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[ { "content": "For the matrix power A^3 where A =\n[[-3, 2, 1, -1],\n [4, 4, 1, 1],\n [-2, -4, 4, 2],\n [4, -2, 4, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
991
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -3, 0, 1],\n [-1, 2, -2, 4],\n [2, 2, 1, 4],\n [0, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
174
MATH
[ { "content": "For the matrix power A^3 where A =\n[[4, 0, -3, -2],\n [0, 2, 0, 0],\n [-3, 0, 2, 0],\n [-2, 0, 0, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
668
MATH
[ { "content": "For the matrix power A^3 where A =\n[[-1, 2, -3, -3],\n [2, -1, 3, 0],\n [-3, 3, 0, 1],\n [-3, 0, 1, 3]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-40
MATH
[ { "content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[1, 2, -3, -2],\n [2, 0, 2, 0],\n [-3, 2, 1, 2],\n [-2, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16
MATH
[ { "content": "Find the sum of all entries of the 3th power of the matrix:\n[[-3, 4, 3, -1],\n [-4, 4, -4, 4],\n [0, 4, 1, -3],\n [-1, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-366
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -2, 4, 4],\n [4, -3, -3, -4],\n [-3, 1, -2, -4],\n [4, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6627
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, -2, 4, -2],\n [-2, 2, 0, 2],\n [4, 0, 4, 0],\n [-2, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3898
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-2, 0, 2, -2],\n [0, 0, 3, 0],\n [2, 3, -2, -2],\n [-2, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
772
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 2, -1, -1],\n [2, -1, 3, -2],\n [-1, 3, -2, -2],\n [-1, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
958
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, 1, -2, 4],\n [-2, 1, 2, -4],\n [0, -2, -4, -2],\n [2, 4, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-339
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-4, 3, 1, 3],\n [-4, -2, -1, -2],\n [2, 4, -1, -2],\n [-3, 4, 2, 3]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-436
MATH
[ { "content": "What is the value at position (4, 2) of the matrix A^4 where A is:\n[[0, -1, -2, 0],\n [-1, 3, 2, 2],\n [-2, 2, 0, 1],\n [0, 2, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
252
MATH
[ { "content": "Calculate the matrix power A^3 and find the value at position (2, 1) of the result:\nA =\n[[2, -4, 2, 2],\n [2, -1, 0, 1],\n [3, 4, -1, -1],\n [-3, -4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-21
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-3, 3, -1, -3],\n [-4, -3, 4, -2],\n [1, 1, 0, -2],\n [-3, 2, 0, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1668
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 1, 2, -4],\n [3, 4, 3, -3],\n [3, -1, -4, 2],\n [2, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1117
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 0, -2, 0],\n [0, -1, 0, 2],\n [-2, 0, 2, 3],\n [0, 2, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4394
MATH
[ { "content": "What is the value at position (2, 4) of the matrix A^3 where A is:\n[[-2, -2, -1, -4],\n [-3, 3, -4, -1],\n [3, -4, -2, 1],\n [-3, -1, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "For the matrix power A^3 where A =\n[[3, -4, 4, -4],\n [-3, -4, 4, 4],\n [-3, 0, 1, 0],\n [1, -3, 0, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
274
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, 0, 0, 0],\n [0, -2, -1, 0],\n [0, -1, -4, 3],\n [0, 0, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
385
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 0, 4, 0],\n [0, 1, -4, -1],\n [4, -4, 1, 2],\n [0, -1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9261
MATH
[ { "content": "What is the value at position (3, 1) of the matrix A^4 where A is:\n[[-4, -1, -3, 3],\n [3, -3, -2, 0],\n [1, 4, 1, 2],\n [-4, -2, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
272
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, -2, 2, -2],\n [-2, -3, 2, 0],\n [2, 2, 1, 2],\n [-2, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-29
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-3, 3, 1, 2],\n [3, -2, 1, 0],\n [1, 1, 0, 0],\n [2, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
536
MATH
