 3, 5, -2, -4, 3],\n [-5, 2, 6, -6, -2, -2],\n [1, -1, -1, -1, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your ans...
-10765
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[-4, 2, 0, 2, 4, 2],\n [2, -2, 0, -2, -1, -4],\n [0, 0, -1, 2, 0, -2],\n [2, -2, 2, 2, -5, -4],\n [4, -1, 0, -5, 0, 2],\n [2, -4, -2, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
3050
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, 3, -1, -5, 1, 2],\n [-4, 6, -1, -1, -5, 3],\n [1, -2, 4, 4, 1, 6],\n [1, 5, -4, -2, 0, -2],\n [-1, -5, 1, -2, -1, -6],\n [3, -5, 4, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7700
MATH
[ { "content": "Find the value at position (3, 3) of the 5th power of the matrix:\n[[-1, 3, 0, -1, 2, 2],\n [3, 6, -1, 2, 4, -3],\n [0, -1, 2, -4, -2, 0],\n [-1, 2, -4, 0, 0, 0],\n [2, 4, -2, 0, -1, 2],\n [2, -3, 0, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10909
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, 5, -4, -6, -2, 1],\n [-2, 3, -4, 2, -5, -4],\n [5, -3, 3, -6, 4, -3],\n [-3, 2, 1, -5, 6, 0],\n [-1, 0, 4, -3, -2, -1],\n [2, -5, 4, 2, 3, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}...
58504
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 5, -2, 2, -1, -3],\n [-5, -2, 1, 1, -1, 4],\n [-6, 1, -3, -5, -6, 0],\n [-5, 6, -3, -3, 6, 3],\n [-6, -5, -6, -1, 6, -4],\n [-6, 5, 1, 5, -3, 3]]\n\nPresent the answer in LaTex format: \\bo...
111441
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, 4, -5, -2, -2, -3],\n [4, -6, 2, -4, -1, 4],\n [-5, 2, -6, -1, -6, -2],\n [-2, -4, -1, -2, 2, 2],\n [-2, -1, -6, 2, 3, -2],\n [-3, 4, -2, 2, -2, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your a...
333674
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[6, -5, 3, 2, 5, -2],\n [4, 1, 3, -3, -5, -3],\n [5, 4, -3, 4, 2, 3],\n [4, -1, 3, -1, -2, -1],\n [-6, 6, -2, 5, -1, 1],\n [-3, -2, -3, 0, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13090
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-3, -1, 6, -3, 5, 1],\n [4, -4, 1, 6, -5, -1],\n [1, -6, -1, 2, 6, 3],\n [3, -5, 4, 6, -6, -5],\n [-2, -1, -6, 0, 4, -3],\n [2, -1, 2, -6, -3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
14369
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-1, -3, 2, -4, -6, 4],\n [6, 4, -6, 5, 2, 2],\n [-2, -5, 2, 6, 5, 6],\n [1, 6, 4, 3, 3, -1],\n [0, 5, -1, -2, -3, 0],\n [-3, 3, 3, 3, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
834352
MATH
[ { "content": "For the matrix power A^5 where A =\n[[1, 1, 0, 0, 0, -2],\n [1, 5, -2, 0, -2, 0],\n [0, -2, -3, -2, 4, 4],\n [0, 0, -2, 1, 0, -2],\n [0, -2, 4, 0, -4, 2],\n [-2, 0, 4, -2, 2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
2759
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-2, 1, 5, -4, 5, 0],\n [1, 0, -5, 1, -1, 3],\n [-4, -3, 0, -4, -6, -1],\n [-4, 4, 3, -1, 3, 5],\n [-4, -1, 4, -3, 6, -3],\n [3, 3, 4, -5, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
276292
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[5, -3, 4, 0, -2, 1],\n [0, 3, 2, 1, 2, -6],\n [3, 6, 5, -4, -2, 2],\n [1, 3, 0, -5, 4, -1],\n [-3, -2, -2, 6, -3, -3],\n [-3, 4, -5, -6, 5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
193117
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 0, -4, -2, 1, -4],\n [0, 0, -4, 2, 2, 2],\n [-4, -4, 3, 5, 3, 2],\n [-2, 2, 5, -3, 0, 1],\n [1, 2, 3, 0, 5, -2],\n [-4, 2, 2, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
585299
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 0, 0, 2, -2, -2],\n [0, 5, 2, 0, -2, -1],\n [0, 2, -1, 2, 0, 4],\n [2, 0, 2, 5, -2, 4],\n [-2, -2, 0, -2, -5, 2],\n [-2, -1, 4, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
18417
MATH
[ { "content": "Find the value at position (4, 5) of the 5th power of the matrix:\n[[0, -2, -4, 3, 1, 1],\n [2, 4, 5, -1, -5, -4],\n [6, 4, 5, 3, 4, -1],\n [-6, -5, 1, 4, 1, -1],\n [-4, -5, 6, -1, -6, 3],\n [-1, 2, 0, 2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
-8480
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-2, 2, 0, 2, 4, -1],\n [0, 3, -2, -1, -6, -6],\n [-5, 4, -3, 4, 2, 0],\n [-1, -6, -2, 4, 5, 6],\n [-3, -2, 4, 2, 5, -4],\n [-3, 1, -4, 6, -4, 6]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
44738
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -2, 3, -6, 0, 0],\n [-1, -1, -4, -4, 3, 4],\n [2, -6, 0, 6, 5, 4],\n [3, 0, 1, -1, 1, -6],\n [-6, 2, 5, -3, -4, -1],\n [3, 5, 6, 5, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your...
