messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[2, 2, 0, -1, 0],\n [2, 2, 0, 0, 0],\n [0, 0, -4, 2, -1],\n [-1, 0, 2, -5, 0],\n [0, 0, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -569 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-5, 0, -4, 2, -1],\n [0, -3, -1, 4, 3],\n [-4, -1, 3, 2, -2],\n [2, 4, 2, 4, 2],\n [-1, 3, -2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 168978 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[1, -2, 4, 4, 4],\n [3, -1, 2, 0, -2],\n [-3, 5, 0, -5, -4],\n [1, -2, -1, 5, 4],\n [-5, -4, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 706 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, 0, -2, 0, -3],\n [0, -1, 2, 0, 0],\n [-2, 2, -3, 2, 2],\n [0, 0, 2, 0, 0],\n [-3, 0, 2, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59509 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, 0, 2, 1, 0],\n [0, -3, 2, 5, 0],\n [2, 2, 4, 2, -2],\n [1, 5, 2, 5, 2],\n [0, 0, -2, 2, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 245704 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 1, -4, 2, -4],\n [1, 3, 4, 1, -2],\n [-4, 4, 0, -2, -2],\n [2, 1, -2, -2, 3],\n [-4, -2, -2, 3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 275520 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -2, -4, -3, 1],\n [0, 0, 2, 2, 0],\n [-5, 4, 1, 2, -1],\n [5, -2, 1, 5, 0],\n [0, -3, 5, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8737 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 1) of the result:\nA =\n[[-1, 3, 2, -3, 0],\n [4, -5, -3, 4, 1],\n [1, -4, -3, 1, 0],\n [1, 4, 3, 2, 0],\n [-2, 4, 3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -21536 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^5 where A is:\n[[-4, 3, 1, 3, 5],\n [3, 4, -1, 1, -1],\n [-3, 4, 2, 2, 3],\n [5, 0, -4, -3, 5],\n [4, 5, 0, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9184 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 0, 2, 0, -2],\n [0, 0, -2, 4, 0],\n [2, -2, 3, -2, 4],\n [0, 4, -2, 3, 2],\n [-2, 0, 4, 2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14774 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, -5, -4, 5, -2],\n [5, 3, 1, 0, -5],\n [-1, 5, -2, -1, 5],\n [3, -3, -2, 2, -3],\n [-3, 3, -1, 4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18541 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 1, 0, 0, -3],\n [-3, 4, 5, 3, -5],\n [1, 5, 4, 1, 2],\n [0, 2, -5, -5, 3],\n [-2, -3, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 393682 | MATH |
[
{
"content": "Find the value at position (2, 4) of the 4th power of the matrix:\n[[4, 5, -2, 3, -1],\n [1, -3, -3, -3, 2],\n [0, 3, 3, 2, -5],\n [0, -2, -2, -3, 3],\n [-4, -5, 4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[-2, 0, -5, -5, -4],\n [-2, 1, 0, 5, 3],\n [1, -1, 0, 4, 3],\n [-5, 5, 3, 0, -2],\n [-1, -5, 1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2399 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-1, -4, 2, 4, 1],\n [4, 3, -2, 5, 3],\n [-2, -3, 5, -3, 4],\n [-4, 4, -3, 2, 5],\n [2, -4, 5, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -78190 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, -2, -2, 0, -4],\n [-2, -5, 0, 0, -1],\n [-2, 0, -4, 4, -2],\n [0, 0, 4, -2, 3],\n [-4, -1, -2, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -37191 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, 5, -5, -4, -4],\n [4, -3, 2, 5, 0],\n [0, 3, 2, -4, 0],\n [-5, 3, -2, -2, 3],\n [-3, -1, -5, 0, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1327171 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 3, 2, 2, -3],\n [3, 5, -4, -2, -4],\n [2, -4, -3, -2, 0],\n [2, -2, -2, 5, 2],\n [-3, -4, 0, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2869 | MATH |
[
{
