messages
listlengths
1
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ground_truth
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1 value
[ { "content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[3, 2, -4, 0, 3, 2],\n [2, 1, -4, -2, 0, -2],\n [-4, -4, 1, 1, 2, 1],\n [0, -2, 1, 1, -4, 0],\n [3, 0, 2, -4, 3, -2],\n [2, -2, 1, 0, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2001
MATH
[ { "content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[-1, -3, -3, -5, 6, 4],\n [-3, -2, 6, 5, -2, -2],\n [-3, -6, 3, 1, -4, -5],\n [2, 0, 2, 6, -5, 2],\n [3, 2, 4, 2, 3, 6],\n [3, -3, 3, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-16409
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, 2, -5, -2, -2, 0],\n [2, 6, -3, 1, 2, 2],\n [-5, -3, 6, 4, 2, 6],\n [-2, 1, 4, 3, -1, 0],\n [-2, 2, 2, -1, 1, 2],\n [0, 2, 6, 0, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
2821086
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[6, -4, -5, -6, -3, -5],\n [-5, 6, 4, 4, -2, -3],\n [-6, 2, -3, -2, 0, -5],\n [1, 4, -5, 4, 3, -2],\n [6, 5, -5, -5, -3, -3],\n [6, 1, 6, -1, 3, 1]]\n\nPresent the answer in LaTex format: \\boxe...
143615
MATH
[ { "content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[6, 1, 0, 0, -2, -4],\n [1, -5, -3, -2, 4, 4],\n [0, -3, -5, -3, 6, 4],\n [0, -2, -3, -5, -2, 4],\n [-2, 4, 6, -2, 4, 2],\n [-4, 4, 4, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
15995
MATH
[ { "content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-5, 3, -2, 2, 0, 5],\n [3, 5, -2, 0, 2, -5],\n [-2, -2, 0, 0, -1, 0],\n [2, 0, 0, 0, -6, 4],\n [0, 2, -1, -6, 0, -2],\n [5, -5, 0, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5136
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-3, -2, -4, 0, 1, -3],\n [-2, -5, 2, -2, 0, 4],\n [-4, 2, 2, -4, -2, 4],\n [0, -2, -4, 4, 0, 4],\n [1, 0, -2, 0, 6, 2],\n [-3, 4, 4, 4, 2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
554848
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, 6, 1, -2, -2, -1],\n [-6, 6, 4, 1, -5, -1],\n [2, 6, -4, -5, 3, -2],\n [4, 2, -1, 1, 1, 0],\n [-2, -5, 3, 3, -2, 5],\n [0, 5, 5, 0, 4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
82954
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, -2, -2, -2, 4, 1],\n [-2, -6, -2, 3, 1, -5],\n [-2, -2, -2, -1, 0, 0],\n [-2, 3, -1, 2, -2, 2],\n [4, 1, 0, -2, 0, 2],\n [1, -5, 0, 2, 2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
721903
MATH
[ { "content": "What is the value at position (4, 6) of the matrix A^4 where A is:\n[[-3, -5, -1, -5, -4, 1],\n [-4, -5, -1, -4, -6, 5],\n [-4, -1, -4, 2, 0, -2],\n [-5, 2, -2, 0, 2, -3],\n [2, -6, 5, -1, -5, 1],\n [-2, -4, -5, 1, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
-847
MATH
[ { "content": "For the matrix power A^5 where A =\n[[1, 4, -3, -5, 6, -5],\n [-5, 4, 5, -1, 0, 5],\n [-1, -5, -3, -4, 4, 6],\n [-3, -2, 0, 2, 4, -5],\n [1, -4, 2, 3, 5, -3],\n [-4, 3, -1, 3, 6, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
-286420
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[0, -3, -4, 3, -3, -4],\n [5, -4, 5, 6, 2, -3],\n [2, 5, 3, -2, 0, -2],\n [-6, -5, 4, -2, -1, 0],\n [-5, 3, 2, -1, -5, -5],\n [-4, -6, 2, 3, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