1310567
MATH
[ { "content": "Find the value at position (5, 5) of the 4th power of the matrix:\n[[4, -4, 2, -2, 4, -3],\n [-4, -4, 4, -4, -2, -4],\n [2, 4, 1, 0, 2, -4],\n [-2, -4, 0, 2, -4, -4],\n [4, -2, 2, -4, -3, 0],\n [-3, -4, -4, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
3509
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 2, 0, 5, -2, -1],\n [3, 2, -6, 4, 2, -1],\n [5, -3, 5, -2, 6, -6],\n [0, 6, 6, 1, 4, -2],\n [-5, 1, 3, 0, 3, 2],\n [-3, 4, 2, -3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
131522
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 3, -5, 3, -4, 1],\n [4, 1, -5, 4, -5, -5],\n [3, 0, -1, 5, 4, -6],\n [-5, -6, 5, 4, 0, -1],\n [-5, -5, -5, 1, 0, -6],\n [-3, 4, -3, 0, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-3895
MATH
[ { "content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[-6, 5, 6, 3, 3, -4],\n [5, -6, -4, -2, 1, 1],\n [6, -4, 1, 0, -2, -2],\n [3, -2, 0, -1, -2, 0],\n [3, 1, -2, -2, -4, 0],\n [-4, 1, -2, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
8029
MATH
[ { "content": "For the matrix power A^5 where A =\n[[5, 4, -4, 2, 6, 3],\n [4, -5, -2, -2, 4, 0],\n [-4, -2, -3, -2, 1, -6],\n [2, -2, -2, -5, -1, 4],\n [6, 4, 1, -1, -1, -1],\n [3, 0, -6, 4, -1, 2]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
200871
MATH
[ { "content": "For the matrix power A^5 where A =\n[[5, 0, 6, 0, 2, 6],\n [0, -1, 3, -3, -1, 2],\n [6, 3, 6, 4, -2, -2],\n [0, -3, 4, 6, 4, 0],\n [2, -1, -2, 4, -5, 0],\n [6, 2, -2, 0, 0, 6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
2253293
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-1, -1, 4, -4, 4, 4],\n [3, 0, 6, 0, 1, -2],\n [-5, 6, -4, 2, -1, 1],\n [1, -2, -6, -1, 0, 2],\n [-5, 5, 6, -5, 3, -6],\n [-2, -5, -4, -5, 4, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
-71090
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (5, 5) of the result:\nA =\n[[4, -4, 2, 3, 5, -5],\n [0, 4, -4, 3, 1, -3],\n [-3, 2, 4, -4, 0, -6],\n [0, 3, 4, -5, 5, -1],\n [6, 2, -1, -4, -6, 5],\n [5, -3, -3, 6, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-4265
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 6, 0, 3, 0, 0],\n [5, -5, 2, -1, -5, -6],\n [4, -6, -6, -3, -3, 5],\n [2, 6, 5, 5, -6, -4],\n [-4, 1, -5, -1, 4, -3],\n [6, 3, -1, 6, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
123805
MATH
[ { "content": "For the matrix power A^5 where A =\n[[2, 4, 0, -2, -4, -2],\n [4, -4, -2, 2, 1, 2],\n [0, -2, -5, 2, 2, 2],\n [-2, 2, 2, -3, -3, 0],\n [-4, 1, 2, -3, 2, 4],\n [-2, 2, 2, 0, 4, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
934925
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 0, -2, 0, 4, -2],\n [0, 5, -3, 0, -2, 0],\n [-2, -3, -4, -2, -6, 2],\n [0, 0, -2, -5, -2, 0],\n [4, -2, -6, -2, 4, 0],\n [-2, 0, 2, 0, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26416
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-5, 2, -3, -2, 4, 4],\n [2, 0, 0, -2, -2, -3],\n [-3, 0, 5, 4, -2, -4],\n [-2, -2, 4, 2, 4, -4],\n [4, -2, -2, 4, -3, 6],\n [4, -3, -4, -4, 6, -5]], determine the value at position (5, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
