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[ { "content": "Find the value at position (5, 1) of the 5th power of the matrix:\n[[-5, 0, -3, -5, -2],\n [0, 3, 4, 4, -1],\n [-3, 4, 3, -5, -2],\n [-5, 4, -5, -1, 2],\n [-2, -1, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-17060
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, 4, -3, -5, -3],\n [5, -4, -4, 3, 2],\n [-5, -2, -5, -5, -2],\n [-4, -3, 5, 3, -4],\n [-2, -5, -4, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
329217
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-5, 4, 2, -2, 2],\n [4, 0, 0, 0, 2],\n [2, 0, 0, -2, 4],\n [-2, 0, -2, 4, 0],\n [2, 2, 4, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3534
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 4, 1, -2, 5],\n [-2, 1, 3, 5, -2],\n [-2, 0, 0, 1, -5],\n [5, -3, 3, 0, 0],\n [-1, 5, -3, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2806
MATH
[ { "content": "Find the value at position (4, 2) of the 5th power of the matrix:\n[[-5, 0, 1, -3, 0],\n [0, -2, -2, 1, -2],\n [1, -2, 1, 4, 1],\n [-3, 1, 4, -1, -2],\n [0, -2, 1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3735
MATH
[ { "content": "For the matrix power A^5 where A =\n[[5, 5, -1, 4, -1],\n [5, 4, 0, -4, 1],\n [-1, 0, -2, -2, -2],\n [4, -4, -2, 2, -2],\n [-1, 1, -2, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
135753
MATH
[ { "content": "For the matrix power A^5 where A =\n[[5, -3, 4, -4, 0],\n [-3, 5, -2, -5, 5],\n [4, -2, 5, -2, 0],\n [-4, -5, -2, 0, 2],\n [0, 5, 0, 2, -2]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2570
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 0, -2, -2, 4],\n [0, 1, 2, 2, 2],\n [-2, 2, -3, -2, -2],\n [-2, 2, -2, -3, -4],\n [4, 2, -2, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-54404
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -4, -1, 2, -2],\n [-4, -3, 0, 4, 0],\n [-1, 0, -5, -4, 1],\n [2, 4, -4, -3, -4],\n [-2, 0, 1, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
51596
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 4, -2, -5, -4],\n [5, -5, 0, -3, 1],\n [-1, 3, 1, -2, -1],\n [-1, 5, -1, 4, 3],\n [4, -3, 0, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
161384
MATH
[ { "content": "For the matrix power A^5 where A =\n[[3, 1, -3, -5, -2],\n [0, -3, -5, 0, -5],\n [3, 5, -5, 0, -5],\n [1, -3, 0, 1, -5],\n [-5, -1, 0, 3, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2203
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 4, 2, 4, 3],\n [-3, 5, -4, -2, -4],\n [-5, -3, 1, -5, -4],\n [-5, 2, -1, 2, -3],\n [1, 2, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7270
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, -1, 1, -5, -1],\n [-5, 2, -2, -2, -4],\n [-1, -5, 3, -1, 0],\n [-4, 4, 4, -5, -2],\n [1, 0, 4, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26701
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 1, -3, 2, -1],\n [1, 1, 0, 0, 0],\n [-3, 0, 3, 0, -4],\n [2, 0, 0, -3, -2],\n [-1, 0, -4, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9293
MATH
[ { "content": "Find the value at position (1, 2) of the 5th power of the matrix:\n[[2, 0, -2, 0, -2],\n [0, 3, 0, 4, -4],\n [-2, 0, -2, 2, 1],\n [0, 4, 2, 3, 0],\n [-2, -4, 1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5192
MATH
[ { "content": "Find the value at position (4, 3) of the 5th power of the matrix:\n[[4, -1, -4, -1, -1],\n [-1, -2, 0, 0, -2],\n [-4, 0, 2, 0, 3],\n [-1, 0, 0, -5, 4],\n [-1, -2, 3, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-4389