[ { "content": "Find the value at position (2, 1) of the 3th power of the matrix:\n[[4, 4, -3, 0],\n [-2, -3, 1, -4],\n [2, 4, -4, -1],\n [-3, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 0, 2, -2],\n [0, 0, -4, -4],\n [2, -4, -4, 3],\n [-2, -4, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8210
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, 2, 0, 0],\n [2, -2, 2, 0],\n [0, 2, 0, -2],\n [0, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
441
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, -3, 2, 1],\n [-2, 4, -4, -4],\n [-4, -3, -3, 0],\n [1, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1753
MATH
[ { "content": "For the matrix power A^3 where A =\n[[3, -1, -1, -2],\n [-1, -4, -3, 0],\n [-1, -3, -2, -1],\n [-2, 0, -1, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-933
MATH
[ { "content": "Calculate the matrix power A^3 and find the value at position (2, 1) of the result:\nA =\n[[-4, 2, -3, -1],\n [-4, -2, 0, -3],\n [-2, -2, 2, -2],\n [-2, 4, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-118
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 0, 0, -1],\n [0, -2, 0, -3],\n [0, 0, -2, 0],\n [-1, -3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
184
MATH
[ { "content": "For the matrix power A^4 where A =\n[[4, -2, 2, 0],\n [-2, 2, 1, 3],\n [2, 1, 2, 0],\n [0, 3, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2237
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, 0, -2, 0],\n [0, -4, 0, 2],\n [-2, 0, -1, -2],\n [0, 2, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2265
MATH
[ { "content": "For the matrix power A^3 where A =\n[[4, 0, 1, -2],\n [0, 3, 2, 0],\n [1, 2, -2, 3],\n [-2, 0, 3, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
565
MATH
[ { "content": "Find the value at position (3, 1) of the 3th power of the matrix:\n[[4, 0, 1, -2],\n [0, 1, -4, 1],\n [1, -4, -4, -2],\n [-2, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
41
MATH
[ { "content": "What is the sum of all entries of the matrix A^3 where A is:\n[[3, 2, 2, 2],\n [2, 1, 2, 2],\n [2, 2, -2, 0],\n [2, 2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
664
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[-1, 3, -2, 2],\n [3, 2, 1, 0],\n [-2, 1, 3, -2],\n [2, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
450
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, 0, 0, -2],\n [0, -2, 2, -2],\n [0, 2, -2, 0],\n [-2, -2, 0, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1469
MATH
[ { "content": "Calculate the matrix power A^3 and find the value at position (1, 4) of the result:\nA =\n[[3, 4, 0, -2],\n [4, -3, -2, -2],\n [0, -2, -1, 2],\n [-2, -2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-150
MATH
[ { "content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[0, -3, -3, -1],\n [-3, 4, -2, 2],\n [-3, -2, 1, -2],\n [-1, 2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-89
MATH
[ { "content": "For the matrix power A^4 where A =\n[[3, 0, 0, -3],\n [0, 3, -2, -3],\n [0, -2, 0, 0],\n [-3, -3, 0, 0]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-210
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, -2, 0, -1],\n [-2, 4, 0, 3],\n [0, 0, -1, 0],\n [-1, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7771
MATH
[ { "content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, 0, 1, 0],\n [0, 4, 1, 0],\n [1, 1, -4, -2],\n [0, 0, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -2, 2, 2],\n [-2, -1, 1, 0],\n [2, 1, 1, -4],\n [2, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
874
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -4, 3, -2],\n [-4, -2, -1, -3],\n [2, -3, 0, 0],\n [1, -1, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4359
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[0, -4, 1, 4],\n [-1, -1, 0, -3],\n [-2, 2, -1, 1],\n [1, -4, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
562
MATH
[ { "content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 0, 3, 1],\n [-3, 0, 3, -4],\n [1, 0, 1, -4],\n [1, -2, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-188
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, 2, 0, 2],\n [2, -2, -1, 2],\n [0, -1, 4, -3],\n [2, 2, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
914
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[-2, 3, -2, 4],\n [0, 4, 4, -2],\n [1, -2, -4, -4],\n [-4, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
420
MATH
