messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "For the matrix power A^4 where A =\n[[5, -3, 2, -2, -4],\n [5, -1, -5, 2, 2],\n [-3, -5, -2, 3, 3],\n [-5, 5, 1, 0, 1],\n [1, 2, 2, 4, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37618 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-4, -2, -2, 5, 4],\n [2, -3, -3, -4, -5],\n [2, 3, 3, 5, 2],\n [-1, -5, 3, 0, 1],\n [2, -1, 0, 1, 1]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4627 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 5, -5, 2, -1],\n [4, -4, -3, 0, 4],\n [0, 2, -1, -1, 1],\n [4, -1, 3, 0, 1],\n [2, -1, 5, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21850 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 3, -5, -3, -2],\n [1, 0, 4, 4, 5],\n [-5, -2, 0, -3, -4],\n [-4, 4, -2, -5, 4],\n [-4, 4, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -363504 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 2, 2, 1, 1],\n [2, 4, -2, 5, 0],\n [2, -2, 1, 4, 0],\n [1, 5, 4, -4, -1],\n [1, 0, 0, -1, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22761 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 0, 0, -2, 0],\n [0, 4, 0, 4, 2],\n [0, 0, -5, 4, 0],\n [-2, 4, 4, -3, 2],\n [0, 2, 0, 2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5666 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, -5, 5, -4, 2],\n [1, -1, 4, -4, 3],\n [-1, 2, -2, 3, 4],\n [1, -4, -3, -4, -1],\n [-4, -1, 3, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69231 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 1, -1, 2, 1],\n [0, -4, 0, -4, -5],\n [3, -1, 4, 4, -2],\n [5, 2, -1, 1, -3],\n [2, 2, -3, 3, 2]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -403 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^4 where A is:\n[[-5, 2, 5, -2, 0],\n [4, 3, -1, 1, -5],\n [3, 0, 5, -2, 0],\n [-1, -3, 1, -3, -4],\n [-2, 1, -1, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2544 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[1, 3, 3, -4, -5],\n [5, -2, -2, -4, -3],\n [-3, -1, -5, 3, 2],\n [2, -3, -4, -5, 0],\n [4, -5, 5, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 145508 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[5, 2, 0, 0, 0],\n [2, -2, 0, 2, 2],\n [0, 0, 4, -1, -1],\n [0, 2, -1, -5, 4],\n [0, 2, -1, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3221 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, 0, 2, -2, 0],\n [5, -3, 1, -4, 2],\n [1, 2, -4, -3, -2],\n [3, -1, 0, -5, -2],\n [-2, 4, 2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42209 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -2, 2, -2, -5],\n [-2, -4, -3, 2, 0],\n [2, -3, -2, 0, 2],\n [-2, 2, 0, -3, 0],\n [-5, 0, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8157 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[-5, 0, -1, -3, 5],\n [5, 5, 3, -3, -4],\n [-1, 3, 2, 0, -3],\n [0, -1, -5, -1, 1],\n [3, -5, -3, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4018 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^5 where A is:\n[[-1, 0, -1, 1, -3],\n [0, 1, -4, 1, 0],\n [-1, -4, -1, 0, 4],\n [1, 1, 0, 2, 0],\n [-3, 0, 4, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4557 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 3, 3, -1, -2],\n [-2, 3, 2, 4, 4],\n [1, -3, -2, 3, 2],\n [-5, -3, 4, -4, -4],\n [2, 0, 0, -2, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31854 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[5, -2, 0, -2, -4],\n [-2, -2, 2, -2, -2],\n [0, 2, 1, 0, 0],\n [-2, -2, 0, -5, 0],\n [-4, -2, 0, 0, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 123173 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -2, 0, 0, 0],\n [-2, -1, 4, -2, 1],\n [0, 4, 4, -2, -1],\n [0, -2, -2, -2, -2],\n [0, 1, -1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2758 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 0, -2, -5, -5],\n [-1, -1, 4, 1, -2],\n [3, -2, 1, -1, -1],\n [0, 2, -1, -3, 0],\n [-4, 2, 2, -3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7184 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, -2, -1, 1, 0],\n [-2, -1, -4, 4, 4],\n [-1, -4, -5, -2, -2],\n [1, 4, -2, 4, 0],\n [0, 4, -2, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 401 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 