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[ { "content": "Calculate the matrix power A^3 and find the value at position (4, 4) of the result:\nA =\n[[-4, 0, 2, -2],\n [0, -2, 1, 1],\n [2, 1, 1, 2],\n [-2, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-45
MATH
[ { "content": "Calculate the matrix power A^2 and find the value at position (1, 4) of the result:\nA =\n[[1, 0, -2, 2],\n [0, 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" } ]
10
MATH
[ { "content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[-4, 1, -3, 0],\n [-4, -1, 3, -2],\n [4, -2, -1, 1],\n [3, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-176
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, 3, 0, 1],\n [3, -3, 0, -3],\n [0, 0, 2, 2],\n [1, -3, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
908
MATH
[ { "content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, -4, -4, 4],\n [3, -3, 4, -1],\n [4, 0, 2, 4],\n [0, 4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-150
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -2, 0, 0],\n [-2, -1, -2, -4],\n [0, -2, -2, 0],\n [0, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4498
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 2, -4, -1],\n [2, -1, 0, 0],\n [-4, 0, -2, 3],\n [-1, 0, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12573
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, -2, 1, 3],\n [-3, -2, -3, 3],\n [4, -3, -3, 3],\n [1, -2, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
33
MATH
[ { "content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[3, 0, 0, -2],\n [0, 3, 4, -2],\n [0, 4, 2, 0],\n [-2, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
63
MATH
[ { "content": "Calculate the matrix power A^2 and find the value at position (3, 4) of the result:\nA =\n[[0, -2, -2, -2],\n [-2, 3, -4, 2],\n [-2, -4, 4, 0],\n [-2, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-4
MATH
[ { "content": "For the matrix power A^3 where A =\n[[-1, -4, 3, -3],\n [3, 0, 0, -3],\n [-2, 2, -2, -2],\n [-4, 1, 2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
592
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, -2, 0, -2],\n [-2, -2, 1, 2],\n [0, 1, 1, 0],\n [-2, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
289
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 2, 2, -4],\n [-2, 2, -4, 2],\n [2, -2, -2, 0],\n [1, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
216
MATH
[ { "content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, 2, -3, -4],\n [-1, 3, 4, -4],\n [3, -2, 3, 2],\n [-1, -1, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1
MATH
[ { "content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, 2, 3, 1],\n [2, 3, 0, 4],\n [-2, 0, -2, 4],\n [1, 4, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1696
MATH
[ { "content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, -3, 2, 3],\n [2, -2, 2, -4],\n [-3, 1, 3, 3],\n [3, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
57
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 3, 4, 0],\n [-1, -3, 3, 2],\n [-1, 3, -1, 4],\n [0, 4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1870
MATH
[ { "content": "For the matrix power A^3 where A =\n[[-4, 3, -2, 3],\n [3, -2, -2, -1],\n [-2, -2, 1, 2],\n [3, -1, 2, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1280
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[1, 2, -2, 3],\n [2, 3, 4, 1],\n [2, -3, 4, 2],\n [3, 3, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
144
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 3, 1, 2],\n [3, 4, 1, -2],\n [1, 1, 3, -2],\n [2, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3564
MATH
[ { "content": "What is the value at position (1, 1) of the matrix A^3 where A is:\n[[-3, -2, 3, -2],\n [-4, 2, 3, 1],\n [-4, -1, -2, 1],\n [-3, -4, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Find the value at position (3, 2) of the 2th power of the matrix:\n[[1, 0, 1, 0],\n [0, 0, 4, 0],\n [1, 4, 2, 2],\n [0, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, -2, 0, 0],\n [-2, 1, 3, 0],\n [0, 3, -3, 0],\n [0, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
84
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-4, 4, 4, 1],\n [4, -2, -1, -2],\n [4, -1, 4, 0],\n [1, -2, 0, -1]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1337
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 0, -4, -3],\n [0, 2, -1, 2],\n [-4, -1, 4, -2],\n [-3, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7247