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-1, 2, -4, -2, 5],\n [2, 2, 0, 2, -1],\n [-4, 0, -2, -2, -2],\n [-2, 2, -2, 5, 1],\n [5, -1, -2, 1, -1]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2732
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 3, 3, 3, 5],\n [-5, 3, 2, -4, 5],\n [-5, -5, 0, 3, 1],\n [-1, 5, -4, -5, -4],\n [-5, -3, 0, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48385
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, 3, 4, -1, 1],\n [2, -3, -4, -4, -1],\n [-5, -4, 3, 1, 0],\n [3, 1, 5, -1, 3],\n [0, 0, 5, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48316
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, 2, 3, 2, 0],\n [2, 3, -2, -4, -5],\n [3, -2, -4, -1, 2],\n [2, -4, -1, 1, 0],\n [0, -5, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
191086
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-1, -1, 2, -2, 0],\n [-1, 5, -2, 2, 0],\n [2, -2, 1, 0, -2],\n [-2, 2, 0, -2, -2],\n [0, 0, -2, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-13471
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-1, 5, 2, 2, 2],\n [5, -5, 0, -2, -2],\n [2, 0, 1, -2, 0],\n [2, -2, -2, 3, -2],\n [2, -2, 0, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-62548
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-1, 2, 5, -4, 2],\n [-2, 4, 4, -5, -1],\n [-5, 1, 2, -3, -3],\n [1, -2, -3, 2, -3],\n [1, -4, 5, 5, -5]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3651
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 0, -1, 0, 4],\n [0, -3, 2, 2, -2],\n [-1, 2, -3, 0, 0],\n [0, 2, 0, -1, -2],\n [4, -2, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1590
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 0, 0, -3, 0],\n [0, -1, 1, -2, 2],\n [0, 1, 5, -2, 0],\n [-3, -2, -2, -3, -2],\n [0, 2, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-24111
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 5, -5, 1, -3],\n [5, 2, 0, -2, 5],\n [2, 3, 4, -4, 0],\n [-1, -1, 4, 5, -3],\n [2, 2, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4970
MATH
[ { "content": "For the matrix power A^4 where A =\n[[2, -3, -4, 3, -4],\n [3, -2, -4, 4, -5],\n [-2, 3, 3, -2, 3],\n [0, -5, 4, 0, 3],\n [-4, 0, -4, -2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-1625
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 0, 2, 2, -3],\n [0, 0, 0, -3, 2],\n [2, 0, 0, -2, -2],\n [2, -3, -2, 4, 0],\n [-3, 2, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-3981
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, 2, -2, 3, 2],\n [1, 1, -3, 0, -1],\n [-5, 5, -3, -5, -2],\n [4, -3, 5, -2, 3],\n [-3, 0, 0, 1, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5585
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, 0, 0, -2, 1],\n [0, -1, 2, -4, 5],\n [0, 2, 3, -2, -4],\n [-2, -4, -2, 3, -2],\n [1, 5, -4, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
25189
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, 3, -4, -1, -2],\n [3, 1, 0, -1, -1],\n [-4, 0, 5, 0, -4],\n [-1, -1, 0, -2, -2],\n [-2, -1, -4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5024
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -5, 3, -3, 4],\n [-3, 5, -4, 2, -3],\n [0, -4, 1, -2, 3],\n [4, 3, 1, 2, -3],\n [5, -1, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
45187
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, 3, 5, 5, 1],\n [4, 4, 2, 3, 0],\n [4, -4, -4, -2, 3],\n [1, -4, 2, 5, 1],\n [3, 2, -3, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
118984
