messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 5) of the result:\nA =\n[[-5, 0, 3, -1, 2],\n [0, -5, 0, -4, -2],\n [3, 0, -1, 0, -2],\n [-1, -4, 0, 3, -2],\n [2, -2, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22418 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, -2, 3, 0, -5],\n [-3, 5, -4, 3, -5],\n [3, 3, 2, 2, 5],\n [-5, 5, 2, 4, -3],\n [5, 1, 5, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -174166 | MATH |
[
{
"content": "Find the value at position (1, 4) of the 4th power of the matrix:\n[[4, 0, -1, -2, -2],\n [0, 0, -2, -4, 0],\n [-1, -2, 0, 0, 0],\n [-2, -4, 0, 5, -1],\n [-2, 0, 0, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1346 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -1, 3, -2, 2],\n [-1, 2, 0, 0, -1],\n [3, 0, -3, -4, 1],\n [-2, 0, -4, 5, -4],\n [2, -1, 1, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1314 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-2, 1, -3, 4, -3],\n [2, 2, 5, -5, 4],\n [-4, 2, -5, 2, 2],\n [-4, -2, 0, 5, 3],\n [2, 2, 1, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 168576 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 4, 0, 2, 2],\n [4, 4, -2, 4, 4],\n [0, -2, 2, -3, -4],\n [2, 4, -3, -3, 2],\n [2, 4, -4, 2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30098 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 1, -2, 1, 1],\n [-5, 0, 3, -4, -3],\n [4, -1, 3, -2, -5],\n [-2, 0, -1, -5, -2],\n [0, 4, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -532 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 1, 4, 3, 2],\n [1, -5, 0, 1, 0],\n [4, 0, -1, -3, -1],\n [3, 1, -3, 2, -4],\n [2, 0, -1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20265 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^5 where A is:\n[[1, 5, -1, 4, -1],\n [1, -1, 2, 5, 0],\n [-1, 3, 5, -4, -5],\n [2, -3, 5, 1, 4],\n [5, 2, 0, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20967 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 4, -1, 2, -4],\n [1, -2, 3, -5, 1],\n [0, 2, -1, -5, -5],\n [3, 4, 0, 4, -1],\n [-5, 0, 0, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 97445 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, -5, 0, 4, -5],\n [0, -5, 0, -3, 2],\n [0, 5, -5, -1, 2],\n [-3, 0, -1, 0, 4],\n [-5, 1, 3, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154214 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, 4, 0, -2, -1],\n [4, -4, -2, -4, -4],\n [0, -2, 1, -3, 4],\n [-2, -4, -3, -3, 0],\n [-1, -4, 4, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 304923 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, 1, 5, -4, -5],\n [-3, -2, 0, 4, -1],\n [-2, 2, 5, -2, 4],\n [-4, -3, 0, 2, 2],\n [5, 3, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 67399 | MATH |
[
{
"content": "What is the value at position (3, 5) of the matrix A^5 where A is:\n[[1, 2, -3, 1, 4],\n [3, -3, 4, 0, -4],\n [-4, -1, -1, 1, -4],\n [5, 1, -1, 0, 2],\n [4, -2, 1, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11286 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[-4, 3, 0, 0, -1],\n [3, -2, 2, 0, 2],\n [0, 2, 5, 0, -2],\n [0, 0, 0, 3, -2],\n [-1, 2, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, -5, -2, 0, 1],\n [5, 5, 4, -3, 3],\n [1, -5, -4, -5, 5],\n [3, 3, 1, 4, -3],\n [-1, -2, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 159018 | MATH |
[
{
"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[2, 4, 1, 4, 2],\n [4, 1, 0, 1, -4],\n [1, 0, 4, -2, 0],\n [4, 1, -2, 0, 2],\n [2, -4, 0, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -604 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 0, 5, 5, -5],\n [-3, -4, -3, -1, 5],\n [4, 0, 3, 5, 4],\n [-2, 1, 0, -4, 4],\n [5, 5, 5, 2, 1]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -285 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^5 where A is:\n[[1, 2, 5, -5, -5],\n [2, -2, -1, 2, -1],\n [4, -2, 0, -1, 1],\n [4, 1, -2, -1, -3],\n [-2, -2, -3, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -228 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-1, 4, -2, 0, -1],\n [4, 0, -2, -4, -1],\n [-2, -2, 0, 2, -2],\n [0, -4, 2, 0, -2],\n [-1, -1, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3413 | MATH |
[
{