[ { "content": "For the matrix power A^3 where A =\n[[2, -4, 3, 2],\n [-1, -4, 2, 2],\n [-2, 4, -4, -4],\n [-2, -4, 0, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
898
MATH
[ { "content": "What is the value at position (1, 1) of the matrix A^3 where A is:\n[[0, 0, 0, -2],\n [0, 4, 0, 0],\n [0, 0, 1, 0],\n [-2, 0, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-16
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-3, 0, 0, 2],\n [0, 3, -1, 0],\n [0, -1, -4, 0],\n [2, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
225
MATH
[ { "content": "Find the value at position (4, 3) of the 3th power of the matrix:\n[[4, 1, 2, 1],\n [-4, -2, 3, -1],\n [-2, 1, -2, 3],\n [2, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, 2, -3, -3],\n [-1, 2, -3, -4],\n [-1, 3, -2, 2],\n [4, -3, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-138
MATH
[ { "content": "Find the sum of all entries of the 3th power of the matrix:\n[[-2, 4, 0, -3],\n [-4, 3, -2, -3],\n [0, -2, 2, 3],\n [-4, 1, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -2, -4, -4],\n [4, -3, 1, -3],\n [-3, 2, -4, 0],\n [-2, -4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
11898
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 4, 2, 2],\n [4, 1, -2, 0],\n [2, -2, 0, -2],\n [2, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5141
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-2, 0, 2, 0],\n [0, -3, 3, 2],\n [2, 3, 4, 0],\n [0, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
689
MATH
[ { "content": "Find the value at position (2, 4) of the 4th power of the matrix:\n[[2, 3, 3, 1],\n [1, 2, 1, 0],\n [1, -3, -4, -4],\n [-1, 0, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-40
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[3, -1, -2, -2],\n [-1, 4, 0, 0],\n [-2, 0, 3, 0],\n [-2, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
631
MATH
[ { "content": "What is the value at position (4, 2) of the matrix A^3 where A is:\n[[2, -4, -2, -1],\n [-1, -3, 3, -4],\n [-2, -2, 2, 0],\n [2, 4, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-8
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, 3, 4, -4],\n [2, 0, -1, -4],\n [0, 3, 3, -4],\n [0, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-150
MATH
[ { "content": "What is the value at position (4, 2) of the matrix A^4 where A is:\n[[-4, -1, 2, 0],\n [-1, -2, 2, 2],\n [2, 2, 3, 0],\n [0, 2, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-56
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -3, 0, 2],\n [-3, -4, 2, -2],\n [0, 2, -2, -2],\n [2, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1060
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -1, -4, 2],\n [1, 0, 0, 0],\n [2, 1, 4, -4],\n [2, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1586
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -4, -4, 4],\n [0, -3, 3, 4],\n [1, -2, -1, 2],\n [0, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
140
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, 3, 3, -1],\n [3, -2, 0, 0],\n [3, 0, -2, -1],\n [-1, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2649
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -2, 0, 0],\n [-2, 0, -2, 0],\n [0, -2, 0, 0],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
870
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 2, -4, 1],\n [1, -3, 2, 1],\n [-2, 2, 0, 0],\n [-2, -3, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5034
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, -1, 1, 0],\n [-1, 4, 1, 0],\n [1, 1, 2, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
192
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -3, 1, 3],\n [-1, 4, 1, -2],\n [2, 0, 1, -4],\n [-1, 4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
926
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 0, -1, 2],\n [0, 4, 1, 0],\n [-1, 1, -2, -4],\n [2, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5741
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 3, 3, -1],\n [2, -1, 0, 4],\n [-3, 1, -2, -1],\n [4, 0, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5776
MATH
[ { "content": "For the matrix power A^3 where A =\n[[3, 1, 0, -2],\n [4, 0, -4, 3],\n [3, -4, 3, 2],\n [1, 1, 3, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
90
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, 1, 1, -1],\n [3, -1, -1, -2],\n [4, 4, -1, 3],\n [-1, -1, 0, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
840
MATH
