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[[4, 3, -3, -2],\n [-1, 0, 4, -3],\n [3, 4, -4, -1],\n [-3, -3, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
598
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, -2, 0, 2],\n [-2, -2, 4, -2],\n [0, 4, -1, 0],\n [2, -2, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
435
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[0, 1, 0, 2],\n [1, 4, -2, 1],\n [0, -2, -3, -2],\n [2, 1, -2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
101
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[-3, -1, 3, 1],\n [3, 0, 0, -2],\n [-2, -1, 2, -2],\n [3, 1, 3, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
35
|
MATH
|
[
{
"content": "Find the value at position (3, 1) of the 3th power of the matrix:\n[[-3, 1, -1, -4],\n [-3, -4, -1, 2],\n [-4, -1, 3, 2],\n [-3, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-130
|
MATH
|
[
{
"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[1, 0, -4, 4],\n [-2, 0, 2, 3],\n [-3, 1, 2, 4],\n [-2, -3, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
284
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 2, -1, 0],\n [2, -1, -2, 0],\n [-1, -2, -2, 1],\n [0, 0, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
289
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 3, -1, 1],\n [-4, -2, 1, -4],\n [-3, -1, 1, -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"
}
] |
502
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, 2, -2, -2],\n [2, 4, 2, -2],\n [-2, 2, 1, 0],\n [-2, -2, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
225
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, 3, 0, -2],\n [1, 4, -4, -2],\n [1, 1, -1, -4],\n [-3, -1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-233
|
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 [0, -1, -2, 4],\n [1, 2, 0, 2],\n [-3, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
288
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 0, -1, 0],\n [0, 4, -1, -4],\n [-1, -1, 1, -2],\n [0, -4, -2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-171
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, 2, 4, -4],\n [1, 0, -2, -2],\n [0, 0, 0, -4],\n [2, -4, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4260
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, -2, 2, 0],\n [-2, 4, 0, -2],\n [2, 0, 0, 1],\n [0, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-128
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 3) of the result:\nA =\n[[0, -1, -2, -1],\n [-1, 1, -1, 1],\n [-2, -1, 1, -2],\n [-1, 1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-29
|
MATH
|
[
{
"content": "What is the value at position (4, 1) of the matrix A^4 where A is:\n[[-3, 0, -1, 1],\n [1, 3, 3, 2],\n [-2, -1, -1, -1],\n [1, 1, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-82
|
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 [-3, -2, 3, -3],\n [0, 3, 4, 0],\n [4, 2, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
354
|
MATH
|
[
{
"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[4, -3, 2, -3],\n [-3, 0, 3, 2],\n [1, 2, 1, 2],\n [1, -4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
243
|
MATH
|
[
{
"content": "What is the value at position (4, 1) of the matrix A^4 where A is:\n[[0, -3, -3, 1],\n [-3, 4, 0, -1],\n [-1, 1, 2, 4],\n [0, -1, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-15
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-2, 4, 4, -1],\n [-3, 4, 0, -4],\n [2, 1, -2, -2],\n [4, 3, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-770
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 1, -4, -1],\n [3, 4, 0, -4],\n [-3, -2, -2, -4],\n [3, -3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
7083
|
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, -2, 0],\n [0, 0, 0, 0],\n [-2, 0, 0, -4],\n [0, 0, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4805
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -1, -2, -2],\n [-1, 2, -3, -4],\n [-3, 3, -4, 0],\n [4, 3, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
4873
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 3) of the result:\nA =\n[[3, 2, 0, -2],\n [2, 0, 0, 0],\n [0, 0, -4, -2],\n [-2, 0, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, -3, 0, 0],\n [-3, 1, -2, -2],\n [0, -2, -3, 1],\n [0, -2, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3033
|
MATH
|
[
{