"content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[0, 0, 3, -4, 0],\n [3, -2, 5, 0, 1],\n [-5, -1, -2, 4, -4],\n [-4, -4, 1, 5, 5],\n [-2, 0, 1, 3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11546 | 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, 0, 4, -4, 4],\n [4, 4, 1, -1, 0],\n [2, -4, -1, 3, -2],\n [0, 4, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 310104 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[1, -1, 0, 0, 4],\n [-1, -1, -3, -4, -1],\n [0, -3, 5, -1, 0],\n [0, -4, -1, 5, -2],\n [4, -1, 0, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16453 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[5, 0, 0, -2, 1],\n [0, 5, -4, 2, 2],\n [0, -4, -5, 1, -3],\n [-2, 2, 1, 1, 4],\n [1, 2, -3, 4, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 254609 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -5, 5, -5, -5],\n [-2, -2, 3, -5, -3],\n [-3, 2, -4, 0, 5],\n [-2, 4, 0, -1, 3],\n [3, -5, -3, -5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19594 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[-3, -5, 0, -1, 2],\n [-4, 2, -1, 2, 4],\n [-2, -2, 4, -2, 5],\n [0, -2, 3, 3, -3],\n [1, -1, 3, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 390 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, -1, -1, 4, 1],\n [2, 2, -5, -5, -3],\n [-5, -5, 4, 2, -5],\n [3, -4, 3, 1, 3],\n [-3, -5, -5, 5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80090 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 1, 3, 0, -1],\n [-4, -4, 2, -5, 2],\n [5, 4, 5, 1, 1],\n [-1, -3, 1, 1, 1],\n [5, -4, -3, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100913 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, 4, -3, 1, -2],\n [4, -2, 0, 0, -2],\n [-3, 0, 1, 2, 1],\n [1, 0, 2, 4, 2],\n [-2, -2, 1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 166444 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, -5, 1, 0, -1],\n [2, 5, -4, -4, 3],\n [-5, 0, -3, -1, 2],\n [1, -2, 2, 5, 5],\n [4, 5, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13418 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[5, 0, -3, 5, 4],\n [1, 1, -4, -5, 4],\n [-4, 2, 5, 4, -3],\n [5, -2, 2, -3, 0],\n [-4, -3, -5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -451 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 1, -4, 2, 3],\n [4, 5, -4, -1, -4],\n [5, -1, 1, 0, -2],\n [-4, 1, 4, 3, -5],\n [-3, 1, 3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1405 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[4, 2, -1, 0, -1],\n [2, -5, -2, -3, 0],\n [-1, -2, 5, 2, -2],\n [0, -3, 2, 1, -4],\n [-1, 0, -2, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -482 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 2, 0, 0, 0],\n [2, 3, 0, -4, 0],\n [0, 0, 4, 0, 2],\n [0, -4, 0, 0, -2],\n [0, 0, 2, -2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2067 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, -1, 1, 0, -3],\n [-1, 4, 3, 0, -4],\n [1, 3, -4, -1, -1],\n [0, 0, -1, -2, 4],\n [-3, -4, -1, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -13334 | MATH |
[
{
"content": "What is the value at position (2, 5) of the matrix A^4 where A is:\n[[5, 2, -2, 4, -4],\n [2, -2, 0, 2, 0],\n [-2, 0, 2, 0, -1],\n [4, 2, 0, -5, -4],\n [-4, 0, -1, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1364 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, -1, -2, -1, -1],\n [4, 2, 4, 1, 3],\n [5, -5, 0, 0, -4],\n [5, 2, 0, 5, 4],\n [3, 4, -1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43780 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[5, -1, 0, -2, -3],\n [-5, -5, 0, 3, 2],\n [-4, 3, 2, 3, -2],\n [3, -4, -5, 3, 4],\n [2, 1, 2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 264840 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 5, 3, 5, 3],\n [0, -2, -4, 5, -2],\n [1, -5, 3, -3, -2],\n [-1, -3, -2, -1, -5],\n [3, 4, 4, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -808 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -5, -1, 3, -3],\n [-1, -3, -3, -5, -4],\n [-4, 3, 1, 2, -4],\n [3, -3, 4, -4, -5],\n [3, 2, 5, -2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 108 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -3, -2, -4, 4],\n [-2, 4, -3, 2, 5],\n [-4, 5, 3, -3, -2],\n [4, 4, -3, -3, 2],\n [2, 0, -2, -5, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3079 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 0, -4, -3, 1],\n [5, 5, -2, -2, -1],\n [2, 1, 3, -1, -5],\n [-2, 0, 0, 3, 4],\n [-1, -1, 0, 5, 0]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 258 | MATH |
[
{
