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[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, 3, 4, 4, -2, 1],\n [3, -6, -1, 0, -5, 1],\n [4, -1, -1, 2, 2, 0],\n [4, 0, 2, -3, 0, -2],\n [-2, -5, 2, 0, 6, -2],\n [1, 1, 0, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
655749
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, 1, 2, -3, 4, -2],\n [1, 5, 0, -2, -1, 1],\n [2, 0, -1, 2, -2, -4],\n [-3, -2, 2, 0, 0, 2],\n [4, -1, -2, 0, 5, 4],\n [-2, 1, -4, 2, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9315
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-5, -4, 1, -1, 6, 0],\n [5, -1, -1, 5, -4, 5],\n [6, 1, 5, 0, 0, -1],\n [-2, 3, 1, -2, 2, 2],\n [-6, -1, 0, -4, 0, 4],\n [4, 0, 6, 4, -5, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-1286
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-6, -2, 2, 0, 0, 4],\n [6, 5, -5, 1, -4, 1],\n [-4, 3, 0, -5, -3, 4],\n [-1, 4, 2, -2, 6, 2],\n [-2, 3, 1, 6, 6, -6],\n [0, -3, -2, -1, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
60508
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-6, 5, 2, -5, 2, 3],\n [-5, 2, -1, 4, 2, 6],\n [-1, -1, 6, 4, -5, 1],\n [-4, 0, -2, -4, -6, 1],\n [-4, -5, -6, -3, 6, 1],\n [6, -4, -6, -3, 2, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
1904579
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-6, 6, 0, -5, 2, -3],\n [6, -4, 1, 0, 4, 0],\n [0, 1, -6, 2, 1, -1],\n [-5, 0, 2, 0, -3, -2],\n [2, 4, 1, -3, -2, 3],\n [-3, 0, -1, -2, 3, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
110291
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (1, 5) of the result:\nA =\n[[2, 2, -2, 1, -2, 0],\n [2, 2, 0, 0, 4, 6],\n [-2, 0, -3, -3, 1, 2],\n [1, 0, -3, -2, -3, -2],\n [-2, 4, 1, -3, 3, 1],\n [0, 6, 2, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-5525
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 4, -4, -2, 6, 3],\n [6, -3, 1, 6, 5, -2],\n [3, 5, 1, 2, -3, 0],\n [-5, -1, 1, 5, 0, 0],\n [1, 0, -2, 0, 6, 3],\n [-4, -2, 0, 2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
-30654
MATH
[ { "content": "For the matrix power A^4 where A =\n[[5, 3, -4, 2, 0, 4],\n [3, 3, -2, 1, 0, 0],\n [-4, -2, 3, -3, -2, 0],\n [2, 1, -3, -4, 0, 2],\n [0, 0, -2, 0, -3, -2],\n [4, 0, 0, 2, -2, -4]], determine the value at position (6, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
1948
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-1, -3, 0, -4, -6, 2],\n [-1, 1, -4, 1, -5, 5],\n [-3, -4, 3, -6, 6, 6],\n [0, 4, 3, -5, -3, 2],\n [-1, 1, -5, 0, -1, 6],\n [2, 0, -6, 1, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
-39532
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 0, 2, 0, 2, -2],\n [0, -4, 4, -1, 0, 0],\n [2, 4, 1, -1, -2, 2],\n [0, -1, -1, 6, -4, 4],\n [2, 0, -2, -4, -4, 2],\n [-2, 0, 2, 4, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
54733
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[-6, 3, -3, -2, 6, 0],\n [3, 4, 0, 0, 2, -6],\n [-3, 0, -2, -1, -1, -6],\n [-2, 0, -1, -3, 0, -2],\n [6, 2, -1, 0, 1, -4],\n [0, -6, -6, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-346007
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 0, -3, 1, 4, 0],\n [0, 2, -6, 4, 0, 2],\n [-3, -6, 6, -6, 0, 0],\n [1, 4, -6, -5, 0, -3],\n [4, 0, 0, 0, -1, 0],\n [0, 2, 0, -3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