MATH
[ { "content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[4, -3, 0, 0],\n [-3, -1, 2, -4],\n [0, 2, 1, 2],\n [0, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
52
MATH
[ { "content": "For the matrix power A^3 where A =\n[[1, 0, 2, 0],\n [0, 3, 0, 2],\n [2, 0, 4, -2],\n [0, 2, -2, 3]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-32
MATH
[ { "content": "For the matrix power A^2 where A =\n[[-1, -1, 4, -1],\n [-4, -2, 1, 1],\n [-3, 4, -4, -1],\n [4, 3, 1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[4, -4, 2, 2],\n [-4, 2, 4, -1],\n [2, 4, 4, -3],\n [2, -1, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
70
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-3, 3, -3, -4],\n [1, -1, 1, 3],\n [-3, -4, 0, 4],\n [-2, -4, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (1, 3) of the result:\nA =\n[[1, -4, 0, -4],\n [2, -4, 1, -3],\n [-1, -1, 3, 3],\n [3, -1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-52
MATH
[ { "content": "What is the value at position (2, 4) of the matrix A^3 where A is:\n[[-4, 0, 2, 4],\n [1, 4, 2, -1],\n [-2, 3, -3, 2],\n [0, -3, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-26
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -1, 0, 2],\n [-1, 3, 0, 2],\n [0, 0, -4, 2],\n [2, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4138
MATH
[ { "content": "Find the sum of all entries of the 2th power of the matrix:\n[[-3, -2, 3, 3],\n [-1, 2, -2, 3],\n [-2, 0, -3, 3],\n [3, 4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
174
MATH
[ { "content": "Find the value at position (3, 3) of the 2th power of the matrix:\n[[2, 0, 0, -3],\n [0, 2, 3, -2],\n [0, 3, 2, 4],\n [-3, -2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
29
MATH
[ { "content": "For the matrix power A^3 where A =\n[[2, 1, 3, 0],\n [3, 0, -2, 3],\n [2, 2, -1, 2],\n [4, -2, 3, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
548
MATH
[ { "content": "For the matrix power A^2 where A =\n[[3, 3, -4, 3],\n [-2, 2, 2, -2],\n [1, 2, -4, -3],\n [3, 1, 0, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
152
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[0, 1, 0, -1],\n [1, 3, 0, -2],\n [0, 0, -4, 3],\n [-1, -2, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 3, 2, -3],\n [3, 1, 1, 0],\n [2, 1, 0, -1],\n [-3, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
775
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 4, -1, -1],\n [-2, -3, -2, 1],\n [-2, 3, 1, 0],\n [-2, 1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3344
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, 2, 2, -2],\n [2, 4, -3, -1],\n [2, -3, -3, 0],\n [-2, -1, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
69
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, 0, 0, -1],\n [0, -3, 0, 2],\n [0, 0, 2, 2],\n [-1, 2, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
285
MATH
[ { "content": "Find the value at position (3, 1) of the 3th power of the matrix:\n[[1, -2, 0, 0],\n [-2, 3, -3, 3],\n [0, -3, 4, 0],\n [0, 3, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "What is the value at position (3, 4) of the matrix A^2 where A is:\n[[-4, -3, 0, 4],\n [2, -2, 0, 4],\n [1, 2, 1, -2],\n [3, 3, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14
MATH
[ { "content": "For the matrix power A^2 where A =\n[[-2, -1, 2, 3],\n [-4, -1, 1, 0],\n [1, 4, 0, 0],\n [-4, 3, 3, -3]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
6
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 0, -1, -2],\n [0, 0, 0, -2],\n [-1, 0, -2, -1],\n [-2, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
540
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, 2, 0, 0],\n [2, 4, 2, 2],\n [0, 2, -2, 0],\n [0, 2, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5290
MATH
[ { "content": "Find the value at position (2, 3) of the 3th power of the matrix:\n[[2, 1, 3, -3],\n [1, 1, -1, -1],\n [-4, 3, 0, -3],\n [3, 4, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
20
MATH
[ { "content": "Calculate the matrix power A^2 and find the sum of absolute values of all entries of the result:\nA =\n[[4, -2, -1, 0],\n [-2, 1, 0, 0],\n [-1, 0, 4, 1],\n [0, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
103
MATH