5, -4, 0, 4],\n [5, -1, 2, -2, 1],\n [-4, 2, -5, -4, 0],\n [0, -2, -4, 0, 2],\n [4, 1, 0, 2, 4]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -632 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[0, -4, 2, 0, -2],\n [-2, 5, 1, -3, 5],\n [-3, 0, 3, -5, -1],\n [-5, -5, -3, -3, -2],\n [-3, 0, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122700 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[2, 5, -5, 5, -5],\n [1, -5, 3, 2, -5],\n [-4, -4, -4, 0, -2],\n [2, -5, 4, -2, 4],\n [5, -1, 3, -1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4256 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 0, 0, 0, -2],\n [0, 5, 0, -1, 0],\n [0, 0, -5, 2, 1],\n [0, -1, 2, 5, -2],\n [-2, 0, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8869 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (4, 2) of the result:\nA =\n[[-1, 2, 1, -4, 0],\n [2, -2, 2, 0, -2],\n [1, 2, -3, 0, -1],\n [-4, 0, 0, -4, -3],\n [0, -2, -1, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1774 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[4, -5, 0, -3, 1],\n [2, -1, -1, -4, 2],\n [4, -5, 4, 3, -5],\n [-5, -5, 1, -2, 1],\n [-1, 1, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1705 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, 2, -4, 3, -1],\n [3, 3, 2, 2, -2],\n [-2, -4, -2, -2, 0],\n [-3, -4, 2, -4, 2],\n [1, -3, 0, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31405 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-1, 1, 4, 0, 0],\n [1, 5, 1, 0, -2],\n [4, 1, 4, -4, -4],\n [0, 0, -4, 0, 0],\n [0, -2, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37616 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, 2, 0, -2, 2],\n [2, -1, 4, -2, 0],\n [0, 4, -2, 4, -2],\n [-2, -2, 4, -3, 1],\n [2, 0, -2, 1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1237 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, -2, 4, 1, 2],\n [-2, 0, -2, 4, 0],\n [4, -2, -4, -2, 4],\n [1, 4, -2, -5, -1],\n [2, 0, 4, -1, 0]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6595 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 4, -3, 0, -4],\n [4, -5, -2, -4, 2],\n [-3, -2, 2, -4, -2],\n [0, -4, -4, -2, -3],\n [-4, 2, -2, -3, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -179919 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -2, 2, 1, 1],\n [4, 1, 4, 5, -1],\n [1, -2, 2, 3, -3],\n [1, 4, 3, -5, -4],\n [1, -4, 1, -5, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27604 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 5, 0, 3, 3],\n [-3, 2, -2, 1, 0],\n [2, 0, -2, -4, 1],\n [5, 5, -2, 3, 3],\n [1, -1, -3, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1390 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 5, -2, 5, -5],\n [4, -1, 2, 4, -2],\n [4, 4, -2, 3, 3],\n [1, 4, 2, -2, 2],\n [0, -3, 1, -3, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 420213 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, -1, -2, -3, 2],\n [-2, 2, 4, -3, 4],\n [3, 0, -1, -1, -3],\n [-4, 0, 5, -5, 1],\n [-1, -2, 3, 4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22340 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (4, 1) of the result:\nA =\n[[5, 0, 1, -2, -1],\n [0, -5, 2, -3, 0],\n [1, 2, -4, 1, 4],\n [-2, -3, 1, -2, 0],\n [-1, 0, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4186 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[5, -3, 0, 4, -2],\n [-3, 0, 5, 0, -4],\n [3, 2, 0, -5, -4],\n [-2, 1, 3, 4, -1],\n [4, -4, 5, 5, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 23323 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[-5, 4, -2, 2, 3],\n [4, 3, 1, -4, 1],\n [-2, 1, -2, -4, -2],\n [2, -4, -4, -2, 1],\n [3, 1, -2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -29883 | MATH |
[
{
"content": "What is the value at position (4, 1) of the matrix A^4 where A is:\n[[-5, -2, -1, -2, -3],\n [-2, -4, 0, -4, -1],\n [-1, 0, 5, 1, 0],\n [-2, -4, 1, -3, 3],\n [-3, -1, 0, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2013 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, -2, 4, -5, -2],\n [-3, -4, -5, 0, 1],\n [0, 3, 3, -4, -4],\n [3, -5, -1, -5, 1],\n [3, 0, -4, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12550 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, 3, 2, 1, 2],\n [4, 0, -3, 1, -2],\n [5, 4, -1, 2, 1],\n [1, 2, 4, -3, -3],\n [-4, -5, 4, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -516 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, 2, 0, 0, -5],\n [1, 1, 4, 3, 1],\n [2, -2, 3, -5, 2],\n [-3, -5, -4, 0, -1],\n [-3, 3, 2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15803 | MATH |