18022
MATH
[ { "content": "For the matrix power A^5 where A =\n[[1, 6, -3, -2, 6, -2],\n [-1, -4, -2, -5, 3, -6],\n [4, -6, 3, 0, -5, -3],\n [-2, 0, -5, -1, -6, 0],\n [2, -2, -2, -3, -4, 2],\n [-2, 1, 2, -2, 3, 2]], determine the value at position (6, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
9051
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, 2, 4, -3, -1, -1],\n [-1, -5, 0, 6, -1, 4],\n [-6, -5, 0, -6, -6, -6],\n [1, -3, -3, 6, -5, 4],\n [4, 4, -6, 5, 3, 2],\n [0, -3, 5, -1, -5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
122474
MATH
[ { "content": "What is the value at position (1, 4) of the matrix A^5 where A is:\n[[-5, 2, 2, 0, -4, 3],\n [2, -5, 0, 2, -5, 0],\n [2, 0, 6, 0, -3, -3],\n [0, 2, 0, 3, -2, 1],\n [-4, -5, -3, -2, -5, 3],\n [3, 0, -3, 1, 3, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
-12711
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -6, -3, -5, 4, 6],\n [-2, 3, 2, 4, 5, 3],\n [-4, 1, -4, -1, -3, 1],\n [4, -1, 1, -6, -1, -6],\n [-6, 1, 0, -4, -1, 2],\n [0, 5, -4, 6, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
59984
MATH
[ { "content": "What is the value at position (3, 4) of the matrix A^5 where A is:\n[[-3, 0, -2, 1, -1, -3],\n [0, -5, 1, 0, 0, -2],\n [-2, 1, 1, 0, -5, -2],\n [1, 0, 0, 5, -4, -4],\n [-1, 0, -5, -4, -2, 0],\n [-3, -2, -2, -4, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
20163
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, 5, 4, 6, -1],\n [1, 3, 5, -6, -3, 3],\n [4, -6, 2, 4, 0, 0],\n [5, -2, 0, 5, -5, 6],\n [-3, 0, -4, -5, 3, -5],\n [6, -6, -2, 5, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Y...
1505359
MATH
[ { "content": "What is the value at position (3, 5) of the matrix A^5 where A is:\n[[2, -3, -6, -1, -2, 3],\n [-1, -4, -5, -1, 6, -6],\n [0, 0, 3, 6, 0, 5],\n [4, 3, -6, -3, 6, 0],\n [4, 2, -2, 6, -5, 0],\n [3, -6, 0, -1, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-39456
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[3, -5, 0, 3, 4, -6],\n [-5, 2, -2, -2, -2, 0],\n [0, -2, 4, 0, 0, -5],\n [3, -2, 0, 0, 0, 2],\n [4, -2, 0, 0, 5, -5],\n [-6, 0, -5, 2, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
670
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 2, 4, 5, -6, 4],\n [-5, 3, -5, -3, -5, 0],\n [6, 2, 0, 5, -1, 3],\n [-6, 4, 3, 2, -2, 4],\n [-2, -1, 2, 6, 1, 1],\n [1, -6, -6, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
810965
MATH
[ { "content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[-5, -2, 4, 1, 0, -4],\n [-2, -6, -2, -1, 0, 4],\n [4, -2, -2, 0, 3, 2],\n [1, -1, 0, -6, -5, -1],\n [0, 0, 3, -5, -6, 3],\n [-4, 4, 2, -1, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
2105
MATH
[ { "content": "What is the value at position (6, 1) of the matrix A^4 where A is:\n[[1, 1, 4, 5, 2, 6],\n [4, 5, -2, 0, -4, 3],\n [-3, 3, 2, 3, 3, 5],\n [-6, -5, -2, -4, -5, -6],\n [3, -4, -6, 5, -6, 5],\n [-6, 1, -4, 4, -6, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
4460
MATH
[ { "content": "Find the value at position (3, 6) of the 4th power of the matrix:\n[[3, -2, -2, -1, -2, -4],\n [-2, 0, -4, 4, 4, 1],\n [-2, -4, 2, 2, 2, 2],\n [-1, 4, 2, 5, 1, 2],\n [-2, 4, 2, 1, 3, -2],\n [-4, 1, 2, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