923842
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-2, 0, -4, 1, -4, 0],\n [0, -2, -2, 0, -2, -1],\n [-4, -2, 4, 2, -2, 2],\n [1, 0, 2, 5, 0, 2],\n [-4, -2, -2, 0, -2, -2],\n [0, -1, 2, 2, -2, -5]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
-9502
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, 2, -2, -2, 5, 0],\n [2, -4, 2, 0, -4, 0],\n [-2, 2, 4, 5, 0, -2],\n [-2, 0, 5, -1, -4, 2],\n [5, -4, 0, -4, -5, -2],\n [0, 0, -2, 2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
22514
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 0, 2, 0, -1, 2],\n [0, -6, -1, 2, -1, -2],\n [2, -1, -3, 2, -1, -1],\n [0, 2, 2, -6, -2, -2],\n [-1, -1, -1, -2, -6, 4],\n [2, -2, -1, -2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
10855
MATH
[ { "content": "For the matrix power A^5 where A =\n[[1, 6, -2, 2, -3, 0],\n [6, 5, 0, 4, -2, -1],\n [-2, 0, -2, 0, -2, 0],\n [2, 4, 0, 4, 2, 1],\n [-3, -2, -2, 2, 1, 2],\n [0, -1, 0, 1, 2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
516909
MATH
[ { "content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[2, -4, -1, -2, 1, -3],\n [-3, 6, 3, 4, 3, 6],\n [-2, 4, 6, 6, -1, 4],\n [-3, -5, 5, 5, -5, 5],\n [-4, -5, -6, 1, 5, -2],\n [3, -6, 6, 2, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-1563
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 6, 5, 6, 3, 0],\n [4, 4, 0, -6, -1, 6],\n [-3, 3, 3, 3, 4, 5],\n [-5, 3, 0, 2, 6, -2],\n [1, -2, 0, 0, 2, -4],\n [-6, -5, 5, -1, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your an...
667732
MATH
[ { "content": "For the matrix power A^4 where A =\n[[5, 5, 4, -2, 4, -6],\n [5, -6, -4, 1, -3, -4],\n [4, -4, -5, 0, 3, 0],\n [-2, 1, 0, 3, -2, -4],\n [4, -3, 3, -2, 4, 2],\n [-6, -4, 0, -4, 2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
57535
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[5, -2, 4, 2, 2, 0],\n [-2, -5, -2, 0, -2, -1],\n [4, -2, 6, 3, -2, 0],\n [2, 0, 3, 4, -4, -4],\n [2, -2, -2, -4, -2, 2],\n [0, -1, 0, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Y...
111532
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, 2, 6, -4, -4, -6],\n [3, 6, -1, -3, 4, 1],\n [-5, 4, -5, 0, 6, -2],\n [6, -6, 0, 0, 3, -1],\n [-3, 5, 6, 1, 5, 4],\n [-5, -5, -5, -4, -1, -6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
58024
MATH
[ { "content": "For the matrix power A^4 where A =\n[[4, -5, 3, -5, 5, -6],\n [-4, 3, 0, 6, -6, 0],\n [-2, 2, -5, -6, 2, 1],\n [3, -1, -2, 1, 1, -2],\n [5, 0, 6, 6, -6, -3],\n [-5, 3, -4, 5, -6, 4]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
732
MATH
[ { "content": "For the matrix power A^4 where A =\n[[4, -5, 6, -6, 1, -3],\n [-4, -6, -5, -4, -4, -1],\n [3, 1, -1, -5, -5, 0],\n [-6, -6, 0, 2, -2, 4],\n [-6, -2, 4, -6, 3, 5],\n [2, -3, 2, -5, 0, 5]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
1752
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[6, -5, 5, -3, -1, -5],\n [-5, -5, -4, -2, 2, -1],\n [5, 2, 3, 6, -2, 4],\n [-1, 3, 5, 1, -4, -5],\n [-4, 2, -1, 3, 5, -3],\n [3, -4, 6, -5, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-46140
