messages
listlengths 1
1
| ground_truth
stringlengths 1
5
| dataset
stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -1, 0, -3],\n [-1, 1, -1, 0],\n [0, -1, 4, 0],\n [-3, 0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2508
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 0, 1, 4],\n [0, 2, 2, 1],\n [1, 2, -3, 0],\n [4, 1, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5238
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 1, 0, -4],\n [1, -3, -2, 0],\n [0, -2, -3, 0],\n [-4, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1178
|
MATH
|
[
{
"content": "What is the value at position (1, 2) of the matrix A^3 where A is:\n[[-1, 3, 4, -1],\n [0, 3, 3, -2],\n [0, 3, 0, 3],\n [2, 2, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
85
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[0, 3, 2, 0],\n [-4, 4, -4, -3],\n [-1, 3, -4, 1],\n [0, -4, -1, 3]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-95
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, 3, 0],\n [0, -2, -1, -2],\n [3, -1, -1, -1],\n [0, -2, -1, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
342
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 2, 4, -3],\n [2, -2, 1, 0],\n [4, 1, -3, -2],\n [-3, 0, -2, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
11522
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[3, -2, -1, -4],\n [-2, -4, -3, -4],\n [-3, 1, 4, 2],\n [2, 4, -3, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3030
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[1, -2, 0, 0],\n [-2, -2, 2, -2],\n [0, 2, 4, 2],\n [0, -2, 2, 4]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
42
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -4, -2, -2],\n [1, 3, 1, 4],\n [1, -3, 4, 0],\n [-4, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3187
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[1, -2, 3, 1],\n [4, 0, -3, -3],\n [3, -4, 4, 0],\n [0, 0, 3, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1444
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, -2, 0, 0],\n [-2, 4, 0, 0],\n [0, 0, -3, 0],\n [0, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
460
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[2, -1, 0, 4],\n [-1, 1, 0, -4],\n [0, 0, 0, -2],\n [4, -4, -2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1653
|
MATH
|
[
{
"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[0, 0, 1, -1],\n [0, -2, 2, 2],\n [1, 2, 2, 2],\n [-1, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
176
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[1, 4, 1, -3],\n [3, 1, -3, 0],\n [2, -2, -2, -4],\n [1, -2, -1, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3908
|
MATH
|
[
{
"content": "What is the value at position (2, 2) of the matrix A^3 where A is:\n[[0, 0, 3, 0],\n [0, 2, 0, 1],\n [3, 0, -1, 3],\n [0, 1, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15
|
MATH
|
[
{
"content": "Find the value at position (3, 4) of the 4th power of the matrix:\n[[1, 0, 1, 4],\n [0, -1, -4, 2],\n [1, -4, 4, 1],\n [4, 2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-45
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[3, -1, -3, 3],\n [1, 3, 4, -3],\n [4, 0, -3, -2],\n [-2, -3, -4, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1130
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 4) of the result:\nA =\n[[-2, 0, 0, 0],\n [0, 0, 0, 2],\n [0, 0, -2, 2],\n [0, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
656
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 4) of the result:\nA =\n[[4, 0, 4, -1],\n [0, -3, -2, 4],\n [4, -2, -2, 0],\n [-1, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
733
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 4, 1, 1],\n [-3, 3, -2, -4],\n [2, 3, -4, 4],\n [-1, 0, -3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-56
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 4, 4, 4],\n [2, -1, 0, 0],\n [-2, 1, 3, -3],\n [2, -2, -4, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7903
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, 2, -3, 3],\n [2, 1, 2, 0],\n [-3, 2, -3, 1],\n [3, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
231
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[2, 4, -1, -3],\n [-4, 3, 4, 3],\n [-4, 0, 4, -4],\n [-3, -3, 2, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1512
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[2, 1, 4, -2],\n [1, 4, 0, -2],\n [4, 0, 1, 0],\n [-2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
513
|
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, 0, 3],\n [2, 1, 4, -3],\n [-3, -1, -1, 1],\n [1, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
727
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 1, 0, -2],\n [1, 4, 0, -2],\n [0, 0, -1, 0],\n [-2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
487
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[-4, -2, -3, -3],\n [-1, 4, -1, 0],\n [-1, -3, -3, -3],\n [3, 0, 3, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
126
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-4, -4, 3, 3],\n [3, -3, -2, 4],\n [4, 2, -4, 0],\n [-4, 0, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2540
|
MATH
|
[
{
"content": "Find the value at position (1, 4) of the 4th power of the matrix:\n[[4, -2, 1, 2],\n [-2, -3, 0, -2],\n [1, 0, -4, -1],\n [2, -2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
574
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, -3, 2, 1],\n [-1, 1, 0, -3],\n [3, 0, 3, 0],\n [-3, -3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-70
|
MATH
|
[
{
"content": "Find the value at position (3, 1) of the 4th power of the matrix:\n[[-1, 0, -2, -2],\n [0, 1, 0, -2],\n [-2, 0, -1, 0],\n [-2, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
80
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, -2, 4, 2],\n [-2, 0, 0, 1],\n [4, 0, 3, 0],\n [2, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9011