-64
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-3, -3, 6, 3, 4, -5],\n [5, -6, 5, 3, 5, -6],\n [6, 1, -5, 5, 3, -2],\n [5, -3, 1, -5, 3, 2],\n [0, 6, 0, -6, 5, -5],\n [-3, -3, 4, -4, 0, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
1611767
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, -5, -3, -4, -5, 5],\n [6, -1, 6, -3, -1, -5],\n [5, -3, 4, -1, -2, -4],\n [1, 0, -4, -1, -3, 4],\n [-2, 4, -2, 0, 4, -2],\n [4, -4, 3, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
2046
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-2, 2, -2, 3, 0, -6],\n [2, -2, 1, -1, -2, 0],\n [-2, 1, 3, 2, 4, -4],\n [3, -1, 2, 5, 1, 0],\n [0, -2, 4, 1, 3, 0],\n [-6, 0, -4, 0, 0, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
61149
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-3, 1, 0, -2, 2, -2],\n [1, 2, 1, 0, -4, -4],\n [0, 1, -6, 0, -2, 1],\n [-2, 0, 0, 4, 2, 2],\n [2, -4, -2, 2, 4, 1],\n [-2, -4, 1, 2, 1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
35702
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-3, 6, 3, 5, 6, -1],\n [-5, -2, -1, -2, 5, -5],\n [0, -3, 1, 0, 0, 2],\n [-6, 3, -1, -1, -1, 6],\n [5, -1, 5, 3, 0, 3],\n [-1, -6, -4, -5, -1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
-1853
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 1, 2, 3, 0, -2],\n [1, -2, -2, 2, 2, -2],\n [2, -2, 1, 4, 2, -3],\n [3, 2, 4, 3, 2, -1],\n [0, 2, 2, 2, 4, 0],\n [-2, -2, -3, -1, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your ...
75926
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -2, -6, 2, -6, -6],\n [-2, -2, 0, 1, 0, 1],\n [-6, 0, -1, -4, -2, 1],\n [2, 1, -4, 3, 2, 0],\n [-6, 0, -2, 2, 3, -3],\n [-6, 1, 1, 0, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "ro...
93836
MATH
[ { "content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[-4, 0, -2, 0, 3, -2],\n [0, -1, -2, 2, 1, 0],\n [-2, -2, 1, 0, 3, 2],\n [0, 2, 0, -4, 4, 0],\n [3, 1, 3, 4, 3, 0],\n [-2, 0, 2, 0, 0, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-5897
MATH
[ { "content": "Find the value at position (5, 3) of the 4th power of the matrix:\n[[-2, 1, 5, -1, 0, -2],\n [1, 3, 2, 1, 0, 0],\n [5, 2, -2, 6, -1, 2],\n [-1, 1, 6, 2, 0, -6],\n [0, 0, -1, 0, 5, -4],\n [-2, 0, 2, -6, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-212
MATH
[ { "content": "For the matrix power A^5 where A =\n[[5, 3, 6, -2, 0, 6],\n [-2, 6, 6, -6, 4, 0],\n [1, 6, 0, 4, 6, -3],\n [1, -2, 3, 2, 5, 5],\n [3, -2, -6, 5, 2, 5],\n [-2, -1, -3, -1, 5, 1]], determine the value at position (3, 6).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
40550
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, -2, -5, -5, 6, 0],\n [3, 6, 3, 4, 3, -1],\n [-3, -2, -6, 0, 1, 2],\n [1, -2, -4, 3, 4, 2],\n [-1, -2, 6, -4, -1, -4],\n [3, 5, -1, -3, -5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
4062
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 0, 2, 1, -1, -4],\n [0, -4, -1, 6, 2, -2],\n [2, -1, 2, 1, -4, 2],\n [1, 6, 1, 6, -4, 0],\n [-1, 2, -4, -4, -5, 4],\n [-4, -2, 2, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "r...