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -2, 2, -2, 3],\n [-2, 0, -2, 4, 5],\n [2, -2, 2, -4, 0],\n [-2, 4, -4, -1, -4],\n [3, 5, 0, -4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3141
MATH
[ { "content": "For the matrix power A^5 where A =\n[[0, -3, 1, 0, 3],\n [-1, -2, -3, 4, -5],\n [-3, -3, 1, 1, -5],\n [-3, 2, 3, 1, 1],\n [5, 2, 0, 5, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
142487
MATH
[ { "content": "Find the value at position (4, 3) of the 4th power of the matrix:\n[[-5, 2, -5, -4, 0],\n [2, 1, 3, -4, 2],\n [-5, 3, 0, -2, 0],\n [-4, -4, -2, -3, -2],\n [0, 2, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2614
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-2, -2, -1, 1, 2],\n [0, -5, 1, -3, 0],\n [2, 1, 4, 0, 3],\n [3, -5, -5, -5, 2],\n [4, 1, -3, -4, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-72836
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -1, 4, 2, -2],\n [-1, 0, -2, 0, 4],\n [4, -2, -2, 0, -2],\n [2, 0, 0, 1, 4],\n [-2, 4, -2, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1283
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-1, -1, 4, 4, 1],\n [-1, -5, 4, 4, 0],\n [4, 4, 0, 0, 0],\n [4, 4, 0, -2, 4],\n [1, 0, 0, 4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
12450
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-1, 0, -2, -4, 2],\n [0, -4, 0, 0, 0],\n [-2, 0, -4, 2, 2],\n [-4, 0, 2, -5, 3],\n [2, 0, 2, 3, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-51382
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-2, -4, 2, 5, -4],\n [3, -2, -5, -2, -3],\n [0, 1, 2, -4, 0],\n [0, 4, -1, 4, 4],\n [1, -3, -2, 4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1599
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 0, -4, -2, 2],\n [0, 1, 2, 0, -2],\n [-4, 2, 3, 2, -3],\n [-2, 0, 2, 0, 0],\n [2, -2, -3, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
970
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 0, 0, -4, 1],\n [0, -5, 0, 2, 0],\n [0, 0, 3, 2, -2],\n [-4, 2, 2, -2, 0],\n [1, 0, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
15972
MATH
[ { "content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[-2, 0, 0, -2, -2],\n [0, 3, -4, 5, 1],\n [0, -4, -2, 0, 2],\n [-2, 5, 0, -5, 2],\n [-2, 1, 2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2252
MATH
[ { "content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 4, 4, 2, 0],\n [4, -5, 0, 0, -1],\n [4, 0, -3, -4, 2],\n [2, 0, -4, 0, 2],\n [0, -1, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
4282
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-3, 2, 4, -1, -2],\n [2, 4, 1, 4, -1],\n [4, 1, 1, 1, 0],\n [-1, 4, 1, -4, 2],\n [-2, -1, 0, 2, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
30509
MATH
[ { "content": "Find the value at position (3, 3) of the 4th power of the matrix:\n[[4, -4, 2, 2, 1],\n [-4, 1, 0, -1, 2],\n [2, 0, 1, 1, 1],\n [2, -1, 1, -2, 0],\n [1, 2, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
276
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 3, -4, 0, -1],\n [-1, -2, 0, -1, 5],\n [-2, 3, 0, 5, 4],\n [4, 4, -3, 4, 0],\n [-5, -1, 4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21086
MATH
[ { "content": "For the matrix power A^5 where A =\n[[2, 0, 0, 2, -3],\n [0, -2, 0, 2, -1],\n [0, 0, -3, 4, 0],\n [2, 2, 4, 5, -3],\n [-3, -1, 0, -3, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
367049
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-5, 1, 0, 1, -3],\n [-3, 5, -5, -2, -4],\n [4, 2, -3, 1, 1],\n [3, 0, -5, 2, -5],\n [-3, 5, -1, 2, 3]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
749
MATH