[ { "content": "Find the value at position (1, 4) of the 4th power of the matrix:\n[[-1, 3, -2, -1],\n [3, -1, -1, -2],\n [-2, -1, 1, 4],\n [-1, -2, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-514
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, 0, -2, 3],\n [-1, 2, 4, 1],\n [0, 2, -4, -3],\n [-2, 3, -2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2036
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, 1, -3, 0],\n [1, 4, -1, 0],\n [-3, -1, -1, -1],\n [0, 0, -1, 3]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
162
MATH
[ { "content": "Find the value at position (3, 1) of the 3th power of the matrix:\n[[4, 0, 4, 0],\n [0, 4, -4, -2],\n [4, -4, 4, -2],\n [0, -2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
336
MATH
[ { "content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-3, 2, 4, 1],\n [2, -4, 0, 2],\n [4, 0, 2, 0],\n [1, 2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
204
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-4, 3, 0, 0],\n [3, 1, 1, 0],\n [0, 1, 3, -2],\n [0, 0, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
565
MATH
[ { "content": "Find the sum of all entries of the 3th power of the matrix:\n[[-2, 1, -2, 0],\n [0, -2, -2, 4],\n [-1, -4, -2, -1],\n [-2, 4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-332
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, -1, -4, 0],\n [1, -2, 0, -4],\n [1, 3, 0, 3],\n [1, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-196
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, -2, 0, 1],\n [-2, 2, 2, -2],\n [0, 2, -2, 0],\n [1, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
546
MATH
[ { "content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, 2, -2, 3],\n [-4, -4, 1, 1],\n [-1, 0, 1, -4],\n [3, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-229
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[0, -1, 0, 4],\n [-2, 2, 0, 0],\n [-1, 4, -1, 1],\n [3, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
606
MATH
[ { "content": "For the matrix power A^3 where A =\n[[-1, 2, 1, 2],\n [2, -3, -2, 0],\n [1, -2, 4, 0],\n [2, 0, 0, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
37
MATH
[ { "content": "What is the value at position (2, 2) of the matrix A^4 where A is:\n[[-1, 4, 4, 4],\n [-1, -1, 2, -1],\n [-3, -3, 0, 0],\n [1, -3, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
232
MATH
[ { "content": "Find the value at position (2, 3) of the 3th power of the matrix:\n[[-1, 0, -4, -2],\n [-1, 0, 0, -1],\n [-4, -3, 3, 0],\n [-1, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16
MATH
[ { "content": "For the matrix power A^4 where A =\n[[3, -1, -2, 1],\n [-3, -3, -4, -2],\n [2, -4, -4, 2],\n [-4, -3, -2, -4]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-63
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 4, 1, 0],\n [4, -2, 2, -2],\n [1, 2, 2, 0],\n [0, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8686
MATH
[ { "content": "For the matrix power A^3 where A =\n[[-4, 0, 1, -2],\n [0, -3, 0, 0],\n [1, 0, -2, 1],\n [-2, 0, 1, 0]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 1, 4, 1],\n [-1, -2, -2, -2],\n [3, -2, 0, 4],\n [0, 2, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4327
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, -4, -2, -2],\n [-4, -1, -2, 0],\n [-2, -2, 1, 0],\n [-2, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-993
MATH
[ { "content": "For the matrix power A^3 where A =\n[[3, 2, -4, 2],\n [2, -4, 0, 2],\n [-4, 0, 0, 2],\n [2, 2, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1067
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -3, -1, 2],\n [4, -3, -3, -4],\n [-1, 0, 3, 0],\n [-3, 1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-28
MATH
[ { "content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[-4, -4, 1, -1],\n [-4, -4, -4, -4],\n [2, 1, 0, 0],\n [4, 0, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
824
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 2, -2, 2],\n [1, 1, -3, 3],\n [0, -3, -2, 3],\n [-4, -3, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
316
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, -3, 4, -3],\n [-2, -4, 4, -2],\n [0, -1, -1, -4],\n [0, -1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6417
MATH
[ { "content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, -1, 1, -1],\n [-1, 3, -1, 0],\n [1, -1, -4, -1],\n [-1, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-126
MATH