"content": "What is the value at position (4, 1) of the matrix A^3 where A is:\n[[3, 0, -3, -2],\n [0, 2, -2, 0],\n [-3, -2, -2, -2],\n [-2, 0, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-48
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[3, 0, 1, -3],\n [0, -4, 2, 0],\n [1, 2, 4, -2],\n [-3, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
87
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[4, -3, -4, -2],\n [-3, 4, -2, 1],\n [-4, -2, 4, -2],\n [-2, 1, -2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1005
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[3, -1, 1, 1],\n [-1, -2, 0, 0],\n [1, 0, 1, 0],\n [1, 0, 0, 0]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-10
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-4, -4, -3, -4],\n [-4, 2, -2, 0],\n [3, 4, 0, 4],\n [4, 2, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
982
|
MATH
|
[
{
"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[-2, -3, 2, 4],\n [1, -4, 3, -4],\n [3, 4, 1, -1],\n [-4, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
556
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[2, 0, -3, 0],\n [0, 0, 2, 2],\n [-3, 2, -3, 3],\n [0, 2, 3, 0]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, 1, -1, -2],\n [1, -4, 0, -1],\n [-1, 0, 3, 0],\n [-2, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-124
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[1, 4, -2, 1],\n [4, 2, -2, 2],\n [-2, -2, 0, 2],\n [1, 2, 2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
3104
|
MATH
|
[
{
"content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[-4, 0, -3, -2],\n [0, 2, -2, 1],\n [4, -4, -1, 1],\n [1, -4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-428
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 0, -3, -2],\n [1, 1, 2, -3],\n [-2, -4, 3, 2],\n [4, -2, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5588
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[4, -1, -3, -3],\n [3, -2, 4, -4],\n [-4, 0, 0, -3],\n [-2, 3, -3, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
818
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[0, 0, 0, -2],\n [0, -2, -1, 2],\n [0, -1, -2, 0],\n [-2, 2, 0, -1]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-20
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 1, 3, -2],\n [-2, -4, -4, -4],\n [-1, 1, 0, -3],\n [2, -3, 2, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5157
|
MATH
|
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -3, 0, 1],\n [-3, -4, -2, 3],\n [-2, -4, 3, 0],\n [1, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2197
|
MATH
|
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, -1, -4, -4],\n [4, -4, -4, -3],\n [-1, -1, -4, 4],\n [4, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5545
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 2, 4, 2],\n [2, 4, 0, 0],\n [4, 0, 1, 2],\n [2, 0, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
6021
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, -2, -3, 3],\n [-2, -2, 3, 2],\n [-3, 3, -2, 1],\n [3, 2, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-71
|
MATH
|
[
{
"content": "What is the value at position (2, 1) of the matrix A^4 where A is:\n[[3, -3, -4, -4],\n [-3, -2, -1, -3],\n [1, -2, -4, 2],\n [-2, 4, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-137
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-1, 0, -4, 1],\n [0, -4, -2, -2],\n [-4, -2, 1, -2],\n [1, -2, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1145
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 2, -4, -3],\n [2, 2, 0, -2],\n [-4, 0, -2, -2],\n [-3, -2, -2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2666
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 0, -2, 0],\n [0, 1, -2, 2],\n [-2, -2, 0, 2],\n [0, 2, 2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
24
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[-3, -2, -2, 2],\n [-1, -4, 4, -1],\n [-1, 2, 1, 4],\n [-1, -4, 4, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2109
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, -3, 4, 0],\n [-3, -2, -3, 0],\n [4, -3, -1, 0],\n [0, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-128
|
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, -1, 2],\n [2, 4, -1, 0],\n [-1, -1, 3, -1],\n [2, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
842
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -2, -4, 2],\n [-2, 0, -2, 2],\n [-4, -2, -1, 2],\n [2, 2, 2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