83970
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, -4, 3, -1, 0, 3],\n [-6, -1, 0, -1, -3, -6],\n [4, 2, -3, 0, 0, -5],\n [-6, 1, 1, 0, 1, -4],\n [4, -5, 0, 1, -6, 5],\n [3, 2, 6, 4, -3, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
45389
MATH
[ { "content": "Find the value at position (6, 6) of the 5th power of the matrix:\n[[-3, -1, 0, -3, -2, -4],\n [-1, -5, -1, 2, -4, 6],\n [0, -1, 1, -2, 0, -1],\n [-3, 2, -2, -3, -2, 1],\n [-2, -4, 0, -2, -2, 2],\n [-4, 6, -1, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "us...
-89253
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-3, 0, 2, 2, 2, 4],\n [0, -2, -2, 1, 0, -6],\n [2, -2, 3, 3, -1, 3],\n [2, 1, 3, 3, 0, -2],\n [2, 0, -1, 0, 1, -4],\n [4, -6, 3, -2, -4, -6]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
122998
MATH
[ { "content": "For the matrix power A^4 where A =\n[[2, 0, -4, 4, 0, -2],\n [0, 1, -4, -1, -1, 1],\n [-4, -4, 6, -1, -6, 4],\n [4, -1, -1, 3, 2, 2],\n [0, -1, -6, 2, 3, 0],\n [-2, 1, 4, 2, 0, -3]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
-4053
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -2, -2, 0, -2, 4],\n [-2, -5, -4, 2, 6, -4],\n [-2, -4, 6, -2, 2, -2],\n [0, 2, -2, -4, 0, 4],\n [-2, 6, 2, 0, -3, 2],\n [4, -4, -2, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed...
160963
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-1, -1, 0, 2, -5, 0],\n [-1, -6, 3, -2, -5, 0],\n [0, 3, -1, -2, 0, 2],\n [2, -2, -2, 4, -2, -4],\n [-5, -5, 0, -2, -5, -1],\n [0, 0, 2, -4, -1, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
-1039133
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, 6, -4, -2, -1, 2],\n [6, -3, 1, 6, 1, -1],\n [-4, 1, -2, -5, -2, 4],\n [-2, 6, -5, -6, -2, 5],\n [-1, 1, -2, -2, 5, -1],\n [2, -1, 4, 5, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
52720
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (6, 5) of the result:\nA =\n[[4, -4, 6, 5, -3, -6],\n [-2, -6, 6, -6, 3, 4],\n [4, 0, 5, -1, -5, 4],\n [5, -5, 4, 0, -6, 6],\n [-5, 5, 1, -1, -5, 0],\n [-3, -5, 5, -1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
-1854
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 2, 1, -4, -4, -5],\n [-2, 5, -3, 0, -3, 2],\n [5, 5, -5, 4, -1, 0],\n [-3, 6, -1, 0, -3, 1],\n [2, -6, 0, 2, 5, 3],\n [-2, 5, -5, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
62906
MATH
[ { "content": "Find the value at position (2, 5) of the 4th power of the matrix:\n[[5, 0, -5, -5, 3, 5],\n [3, -6, -3, 0, 2, -4],\n [5, 4, 0, 0, 0, -5],\n [-1, -5, -1, 6, 3, -4],\n [-5, 5, -1, -5, -2, -5],\n [-4, -4, -1, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
-2616
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, 6, 5, 6, -6, 0],\n [6, 1, -5, -3, 3, 0],\n [1, -6, -3, -1, -4, -2],\n [3, 2, 4, 6, -4, -2],\n [1, -1, -3, 1, 4, -4],\n [-4, -3, 2, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-38052
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -1, 3, 2, 2, 1],\n [-1, 6, -1, 2, -1, -4],\n [3, -1, -4, -4, 2, 0],\n [2, 2, -4, -5, -2, 4],\n [2, -1, 2, -2, 4, 2],\n [1, -4, 0, 4, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6380
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[-2, -3, 0, 0, 6, 2],\n [2, -2, 6, 5, 6, 1],\n [3, -6, 2, 1, -1, 6],\n [-4, -4, 1, -2, 3, 4],\n [0, -2, 1, 3, 3, -3],\n [-5, -4, 1, 4, 6, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
1313
MATH
[ { "content": "Find the value at position (3, 1) of the 4th power of the matrix:\n[[6, -5, -4, 3, 0, -2],\n [-5, -5, 4, 2, 2, -2],\n [-4, 4, 4, -1, 0, -3],\n [3, 2, -1, -5, 2, -2],\n [0, 2, 0, 2, 1, -4],\n [-2, -2, -3, -2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-8613
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, -4, 0, 2, -1, 0],\n [-4, 3, -2, 0, 5, 0],\n [0, -2, -1, 2, -3, 0],\n [2, 0, 2, 2, 2, 0],\n [-1, 5, -3, 2, 6, 2],\n [0, 0, 0, 0, 2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
23712
MATH
[ { "content": "For the matrix power A^4 where A =\n[[3, 0, 3, -2, 4, -1],\n [-2, 0, 5, -5, -2, 3],\n [-4, 2, 6, -1, 6, 3],\n [-4, 0, -3, -4, 1, 6],\n [-3, 4, -6, -1, 3, 4],\n [4, -6, -2, 0, -1, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"...