[
{
"content": "Find the value at position (5, 5) of the 5th power of the matrix:\n[[2, -2, 0, -1, 4],\n [-2, -1, 0, 1, -1],\n [0, 0, 3, -2, 2],\n [-1, 1, -2, 5, -3],\n [4, -1, 2, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11481 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 0, 2, -2, 2],\n [0, -4, -2, 0, 2],\n [2, -2, 0, 0, -2],\n [-2, 0, 0, 5, 4],\n [2, 2, -2, 4, 1]], determine the value at position (1, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1132 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[4, 3, 1, 2, -2],\n [3, 1, -2, 2, 0],\n [1, -2, -3, 0, -1],\n [2, 2, 0, 4, -4],\n [-2, 0, -1, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -842 | MATH |
[
{
"content": "What is the value at position (5, 5) of the matrix A^5 where A is:\n[[1, -2, -4, 5, 2],\n [-2, -2, -4, -5, -5],\n [-3, 0, 1, 3, -1],\n [3, 2, -5, 5, -3],\n [2, 3, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2197 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 0, 2, 0, 0],\n [0, -2, -1, 2, 2],\n [2, -1, -5, 2, 2],\n [0, 2, 2, -4, 0],\n [0, 2, 2, 0, -2]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10207 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[2, -1, -2, 2, -2],\n [-1, 4, 1, 0, -4],\n [-2, 1, -1, -1, -2],\n [2, 0, -1, 4, -1],\n [-2, -4, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 70755 | MATH |
[
{
"content": "What is the value at position (5, 3) of the matrix A^5 where A is:\n[[5, 3, -4, 2, 3],\n [-4, 3, 1, 3, 0],\n [-4, 2, 4, 3, 2],\n [-4, 2, -3, -3, 3],\n [3, 3, -2, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6457 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, -5, 3, 0, -3],\n [-3, 4, -5, 2, -4],\n [-5, 1, 5, 3, 0],\n [2, 2, 3, 1, 3],\n [3, 5, -5, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2392 | MATH |
[
{
"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[4, 3, -3, -4, 4],\n [3, 3, 0, -3, -2],\n [-3, 0, -5, -1, -1],\n [-4, -3, -1, 0, 3],\n [4, -2, -1, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 601 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, -2, -1, 1, 0],\n [2, 0, 4, 2, -2],\n [1, -3, -5, 3, 3],\n [0, -4, 2, 4, 0],\n [1, -5, -3, -5, 4]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1176 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, 3, -2, -2, 1],\n [3, -1, 2, 0, 0],\n [-2, 2, 0, 2, -2],\n [-2, 0, 2, 5, -2],\n [1, 0, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6040 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-4, 2, -5, 2, -3],\n [3, 5, -4, 4, 3],\n [0, -5, -1, 4, 3],\n [0, 1, -2, -5, -1],\n [-4, 2, -2, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99251 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 5, -4, -3, 3],\n [3, -4, -3, 5, 3],\n [-5, -4, 5, -4, 4],\n [-3, 4, -3, 4, -4],\n [2, 2, 2, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90772 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[5, 2, -2, 1, 3],\n [2, -4, -2, 4, -1],\n [-2, -2, -3, 4, 2],\n [1, 4, 4, -3, 0],\n [3, -1, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4173 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 0, 1, -2, 0],\n [0, -3, 0, 0, 0],\n [1, 0, -1, -2, 0],\n [-2, 0, -2, -3, 1],\n [0, 0, 0, 1, 3]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 64 | MATH |
[
{
"content": "Find the value at position (5, 4) of the 4th power of the matrix:\n[[-4, -5, -3, 1, 3],\n [-4, 0, -3, -1, 3],\n [-3, -5, -1, -5, 2],\n [1, 5, -4, 5, 3],\n [-1, 1, -2, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -735 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, -4, -2, 0, -2],\n [-4, 3, 1, -2, 0],\n [-2, 1, 1, 5, 4],\n [0, -2, 5, 3, 0],\n [-2, 0, 4, 0, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24320 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^5 where A is:\n[[1, 4, 4, 0, -4],\n [4, -1, 1, 0, 2],\n [4, 1, 0, 2, 4],\n [0, 0, 2, 3, -2],\n [-4, 2, 4, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22223 