[ { "content": "Find the value at position (4, 2) of the 2th power of the matrix:\n[[-2, 2, -3, 3],\n [-1, -1, 3, 0],\n [4, 0, -4, 0],\n [1, -1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Find the sum of all entries of the 2th power of the matrix:\n[[2, 0, 0, 0],\n [0, 2, 0, -4],\n [0, 0, 0, 1],\n [0, -4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
34
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 2, 4, -2],\n [4, -1, 1, -4],\n [1, 1, -1, -1],\n [-4, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1152
MATH
[ { "content": "Find the value at position (4, 3) of the 2th power of the matrix:\n[[-2, 2, -1, -2],\n [2, -1, 2, 0],\n [-1, 2, 1, 0],\n [-2, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "For the matrix power A^3 where A =\n[[3, -1, 1, 0],\n [-1, 3, 0, 0],\n [1, 0, 0, 4],\n [0, 0, 4, -1]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
42
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-4, -2, -2, 0],\n [-2, 0, -2, 2],\n [-2, -2, 3, 0],\n [0, 2, 0, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2073
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[4, -2, 2, 0],\n [-2, -1, 2, -2],\n [2, 2, 2, 0],\n [0, -2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-114
MATH
[ { "content": "What is the value at position (4, 3) of the matrix A^3 where A is:\n[[-3, -2, -2, 0],\n [-2, 4, -1, 2],\n [-2, -1, -2, -2],\n [0, 2, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-30
MATH
[ { "content": "What is the value at position (4, 4) of the matrix A^3 where A is:\n[[-2, -4, -2, -2],\n [-4, 1, -1, 2],\n [-2, -1, -4, -4],\n [-2, 2, -4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-52
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-2, -4, 2, -3],\n [-4, 4, 2, -3],\n [-1, -3, 2, 0],\n [4, -4, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-146
MATH
[ { "content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-4, -3, -1, -1],\n [-4, -1, -3, 2],\n [-4, -4, -3, -2],\n [4, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
437
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, 2, -2, -4],\n [0, -2, 0, 0],\n [-4, -4, 0, -2],\n [0, -3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2625
MATH
[ { "content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, 0, 3, -3],\n [3, -4, -2, -2],\n [0, -4, 3, 3],\n [-3, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1186
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-2, 4, 0, 3],\n [0, 1, -4, -2],\n [3, -2, -4, -4],\n [4, 2, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
58
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 2, 2, -1],\n [3, 1, -1, 0],\n [1, -1, -3, -1],\n [3, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
158
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, -2, 1, -1],\n [-2, 3, 0, 2],\n [1, 0, 0, 1],\n [-1, 2, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
625
MATH
[ { "content": "For the matrix power A^3 where A =\n[[0, -1, 4, 4],\n [3, -4, -4, 4],\n [-4, -1, -2, 4],\n [3, 4, -3, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2074
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, 0, 0, -4],\n [0, 1, -2, 2],\n [0, -2, 0, -3],\n [-4, 2, -3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1048
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[3, 1, 0, 1],\n [1, -1, -2, 0],\n [0, -2, -4, 0],\n [1, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
66
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-3, -2, -1, 0],\n [-2, -2, -2, -1],\n [-1, -2, -3, -4],\n [0, -1, -4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
19074
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 0, 2, 0],\n [1, 0, 3, 4],\n [0, 4, 0, -3],\n [3, -1, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1170
MATH
[ { "content": "Find the sum of all entries of the 2th power of the matrix:\n[[4, 2, -4, 1],\n [-2, 4, -4, -1],\n [3, 3, -4, -2],\n [1, -3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2
MATH
[ { "content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[4, 1, -2, 3],\n [1, -4, -2, 2],\n [-2, -2, 2, 0],\n [3, 2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "Find the value at position (2, 4) of the 3th power of the matrix:\n[[-4, 2, -3, 1],\n [2, -3, 0, 4],\n [-3, 0, 2, -2],\n [1, 4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
170
MATH
[ { "content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 2, 3, -1],\n [2, -3, 1, -2],\n [3, 1, -1, 2],\n [-1, -2, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
147
MATH