"content": "Find the value at position (5, 3) of the 5th power of the matrix:\n[[1, -3, -3, 0, 0],\n [-2, 3, -2, 3, -2],\n [-4, -4, -1, -2, 1],\n [5, -1, 0, 4, -2],\n [-4, 4, 3, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1992 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-2, -2, 1, -4, -1],\n [-2, -3, 2, -2, 5],\n [1, 2, -4, -2, 2],\n [-4, -2, -2, 5, 0],\n [-1, 5, 2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 174515 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, 4, -4, -5, -5],\n [5, -5, -1, 4, 1],\n [-4, 4, 2, -2, -3],\n [4, 5, 2, -4, 5],\n [5, -3, -3, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4012 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, 0, -4, -5, -4],\n [0, -2, 0, 3, 4],\n [4, 2, -5, 2, 3],\n [0, 4, -1, 0, 0],\n [3, -2, -4, 5, 5]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6907 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^5 where A is:\n[[3, -4, 4, 3, -4],\n [2, 3, 4, 3, 4],\n [3, -4, -2, 1, -4],\n [-5, -3, -2, 2, 0],\n [5, -4, 3, -4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14799 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[-2, 0, 1, 0, 1],\n [0, -4, 2, -3, 1],\n [1, 2, 0, 0, -3],\n [0, -3, 0, 3, -2],\n [1, 1, -3, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1517 | MATH |
[
{
"content": "Find the value at position (5, 3) of the 4th power of the matrix:\n[[1, 2, 0, 0, 0],\n [2, 2, -1, -2, 1],\n [0, -1, 1, -3, 4],\n [0, -2, -3, 5, 2],\n [0, 1, 4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1648 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[-1, -3, -5, -3, 0],\n [1, 2, 5, -2, -3],\n [-1, 3, 0, 3, 0],\n [-4, -1, 5, 3, 2],\n [1, -5, -2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6297 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 0, 2, 5, 0],\n [4, -3, -2, -3, -5],\n [4, -1, -5, -5, -4],\n [-2, 0, 2, -3, -5],\n [-3, -3, -1, 5, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15417 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, 2, 2, 2, 0],\n [2, -3, 0, 1, 4],\n [2, 0, -2, 0, -2],\n [2, 1, 0, -2, 3],\n [0, 4, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2520 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, 3, -2, 2, -3],\n [1, -3, 1, 5, 4],\n [4, 5, 5, 0, -4],\n [5, -3, 0, -2, 0],\n [-5, 4, -5, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 392107 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 3, 1, 0, 1],\n [3, 5, 0, -2, 2],\n [1, 0, 5, 0, 1],\n [0, -2, 0, 3, 0],\n [1, 2, 1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18603 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 5, -4, 0, 0],\n [5, 0, 4, -1, -1],\n [-4, 4, 3, 0, 0],\n [0, -1, 0, -2, 0],\n [0, -1, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 183358 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 0, 4, 0, 1],\n [0, -2, 4, -2, 1],\n [4, 4, 1, 2, -4],\n [0, -2, 2, 4, 2],\n [1, 1, -4, 2, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27563 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, -5, -5, -1, -4],\n [-2, -5, -2, 5, 0],\n [4, -2, -5, 1, -4],\n [3, -3, 2, 2, -3],\n [-2, -4, -2, 5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -43778 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, 4, 0, 1, 2],\n [4, -2, 0, -4, 1],\n [0, 0, 3, -2, -2],\n [1, -4, -2, -4, 4],\n [2, 1, -2, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30972 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 4, 0, 0, 2],\n [2, 0, -3, -1, -4],\n [-1, 3, 4, -5, 4],\n [-1, 0, 5, 1, 3],\n [0, -1, 1, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20085 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, -4, -2, 1, -1],\n [0, -4, -3, 1, 5],\n [-4, 0, -1, 4, -5],\n [5, 4, 5, -2, 5],\n [-4, -2, -5, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9018 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[0, -4, 0, 4, 3],\n [1, 3, -1, 1, 5],\n [1, -3, 1, -5, 3],\n [4, 0, -1, 1, -1],\n [4, -1, 5, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2029 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 4, 1, 5, -3],\n [-3, 4, -3, 0, 0],\n [-3, -3, 2, 2, 1],\n [4, -2, -2, -3, -1],\n [-3, 2, 1, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14233 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-1, 