MATH
[ { "content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[-3, 6, 1, -4, -2, -4],\n [6, 4, -5, -4, 3, -3],\n [1, -5, 0, 4, 2, -6],\n [-4, -4, 4, 0, 0, 1],\n [-2, 3, 2, 0, 5, 0],\n [-4, -3, -6, 1, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
8750
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-2, 2, 0, -4, -4, 2],\n [2, -2, 0, 2, 4, 3],\n [0, 0, 4, -1, -4, -2],\n [-4, 2, -1, -5, 2, 2],\n [-4, 4, -4, 2, 1, 4],\n [2, 3, -2, 2, 4, 6]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
301726
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 3, 3, 4, 5, 4],\n [6, -1, 1, 6, -6, -1],\n [-1, 4, 6, -2, -3, -6],\n [4, 3, 4, 1, -1, -4],\n [5, -4, 5, -1, 5, 0],\n [1, -2, 3, -1, 5, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
-2775
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, 2, 3, -3, 3, 6],\n [-6, 4, 2, -3, -5, -6],\n [-4, 0, 4, 3, -5, 2],\n [5, 6, 4, -5, -2, 1],\n [6, 6, 5, 3, 1, -4],\n [-5, 2, -4, 1, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
804094
MATH
[ { "content": "Find the value at position (6, 4) of the 5th power of the matrix:\n[[-6, 4, -1, 6, 0, -3],\n [-6, -4, 2, -2, -1, -3],\n [-6, -2, -2, -2, -1, 4],\n [-5, -6, -5, 6, 3, -1],\n [-2, -2, 5, 5, -1, 3],\n [0, 2, 0, -5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
-34323
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -5, -4, 1, 4, 2],\n [-3, 2, -5, 6, 4, -2],\n [4, -5, 4, -6, 6, -2],\n [-5, 6, 0, 1, -5, 0],\n [-3, -6, 4, -4, 4, 5],\n [-6, -2, 6, 1, -6, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
1027
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, 0, 2, -2, -2, 0],\n [0, 0, 2, -5, 1, -2],\n [2, 2, -3, 2, -5, 2],\n [-2, -5, 2, 4, 1, -3],\n [-2, 1, -5, 1, -1, -1],\n [0, -2, 2, -3, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
465363
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -6, 6, 4, 3, -4],\n [1, -2, 1, -5, 0, 2],\n [0, -4, 0, 1, -6, 6],\n [6, -4, -2, 5, -1, -4],\n [-3, -2, -4, -3, -2, -5],\n [3, 2, 3, 1, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed...
61981
MATH
[ { "content": "What is the value at position (1, 6) of the matrix A^5 where A is:\n[[3, 4, -4, 4, -5, 0],\n [1, 3, -6, -1, 0, 6],\n [2, 5, -4, -5, -2, 6],\n [3, -6, 6, -1, 2, 3],\n [2, 0, 4, 0, 1, 3],\n [-5, -1, -2, -2, 6, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
-2154
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[-4, -1, 5, 3, 6, 3],\n [0, -6, -4, 5, -6, 3],\n [-4, -2, 2, -4, 3, 3],\n [2, -6, -1, 2, 5, -2],\n [4, 3, -5, -2, -6, 2],\n [3, 6, 3, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
1738
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -4, -3, 6, -1, -3],\n [-6, 0, -2, 1, 2, -2],\n [1, 6, -6, -6, 0, -1],\n [-2, -2, 2, -6, 1, -5],\n [0, -1, 3, -5, 5, 6],\n [-4, -3, 0, 1, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed...
1162060
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (5, 1) of the result:\nA =\n[[-5, 1, 4, 2, 0, -6],\n [-1, 1, -2, 5, -5, -2],\n [1, -5, -6, -3, -3, 2],\n [-4, -3, -4, -5, -3, 1],\n [-6, 1, 1, -4, 3, 3],\n [5, 5, -1, 6, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer...