-6862
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 3, 3, 0, 5, 3],\n [-2, 5, 3, -1, -6, -3],\n [-3, 4, 1, -5, -6, 0],\n [-1, -2, 5, 6, 6, 6],\n [1, 4, 6, -5, -5, 2],\n [-6, -1, 6, 6, -4, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
1512348
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-2, 1, 0, 6, 5, -3],\n [1, 4, 4, 3, 4, -5],\n [0, -2, 4, -1, -4, 4],\n [3, 0, 0, -5, -6, 3],\n [-5, 5, 1, 4, 3, -4],\n [4, -3, 1, -4, -1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
268965
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, -6, 2, -3, -1, 0],\n [-5, 1, 5, 2, 3, 4],\n [-5, -2, -5, 4, -2, 0],\n [-1, -3, -5, 0, 5, 3],\n [2, -6, -4, 0, 2, 6],\n [-2, 0, 3, 0, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
255236
MATH
[ { "content": "Find the value at position (6, 1) of the 5th power of the matrix:\n[[-5, -2, 1, -6, 0, 0],\n [-2, 0, 0, 2, 0, 0],\n [1, 0, -4, 6, 0, 3],\n [-6, 2, 6, 1, 2, 2],\n [0, 0, 0, 2, -4, 2],\n [0, 0, 3, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-17420
MATH
[ { "content": "What is the value at position (4, 3) of the matrix A^5 where A is:\n[[2, 6, 0, -4, 4, 3],\n [-3, 5, 3, -5, 2, -2],\n [5, -5, 3, -1, 0, 6],\n [-5, -6, 6, 0, -6, -4],\n [-3, -5, 0, -2, -6, 5],\n [5, 1, 3, 0, -3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
10512
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, 2, -5, -2, -2, -2],\n [2, 5, 0, 0, 1, 1],\n [-5, 0, 3, -4, 0, 0],\n [-2, 0, -4, 0, -3, 0],\n [-2, 1, 0, -3, 1, -3],\n [-2, 1, 0, 0, -3, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
18587
MATH
[ { "content": "What is the value at position (4, 5) of the matrix A^5 where A is:\n[[-5, -3, -1, -1, -6, 1],\n [-5, 6, -2, -3, -2, -2],\n [3, 1, 3, 0, 5, 2],\n [5, 4, 6, -6, -1, -1],\n [-5, 4, 1, -1, 4, 6],\n [3, 2, 3, -2, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
12939
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[4, -2, -1, -3, -4, 6],\n [-6, -6, -1, 2, 1, 5],\n [-5, 2, 1, 5, 2, -3],\n [2, -5, 6, -6, 6, 2],\n [3, 1, 0, 6, 1, 5],\n [-6, 2, 5, 3, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42156
MATH
[ { "content": "Find the value at position (5, 1) of the 4th power of the matrix:\n[[5, 5, 2, 2, 2, 2],\n [5, -5, 0, 1, -3, -4],\n [2, 0, 6, 6, 0, 6],\n [2, 1, 6, -4, 0, 0],\n [2, -3, 0, 0, 6, 0],\n [2, -4, 6, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
764
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, -2, 6, 2, -4, -2],\n [-4, 5, -4, -6, -5, -5],\n [2, 0, 1, -5, 2, 6],\n [-4, 3, 6, -5, 5, -6],\n [2, 1, 6, 5, 4, -3],\n [0, 5, -4, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13658
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[3, -3, 3, -4, 1, 4],\n [-5, 4, 2, -4, -3, 6],\n [3, 3, -4, -4, 1, 1],\n [6, 6, -1, -3, -6, -3],\n [1, -1, -5, -4, 5, 0],\n [4, 4, -3, -3, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-42354
MATH
[ { "content": "For the matrix power A^5 where A =\n[[0, 2, -2, -6, -3, -1],\n [-1, 2, 3, 6, -2, -2],\n [-1, 4, -1, -4, -1, 1],\n [5, -1, 5, 4, -2, -4],\n [-6, -2, -1, -1, -1, -4],\n [-3, -4, -5, 1, 0, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your an...