3, 1, 1, 0],\n [-4, 3, 0, 2, -5],\n [-1, -5, 4, 5, 2],\n [2, -5, 3, -4, 3],\n [-5, 4, 3, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22909 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, 4, 2, 0, 0],\n [4, -4, 1, -3, 1],\n [2, 1, 2, 0, 4],\n [0, -3, 0, -2, 2],\n [0, 1, 4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8541 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 1, -1, 3, -2],\n [0, -4, -4, -4, 4],\n [1, -4, -4, 3, 1],\n [5, -3, -3, 1, -1],\n [4, 0, 2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38804 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 4, 3, -2, -1],\n [4, 0, -4, -2, 2],\n [3, -4, -3, 4, -1],\n [-2, -2, 4, -3, -2],\n [-1, 2, -1, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 645 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[0, -3, 2, 1, 1],\n [0, -1, 4, 2, -1],\n [3, 3, -5, 0, 1],\n [-3, 1, 5, 5, 1],\n [5, -4, 1, -5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 348 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 1, 1, 5, -4],\n [2, -3, 2, -3, 4],\n [1, -4, -2, 5, 0],\n [5, 3, -1, 3, -1],\n [4, 2, -5, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 138489 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (2, 5) of the result:\nA =\n[[-1, 0, -1, -5, 3],\n [-4, 3, 4, -4, 3],\n [0, 5, 3, 0, 0],\n [5, -4, 2, -3, 1],\n [-1, -3, -5, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3245 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-4, -5, -3, 0, -4],\n [-5, -2, 3, -1, 4],\n [-3, 3, -4, -2, -1],\n [0, -1, -2, -3, -1],\n [-4, 4, -1, -1, -4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -36873 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, 0, 0, -3, 0],\n [0, -1, 2, -2, 2],\n [0, 2, 4, 3, 3],\n [-3, -2, 3, -2, 3],\n [0, 2, 3, 3, 4]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5553 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -5, -3, 3, -2],\n [-1, 1, -1, -2, -4],\n [-4, -2, 4, 4, 3],\n [2, -3, 3, -1, 5],\n [-3, -1, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31986 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 4, 2, 3, -2],\n [1, -4, 0, 2, 1],\n [1, 2, 1, -1, 1],\n [4, -3, -1, 1, 3],\n [-4, -2, 1, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4834 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 2, 3, 2, 0],\n [2, -3, 2, 1, 0],\n [3, 2, -2, -2, -1],\n [2, 1, -2, 2, 0],\n [0, 0, -1, 0, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29895 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, -3, 0, -2, 1],\n [-3, -5, 3, 0, 2],\n [-3, 2, -4, -2, -3],\n [4, -5, 1, 5, 4],\n [-4, -2, 3, 0, 2]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 774 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, -2, -2, 4, 3],\n [-2, 2, 1, 2, 0],\n [-2, 1, 5, 0, -3],\n [4, 2, 0, 2, 0],\n [3, 0, -3, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20657 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 2, 0, -5, 2],\n [2, 0, -1, 1, 5],\n [0, -1, 2, 0, 5],\n [-5, 1, 0, 1, 2],\n [2, 5, 5, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 249673 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, 0, -2, -2, 0],\n [0, -5, -3, 0, -2],\n [-2, -3, -2, -4, 4],\n [-2, 0, -4, -4, -2],\n [0, -2, 4, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 357270 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[1, 2, -4, 2, 0],\n [2, 2, 0, -2, -2],\n [-4, 0, -4, 0, -2],\n [2, -2, 0, 0, -2],\n [0, -2, -2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -114 | 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, -2, -1, -1],\n [0, -3, -1, -4, 4],\n [-5, 5, -5, 4, 1],\n [-4, -2, -1, 1, -4],\n [0, -5, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12193 | MATH |
[
{