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-4, 2, 0, 4, 5],\n [5, 2, -4, 5, 0],\n [1, 2, 3, -1, 5],\n [-3, -4, 2, -5, 4],\n [0, -4, -3, 2, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37473 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -3, 0, -3, 5],\n [5, 2, -1, -2, 3],\n [-1, -2, 2, 2, 2],\n [-2, -5, -4, -2, 4],\n [-4, 5, 4, -3, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21983 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, 5, 3, 1, -2],\n [-5, -3, 2, -2, 4],\n [4, -4, 2, 1, 5],\n [4, 3, -4, -1, 0],\n [-4, -4, 4, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5512 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[5, -1, 3, -2, -3],\n [4, 2, -5, 3, -2],\n [5, 3, 2, -3, -3],\n [3, -3, -2, 3, -2],\n [5, -3, 1, 0, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14450 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 1, -4, -4, -2],\n [1, 1, 2, 1, 2],\n [-4, 2, 1, 3, 1],\n [-4, 1, 3, 1, 2],\n [-2, 2, 1, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78171 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 0, 4, -2, 3],\n [0, 3, -1, 4, 0],\n [4, -1, -5, 0, 2],\n [-2, 4, 0, 4, 5],\n [3, 0, 2, 5, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44076 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -5, -1, -2, -5],\n [4, 3, 0, 0, 5],\n [-4, 1, 3, 0, 5],\n [2, -1, -4, -2, -5],\n [-5, 0, -4, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7141 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, 4, -3, 3, -4],\n [2, 0, 0, 1, -1],\n [5, -2, 0, 2, -2],\n [-1, 1, 0, -2, -2],\n [4, -2, -5, -1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29848 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (2, 2) of the result:\nA =\n[[1, -1, -3, 5, -5],\n [1, 5, -3, -2, -1],\n [2, 1, 3, 5, -3],\n [5, 4, -5, -5, 4],\n [-5, -4, -4, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5159 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (5, 4) of the result:\nA =\n[[2, -2, -4, -3, 4],\n [-1, 3, 2, -3, 3],\n [4, -3, 4, 2, -5],\n [-2, -2, 0, -4, 1],\n [-1, 4, 0, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13000 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, -1, 0, 4, 0],\n [-1, 4, 0, 0, -2],\n [0, 0, -5, -2, -2],\n [4, 0, -2, -4, 1],\n [0, -2, -2, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6608 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-1, -2, 2, 0, -4],\n [-2, 2, 0, 4, 0],\n [2, 0, -2, -2, -4],\n [0, 4, -2, -4, 0],\n [-4, 0, -4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108128 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 0, 0, -2, 1],\n [0, -3, -1, -1, 2],\n [0, -1, -5, -1, 3],\n [-2, -1, -1, 2, -2],\n [1, 2, 3, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2943 | MATH |
[
{
"content": "Find the value at position (5, 5) of the 4th power of the matrix:\n[[3, 4, 0, 0, 0],\n [4, -3, -1, 0, 0],\n [0, -1, -1, -2, 2],\n [0, 0, -2, -3, -2],\n [0, 0, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[0, -4, 0, 0, 0],\n [-1, 1, -1, 5, -5],\n [3, -3, -4, 4, 0],\n [2, -4, -2, -4, 3],\n [4, -4, 4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79302 | MATH |
[
{
"content": "What is the value at position (3, 1) of the matrix A^5 where A is:\n[[-1, 3, -2, -2, 2],\n [3, 0, -2, -2, 0],\n [-2, -2, 4, -2, 1],\n [-2, -2, -2, 0, -2],\n [2, 0, 1, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2782 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[1, -2, -3, -2, 1],\n [-2, -1, -2, -4, 0],\n [-3, -2, 4, 0, 0],\n [-2, -4, 0, 3, -3],\n [1, 0, 0, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -33671 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[1, -2, -4, -1, -1],\n [-4, 5, 0, 4, -2],\n [-5, -3, 3, 4, 1],\n [0, -5, 3, 3, -5],\n [0, 1, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1603 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 0, 3, -3, -4],\n [-4, 0, 1, 0, 5],\n [-3, -1, 2, 0, -4],\n [1, 2, -2, -5, -4],\n [-2, 1, -4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14645 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, -2, -3, 0, -3],\n [-2, 3, 3, -1, 0],\n [-3, 3, 5, 1, 2],\n [0, -1, 1, 0, -1],\n [-3, 0, 2, -1, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11058 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -1, 