39738
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -4, 4, -5, 0, -6],\n [-4, -4, 2, 2, -6, 4],\n [4, 2, -3, 1, 0, -4],\n [-5, 2, 1, 3, -2, 0],\n [0, -6, 0, -2, 6, 0],\n [-6, 4, -4, 0, 0, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role"...
215986
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, -4, 3, -2, 3],\n [6, -2, 6, 3, -1, 5],\n [3, 1, -2, 4, -6, -2],\n [-4, -3, 6, 1, 0, 4],\n [-2, -5, -1, 4, -1, 3],\n [3, 4, -1, 2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Y...
323725
MATH
[ { "content": "For the matrix power A^5 where A =\n[[1, -6, -2, 0, -1, -2],\n [1, -4, -1, -2, 1, -3],\n [1, 3, -5, 2, 6, 2],\n [3, 3, 6, -1, -3, -3],\n [6, -1, -2, -1, 0, 0],\n [2, 1, 6, -1, 5, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"...
425289
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (4, 1) of the result:\nA =\n[[-2, -6, 2, 2, 2, 4],\n [1, 6, 3, 6, -4, -6],\n [4, 5, 5, 1, 0, 6],\n [-2, 3, 0, 3, -3, 2],\n [4, 3, -5, 2, 2, -2],\n [4, -6, 0, 3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
-675
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 1, 0, -4, -4, 4],\n [1, -1, -1, -2, 4, 0],\n [0, -1, -5, 3, -4, -1],\n [-4, -2, 3, -3, -4, -1],\n [-4, 4, -4, -4, -3, 4],\n [4, 0, -1, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
26227
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, 4, 4, 5, -4, -2],\n [4, -4, -2, 0, -4, 0],\n [4, -2, -4, 1, 4, -2],\n [5, 0, 1, -4, 0, 4],\n [-4, -4, 4, 0, 4, -5],\n [-2, 0, -2, 4, -5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "rol...
1354910
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[0, -1, 0, 0, 2, -2],\n [-1, 3, -4, 2, -4, -2],\n [0, -4, -3, -6, 0, -2],\n [0, 2, -6, 5, 0, -4],\n [2, -4, 0, 0, 2, 1],\n [-2, -2, -2, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-193018
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 6, -3, -2, -2, -3],\n [-3, -3, -3, -3, -2, -5],\n [-5, 2, -5, -1, -5, -2],\n [-3, 5, 0, 0, 6, -1],\n [3, -2, -6, 5, -4, 2],\n [-6, -2, -5, -3, 4, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
1091289
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-4, -1, -2, 4, 0, 0],\n [-1, -4, 0, -4, 4, -4],\n [-2, 0, 5, 2, -3, -3],\n [4, -4, 2, -6, 0, 0],\n [0, 4, -3, 0, 6, 0],\n [0, -4, -3, 0, 0, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
1049383
MATH
[ { "content": "For the matrix power A^4 where A =\n[[2, 0, 0, 5, 0, 2],\n [0, 1, -1, 1, 4, 0],\n [0, -1, 2, -5, 0, 0],\n [5, 1, -5, -5, 3, 2],\n [0, 4, 0, 3, -3, 0],\n [2, 0, 0, 2, 0, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
52755
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-6, 0, 0, 2, 2, 6],\n [0, 5, 0, -2, -4, 3],\n [0, 0, -6, 0, -4, 5],\n [2, -2, 0, 2, 2, -1],\n [2, -4, -4, 2, 2, -2],\n [6, 3, 5, -1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "...