248751
MATH
[ { "content": "What is the value at position (1, 2) of the matrix A^4 where A is:\n[[1, 0, -3, 0, 4, 0],\n [0, 3, 0, -4, -2, 1],\n [-3, 0, 1, 0, 0, 2],\n [0, -4, 0, 0, 0, 0],\n [4, -2, 0, 0, 0, -2],\n [0, 1, 2, 0, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-534
MATH
[ { "content": "For the matrix power A^5 where A =\n[[6, -4, -3, 0, -2, -1],\n [-4, 3, 2, -4, -3, 2],\n [-3, 2, -4, -1, 2, 0],\n [0, -4, -1, -4, -4, 2],\n [-2, -3, 2, -4, 0, -2],\n [-1, 2, 0, 2, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
-147337
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, -6, -2, 4, 2, -4],\n [-6, 6, 0, 0, -4, 1],\n [-2, 0, -2, 2, -3, -4],\n [4, 0, 2, -6, 0, 2],\n [2, -4, -3, 0, -5, 2],\n [-4, 1, -4, 2, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-94680
MATH
[ { "content": "For the matrix power A^5 where A =\n[[5, -6, -1, -5, 1, -2],\n [-4, 3, 0, 4, -5, -2],\n [4, 1, 6, 4, -6, -6],\n [-4, -4, 6, 0, -1, 0],\n [-3, 4, -5, -5, 3, -6],\n [6, 2, 0, 3, -4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
105423
MATH
[ { "content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[-4, 0, -2, 5, -4, 2],\n [-5, 0, 3, -1, -1, 0],\n [-1, -5, 4, -2, -4, 2],\n [1, 3, 4, -5, -6, -3],\n [-3, 5, 3, 4, -5, 0],\n [6, -4, 0, 0, -6, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
746
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[-3, 4, 1, 1, -4, -3],\n [-6, 3, -5, 0, 4, 5],\n [0, 6, 2, 3, 2, 2],\n [-1, 1, 2, 5, 0, -3],\n [-3, -1, 4, -3, 4, 0],\n [1, 1, 1, -5, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
11579
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, -5, -3, -2, -3, -2],\n [-3, 0, 3, -6, 6, -6],\n [-5, 6, -6, 5, 3, 5],\n [5, 3, 6, 4, -4, -1],\n [3, 4, -1, -6, -1, -2],\n [0, -1, 5, 5, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-137309
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, -6, 0, 2, -5, 5],\n [0, -4, -1, -4, 6, 3],\n [6, 4, 4, 4, -2, -5],\n [1, 1, 0, -1, -6, 1],\n [-6, 1, 4, -5, 1, 3],\n [5, -3, 0, -2, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
122215
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, 0, -6, -1, 0, 4],\n [0, -2, 0, -2, 0, -4],\n [-6, 0, -2, -2, 2, 0],\n [-1, -2, -2, -1, 0, -1],\n [0, 0, 2, 0, -4, -1],\n [4, -4, 0, -1, -1, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
743432
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-2, 1, -1, 0, -2, -2],\n [1, -6, 5, -5, 1, 2],\n [-1, 5, -6, 1, -2, 2],\n [0, -5, 1, 3, -6, 2],\n [-2, 1, -2, -6, -5, -6],\n [-2, 2, 2, 2, -6, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
-311633
MATH
[ { "content": "What is the value at position (1, 1) of the matrix A^5 where A is:\n[[5, 2, -2, 3, 2, -2],\n [2, -5, 2, 0, -5, -4],\n [-2, 2, -5, 2, -4, -2],\n [3, 0, 2, -5, -2, -1],\n [2, -5, -4, -2, -6, -4],\n [-2, -4, -2, -1, -4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
9851
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (1, 4) of the result:\nA =\n[[5, -1, 1, -4, 3, -2],\n [-1, 1, 4, 3, 6, 1],\n [1, 4, 5, 3, 2, 3],\n [-4, 3, 3, -4, 0, -2],\n [3, 6, 2, 0, -2, -2],\n [-2, 1, 3, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-12768
MATH
[ { "content": "What is the value at position (3, 3) of the matrix A^5 where A is:\n[[-5, 2, -4, 2, -2, -3],\n [2, -5, -1, 5, 0, 0],\n [-4, -1, 0, 2, 0, -2],\n [2, 5, 2, 5, -1, -3],\n [-2, 0, 0, -1, 1, 3],\n [-3, 0, -2, -3, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-9004