"content": "Find the value at position (5, 4) of the 4th power of the matrix:\n[[-3, 0, 1, -2, 2],\n [0, -3, -2, 0, 2],\n [1, -2, -3, 0, -1],\n [-2, 0, 0, 5, -2],\n [2, 2, -1, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1420 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 0, 0, 1, -2],\n [0, 2, 0, 0, 0],\n [0, 0, -1, -2, 0],\n [1, 0, -2, 5, -2],\n [-2, 0, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26286 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -4, -2, 2, -2],\n [-4, -3, 2, 2, -2],\n [-2, 2, 0, -2, 4],\n [2, 2, -2, -4, -3],\n [-2, -2, 4, -3, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43039 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, -2, 1, -1, 4],\n [0, 4, -2, -4, 3],\n [-4, -4, -4, -5, -3],\n [0, 1, -5, -1, -1],\n [-5, -2, 4, -5, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24848 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[1, -2, -1, 0, -4],\n [-2, 4, -4, 0, -2],\n [-1, -4, 0, 0, 4],\n [0, 0, 0, 1, 4],\n [-4, -2, 4, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11299 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-5, -5, -3, -3, 1],\n [0, 1, -2, 5, -4],\n [-4, 4, -5, 3, 1],\n [4, -3, -4, -3, 1],\n [-1, -3, 3, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25749 | 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, 1, 0, 0],\n [-2, 5, 2, -2, 0],\n [1, 2, 5, 0, -2],\n [0, -2, 0, 5, -2],\n [0, 0, -2, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 137840 | MATH |
[
{
"content": "What is the value at position (5, 3) of the matrix A^5 where A is:\n[[0, -2, 5, 2, 2],\n [-3, -2, -5, 4, -4],\n [1, 5, 1, 3, 4],\n [3, 3, 0, 2, 3],\n [1, -2, -2, 0, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -609 | MATH |
[
{
"content": "Find the value at position (3, 4) of the 5th power of the matrix:\n[[-2, 4, -2, 0, -1],\n [4, -4, 1, -2, -4],\n [-2, 1, -1, 1, 2],\n [0, -2, 1, -5, 0],\n [-1, -4, 2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8411 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-3, -2, 2, 0, 2],\n [-2, 0, -2, 1, 2],\n [2, -2, -5, -1, 4],\n [0, 1, -1, 0, 1],\n [2, 2, 4, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -22119 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, -2, -1, 0, -2],\n [-2, 2, -2, 2, 4],\n [-1, -2, 4, -1, 2],\n [0, 2, -1, -1, -1],\n [-2, 4, 2, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40156 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 0, -3, 0, -2],\n [0, 3, -1, 1, 0],\n [-3, -1, 4, 0, -2],\n [0, 1, 0, -3, 0],\n [-2, 0, -2, 0, -5]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 136 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 0, 4, -1, -5],\n [-1, 4, -5, 5, -3],\n [-4, -5, -2, -4, -1],\n [4, -5, 4, -5, 5],\n [4, -2, 1, -4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1765 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, 0, 2, -2, -4],\n [0, 0, -1, -1, 3],\n [2, -1, 1, -2, 0],\n [-2, -1, -2, 1, -4],\n [-4, 3, 0, -4, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14352 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -3, -1, 0, -5],\n [-4, -5, -3, 2, 2],\n [-2, 0, 3, 1, -4],\n [5, -4, -3, 2, 4],\n [3, -3, 3, 4, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4685 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 3, 2, -4, 2],\n [3, 3, 1, -3, -2],\n [2, 1, -2, -1, 4],\n [-4, -3, -1, -5, 0],\n [2, -2, 4, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9707 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 1, 1, 4, -5],\n [4, 5, 5, -2, 0],\n [2, -3, -3, 2, 2],\n [2, -5, 2, 2, -4],\n [3, 1, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -45144 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (5, 3) of the result:\nA =\n[[1, 0, 1, -1, 2],\n [0, -2, -2, 0, 1],\n [1, -2, 4, 0, -2],\n [-1, 0, 0, -3, 4],\n [2, 1, -2, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5018 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 5, -1, 0, -3],\n [0, 2, 4, 5, 3],\n [-3, 2, -3, -4, -1],\n [-2, -1, 0, -3, -5],\n [-2, 0, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1016317 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, -3, -4, -2, 0],\n [-5, 3, 3, 2, 0],\n [-2, -4, 2, 1, -2],\n [-3, 0, -5, -4, 1],\n [5, -3, -5, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6755 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 4th power of the matrix:\n[[4, 3, 1, 1, 4],\n [2, 2, 3, -4, 2],\n [2, -1, -1, -2, -1],\n [-4, -4, -1, 5, -3],\n [-5, 3, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -53 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -4, 1, 4, -5],\n [5, -4, 5, -1, -4],\n [3, -2, 3, 5, -5],\n [-5, -5, -2, 3, 2],\n [1, -5, -3, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2295 