"content": "What is the value at position (1, 5) of the matrix A^4 where A is:\n[[-1, 0, -4, 2, 2],\n [0, 3, 1, 2, -1],\n [-4, 1, 5, -3, -2],\n [2, 2, -3, 1, 0],\n [2, -1, -2, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 94 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, -5, 2, -2, -2],\n [-4, 5, 5, 5, -5],\n [4, 3, 1, -2, 0],\n [-4, 1, -4, 4, 2],\n [2, -5, 2, -4, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 573870 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (3, 3) of the result:\nA =\n[[-5, -1, 5, 1, 4],\n [-5, -4, 1, 0, -3],\n [4, -4, 4, -2, -3],\n [1, 2, -4, 4, 1],\n [2, 0, 0, 4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16878 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[-2, -5, -2, -4, 5],\n [-1, 4, 3, 5, 4],\n [-3, 2, -3, 0, -2],\n [2, 5, 0, 2, -5],\n [0, -5, -5, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2827 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 0, 4, 2, 0],\n [0, 5, -3, -4, 2],\n [4, -3, -5, -2, -1],\n [2, -4, -2, 1, 2],\n [0, 2, -1, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -46233 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (5, 5) of the result:\nA =\n[[-3, 3, -4, -3, -4],\n [-5, -2, -1, 0, -1],\n [-5, -3, -5, 5, -1],\n [-1, 5, 0, 2, 4],\n [-5, -2, 4, 5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16775 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 3, -2, 0, 0],\n [3, -4, 1, 0, -2],\n [-2, 1, -4, -1, 2],\n [0, 0, -1, -2, -2],\n [0, -2, 2, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1890 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 2, -4, -2, 0],\n [2, 1, 3, 2, -2],\n [-4, 3, 5, 4, 2],\n [-2, 2, 4, -5, -1],\n [0, -2, 2, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 250728 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 4th power of the matrix:\n[[1, -4, -5, 3, 3],\n [1, 1, -3, 4, -4],\n [5, 1, 3, -5, -2],\n [0, 1, 4, 1, 4],\n [-4, -2, -1, -5, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -372 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -3, 4, -3, 2],\n [3, 5, -5, 5, -4],\n [4, -4, -2, -4, 1],\n [3, 1, 0, 4, -5],\n [5, 4, 3, -1, 5]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1780 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, 1, 3, 0, 2],\n [1, -5, -4, -2, 2],\n [3, -4, 3, -2, 4],\n [0, -2, -2, -1, -2],\n [2, 2, 4, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 244019 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (3, 5) of the result:\nA =\n[[-4, -2, -2, 4, -1],\n [-2, 4, 0, -2, 0],\n [-2, 0, -5, 0, -2],\n [4, -2, 0, 2, 3],\n [-1, 0, -2, 3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14470 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -2, 4, 3, 4],\n [4, -5, -4, -1, -3],\n [-4, -5, 4, -3, -5],\n [-5, -5, 2, -3, 5],\n [-5, 1, 4, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16974 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, -2, -1, 0, 1],\n [-2, 2, 0, -5, -5],\n [3, 4, 0, 4, 2],\n [1, 0, -2, 1, 3],\n [5, 4, 4, 1, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35818 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, 0, 1, -2, 0],\n [0, 4, 0, -3, -2],\n [1, 0, 2, -1, 2],\n [-2, -3, -1, -4, 0],\n [0, -2, 2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37372 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -2, 5, -3, 1],\n [2, -4, -2, -3, -4],\n [0, -2, 0, -4, -2],\n [5, 0, -1, -3, 2],\n [1, -3, 0, -2, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11376 | MATH |
[
{
"content": "What is the value at position (5, 4) of the matrix A^5 where A is:\n[[-1, 5, -1, 1, 5],\n [-1, 5, -3, 4, -1],\n [1, -1, -1, 3, -3],\n [0, -5, 4, -1, 2],\n [-1, 3, 5, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -114 | 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, -3, 1, 1],\n [4, 0, 1, -4, 3],\n [4, 4, -5, -5, -3],\n [-3, -5, 1, -2, 4],\n [-4, 4, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15713 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, -4, -1, -3, -4],\n [-5, 4, -4, 0, 2],\n [-3, 5, 3, 3, -4],\n [2, 4, 5, -1, -2],\n [4, -1, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20716 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, 0, -4, -1, 0],\n [-1, -4, 1, -2, 2],\n [1, 1, 3, -5, 4],\n [0, 0, 0, 0, 4],\n [1, 4, 0, -5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33388 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 0, 2, -3, 4],\n [2, 2, -1, 2, 0],\n [-1, 3, 1, 2, -5],\n [5, -4, 2, 3, -2],\n [4, 5, 4, 3, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6082 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 4, 4, 3, 5],\n [1, -4, 3, -2, 2],\n [1, 1, 2, -5, -1],\n [-4, -4, -5, -1, -4],\n [-2, -3, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21384 | 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, 3, 1, 2],\n [2, -2, 0, 2, -4],\n [3, 0, -2, 0, 3],\n [1, 2, 0, -3, -2],\n [2, -4, 3, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20328 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[0, -1, 3, -1, 2],\n [-1, 2, -2, 4, -2],\n [3, -2, -3, 0, 2],\n [-1, 4, 0, 4, -2],\n [2, -2, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24467 | MATH |