1416069
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 0, 4, -3, -1, 2],\n [0, -5, 0, 2, 2, 1],\n [4, 0, 3, 0, 0, 3],\n [-3, 2, 0, -1, 1, 2],\n [-1, 2, 0, 1, 2, 2],\n [2, 1, 3, 2, 2, -6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "u...
6971
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[3, 5, -6, -3, -5, 4],\n [0, -5, 3, -5, -2, -3],\n [1, -3, 5, -1, -2, 4],\n [-5, 4, 6, 5, 1, -5],\n [2, 2, -4, -3, 1, 2],\n [-4, -2, 4, 1, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
83412
MATH
[ { "content": "What is the value at position (5, 5) of the matrix A^4 where A is:\n[[4, 1, 3, 4, -4, -5],\n [3, 6, 0, 5, 2, -6],\n [-4, -2, -4, -6, 0, 0],\n [3, 5, 1, -2, 3, 5],\n [-2, -2, -6, 3, -2, -1],\n [6, 5, -6, 4, 0, -6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
171
MATH
[ { "content": "For the matrix power A^5 where A =\n[[4, -5, -5, -2, 3, 6],\n [0, -6, 3, -6, -6, -1],\n [-5, -6, -1, -5, -1, 3],\n [1, -5, 4, 2, 1, 5],\n [3, -6, 0, 6, 3, -1],\n [-1, -1, -1, 3, 0, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}...
1527998
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (3, 3) of the result:\nA =\n[[-4, -1, -4, 0, 0, 1],\n [-5, 2, 6, -2, 2, 3],\n [-2, 0, 4, 2, -3, -5],\n [2, 6, -5, -4, 3, -5],\n [-4, -1, -4, 3, 1, 4],\n [-1, 0, -6, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer...
22080
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[0, 2, -3, 5, -2, -4],\n [4, 2, -3, -2, -6, 4],\n [5, 6, -5, 5, 6, 2],\n [-5, -2, 6, 1, -4, -1],\n [-3, 4, 0, 3, 6, -4],\n [-1, 5, 3, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
262
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-6, -2, -1, 2, 1, -3],\n [-2, -4, 2, -1, 0, -2],\n [-1, 2, -6, 0, -3, 2],\n [2, -1, 0, -1, 2, -2],\n [1, 0, -3, 2, 3, 4],\n [-3, -2, 2, -2, 4, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14049
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (5, 5) of the result:\nA =\n[[-6, 4, 1, 3, -3, -4],\n [5, 0, 5, -5, 1, -1],\n [0, -2, 2, -2, 4, -2],\n [-4, 4, -6, -5, 1, -6],\n [0, -2, -4, 5, 5, 4],\n [0, 2, -5, 1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
-6218
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -4, 3, 0, -4, 4],\n [-4, -3, 2, 0, 0, 0],\n [3, 2, -3, -3, -1, -2],\n [0, 0, -3, 2, 0, -4],\n [-4, 0, -1, 0, 6, -4],\n [4, 0, -2, -4, -4, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2435
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -3, 0, -2, 6, 4],\n [-3, -4, 3, -2, 2, 0],\n [0, 3, -1, 0, 2, 1],\n [-2, -2, 0, -5, -2, 0],\n [6, 2, 2, -2, 2, 0],\n [4, 0, 1, 0, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your...
716657
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (6, 4) of the result:\nA =\n[[6, 5, 4, -5, -3, -6],\n [-2, -1, 2, 3, 1, -5],\n [-6, -5, 0, -3, 3, -2],\n [5, 0, -4, 3, -5, 6],\n [0, -2, -6, -6, 2, -2],\n [-6, 0, 2, 4, -6, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}...