3, 5, 4],\n [-4, -5, -5, 2, 4],\n [4, 4, -4, 3, 3],\n [-4, -3, -4, 0, 1],\n [0, -3, -3, -4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1400 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[5, 0, 2, 0, 1],\n [0, 3, 4, -1, 2],\n [2, 4, 4, 2, -2],\n [0, -1, 2, -1, 0],\n [1, 2, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15837 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 5, 4, 5, -3],\n [3, 5, 5, -2, -3],\n [1, 2, 1, -5, -5],\n [-1, 2, 4, 5, -3],\n [2, -3, -2, 4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48925 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-3, -2, 2, -2, 3],\n [-2, -2, -1, -5, 1],\n [3, 3, -5, 0, -3],\n [-2, 2, -2, 2, -2],\n [3, 0, -5, 4, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 497997 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[1, 3, 1, -4, -2],\n [3, 4, 4, 0, 2],\n [1, 4, 2, -3, 0],\n [-4, 0, -3, -3, 4],\n [-2, 2, 0, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 332559 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 5) of the result:\nA =\n[[5, 0, -4, 3, -4],\n [-3, 0, -4, -1, -4],\n [-2, 5, 5, -3, -1],\n [0, 1, 4, 2, 3],\n [-2, -2, 1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4476 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 3) of the result:\nA =\n[[5, 3, 5, -4, 5],\n [0, 4, 4, 2, -1],\n [-1, 2, -5, 0, 4],\n [3, 0, 1, -2, 4],\n [-5, 3, 0, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -440 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, 0, 2, 1, -2],\n [0, -1, 0, 0, -2],\n [2, 0, 4, 4, 1],\n [1, 0, 4, -2, -4],\n [-2, -2, 1, -4, 5]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13036 | MATH |
[
{
"content": "Find the value at position (1, 4) of the 5th power of the matrix:\n[[-5, 4, 4, 2, -1],\n [4, 0, 1, 3, 4],\n [4, 1, -3, -2, 0],\n [2, 3, -2, 3, 2],\n [-1, 4, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15632 | MATH |
[
{
"content": "What is the value at position (4, 5) of the matrix A^4 where A is:\n[[-2, -2, 0, 3, 1],\n [-1, -1, 2, 0, -5],\n [-5, 3, 2, 0, -5],\n [-4, 4, -3, 4, -3],\n [-4, -4, 0, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[-5, 0, 1, -2, 0],\n [3, -2, 4, -2, 4],\n [-1, -3, 4, -4, 3],\n [-5, -1, -1, 2, 0],\n [0, 0, -2, -5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3257 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 5, 0, -1, 4],\n [-5, -1, -4, -5, -2],\n [0, 1, 3, -1, 2],\n [2, 5, 3, -3, -3],\n [3, 1, -2, -5, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9788 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[4, 0, -3, -1, -3],\n [2, -1, 4, 4, 0],\n [-4, 2, 3, -3, 0],\n [0, -4, 4, 2, -1],\n [5, 5, 2, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18749 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 5th power of the matrix:\n[[-1, 1, -1, 0, -4],\n [2, -1, 0, -5, 4],\n [-4, 5, -2, 5, 3],\n [0, 2, -4, 4, -1],\n [-5, -2, 4, -5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4236 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[5, 3, -4, 1, -3],\n [-4, -2, 1, 1, 3],\n [-3, 1, 0, 4, 1],\n [1, 4, -1, 3, 1],\n [1, -3, -5, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -349 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[-1, 4, -3, 3, -4],\n [-3, -2, 4, -5, 5],\n [-2, -2, 3, 2, -4],\n [1, 0, 1, 5, -2],\n [-1, 0, 3, -4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1644 | 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, 0, -2],\n [4, 0, 0, -3, -2],\n [-2, 0, 0, 0, -4],\n [0, -3, 0, -5, 2],\n [-2, -2, -4, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25791 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, -5, 0, -3, -5],\n [2, -2, 4, 1, 4],\n [-4, 0, 0, 1, -5],\n [-5, -4, 5, -4, -1],\n [-5, 5, -4, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 744215 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -5, -1, -2, 2],\n [-3, 4, -5, 4, -1],\n [-5, 5, -1, 3, -1],\n [-4, -4, 4, 3, -1],\n [5, 2, 4, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 697 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 5, -2, 5, 3],\n [4, 5, 0, 4, 0],\n [-1, 0, -5, -1, 0],\n [2, -2, -1, -2, 1],\n [4, 0, -2, 0, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16098 | MATH |
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