[ { "content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[1, 4, 0, -4, 0],\n [4, 2, 0, 0, 2],\n [0, 0, 4, -2, -2],\n [-4, 0, -2, 4, -2],\n [0, 2, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1953
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, 5, -3, -5, -4],\n [-1, 4, -1, 4, -5],\n [-5, 3, -4, 1, 4],\n [-2, 1, 2, -1, -5],\n [-2, 4, -3, 4, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
13459
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (5, 4) of the result:\nA =\n[[4, 4, 0, -4, 1],\n [-3, -5, 4, -3, 3],\n [4, 5, 5, 0, 5],\n [0, -2, 2, -1, 1],\n [3, -1, 5, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -4, -2, -4, 0],\n [-4, 2, 0, -4, -1],\n [-2, 0, -1, -2, -2],\n [-4, -4, -2, 1, -4],\n [0, -1, -2, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31496
MATH
[ { "content": "For the matrix power A^5 where A =\n[[2, -2, 0, 2, 4],\n [-2, -1, 3, 3, 2],\n [0, 3, 1, -2, 2],\n [2, 3, -2, 0, 4],\n [4, 2, 2, 4, -2]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8296
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, -4, 0, 0, 0],\n [-4, -4, 2, 4, -2],\n [0, 2, 0, 0, -2],\n [0, 4, 0, -1, 3],\n [0, -2, -2, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26144
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-1, 4, -3, 2, 0],\n [-4, -4, 3, 1, 4],\n [3, 0, -1, -5, 0],\n [0, -3, -3, -3, -3],\n [1, 4, 5, -4, 4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-334
MATH
[ { "content": "For the matrix power A^4 where A =\n[[4, -4, 1, 3, 0],\n [-4, 1, 0, 4, 3],\n [1, 0, 1, 1, 0],\n [3, 4, 1, -1, -2],\n [0, 3, 0, -2, 2]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2252
MATH
[ { "content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 0, -1, -1, 4],\n [-4, -2, 2, 2, 5],\n [-5, -4, -1, 3, 4],\n [5, 5, 1, 4, -1],\n [-5, 0, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
61622
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-1, 5, -2, 3, 4],\n [-5, 0, -3, 5, 3],\n [-1, 0, 5, 3, 3],\n [2, 3, -2, 0, -1],\n [-1, -2, -4, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
28525
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 0, -2, -3, -2],\n [0, 3, 0, -1, -4],\n [-2, 0, 5, 4, 2],\n [-3, -1, 4, -3, -4],\n [-2, -4, 2, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
407992
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, -3, 1, 0, 2],\n [-3, -3, -2, -3, 3],\n [5, -2, 0, 2, 5],\n [2, -1, -1, 0, 4],\n [1, 4, 1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-7328
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[1, 0, -2, -1, 0],\n [0, 5, -2, 2, 0],\n [-2, -2, 5, 4, -1],\n [-1, 2, 4, -3, 2],\n [0, 0, -1, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
294
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-2, -2, 0, 5, 1],\n [-2, 0, 4, -2, 3],\n [0, 4, 2, 1, -4],\n [5, -2, 1, -1, 2],\n [1, 3, -4, 2, -5]], determine the value at position (5, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
21542
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 1, 2, -5, -3],\n [1, 3, 2, 2, 3],\n [4, -3, 2, -5, 2],\n [1, 2, -5, 0, 1],\n [5, -1, -1, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
14344
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 0, 1, -5, -4],\n [-2, 2, 5, 4, 0],\n [-5, 4, -1, 1, 0],\n [3, 2, -2, 5, -1],\n [1, 2, -1, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22933
MATH
[ { "content": "Find the value at position (1, 2) of the 5th power of the matrix:\n[[-2, -2, 2, -5, 2],\n [-1, 5, -5, -2, -4],\n [-2, 2, -1, -5, 1],\n [-5, 3, -3, -3, 0],\n [4, 0, 5, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3036