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 3, 0, 0],\n [2, -1, -4, 4],\n [-3, 3, 0, 0],\n [-2, 3, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1068
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -1, 0, 2],\n [-1, 4, 0, 0],\n [0, 0, 0, 0],\n [2, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2041
|
MATH
|
[
{
"content": "Find the value at position (1, 3) of the 4th power of the matrix:\n[[-2, -1, -4, 3],\n [1, 2, 3, 0],\n [4, -2, -3, 4],\n [2, 3, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-475
|
MATH
|
[
{
"content": "Find the value at position (1, 2) of the 3th power of the matrix:\n[[-4, 1, 1, 0],\n [1, -1, -2, -3],\n [1, -2, -2, -2],\n [0, -3, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
56
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[0, 2, 2, 0],\n [2, 4, 4, 3],\n [2, 4, 0, 0],\n [0, 3, 0, -4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
420
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -1, 0, -4],\n [-1, 1, -2, 4],\n [4, -3, 0, 3],\n [0, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4505
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, 4, -1, 3],\n [-3, -2, 1, 4],\n [1, 3, 3, 1],\n [-1, 2, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1121
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -1, 4, -2],\n [1, -4, 1, -1],\n [-3, 1, 0, 1],\n [-3, 1, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-190
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[1, -3, 2, 0],\n [-3, -1, -2, -3],\n [-1, 4, 2, -1],\n [-1, 2, -3, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
13
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[1, -1, -1, -4],\n [-1, 4, -2, -2],\n [-1, -2, -1, 2],\n [-4, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1327
|
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, 4],\n [-3, 3, -1, 2],\n [0, -1, 1, 2],\n [4, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
967
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[-2, 2, 2, 0],\n [2, -2, -3, -1],\n [2, -3, 3, 0],\n [0, -1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
111
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 1, 0, -2],\n [1, 2, -1, -2],\n [0, -1, 4, -3],\n [-2, -2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
582
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[1, 0, 4, -2],\n [0, -4, 0, -4],\n [3, -4, 0, -1],\n [1, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
65
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, 1, 0, -2],\n [1, -2, 2, 2],\n [0, 2, -4, 0],\n [-2, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3925
|
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, 0, 0],\n [2, 0, -3, 0],\n [-2, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
509
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, -2, -1, -2],\n [-2, -1, 2, 0],\n [-1, 2, 4, 0],\n [-2, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-12
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, 4, 2, 0],\n [4, 4, 2, -3],\n [2, 2, -1, 0],\n [0, -3, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
18196
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, -2, 0, 2],\n [-2, 2, -2, -2],\n [0, -2, -1, 0],\n [2, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
466
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 2, 0, -1],\n [2, -4, -2, 2],\n [0, -2, -4, -2],\n [-1, 2, -2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2081
|
MATH
|
[
{
"content": "Find the value at position (4, 2) of the 3th power of the matrix:\n[[-1, -2, 2, -2],\n [-2, -3, -4, 2],\n [2, -4, -2, -3],\n [-2, 2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-4, -2, -3, 1],\n [-2, 1, 4, -4],\n [-3, -1, 2, -3],\n [1, 1, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2082
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -3, -3, 0],\n [2, 2, -3, 2],\n [0, 0, 0, -2],\n [4, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-788
|
MATH
|
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 3, -1, 0],\n [-3, -4, -1, -3],\n [1, -3, 2, 3],\n [-4, 4, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
131
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[4, 0, 3, 0],\n [0, -1, 0, -1],\n [3, 0, -3, -4],\n [0, -1, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2450
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 0, -3, 2],\n [0, -4, -3, -3],\n [3, 3, 2, -1],\n [0, -4, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2403
|
MATH
|
[
{
"content": "What is the value at position (3, 2) of the matrix A^3 where A is:\n[[-3, 1, -1, 4],\n [3, -1, 2, 0],\n [4, -3, 2, 1],\n [4, -1, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-17
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 0, -3, 4],\n [3, 4, 4, 0],\n [-1, -3, 0, -2],\n [3, 0, -1, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
707
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[4, -1, 2, -2],\n [-1, -3, 1, 0],\n [2, 1, -4, 1],\n [-2, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
747
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, -4, 1, -1],\n [-3, 0, 0, -3],\n [-4, -1, -4, 3],\n [-4, 2, 4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1933
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, 3, 4, -3],\n [4, 0, 1, 0],\n [-2, 3, -1, 3],\n [-3, -4, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-997
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, -1, 4, -4],\n [0, -4, 4, -2],\n [-4, -1, 3, -1],\n [3, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
431
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[4, 0, 0, -2],\n [0, 1, -3, 0],\n [0, -3, 4, -2],\n [-2, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-107
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -2, 4, 0],\n [-3, 0, 1, 0],\n [3, 2, 4, 1],\n [-1, -3, 1, -4]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