13960
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[6, -3, -4, -2, 0, 1],\n [6, -5, 0, -6, 0, 1],\n [-5, 2, -6, 6, -1, -6],\n [-4, 4, -1, -4, 1, -2],\n [-5, -3, 2, -3, 3, 3],\n [1, -2, 4, 4, 3, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3908
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[6, 0, -2, -4, 4, -2],\n [0, -4, -6, 0, -3, 2],\n [-2, -6, 2, -3, -2, -1],\n [-4, 0, -3, 2, 1, -2],\n [4, -3, -2, 1, -1, 0],\n [-2, 2, -1, -2, 0, 6]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
538748
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, 6, 3, 2, 3, -1],\n [0, 3, 1, 4, 6, 3],\n [-6, 1, -3, 3, 1, 6],\n [-1, 4, 2, 4, -3, -5],\n [-5, -2, 3, 2, 5, -4],\n [1, -3, -1, 3, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role...
237182
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, 5, -4, 4, 4, -6],\n [0, -3, 0, -4, 5, 4],\n [-2, -2, 6, -5, 4, 3],\n [5, -5, -3, -3, -3, -1],\n [-5, -1, 0, 4, 3, -4],\n [4, 5, 1, -5, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11204
MATH
[ { "content": "For the matrix power A^4 where A =\n[[6, 4, -2, -5, 0, -5],\n [-1, 3, -4, 2, -4, 4],\n [5, 5, -4, -2, 0, 1],\n [5, 4, 0, 2, -2, 3],\n [4, -4, -1, -2, 5, -3],\n [5, -5, 0, 6, -2, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",...
74676
MATH
[ { "content": "What is the value at position (4, 4) of the matrix A^5 where A is:\n[[5, 0, -1, 0, -4, 0],\n [0, -2, -2, -4, -6, 3],\n [-1, -2, -6, 4, -2, -4],\n [0, -4, 4, -3, 6, 2],\n [-4, -6, -2, 6, -6, -2],\n [0, 3, -4, 2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "use...
-165627
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-1, 4, -5, 1, -2, 1],\n [1, -1, -5, 1, 4, -1],\n [-1, 1, -6, -5, 5, 5],\n [2, 4, 5, 1, 5, 0],\n [0, -2, -5, 4, -1, 3],\n [-4, -3, 6, 3, 5, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
85020
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-5, -5, 5, 1, 1, 3],\n [-1, 6, -2, 1, -3, 4],\n [-3, -2, -6, -6, -5, 1],\n [0, 3, 2, -2, -5, 0],\n [1, 5, 0, 0, 5, -2],\n [-5, -1, -3, 3, -5, 5]], determine the value at position (6, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
-4920
MATH
[ { "content": "For the matrix power A^4 where A =\n[[2, 2, 2, 6, 0, -1],\n [2, 3, 2, -2, -4, 1],\n [2, 2, -4, -2, -2, 2],\n [6, -2, -2, 3, -1, 2],\n [0, -4, -2, -1, 6, 0],\n [-1, 1, 2, 2, 0, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
13246
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 4, 1, 3, -3, -4],\n [-4, 5, -2, 4, -6, 3],\n [-4, -1, -4, -2, 2, -5],\n [4, -5, 5, -1, -1, 4],\n [4, 1, 5, 6, 4, -5],\n [2, -5, 6, -6, 3, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16314
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, 0, 1, -2, -1, 5],\n [-6, -1, 5, 1, 6, -4],\n [4, -6, 4, -3, -6, 1],\n [-2, -6, 1, 2, 3, -5],\n [2, 1, 0, -4, -5, 0],\n [-2, -1, -3, -5, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "...
36808
MATH
[ { "content": "For the matrix power A^4 where A =\n[[5, 0, 1, -5, 2, 5],\n [0, 0, 2, 0, -2, -2],\n [1, 2, -2, -1, 0, 2],\n [-5, 0, -1, -6, 1, -2],\n [2, -2, 0, 1, -6, 2],\n [5, -2, 2, -2, 2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
31192
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-1, -1, -1, -2, 3, -6],\n [-1, 2, -2, -2, 0, -2],\n [-1, -2, 4, 4, 3, 0],\n [-2, -2, 4, 4, 0, -3],\n [3, 0, 3, 0, 1, 4],\n [-6, -2, 0, -3, 4, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user...