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (1, 4) of the result:\nA =\n[[-5, -1, 0, 2, -5],\n [-1, -3, -4, 5, 2],\n [1, 4, 1, -1, 3],\n [-1, -4, -3, -2, -1],\n [-3, 1, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-123
MATH
[ { "content": "For the matrix power A^4 where A =\n[[1, 4, 4, 2, 3],\n [5, -2, -1, -1, 2],\n [3, 1, -1, -3, -5],\n [5, 3, -1, 3, 4],\n [-2, -1, -2, -4, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
16799
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -2, -1, 0, 2],\n [5, 2, 1, -2, 0],\n [-2, 1, 5, -5, -1],\n [4, 4, -2, 5, 1],\n [3, -1, -2, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
723
MATH
[ { "content": "What is the value at position (5, 3) of the matrix A^4 where A is:\n[[3, 2, -2, 2, 2],\n [2, -1, 4, -3, 2],\n [-2, 4, 3, 0, 0],\n [2, -3, 0, -4, -2],\n [2, 2, 0, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, -2, 4, -4, -3],\n [-3, 3, -2, -5, -5],\n [1, 1, -4, 3, 3],\n [-1, -3, -3, -3, 0],\n [-2, 2, 5, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-10400
MATH
[ { "content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -5, 2, 0, -1],\n [-5, -3, 4, 1, 4],\n [2, 4, 2, 2, 0],\n [0, 1, 2, 3, 2],\n [-1, 4, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
326312
MATH
[ { "content": "What is the value at position (4, 1) of the matrix A^5 where A is:\n[[-5, -4, 4, -3, 2],\n [0, 4, 5, -1, -5],\n [5, 3, -3, -3, -4],\n [-2, -4, 3, 4, 1],\n [2, -3, 0, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-25959
MATH
[ { "content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-5, -2, 1, 4, -1],\n [-2, 4, 4, 0, 0],\n [1, 4, -1, -3, 4],\n [4, 0, -3, 2, -1],\n [-1, 0, 4, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2968
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-3, 1, -4, 0, 4],\n [1, -2, -1, 2, 0],\n [-4, -1, -3, -1, -2],\n [0, 2, -1, -3, 2],\n [4, 0, -2, 2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-26031
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -3, 4, 4, -2],\n [1, -4, -3, 1, 1],\n [4, -3, -5, -3, -1],\n [1, -2, 5, 5, -5],\n [0, -4, -3, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
26584
MATH
[ { "content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[0, -2, 2, -1, -4],\n [-2, 4, 3, -2, 0],\n [2, 3, 0, -2, 4],\n [-1, -2, -2, -2, -2],\n [-4, 0, 4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
597
MATH
[ { "content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, -2, -2, -2, 4],\n [-2, 5, 3, 0, -3],\n [-2, 3, -1, -1, 0],\n [-2, 0, -1, -5, 0],\n [4, -3, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
35627
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, -4, 1, 2, 0],\n [-4, 2, 2, 4, 4],\n [1, 2, 4, 2, -2],\n [2, 4, 2, -4, 0],\n [0, 4, -2, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
32351
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -3, 3, -2, -2],\n [-3, -1, -3, 3, -3],\n [-4, -1, 0, -5, 5],\n [0, 4, -3, -2, 0],\n [2, 3, 0, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-344
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, -2, 0, 2, 0],\n [-2, -5, -1, 0, 3],\n [0, -1, 1, 2, 1],\n [2, 0, 2, -1, 4],\n [0, 3, 1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
3886
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, 4, -1, -3, 2],\n [1, -1, 4, -3, -1],\n [-3, 4, -1, -5, 0],\n [4, -2, -2, 2, -4],\n [-2, -4, -5, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-12278
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 1, 2, 0, -1],\n [1, 2, 0, -2, 0],\n [2, 0, -4, -2, -1],\n [0, -2, -2, -2, 0],\n [-1, 0, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2326