15454
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, 0, 2, -2],\n [0, 0, 2, 1],\n [2, 2, -4, 0],\n [-2, 1, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-64
|
MATH
|
[
{
"content": "Find the value at position (2, 3) of the 4th power of the matrix:\n[[1, 1, 0, 0],\n [-3, 4, 1, -4],\n [4, 0, 2, 0],\n [0, -4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1387
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, -4, 2, 1],\n [-1, -4, -3, 4],\n [1, 1, -4, -4],\n [-4, 4, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-173
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[-3, 0, 2, -2],\n [4, 0, 0, -1],\n [3, 3, -3, -1],\n [1, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
203
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[0, 0, -1, 1],\n [0, 3, 1, 0],\n [-1, 1, -2, -2],\n [1, 0, -2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1837
|
MATH
|
[
{
"content": "What is the value at position (4, 1) of the matrix A^3 where A is:\n[[3, -1, -2, -1],\n [-1, -4, 2, 0],\n [-2, 2, -4, 0],\n [-1, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-25
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 3, 0, 0],\n [2, -1, 1, -4],\n [-3, -4, 1, 3],\n [3, -4, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1032
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-4, -1, 0, 0],\n [-1, 2, 0, 2],\n [0, 0, -1, 1],\n [0, 2, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[3, 1, 0, -2],\n [1, 3, 2, -2],\n [0, 2, -1, 0],\n [-2, -2, 0, -3]], determine the sum of all entries.\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^4 where A is:\n[[-1, -2, 1, 0],\n [-2, -3, -1, -2],\n [1, -1, 1, -1],\n [0, -2, -1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1817
|
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, -4, -2],\n [-2, 3, -4, 1],\n [0, 0, 4, 1],\n [3, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
568
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, -1, 2, -2],\n [-1, 0, 3, 1],\n [2, -4, -1, -1],\n [-4, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
29
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 0, -2, -2],\n [2, 1, -2, 3],\n [-2, -1, -3, -1],\n [-4, 0, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2091
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[3, 0, 2, 1],\n [0, 2, -2, 1],\n [2, -2, -2, 0],\n [1, 1, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
348
|
MATH
|
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, 3, 3, 4],\n [-3, -4, 2, 1],\n [-3, 4, 3, 0],\n [-4, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-5036
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, 0, 0, -2],\n [0, 4, 2, 4],\n [0, 2, 4, -4],\n [-2, 4, -4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
32
|
MATH
|
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, -1, 0, -1],\n [4, 0, 1, -2],\n [-1, -2, 0, 0],\n [-2, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
170
|
MATH
|
[
{
"content": "Find the value at position (1, 2) of the 4th power of the matrix:\n[[-1, 0, -2, 0],\n [0, -3, -1, 3],\n [-2, -1, -2, 0],\n [0, 3, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
78
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[3, -4, 0, 4],\n [-4, 1, -3, 0],\n [0, -3, -1, -2],\n [4, 0, -2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-45
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, 2, 2],\n [0, 2, -2, 0],\n [2, -2, 1, -2],\n [2, 0, -2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-15
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, -1, -1, -1],\n [1, -4, -4, 4],\n [-3, 3, 2, 2],\n [-3, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1100
|
MATH
|
[
{
"content": "Find the value at position (3, 4) of the 3th power of the matrix:\n[[1, -1, 0, 4],\n [-1, 4, -1, -2],\n [0, -1, 0, 0],\n [4, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[-4, -1, -1, 2],\n [-1, -2, -2, 0],\n [-1, -2, -1, 0],\n [2, 0, 0, 3]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
301
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 1, 3, 2],\n [0, 1, 1, 2],\n [-4, 1, 4, 3],\n [-3, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-3696
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[-2, -1, -2, 0],\n [-1, 1, -4, -1],\n [-2, -4, -2, 1],\n [0, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
317
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 3) of the result:\nA =\n[[-1, -2, 3, 0],\n [-2, -4, -1, -1],\n [1, 2, -2, -1],\n [-2, -2, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
