messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-4, 3, -3, 0],\n [3, -1, -2, 1],\n [-3, -2, -2, -2],\n [0, 1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 957 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, -3, 2, -2],\n [-3, 1, -4, -2],\n [2, -4, -2, 2],\n [-2, -2, 2, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6413 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, -4, -2, 4],\n [1, 1, 3, 2],\n [0, 0, -4, 2],\n [2, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -131 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 2, 0, 0],\n [-1, -2, 3, 0],\n [-1, 2, -3, -2],\n [-1, 3, 4, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1919 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 1, 1, 0],\n [1, 2, 4, 0],\n [1, 4, -4, -1],\n [0, 0, -1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 326 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, -2, -2, -2],\n [-2, -3, -2, 0],\n [-2, -2, -4, 2],\n [-2, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -646 | 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, 0, -4],\n [-2, 2, -2, 4],\n [1, 4, -4, 0],\n [3, -1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 889 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -1, 2, 3],\n [-2, 3, 4, 0],\n [0, -1, 3, 0],\n [2, 1, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3016 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[4, 0, 0, 0],\n [0, -3, 2, -1],\n [0, 2, -3, -2],\n [0, -1, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 525 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 3, 0, -3],\n [3, 4, 4, 0],\n [0, 4, -4, -1],\n [-3, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1924 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 0, 1, 2],\n [0, -2, 0, 0],\n [1, 0, -4, -3],\n [2, 0, -3, 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^4 where A is:\n[[-1, 2, -2, 0],\n [2, -1, 0, -2],\n [-2, 0, 1, -1],\n [0, -2, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 3, 4, -1],\n [2, 1, -4, 0],\n [1, 4, 1, 3],\n [0, 0, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 654 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 3th power of the matrix:\n[[-2, 2, -2, -4],\n [4, 4, 0, -4],\n [-2, -2, 0, -4],\n [-3, 3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -88 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[3, 3, -3, 0],\n [0, 2, 4, 2],\n [-4, 2, 0, 4],\n [-2, 0, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 66 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, 2, 0, 2],\n [2, -2, 1, 0],\n [0, 1, 3, -2],\n [2, 0, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 488 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 3) of the result:\nA =\n[[-3, 4, 2, 0],\n [4, 3, 3, 0],\n [2, 3, -2, 0],\n [0, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 3, -4, -1],\n [2, -1, -1, -4],\n [3, 2, -3, 3],\n [3, 0, -2, 0]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -50 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[-2, 0, 0, 0],\n [0, -4, -1, -3],\n [0, -1, 4, 1],\n [0, -3, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -68 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, -4, 1, 0],\n [-4, 0, 2, 2],\n [1, 2, 4, -2],\n [0, 2, -2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1140 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, 1, -3, -2],\n [1, 2, -2, -2],\n [-3, -2, -4, 2],\n [-2, -2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -197 | MATH |
[
{
"content": "Find the value at position (2, 2) of the 3th power of the matrix:\n[[0, 2, 0, 0],\n [1, 3, -2, 1],\n [3, -4, 2, 2],\n [4, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[4, -2, 0, 0],\n [-2, -1, -2, 1],\n [0, -2, 4, -2],\n [0, 1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -196 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -4, -2, 2],\n [-4, -1, 2, 0],\n [-2, 2, -4, -3],\n [2, 0, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2942 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, -3, -1, -2],\n [3, -2, -4, -4],\n [0, 4, -2, 0],\n [1, 2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, -3, -3, -4],\n [-4, -3, 0, 4],\n [-1, -1, 4, -4],\n [0, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -227 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -4, 0, 3],\n [4, -3, 3, 3],\n [-3, -4, 0, -1],\n [3, 1, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2023 | 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, -4, -3],\n [-1, 2, 2, -3],\n [-1, -2, -3, -1],\n [1, 1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 417 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, 0, -2, 2],\n [0, 4, 0, 0],\n [-2, 0, 3, 1],\n [2, 0, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 146 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, -2, -1, -1],\n [1, -1, -3, 3],\n [-4, -2, -2, 1],\n [2, -2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 388 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 2, 0, 2],\n [2, -2, 2, -1],\n [0, 2, 4, 2],\n [2, -1, 2, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4173 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, -3, -1, 4],\n [-3, 4, -3, -1],\n [0, 3, 1, 3],\n [-2, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 0, 0, -2],\n [0, -3, 0, 2],\n [0, 0, 3, 2],\n [-2, 2, 2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, 4, 0, 2],\n [4, -1, -1, -1],\n [0, -1, 1, 0],\n [2, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 498 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, -4, 0, -3],\n [0, -2, 3, -4],\n [2, -3, 3, 2],\n [-3, -2, -1, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1991 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 2, -2, 1],\n [-2, -3, -2, -4],\n [0, -4, -4, -1],\n [2, -4, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1321 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, -2, 4, -2],\n [-4, -2, 1, 3],\n [4, -3, -4, -2],\n [2, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7700 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, 3, -2, -1],\n [-2, 1, 0, 1],\n [-3, -3, 3, -4],\n [2, 2, -4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -48 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -2, 4, 0],\n [-2, -3, 2, 0],\n [4, 2, -1, 2],\n [0, 0, 2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7791 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 4, -4, 2],\n [4, -2, 0, -2],\n [-4, 0, 4, 0],\n [2, -2, 0, 3]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2188 | MATH |
[
{
"content": "Find the value at position (3, 4) of the 4th power of the matrix:\n[[1, 0, 2, 2],\n [1, -3, -4, 3],\n [-3, -3, -4, 4],\n [-1, -3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1022 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, 1, 2, 0],\n [3, -4, 3, -3],\n [3, -1, 1, -3],\n [1, 3, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 412 | MATH |
[
{
"content": "What is the value at position (4, 1) of the matrix A^3 where A is:\n[[2, 4, -4, 2],\n [-3, -4, -1, 3],\n [3, 0, 2, 4],\n [0, -4, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | 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, -3, 0, 1],\n [-2, 0, 0, 2],\n [0, 1, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3829 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 4) of the result:\nA =\n[[-3, 2, -3, -4],\n [-4, -4, -3, 0],\n [2, 2, -1, 3],\n [0, 4, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 166 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-2, 2, -4, 4],\n [-2, 2, 3, 4],\n [-2, -4, -2, -4],\n [4, 3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -146 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, 0, 0, 0],\n [0, 3, -4, 2],\n [0, -4, 3, -1],\n [0, 2, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -43 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 1) of the result:\nA =\n[[-2, -2, -3, 3],\n [2, -2, -3, -1],\n [4, -4, -1, 2],\n [-2, 3, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 186 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, -2, 0, 0],\n [-2, 1, -2, -3],\n [0, -2, 4, -2],\n [0, -3, -2, -1]], determine the value at position (1, 1).\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 absolute values of all entries of the result:\nA =\n[[2, -3, -4, -3],\n [1, -3, -1, 3],\n [-2, 1, -1, -2],\n [1, -3, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[0, 4, 4, 3],\n [4, 1, -4, 3],\n [0, 3, 0, 4],\n [-2, -4, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 836 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, -1, 3, 2],\n [-2, 1, -1, 4],\n [0, 1, 4, 0],\n [-1, -3, -4, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 598 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, 4, -2, -3],\n [0, 2, 2, -2],\n [3, -1, 1, 2],\n [-2, 3, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1181 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, -1, 2, -3],\n [2, 3, -1, -1],\n [-3, 4, -1, 0],\n [-1, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4060 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[1, 3, 1, 2],\n [-4, -4, -2, 2],\n [-3, 0, 2, 1],\n [2, 1, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 4) of the result:\nA =\n[[3, 2, -2, -1],\n [2, -3, -1, -2],\n [-2, -1, -3, -2],\n [-1, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -36 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[0, 0, 4, 2],\n [2, 0, 2, 0],\n [-2, 2, -2, 4],\n [3, 3, 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 value at position (1, 4) of the result:\nA =\n[[0, 0, -2, 1],\n [-4, -3, 1, 3],\n [-4, -2, 3, 0],\n [1, 3, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -295 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, 1, -4, -4],\n [4, 2, 2, -2],\n [1, 0, 4, 2],\n [-2, 4, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 530 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, -2, -2, -2],\n [-2, -1, 2, -1],\n [-2, 2, 1, -1],\n [-2, -1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5560 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 3, -1, -4],\n [-1, 2, -4, 3],\n [-2, -2, -3, 4],\n [3, -1, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3733 | 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, 4, -2],\n [0, 1, 0, 0],\n [4, 0, 1, 3],\n [-2, 0, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5694 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, -3, -4, -1],\n [-1, -1, -4, -1],\n [3, 3, 0, 3],\n [-2, -4, 0, -1]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 4) of the result:\nA =\n[[-2, -2, -2, -1],\n [-2, 1, 2, -2],\n [-2, 2, 1, 0],\n [-1, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, 2, -2, 0],\n [2, -1, 0, -2],\n [-2, 0, 4, 0],\n [0, -2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 138 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -2, 2, -2],\n [-2, -1, -2, -2],\n [2, -2, 3, 4],\n [-2, -2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14471 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -3, 0, -3],\n [1, 3, -4, 2],\n [-2, -3, -2, 3],\n [0, -3, 3, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -227 