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 0, 2, 2, 1],\n [0, 0, 4, 5, 0],\n [2, -5, -1, -3, 2],\n [5, 0, -4, 1, 1],\n [-1, 2, -1, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-11023
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-2, -3, -3, -1, -1],\n [-3, -4, 1, -2, 3],\n [-3, 1, -1, 2, 0],\n [-1, -2, 2, -5, 1],\n [-1, 3, 0, 1, -3]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
426
MATH
[ { "content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 2, 1, 2, 4],\n [2, 0, 3, 0, 4],\n [1, 3, -4, 1, 0],\n [2, 0, 1, 4, 0],\n [4, 4, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
417721
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, -4, 1, 2],\n [-2, 0, 0, 0, 0],\n [-4, 0, 5, 2, 1],\n [1, 0, 2, 2, -1],\n [2, 0, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
134300
MATH
[ { "content": "What is the sum of all entries of the matrix A^5 where A is:\n[[5, 2, -3, -2, -4],\n [2, 2, 0, 2, 0],\n [-3, 0, 1, 2, 2],\n [-2, 2, 2, -5, 4],\n [-4, 0, 2, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5766
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[3, 4, 2, 2, -2],\n [4, 1, -1, 0, 2],\n [2, -1, 1, -3, -2],\n [2, 0, -3, 2, -1],\n [-2, 2, -2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
31951
MATH
[ { "content": "For the matrix power A^4 where A =\n[[3, -3, 0, 1, 2],\n [1, -3, 0, -1, 4],\n [-2, -5, 1, 2, -4],\n [1, 0, -1, -2, -4],\n [4, 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" } ]
14237
MATH
[ { "content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 2, 2, 4, 2],\n [2, -1, 3, 2, -4],\n [2, 3, 1, -2, -2],\n [4, 2, -2, -2, -1],\n [2, -4, -2, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7911
MATH
[ { "content": "What is the value at position (2, 4) of the matrix A^5 where A is:\n[[0, 1, 2, 5, 3],\n [3, 2, 4, 5, -3],\n [-4, -1, -5, -3, -5],\n [-3, -2, 1, -1, -1],\n [-5, 2, -2, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8416
MATH
[ { "content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-4, -5, 4, -1, -2],\n [-5, -5, 1, -4, 4],\n [4, 1, 1, -1, 0],\n [-1, -4, -1, -3, 0],\n [-2, 4, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-32001
MATH
[ { "content": "For the matrix power A^4 where A =\n[[-5, -3, -1, 1, -4],\n [-3, -3, 2, 0, -2],\n [-1, 2, 5, 2, 0],\n [1, 0, 2, 1, 2],\n [-4, -2, 0, 2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
22440
MATH
[ { "content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[-3, 3, -2, 4, -4],\n [0, -5, 0, 4, -5],\n [2, -1, 0, -4, -4],\n [3, -3, 0, 4, -1],\n [-2, 4, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-555
MATH
[ { "content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 5, -4, 0, 2],\n [1, -5, -1, -4, 0],\n [1, 1, -3, 1, -1],\n [2, 2, 1, 0, -4],\n [0, 5, 3, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
54517
MATH
[ { "content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, -1, 5, 0, -3],\n [2, 1, -4, 1, -5],\n [3, 1, 0, -4, -3],\n [-5, 4, -1, 3, 0],\n [-1, -3, -1, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
7080
MATH
[ { "content": "For the matrix power A^5 where A =\n[[-1, 0, 2, 1, 1],\n [0, 3, -1, 0, 0],\n [2, -1, -2, -2, 2],\n [1, 0, -2, 4, -2],\n [1, 0, 2, -2, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-2314
MATH
[ { "content": "For the matrix power A^4 where A =\n[[0, 0, 0, -2, 0],\n [0, -3, 0, 3, 4],\n [0, 0, 2, -2, 0],\n [-2, 3, -2, 0, 4],\n [0, 4, 0, 4, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
5234
MATH