19
|
MATH
|
[
{
"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[-3, -2, 3, 0],\n [-2, -3, 1, 1],\n [3, 1, 0, 3],\n [0, 1, 3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-367
|
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, -1, 2],\n [2, -2, -2, 0],\n [-1, -2, 4, 4],\n [2, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
9954
|
MATH
|
[
{
"content": "What is the value at position (1, 1) of the matrix A^3 where A is:\n[[1, 4, 2, 4],\n [-4, -4, -3, -4],\n [2, 4, -3, 3],\n [1, 3, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-81
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, 1, -3, 1],\n [1, -2, -4, -1],\n [0, -3, 1, 2],\n [-3, 1, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
1748
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 1) of the result:\nA =\n[[3, 2, 0, -2],\n [2, -1, 0, -1],\n [0, 0, -1, -1],\n [-2, -1, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-52
|
MATH
|
[
{
"content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[-3, -2, 0, -1],\n [-2, -2, 0, 0],\n [0, 0, -3, 0],\n [-1, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
76
|
MATH
|
[
{
"content": "What is the value at position (2, 1) of the matrix A^4 where A is:\n[[-3, -1, -2, -2],\n [-1, 2, -2, 0],\n [-2, -2, -3, 2],\n [-2, 0, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
159
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[1, -4, -1, 0],\n [-4, 1, 0, 2],\n [-1, 0, 2, 0],\n [0, 2, 0, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
402
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, 3, 2, 2],\n [3, -1, 0, 2],\n [2, 0, -1, -3],\n [2, 2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5057
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[3, 1, 2, 1],\n [4, 0, -3, 2],\n [-2, -2, -2, 3],\n [-4, 2, -3, 3]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
37
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[3, 0, -2, -1],\n [0, 1, 2, -2],\n [-2, 2, 3, -2],\n [-1, -2, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2043
|
MATH
|
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-4, -1, 2, 3],\n [3, 0, 0, -2],\n [-1, -4, 0, -2],\n [0, 4, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
216
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[4, 0, 3, 0],\n [0, -2, -3, 1],\n [3, -3, -3, -2],\n [0, 1, -2, 4]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
20
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, -2, -4, 0],\n [-2, -4, 2, 2],\n [-4, 2, 1, -1],\n [0, 2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
2152
|
MATH
|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[0, 2, -4, -1],\n [-4, 4, -2, 4],\n [-3, -3, -1, -2],\n [-2, 0, 1, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
994
|
MATH
|
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 1) of the result:\nA =\n[[-2, -1, -2, -2],\n [4, 1, 0, 0],\n [-4, -3, -2, -1],\n [-2, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
12
|
MATH
|
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[2, 0, 1, 1],\n [0, -3, 2, 0],\n [1, 2, 4, 0],\n [1, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
261
|
MATH
|
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[1, 2, -3, -3],\n [2, -3, -3, 0],\n [3, 1, 2, -2],\n [1, -3, 4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
369
|
MATH
|
[
{
"content": "For the matrix power A^4 where A =\n[[1, 0, -1, -4],\n [1, -1, -1, 1],\n [-3, 4, 1, 4],\n [-1, 0, -3, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
764
|
MATH
|
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -2, -2, 0],\n [-2, 0, -2, 2],\n [-2, -2, 4, 2],\n [0, 2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
5920
|
MATH
|
[
{
"content": "For the matrix power A^3 where A =\n[[3, 2, -2, 3],\n [2, -1, 1, -2],\n [1, 3, 0, -2],\n [0, 4, 3, 0]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
8
|
MATH
|
[
{
"content": "Find the value at position (4, 3) of the 3th power of the matrix:\n[[3, -2, 0, 2],\n [-2, 3, 0, 2],\n [0, 0, -4, 1],\n [2, 2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
30
|
MATH
|
[
{
"content": "Find the value at position (4, 3) of the 4th power of the matrix:\n[[-2, -3, 2, 3],\n [-2, -3, -2, -3],\n [-2, 2, 3, 1],\n [-1, 0, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] |
-20
|
MATH
|
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