64845
MATH
[ { "content": "For the matrix power A^5 where A =\n[[6, -6, -1, 2, 4, -2],\n [-6, -5, 2, -2, 0, -4],\n [-1, 2, 6, 4, -4, 2],\n [2, -2, 4, -5, -2, 4],\n [4, 0, -4, -2, 0, -3],\n [-2, -4, 2, 4, -3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
-149724
MATH
[ { "content": "For the matrix power A^5 where A =\n[[5, 2, 2, -4, -2, -2],\n [2, -1, -2, -4, -4, 2],\n [2, -2, 6, 4, 4, 2],\n [-4, -4, 4, -4, -1, -3],\n [-2, -4, 4, -1, 3, 0],\n [-2, 2, 2, -3, 0, -6]], determine the value at position (6, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
-6052
MATH
[ { "content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[-1, -6, -6, 1, -5, 3],\n [6, -1, -1, -1, 1, -3],\n [-4, -1, -3, -5, -1, 3],\n [-2, 4, 2, 4, -1, -4],\n [4, -2, 3, 1, 2, 1],\n [-4, 2, -4, 1, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
2957
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, -3, 3, 2, -4, -4],\n [-5, 3, -4, -6, -3, 1],\n [-2, -5, -4, -6, -5, -6],\n [-5, -4, -6, 4, 2, 3],\n [-2, 1, -2, 1, 0, 5],\n [-3, 0, -1, -4, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
53536
MATH
[ { "content": "For the matrix power A^5 where A =\n[[3, 4, 0, -3, -2, -2],\n [4, 0, 0, -1, 4, 2],\n [0, 0, 3, 0, 0, -4],\n [-3, -1, 0, -3, 0, 0],\n [-2, 4, 0, 0, 3, 0],\n [-2, 2, -4, 0, 0, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
235056
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, -3, -6, 6, 6, 1],\n [-6, 5, -1, 0, 3, 5],\n [-5, -3, 4, -4, 6, 6],\n [2, 0, -5, 4, 5, -1],\n [2, 5, -4, 4, -1, -4],\n [-4, -3, 2, 4, 6, 1]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
101324
MATH
[ { "content": "What is the value at position (2, 2) of the matrix A^4 where A is:\n[[-6, 1, 0, 2, -6, 2],\n [1, 4, 2, 3, -2, 0],\n [0, 2, -6, 0, 0, 0],\n [2, 3, 0, 2, 0, -2],\n [-6, -2, 0, 0, 3, 2],\n [2, 0, 0, -2, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2292
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, -4, 0, -2, 0, 2],\n [-4, 1, 0, 0, 2, 0],\n [0, 0, 3, 2, 5, 2],\n [-2, 0, 2, 6, -1, 6],\n [0, 2, 5, -1, -1, 4],\n [2, 0, 2, 6, 4, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
79047
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 0, 4, 3, -3, -6],\n [-4, 0, 4, 4, 0, 4],\n [6, -4, -6, 3, 2, 5],\n [-1, 6, 6, 5, 0, -6],\n [-6, -3, 0, 4, 4, 1],\n [3, 2, -6, -3, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
8579
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[0, -6, 2, 3, 0, 0],\n [-6, 1, 4, -2, 1, -2],\n [2, 4, -4, -3, -4, 0],\n [3, -2, -3, -4, -1, -2],\n [0, 1, -4, -1, 3, -2],\n [0, -2, 0, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxe...