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 3th power of the matrix:\n[[-4, -4, -2, 4],\n [-4, -1, 0, 1],\n [-2, 0, 2, 0],\n [4, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -96 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -4, 0, -2],\n [-4, 0, 1, 3],\n [0, 1, -1, 2],\n [-2, 3, 2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 280 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, -3, -3, 4],\n [4, 2, -1, 2],\n [-3, 2, -3, -4],\n [-1, -4, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1596 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 0, 1, -2],\n [0, 4, 2, 0],\n [1, 2, -1, 4],\n [-2, 0, 4, -1]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 426 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[0, -3, 3, -1],\n [4, -2, 2, 4],\n [-4, 3, 3, 0],\n [4, 2, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1108 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 3th power of the matrix:\n[[-2, -2, -4, -3],\n [-3, 0, 3, -3],\n [-3, -3, 1, 1],\n [-2, -3, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -59 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, 3, 0, 4],\n [3, -4, 3, -1],\n [0, 3, -4, 2],\n [4, -1, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, -3, 0, 4],\n [-4, 0, 4, -2],\n [2, 0, -2, -2],\n [3, 2, -4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1784 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 2, 0, -2],\n [2, 2, 0, 2],\n [0, 0, 0, 3],\n [-2, 2, 3, 0]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[3, 2, -4, -4],\n [-3, -4, -1, 3],\n [-1, -1, 4, -2],\n [-4, -4, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1193 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, -1, 0, 2],\n [-1, 2, 0, 3],\n [0, 0, 1, 2],\n [2, 3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 701 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 1, -2, -2],\n [-4, -1, -4, 2],\n [-3, -3, 0, 0],\n [-4, -4, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3444 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, -3, 4, -1],\n [-1, -4, -3, 1],\n [-4, -1, 1, -2],\n [4, -2, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4206 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 2, 0, 2],\n [2, -3, 2, 0],\n [0, 2, -4, 0],\n [2, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4306 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, -4, 2, 1],\n [-4, 1, 0, 2],\n [2, 0, 1, 2],\n [1, 2, 2, -2]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 113 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, -3, 2, -2],\n [2, -1, -1, -2],\n [0, -3, 2, 3],\n [-3, -4, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2850 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 3th power of the matrix:\n[[-1, 0, 3, 2],\n [3, 4, -1, -2],\n [3, -2, -2, -4],\n [-3, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -40 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, 1, 3, -2],\n [-1, -4, -3, -4],\n [1, 0, 3, -1],\n [-1, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[2, 2, -4, 3],\n [-4, 0, 4, -3],\n [4, 3, 0, -4],\n [0, 2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 2, 0, 3],\n [2, -1, 0, 2],\n [0, 0, -1, 0],\n [3, 2, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 387 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -4, -2, -1],\n [1, -4, 4, -2],\n [-4, -4, -4, 3],\n [3, 4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15437 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, -2, 4, 0],\n [-2, -4, 2, 2],\n [4, 2, -3, 1],\n [0, 2, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21784 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-2, 2, 4, 0],\n [-4, -4, 3, 4],\n [-1, -4, -4, 2],\n [-2, -3, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 947 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, -3, 4, 3],\n [-1, 1, 4, 0],\n [-4, 0, 1, 2],\n [0, 0, -2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -119 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, -4, -1, -4],\n [2, -4, 2, 3],\n [-1, 0, 1, -1],\n [-2, -4, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 441 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 4, -3, 4],\n [4, -1, 3, 0],\n [0, 0, -1, 2],\n [-4, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1436 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 0, -4, 1],\n [0, 2, -2, 2],\n [-4, -2, -3, 1],\n [1, 2, 1, 2]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -40 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, -2, -1, 0],\n [-2, 3, -1, -2],\n [-1, -1, -4, 0],\n [0, -2, 0, 1]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -37 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 4th power of the matrix:\n[[-1, -1, 0, 4],\n [-3, 4, 1, -4],\n [-4, -4, -1, 0],\n [0, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, -4, -3, 1],\n [-4, 2, -1, -1],\n [1, 4, 0, 1],\n [3, 3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -134 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, -3, 0, -2],\n [-3, 2, 1, 1],\n [0, 1, 0, 4],\n [-2, 1, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1034 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-2, 0, -4, -4],\n [1, 3, -1, 0],\n [-4, -4, 0, -1],\n [-2, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1270 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, -1, -2, 0],\n [-1, -1, 2, 0],\n [-2, 2, 2, 2],\n [0, 0, 2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 624 | MATH |
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