[
{
"content": "What is the value at position (4, 4) of the matrix A^5 where A is:\n[[-1, 1, 4, 0, 0],\n [1, 2, 4, 2, -2],\n [4, 4, -2, 2, -1],\n [0, 2, 2, 1, 1],\n [0, -2, -1, 1, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1918 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-2, 5, 4, -1, 1],\n [-1, -5, 5, 1, 2],\n [1, 5, -2, 2, -1],\n [4, 3, 4, -1, -5],\n [3, -1, 0, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6623 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, -3, -1, -4, -4],\n [1, 4, 4, 5, 4],\n [0, -2, -1, -5, 1],\n [2, 3, 2, -1, -3],\n [4, 5, 3, 0, -1]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 295 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 0, -3, 4, 0],\n [-2, -4, 2, -2, 3],\n [1, -4, -2, -1, -3],\n [3, -1, -4, 5, -3],\n [3, 1, -4, 3, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8851 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, -4, 4, -2, -1],\n [-4, 4, -5, 1, 4],\n [-5, 5, 5, 2, -3],\n [4, 0, 1, 4, -5],\n [0, 1, 0, -2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 343132 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, 3, -2, 1, 1],\n [-4, -5, 2, 2, 1],\n [2, -3, 5, -4, 1],\n [2, -5, 4, 3, 5],\n [-2, -2, -3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3724 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -4, 3, -4, 1],\n [-5, 1, -1, 2, -2],\n [4, 1, 0, -1, -2],\n [1, -1, -1, -5, -4],\n [-1, -3, -4, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15245 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, -2, -3, 1, 3],\n [-1, -2, 5, -4, -4],\n [-1, 1, 4, 4, 3],\n [1, -1, 4, 4, 4],\n [0, 5, -3, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4157 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-5, -5, 2, -2, -3],\n [-5, 3, -4, -2, 4],\n [2, -4, 2, -2, 0],\n [-2, -2, -2, -5, 0],\n [-3, 4, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28915 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 0, 3, -5, 1],\n [4, 5, -1, 2, 1],\n [-2, -2, 0, 0, 3],\n [-1, 2, -1, -4, 0],\n [3, -3, -5, -5, -3]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 464 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, -2, -2, 2, 2],\n [-2, 3, -2, 0, 0],\n [-2, -2, -1, 0, -2],\n [2, 0, 0, -1, -4],\n [2, 0, -2, -4, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -27210 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-3, 2, 1, 0, 4],\n [4, 5, -2, 3, -5],\n [5, -4, -2, -3, -5],\n [-1, 1, -4, -1, 0],\n [5, 1, -5, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 827886 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -2, 1, 0, -2],\n [-2, 2, 1, -3, -1],\n [1, 1, -4, 0, -1],\n [0, -3, 0, 2, 0],\n [-2, -1, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4717 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -2, 2, 0, -4],\n [-2, -5, 2, 0, -4],\n [2, 2, 5, -2, 1],\n [0, 0, -2, 5, 0],\n [-4, -4, 1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 473817 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, -2, -4, 0, 5],\n [3, 5, 3, 2, -3],\n [-3, -4, -1, -2, 1],\n [-2, 3, -4, 5, 0],\n [1, -2, 0, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109113 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 3, -5, 1, 3],\n [4, -1, -4, 4, 0],\n [1, -4, -4, 4, 4],\n [-5, -2, 1, 3, -3],\n [5, 1, 1, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178780 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -4, -2, 0, -4],\n [-4, 0, -4, -2, -3],\n [-2, -4, 0, -2, 4],\n [0, -2, -2, 1, 2],\n [-4, -3, 4, 2, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24735 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-5, -2, 0, -3, -1],\n [4, 3, 5, -3, -1],\n [2, 0, -2, 2, 5],\n [-3, -3, -2, 3, -1],\n [2, 0, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5655 | MATH |
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