77509
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, 2, 2, -1, 2, 4],\n [2, 3, 1, -5, 6, 0],\n [2, 1, -5, -1, 3, 2],\n [-1, -5, -1, -3, 0, 0],\n [2, 6, 3, 0, -2, -6],\n [4, 0, 2, 0, -6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
14302
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, 1, -1, 0, 3, 4],\n [-5, -2, 5, 0, 2, -6],\n [-4, -1, 0, -1, -6, -3],\n [-1, 1, 3, -3, 0, 4],\n [-4, 1, -6, -3, 1, 3],\n [-3, -5, -5, -3, 6, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
-9334
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-5, 0, 2, 4, -4, 2],\n [0, -6, -3, -4, -4, 3],\n [2, -3, 4, 0, 0, 0],\n [4, -4, 0, 3, -2, 1],\n [-4, -4, 0, -2, 0, -2],\n [2, 3, 0, 1, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-258333
MATH
[ { "content": "What is the value at position (1, 1) of the matrix A^5 where A is:\n[[6, -5, -4, 4, 4, -3],\n [-2, 2, -1, -6, -4, 0],\n [1, 0, -2, 3, 1, 2],\n [0, 4, 2, -6, 2, -4],\n [-1, 1, -4, -3, 0, 5],\n [0, -3, 2, 6, -4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
4084
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (1, 3) of the result:\nA =\n[[1, 4, 2, -4, 1, -4],\n [4, 5, 0, -2, -4, -2],\n [2, 0, 3, 3, 2, 5],\n [-4, -2, 3, 0, 2, 4],\n [1, -4, 2, 2, -2, -2],\n [-4, -2, 5, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-36374
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-4, 3, 2, 4, 1, 5],\n [3, 3, 2, 0, 1, 0],\n [2, 2, -4, -3, 4, 2],\n [4, 0, -3, -1, -2, 4],\n [1, 1, 4, -2, 4, -4],\n [5, 0, 2, 4, -4, -5]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
-3708
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 6, -3, 3, 6, -1],\n [-2, -4, 3, 1, 1, 0],\n [-4, -6, -2, -6, -1, 4],\n [0, 5, -2, -3, -5, -2],\n [2, -3, -5, 6, -1, 1],\n [-5, 2, 0, 6, -5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
8015
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, -2, 0, 6, -2, 4],\n [-1, 2, -4, -4, 1, 3],\n [5, -1, 5, 3, -4, -5],\n [6, -5, -5, -2, 5, -2],\n [-6, -5, -5, -3, 0, -4],\n [-2, 4, 2, -2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-7182
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, -2, 1, -2, 5, -1],\n [1, -5, -4, 4, 2, -2],\n [-2, 2, 3, -4, -3, 0],\n [-5, 1, -2, -6, -4, 2],\n [-2, 1, -6, 0, 0, 1],\n [-4, -6, 4, 2, -6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
6229
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, -2, -4, 1, 0, 1],\n [-2, 5, -4, 4, -2, 0],\n [-4, -4, -2, 2, -2, 1],\n [1, 4, 2, -1, 4, 1],\n [0, -2, -2, 4, -4, 2],\n [1, 0, 1, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
1017692
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-2, 0, -6, -6, 4, 6],\n [-6, -5, 2, 6, -2, 2],\n [6, -2, 0, -1, -5, -4],\n [-2, -3, 4, -1, 1, 1],\n [-4, -3, -6, -5, 6, 2],\n [5, 3, 3, -5, 5, -1]], determine the value at position (6, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
1072
MATH
[ { "content": "For the matrix power A^5 where A =\n[[0, -1, 1, 2, 1, -2],\n [1, 3, 3, 2, 1, -5],\n [-5, 5, -4, 0, 2, 1],\n [2, -1, -6, 5, -3, 6],\n [-1, 5, -1, 1, -6, 6],\n [4, -5, -5, 6, -1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-24518
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[0, -4, 0, 0, -4, -2],\n [-4, 3, 0, 6, 2, -4],\n [0, 0, 4, 5, 0, -2],\n [0, 6, 5, -4, -2, -3],\n [-4, 2, 0, -2, 6, 2],\n [-2, -4, -2, -3, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
184155
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[-6, 4, 0, -1, 0, 0],\n [1, 1, 3, 4, -5, 5],\n [5, 5, -3, -3, 6, 4],\n [3, 5, 6, 1, 6, 6],\n [-4, 5, 6, 6, 5, -4],\n [6, -5, -6, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
71581
MATH
[ { "content": "For the matrix power A^5 where A =\n[[4, 1, -2, -6, 2, -1],\n [5, 0, 1, 6, -2, -1],\n [5, 6, 0, 0, -5, 4],\n [5, -6, 1, -2, 3, -5],\n [-4, -1, 3, -1, 1, -2],\n [-2, 0, 3, 6, -2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
545
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 2, 4, 0, 2, 2],\n [2, -3, 0, 0, 2, 4],\n [4, 0, -4, 4, -4, 2],\n [0, 0, 4, 3, 0, 0],\n [2, 2, -4, 0, -5, -2],\n [2, 4, 2, 0, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answ...