196
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 0, 1, 0],\n [0, -2, -1, -2],\n [1, -1, -4, -2],\n [0, -2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3388
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -3, 1, 1],\n [-1, 4, 1, 4],\n [-1, 4, 3, 3],\n [0, -3, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4819
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[-1, -2, -3, 4],\n [-2, -4, 0, 0],\n [-1, -4, -4, 0],\n [1, 2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1614
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[4, 0, -4, -2],\n [3, -1, -2, -2],\n [3, 0, -2, 4],\n [-1, -1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-47
|
MATH
|
[
{
"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[-4, -2, 2, -2],\n [-2, 3, -2, -2],\n [2, -2, -2, -2],\n [-2, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
394
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[4, 2, -4, -4],\n [-1, 3, 4, 0],\n [-1, -3, -2, 1],\n [-1, -3, 1, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3091
|
MATH
|
[
{
"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[-4, -2, 4, -1],\n [-2, 1, 1, 4],\n [4, 1, -4, 1],\n [-1, 4, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-617
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[2, 0, -1, -1],\n [0, 1, 0, -1],\n [-1, 0, 3, -2],\n [-1, -1, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1408
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 1, -2, 0],\n [1, -3, 0, -2],\n [-2, 0, 0, 0],\n [0, -2, 0, 0]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-72
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 2, 0, 4],\n [2, -1, -2, -2],\n [0, -2, 1, 2],\n [4, -2, 2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
302
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-4, 0, 1, 3],\n [0, 4, 2, -4],\n [1, 2, -4, -1],\n [3, -4, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1608
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[4, -2, -2, -2],\n [-2, 2, 0, -2],\n [-2, 0, 2, 1],\n [-2, -2, 1, -3]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-534
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, -3, 1, 2],\n [-1, 1, 2, -3],\n [4, -2, -3, -2],\n [4, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
266
|
MATH
|
[
{
"content": "What is the value at position (4, 1) of the matrix A^3 where A is:\n[[1, 0, 0, 0],\n [0, -3, 2, 0],\n [0, 2, -4, 0],\n [0, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
0
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-1, -1, -2, 0],\n [-1, 2, 0, -2],\n [-2, 0, 0, -1],\n [0, -2, -1, -4]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
70
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[4, 3, -2, 2],\n [3, -3, -1, -4],\n [-2, -1, -3, -2],\n [2, -4, -2, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9098
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -2, -2, -3],\n [-2, 2, 0, 3],\n [-2, 0, 4, 2],\n [-3, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1621
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[3, -1, 2, -2],\n [-1, -4, -4, 3],\n [2, -4, 1, -2],\n [-2, 3, -2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-267
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[0, -4, 2, 1],\n [-4, -2, -2, -2],\n [2, -2, -3, -1],\n [1, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-72
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, 0, -1, -2],\n [0, -1, 2, 2],\n [-1, 2, 3, -2],\n [-2, 2, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-48
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, -3, -2, 2],\n [0, 0, 3, 1],\n [2, 1, 4, -1],\n [0, 1, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 4) of the result:\nA =\n[[-3, 0, 2, 2],\n [0, 4, -2, -2],\n [2, -2, 1, 2],\n [2, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1018
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[4, -2, 0, -2],\n [0, -1, 2, 0],\n [0, -3, -3, -3],\n [-4, -3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-1011
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -3, 0, -4],\n [-3, -2, 2, -1],\n [0, 2, 4, -4],\n [-4, -1, -4, -3]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1005
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 3, 2, -4],\n [-3, 2, 3, -3],\n [-1, 3, 2, 2],\n [2, -4, -4, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2336
|
MATH
|
[
{
"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[0, 0, -1, 4],\n [0, 3, -4, 0],\n [-1, -4, -4, 0],\n [4, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
280
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[0, 0, -4, -1],\n [3, 1, -3, -4],\n [0, 3, -4, 4],\n [0, -4, 0, -2]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
92
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, 2, 0, 0],\n [2, 3, 0, -2],\n [0, 0, -4, -2],\n [0, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-81
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[1, 0, 3, -2],\n [2, -4, 2, -2],\n [-1, -4, -4, 1],\n [-2, 1, -4, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-219
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[1, -2, 1, 2],\n [-2, -2, -1, -3],\n [3, 1, -4, 1],\n [3, -3, -2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-174
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, -2, 0, -3],\n [-2, -4, -2, -2],\n [0, -2, 3, 0],\n [-3, -2, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3762
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-3, -4, -4, 0],\n [-4, 4, -2, 0],\n [-4, -2, 0, 2],\n [0, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1851
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-4, -3, 2, -4],\n [-4, -3, -2, -3],\n [-4, 4, -3, 4],\n [0, -3, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-1557
|
MATH
|
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