22683
MATH
[ { "content": "For the matrix power A^5 where A =\n[[1, -4, 6, -3, -1, 4],\n [0, -3, -3, 0, -1, 6],\n [4, 1, -6, 3, 6, 4],\n [0, 5, 0, 4, 0, 0],\n [3, 3, 1, 2, 2, -5],\n [6, 6, 0, 0, -3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
84236
MATH
[ { "content": "For the matrix power A^5 where A =\n[[1, 5, -6, -5, 6, 6],\n [-5, 5, 5, 4, 1, -6],\n [-3, 3, 5, -2, 2, 0],\n [1, 4, 2, 6, 0, -2],\n [6, -2, 3, 4, -1, -2],\n [6, 5, 4, 2, -4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" }...
44445
MATH
[ { "content": "For the matrix power A^5 where A =\n[[0, 0, -1, -4, 6, 0],\n [-2, 0, -5, -1, 1, -6],\n [-3, 4, -6, -6, 3, 5],\n [4, 1, 0, 5, 3, 6],\n [-6, 4, 6, -5, -3, -6],\n [-4, 1, 1, 1, -1, -1]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": ...
7104
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-2, 6, 2, 0, 1, 3],\n [6, 5, 2, 0, 2, 1],\n [2, 2, 2, 2, -3, 1],\n [0, 0, 2, -3, -1, -4],\n [1, 2, -3, -1, -2, -3],\n [3, 1, 1, -4, -3, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ...
418476
MATH
[ { "content": "For the matrix power A^5 where A =\n[[3, 1, 2, 5, -2, 5],\n [-1, 4, -3, -2, 0, 2],\n [3, 4, 6, -1, -1, 1],\n [4, -3, -4, 0, -2, -5],\n [-5, 4, -1, 1, -6, 4],\n [-1, 5, -5, -5, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"...
-122538
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-6, 0, -2, 2, 2, 1],\n [0, 6, -5, 0, 2, 0],\n [-2, -5, 5, 1, -1, 2],\n [2, 0, 1, -5, 0, 2],\n [2, 2, -1, 0, -3, 2],\n [1, 0, 2, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your ans...
60079
MATH
[ { "content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[-5, -3, -2, -6, 1, 1],\n [-1, 5, -2, 1, -4, -4],\n [-5, -2, -4, -4, -1, 1],\n [-5, -3, 4, 0, -6, -6],\n [5, 6, 3, 0, 0, -6],\n [-6, -3, -2, -2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your an...
-9881
MATH
[ { "content": "What is the value at position (3, 2) of the matrix A^5 where A is:\n[[0, 1, 1, 2, -3, 5],\n [1, -6, 2, 4, 1, 5],\n [1, 2, -4, -2, -4, 6],\n [2, 4, -2, -4, 4, -4],\n [-3, 1, -4, 4, -5, 0],\n [5, 5, 6, -4, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7377
MATH
[ { "content": "Find the value at position (6, 1) of the 4th power of the matrix:\n[[4, -5, 0, -3, 4, 6],\n [-5, 6, 0, 6, -2, -6],\n [-2, 5, 5, -4, 0, -1],\n [1, 6, -2, -5, 2, 4],\n [1, -1, 6, 3, 0, 2],\n [0, -4, -1, 4, 6, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4051
MATH
[ { "content": "Find the value at position (6, 2) of the 5th power of the matrix:\n[[0, -6, -1, -4, 4, -3],\n [-6, 2, 0, 4, 2, 1],\n [-1, 0, -6, 0, -4, 2],\n [-4, 4, 0, 4, -6, -6],\n [4, 2, -4, -6, -3, -2],\n [-3, 1, 2, -6, -2, 6]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" ...
-12231
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, -2, 3, -2, -6, -1],\n [6, 2, -5, 0, -1, -2],\n [-3, -3, -1, -3, -2, 6],\n [-1, -2, 0, 2, 3, 0],\n [0, -3, -6, 1, -3, -6],\n [-2, 1, -3, 6, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", ...
47917
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, -4, 2, -4, -6, -5],\n [-1, 5, 3, -5, -1, -6],\n [4, 6, -6, -2, 3, 6],\n [4, 2, 1, -4, -4, -6],\n [-4, 5, 5, 5, 6, 4],\n [-6, 1, -6, -2, 2, 0]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role":...
-7398
MATH