685165
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-5, 0, 3, -2, -1, 1],\n [0, 0, -3, 4, 0, 0],\n [3, -3, 4, 0, 2, -1],\n [-2, 4, 0, 5, -4, 2],\n [-1, 0, 2, -4, -4, 3],\n [1, 0, -1, 2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
69365
MATH
[ { "content": "For the matrix power A^5 where A =\n[[0, 2, -2, -2, 2, 0],\n [2, 2, -2, -2, 0, -1],\n [-2, -2, -6, 4, 3, 0],\n [-2, -2, 4, 6, 0, 2],\n [2, 0, 3, 0, 1, 3],\n [0, -1, 0, 2, 3, -2]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
-1338
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[6, 4, -4, 2, 0, -2],\n [4, -3, -2, -1, 0, -2],\n [-4, -2, -2, -2, -2, 6],\n [2, -1, -2, 0, -2, -2],\n [0, 0, -2, -2, -1, -1],\n [-2, -2, 6, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-12283
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, 4, 1, -2, 0],\n [-4, 1, 1, -4, 2, 1],\n [-6, 1, 5, 4, -3, -1],\n [6, 3, 2, -2, 0, 6],\n [-6, 2, -1, 4, -3, -1],\n [-2, -4, 0, -4, 6, 6]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
29226
MATH
[ { "content": "What is the value at position (6, 1) of the matrix A^5 where A is:\n[[-5, -3, 0, -2, 2, 3],\n [0, 5, 2, 2, 5, -5],\n [-6, 4, -3, -3, 6, -5],\n [-4, -4, -2, -6, 2, 1],\n [1, -4, -5, -6, 5, -1],\n [6, 3, -6, 4, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
-9685
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (6, 3) of the result:\nA =\n[[4, 2, 6, 5, -3, 0],\n [4, 0, -3, -2, 4, 2],\n [0, 0, 3, 0, 2, -2],\n [-1, -4, -6, 4, 5, -5],\n [1, 6, -6, 3, 0, -2],\n [6, -1, 1, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
4552
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-4, 0, -5, 5, 1, 6],\n [0, 5, 5, 1, -5, -4],\n [5, -3, 5, 2, 5, 5],\n [-2, -1, -6, -3, -3, 3],\n [1, 1, 3, -1, 1, 2],\n [-2, -6, -6, -5, -5, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"...
74017
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (3, 1) of the result:\nA =\n[[0, 0, -3, 6, -3, 4],\n [3, -4, 4, -5, -4, 1],\n [-6, -3, 0, -2, -5, -6],\n [-1, 6, 6, -2, -4, 4],\n [4, 4, 2, -4, -5, -2],\n [2, 1, -1, -4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answe...
-845
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[-6, -2, 0, 2, 5, -6],\n [-4, 1, -1, 6, -2, 6],\n [3, -5, -4, 5, -5, -6],\n [0, -4, 0, 5, 0, 1],\n [-6, -2, 3, 2, 5, 4],\n [0, -6, 1, -4, 6, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
-5844
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[-3, 3, 5, 1, -6, 1],\n [2, 2, -2, -3, -3, 2],\n [1, 3, 3, 5, 0, 5],\n [-4, -3, 2, 6, 1, 5],\n [5, -6, -4, 5, 3, -5],\n [-5, 6, 6, 1, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-3037
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 4, 2, 0, -3, -2],\n [4, 0, 0, -2, -6, 0],\n [2, 0, -2, -4, -2, 4],\n [0, -2, -4, 6, -3, -2],\n [-3, -6, -2, -3, -3, 2],\n [-2, 0, 4, -2, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31631
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-2, 3, 4, -2, -4, -2],\n [3, 3, 0, 0, 4, -2],\n [4, 0, 3, -3, -2, 0],\n [-2, 0, -3, -3, -3, -4],\n [-4, 4, -2, -3, 0, -4],\n [-2, -2, 0, -4, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
1099950
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, -2, 2, 5, 0, 0],\n [-2, 0, -3, 0, -2, -2],\n [2, -3, -1, 3, -4, 4],\n [5, 0, 3, -4, 2, 2],\n [0, -2, -4, 2, 0, -3],\n [0, -2, 4, 2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
562141
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-6, 0, -6, 6, 1, 3],\n [5, -5, 3, 6, 5, -2],\n [6, -1, 2, 0, -1, -2],\n [-1, 4, -3, -6, 5, 2],\n [4, -2, 1, 0, 1, -6],\n [2, -6, -4, 1, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
-1428
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-6, -6, -1, -2, 4, -1],\n [-4, 3, 5, 3, -1, -5],\n [1, 5, -1, 6, 6, -3],\n [-3, 4, 0, -4, 4, -4],\n [-1, 2, -6, -2, -6, -6],\n [-4, -4, -3, -4, -1, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
5773
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, 2, 0, -1, 4, -5],\n [2, -6, -3, -2, 0, 2],\n [0, -3, -5, -6, -2, -2],\n [-1, -2, -6, 3, -2, 3],\n [4, 0, -2, -2, 6, 2],\n [-5, 2, -2, 3, 2, -6]]\n\nPresent the answer in LaTex format: \\box...