[ { "content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-2, 0, 2, -2],\n [0, 1, 0, 2],\n [2, 0, -3, 1],\n [-2, 2, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[4, -4, 0, -1],\n [-3, -2, -3, 0],\n [-1, 3, -1, 1],\n [1, -3, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
435
MATH
[ { "content": "Calculate the matrix power A^2 and find the value at position (2, 2) of the result:\nA =\n[[4, 2, -2, -4],\n [2, 2, 2, 1],\n [-2, 2, -1, 2],\n [-4, 1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-4, -3, -1, -3],\n [-3, 3, -3, 1],\n [-4, -3, 4, 4],\n [4, -2, 0, 0]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
240
MATH
[ { "content": "Find the sum of absolute values of all entries of the 2th power of the matrix:\n[[-3, 2, -2, 0],\n [2, 4, 0, 0],\n [-2, 0, 3, 2],\n [0, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
86
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -3, 0, 0],\n [-3, 4, 1, -2],\n [0, 1, 1, 0],\n [0, -2, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
728
MATH
[ { "content": "For the matrix power A^3 where A =\n[[-2, 2, 2, 0],\n [2, 0, 2, -1],\n [2, 2, -3, -3],\n [0, -1, -3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-144
MATH
[ { "content": "For the matrix power A^4 where A =\n[[4, 1, 2, 0],\n [1, 4, 1, 0],\n [2, 1, -2, 2],\n [0, 0, 2, -2]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
60
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 3, 1, -1],\n [-1, 3, -4, 0],\n [-2, 3, -4, 0],\n [-2, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
895
MATH
[ { "content": "For the matrix power A^2 where A =\n[[0, 4, 3, 2],\n [-2, 2, 2, 3],\n [-2, 4, 3, 4],\n [0, -2, -1, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
40
MATH
[ { "content": "Find the value at position (1, 4) of the 3th power of the matrix:\n[[0, 1, -3, -1],\n [0, 1, -2, 0],\n [4, -2, -1, 0],\n [1, 4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -2, 4, -2],\n [-2, 2, 0, 0],\n [4, 0, 1, -2],\n [-2, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
745
MATH
[ { "content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, -1, 0, 2],\n [-1, -3, 0, 0],\n [0, 0, -2, 2],\n [2, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
217
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, -1, 2, 4],\n [-1, 2, -2, -4],\n [2, -2, -3, 2],\n [4, -4, 2, 4]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
845
MATH
[ { "content": "Calculate the matrix power A^2 and find the sum of all entries of the result:\nA =\n[[1, 0, -3, -2],\n [0, 2, 4, -2],\n [-3, 4, -3, -2],\n [-2, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
64
MATH
[ { "content": "Find the value at position (1, 1) of the 3th power of the matrix:\n[[4, 2, 0, 0],\n [2, 4, 1, -4],\n [0, 1, 2, 2],\n [0, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
112
MATH
[ { "content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, -1, 1, 0],\n [2, -4, -4, -4],\n [3, -3, 2, 4],\n [-2, -4, 1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-24
MATH
[ { "content": "Calculate the matrix power A^2 and find the value at position (2, 2) of the result:\nA =\n[[2, -2, -2, 3],\n [-2, -4, -1, 1],\n [-3, 2, 3, 2],\n [0, -1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
17
MATH
[ { "content": "Calculate the matrix power A^2 and find the value at position (1, 2) of the result:\nA =\n[[0, -2, 4, -3],\n [0, 4, 0, 2],\n [2, 3, -3, -3],\n [3, 4, 3, -3]]\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[[-2, 4, -3, -1],\n [0, -2, 2, -4],\n [-4, 0, 1, 2],\n [0, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
98
MATH
[ { "content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[0, -2, -3, 3],\n [3, 3, -3, 2],\n [4, 2, 0, 1],\n [4, 4, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-4, 3, 2, -1],\n [3, -2, 2, -2],\n [0, 2, 2, -4],\n [0, 1, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, -3, -3, 4],\n [-3, -1, -3, 3],\n [2, 3, -3, 1],\n [3, -2, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
152
MATH
[ { "content": "For the matrix power A^3 where A =\n[[0, 0, 0, 4],\n [0, -4, 3, 0],\n [0, 3, 3, -1],\n [4, 0, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
81
MATH
[ { "content": "What is the sum of all entries of the matrix A^2 where A is:\n[[-4, -2, -2, 0],\n [-2, -3, 0, 0],\n [-2, 0, -2, -4],\n [0, 0, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
217
MATH
[ { "content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[4, 1, -2, -2],\n [1, -4, -2, 0],\n [-2, -2, -4, 0],\n [-2, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
164
MATH