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 0, -4, 0, 2, -2],\n [0, -6, -2, 0, 2, 2],\n [-4, -2, 1, 0, -2, 2],\n [0, 0, 0, 2, 0, 4],\n [2, 2, -2, 0, 6, 1],\n [-2, 2, 2, 4, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17367
MATH
[ { "content": "Find the value at position (3, 6) of the 5th power of the matrix:\n[[-2, -1, -4, -1, 6, 1],\n [3, 6, 4, 2, -4, 1],\n [5, -4, -5, -2, -3, 6],\n [-2, -1, -4, -6, -3, -1],\n [-5, -5, -6, 2, -4, -5],\n [-3, -1, -6, 2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
63892
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, -3, -5, 1, 0, 5],\n [-3, -4, -1, -6, -5, 0],\n [4, -4, 6, -6, -5, 3],\n [3, 2, 0, 0, 3, 1],\n [5, 5, 1, 2, -5, 1],\n [1, 6, -2, -2, -3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
138447
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -6, -2, 4, 2, -5],\n [-6, 2, -5, 0, 2, -4],\n [-2, -5, 0, 4, 4, -2],\n [4, 0, 4, -2, 0, 2],\n [2, 2, 4, 0, -6, -3],\n [-5, -4, -2, 2, -3, -6]]\n\nPresent the answer in LaTex format: \\boxed...
7892166
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-4, 2, 2, -2, 5, 6],\n [-1, 4, 6, -1, 3, -3],\n [-6, -2, 6, -6, -6, 4],\n [-2, -2, 0, -5, -1, -5],\n [6, 3, -2, -3, 4, 3],\n [-2, -5, 1, 1, -1, -4]], determine the value at position (6, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
15297
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[-3, -5, -1, 2, -3, 2],\n [-5, -3, -2, -1, 0, -2],\n [-1, -2, 2, -2, 0, -2],\n [2, -1, -2, -6, 0, -4],\n [-3, 0, 0, 0, -5, 2],\n [2, -2, -2, -4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
-272507
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -3, 0, 0, 2, 2],\n [-3, -3, 3, 1, 4, 2],\n [0, 3, -6, 0, 1, 3],\n [0, 1, 0, 0, -4, -4],\n [2, 4, 1, -4, -1, 0],\n [2, 2, 3, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
71823
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (3, 6) of the result:\nA =\n[[-6, 6, 0, -4, 0, 0],\n [6, 2, 4, -6, 3, 0],\n [0, 4, -4, 3, 0, 4],\n [-4, -6, 3, 6, 1, -2],\n [0, 3, 0, 1, 4, 1],\n [0, 0, 4, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
-1355
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, 6, -1, 0, 4, 2],\n [5, 5, 0, -3, 3, -2],\n [6, -1, 6, 2, -2, -2],\n [0, -5, -4, 5, -5, 3],\n [3, 5, -5, -4, -1, -2],\n [4, 6, -2, -5, -5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
241704
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-6, 0, 0, 1, 2, 1],\n [0, -2, -3, 4, -1, -4],\n [0, -3, 3, -2, 0, -2],\n [1, 4, -2, 3, -1, -5],\n [2, -1, 0, -1, -6, -2],\n [1, -4, -2, -5, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
822800
MATH
[ { "content": "For the matrix power A^5 where A =\n[[6, -2, 0, -1, -1, 0],\n [-2, -2, -5, 0, 0, 2],\n [0, -5, -5, -4, 0, 4],\n [-1, 0, -4, 4, 2, 2],\n [-1, 0, 0, 2, -3, 3],\n [0, 2, 4, 2, 3, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-277071
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 3, 6, -1, -3, -1],\n [3, 0, -1, 4, -6, -2],\n [1, 1, 5, 3, 2, -3],\n [3, -1, 0, -2, 4, 1],\n [-4, 1, -2, -6, 6, -1],\n [-5, 0, 2, -4, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
56700
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[-3, -3, -4, -2, 2, 4],\n [1, 3, -5, 5, 2, 5],\n [3, -5, 0, -2, 6, 0],\n [-2, 5, -1, 1, -6, 6],\n [4, 6, 5, -6, -2, -6],\n [-4, 3, 2, 6, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-125261
MATH