2034881
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, -4, 2, -4, -2, 0],\n [-4, 2, 0, -4, -2, -2],\n [2, 0, -6, 0, 2, -4],\n [-4, -4, 0, 2, 2, 0],\n [-2, -2, 2, 2, 0, -2],\n [0, -2, -4, 0, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
35088
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, -4, 0, 0, 0, 0],\n [-4, 0, -4, -6, 2, 0],\n [0, -4, 0, 1, -4, -1],\n [0, -6, 1, 3, 0, -4],\n [0, 2, -4, 0, -6, 2],\n [0, 0, -1, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
-198912
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (6, 5) of the result:\nA =\n[[3, 0, -3, -5, 1, -5],\n [2, -2, 2, 2, 1, 1],\n [-3, -3, -5, -3, -3, -1],\n [-4, -5, 1, -5, 1, 0],\n [-4, -1, -1, 3, -2, 6],\n [1, 4, 5, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer...
2006
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, 0, 6, 2, -4, 3],\n [0, 6, 3, -4, 6, -5],\n [5, 0, -3, -6, -1, 4],\n [-1, -1, -5, -6, -4, 5],\n [-5, -1, 6, 5, -1, 6],\n [-2, 3, 3, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
147831
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[6, 3, -1, 4, -3, 3],\n [-6, -3, -5, 3, -4, 0],\n [0, -6, 1, 0, -6, 1],\n [-5, 1, -4, 3, 0, 6],\n [-1, -2, 4, 3, 4, -5],\n [-5, 6, 5, -6, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Yo...
842025
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[1, -2, -6, -4, 2, -3],\n [-2, 3, 2, -4, 4, 0],\n [-6, 2, 3, -5, 3, 4],\n [-4, -4, -5, 0, 6, -3],\n [2, 4, 3, 6, -5, 6],\n [-3, 0, 4, -3, 6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
-1327223
MATH
[ { "content": "Find the value at position (6, 5) of the 5th power of the matrix:\n[[-3, -1, -1, 0, 0, -2],\n [-1, -3, -2, 1, 2, 3],\n [-1, -2, 3, 3, 0, -2],\n [0, 1, 3, 6, 4, -2],\n [0, 2, 0, 4, -6, -6],\n [-2, 3, -2, -2, -6, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-148796
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 5, 4, -1, 6, 2],\n [2, -4, 1, 6, -3, 0],\n [-1, 1, -1, -3, -5, 0],\n [4, 6, 4, -3, 6, 2],\n [2, 0, -2, -4, -4, 2],\n [2, 5, 6, 4, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
100619
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[-6, 6, 3, -2, 1, 3],\n [-3, 3, 3, -3, 6, 5],\n [2, 2, 0, 3, 1, 5],\n [5, -3, 1, -1, 6, -4],\n [0, -4, 4, 0, -2, -3],\n [-4, 1, -3, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1793
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 6, 2, -1, -2, -2],\n [6, -4, -5, -1, 4, -6],\n [0, -2, -3, 2, 3, -6],\n [4, -3, -4, -1, -2, 0],\n [6, -6, 6, -2, -5, -5],\n [4, 4, -5, 2, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
162592
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, -2, -3, -3, -2, 3],\n [2, 5, 2, -1, 4, 5],\n [-4, -1, 3, -3, -4, -1],\n [4, -1, -5, 2, 1, -1],\n [-6, 5, -5, -3, 0, 2],\n [3, -2, 3, -5, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-1867
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[4, 4, -6, 3, 6, -6],\n [-2, 0, 2, 2, 1, -6],\n [-2, -1, -1, -3, -6, -4],\n [3, -3, -3, 6, -3, -2],\n [6, 4, 2, -3, 2, 2],\n [-6, -2, 2, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answe...
2212
MATH
[ { "content": "For the matrix power A^4 where A =\n[[6, -6, -2, 0, -1, 2],\n [-6, -4, 0, 2, -6, 1],\n [-2, 0, -4, 4, -4, 0],\n [0, 2, 4, 0, -5, -2],\n [-1, -6, -4, -5, -5, -2],\n [2, 1, 0, -2, -2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
117708
MATH
[ { "content": "For the matrix power A^4 where A =\n[[2, -5, -5, 2, -6, -2],\n [-6, 0, 2, -1, -5, -1],\n [2, -4, 2, 1, 6, 5],\n [0, 1, 3, -1, -4, 0],\n [-3, 4, 3, -2, 1, 0],\n [0, 1, 3, -4, -4, -5]], determine the value at position (4, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
75
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-6, 4, 0, 0, 0, 2],\n [4, 1, 0, -2, -6, 6],\n [0, 0, 3, 2, 2, -2],\n [0, -2, 2, -6, 0, -4],\n [0, -6, 2, 0, -4, 2],\n [2, 6, -2, -4, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
95882
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[2, -6, 3, -4, -2, -5],\n [-4, -3, -3, 4, 2, -6],\n [5, 2, 2, 4, -1, 4],\n [-6, 4, 6, 5, -1, 1],\n [-2, -2, -6, -6, 1, 6],\n [-2, 1, 3, -5, -3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2547
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 4, 2, 3, -2, 0],\n [4, 0, -2, -2, -2, 0],\n [2, -2, 0, 4, -6, 0],\n [3, -2, 4, -1, 4, 0],\n [-2, -2, -6, 4, -2, -1],\n [0, 0, 0, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
642616
MATH
[ { "content": "For the matrix power A^4 where A =\n[[2, 3, -5, -5, -1, -4],\n [-6, -5, 6, 0, -3, 5],\n [-5, 4, 5, 5, 1, -3],\n [-3, -5, -6, -6, -4, -1],\n [0, 6, 2, -2, 2, 1],\n [-6, 4, 5, -4, 1, 2]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
-211
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 0, -2, -4, 0, 0],\n [0, -1, 0, 4, -1, 0],\n [-2, 0, 4, 0, 2, 3],\n [-4, 4, 0, -6, 0, 0],\n [0, -1, 2, 0, 3, 0],\n [0, 0, 3, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14226
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, 2, -2, 2, 2, 4],\n [2, -5, -4, -4, 2, -4],\n [-2, -4, 3, -2, 2, 3],\n [2, -4, -2, -5, 0, 0],\n [2, 2, 2, 0, 6, -2],\n [4, -4, 3, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
81663
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 2, -1, -5, 1, 3],\n [2, 5, 1, -5, 1, -4],\n [-4, 2, 6, 2, 2, -3],\n [5, 0, 6, 1, 6, 6],\n [-2, 6, -6, 2, -1, -4],\n [-4, 3, -6, 6, 1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
68224
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, -2, 2, 4, 2, -3],\n [-2, 1, 3, 1, 2, -1],\n [2, 3, -6, -2, 5, -2],\n [4, 1, -2, 6, -2, 0],\n [2, 2, 5, -2, -4, -2],\n [-3, -1, -2, 0, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
776266
MATH