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-1, -1, 5, 0, 4],\n [-1, -5, -1, -4, 0],\n [5, -1, -1, 2, -2],\n [0, -4, 2, -1, -3],\n [4, 0, -2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6738 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 0, -3, -2, -5],\n [3, 4, -1, 2, -3],\n [-2, -2, 2, 3, -3],\n [1, 3, -4, -2, -3],\n [2, -2, 3, -5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5531 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, 0, 0, 2, -2],\n [0, 4, 0, 0, 0],\n [0, 0, -3, -2, 3],\n [2, 0, -2, -2, 0],\n [-2, 0, 3, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 124936 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 4, 3, -1, 1],\n [-5, -2, 4, -2, -1],\n [0, -2, 0, 4, 1],\n [-3, 3, 2, -5, -4],\n [-4, 4, 3, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81125 | 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, 4, 1, 2],\n [2, 2, -4, 0, 4],\n [4, -4, -3, -1, 0],\n [1, 0, -1, -4, 2],\n [2, 4, 0, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38577 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 3, 1, -2, 4],\n [-1, 0, 3, -1, -1],\n [1, -4, -3, -4, 4],\n [4, -4, -3, 0, -1],\n [5, -1, -4, -4, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 124401 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-3, 3, -2, 2, 0],\n [3, 3, 2, -4, -2],\n [-2, 2, 3, 2, 0],\n [2, -4, 2, -3, 0],\n [0, -2, 0, 0, -5]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16951 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-4, 3, -1, -2, -5],\n [3, 5, 3, -2, 3],\n [4, -5, -1, -5, -2],\n [-1, 5, -3, -4, 0],\n [5, -3, 4, -5, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 299571 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[-1, -4, -4, -2, -2],\n [-2, 1, -5, 2, 4],\n [3, 4, 0, -2, 0],\n [4, 1, 0, 5, -5],\n [-1, 2, 2, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -64781 | MATH |
[
{
"content": "What is the value at position (2, 2) of the matrix A^5 where A is:\n[[-2, 4, 0, 1, -1],\n [5, 2, -3, 2, -1],\n [-5, 0, -4, 1, 3],\n [-3, 4, -2, -2, -2],\n [-3, -1, 3, 5, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8068 | MATH |
[
{
"content": "What is the value at position (5, 1) of the matrix A^5 where A is:\n[[4, -2, 2, 0, -2],\n [-2, -1, -2, -2, 1],\n [2, -2, 5, 0, 0],\n [0, -2, 0, 3, 0],\n [-2, 1, 0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2970 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, -2, 0, -5, -4],\n [0, 5, -5, 3, 0],\n [1, -5, 2, -1, -1],\n [0, 1, 1, -1, -5],\n [5, 3, 0, 3, 5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2055 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[-2, -1, -1, -2, 2],\n [-1, -3, 4, 2, 0],\n [-1, 4, -1, -2, 2],\n [-2, 2, -2, -1, -1],\n [2, 0, 2, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -872 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[-4, -3, 1, 5, -3],\n [-3, 4, -2, 1, -2],\n [1, -2, 0, -2, 1],\n [5, 1, -2, 1, 1],\n [-3, -2, 1, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -775 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, 4, 0, -4, 2],\n [4, -4, 0, 3, 2],\n [0, 0, 0, 0, 0],\n [-4, 3, 0, 4, -2],\n [2, 2, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1268 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, 1, -4, -4, -3],\n [1, 3, -2, -2, -2],\n [-4, -2, -3, -4, -2],\n [-4, -2, -4, -5, 1],\n [-3, -2, -2, 1, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88439 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[2, 4, 5, 0, 1],\n [3, 0, 3, -4, -4],\n [-4, 0, -4, -3, 2],\n [2, 5, -2, 3, 2],\n [-5, 2, -5, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 879 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[0, 1, 4, -2, 2],\n [2, 3, 0, -2, -4],\n [1, 4, -3, 5, -3],\n [-3, -2, -4, -1, -3],\n [4, -1, 1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -40 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 4, 0, 0, 5],\n [-3, 4, 3, -2, -1],\n [-3, -1, 2, 2, 2],\n [0, -5, 5, 4, 0],\n [5, 4, 1, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 201465 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[5, -1, 2, -2, -1],\n [-1, 0, -4, 0, -1],\n [2, -4, 0, 0, 4],\n [-2, 0, 0, 5, 0],\n [-1, -1, 4, 0, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 158985 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, -2, 0, 2, -2],\n [-2, 1, 1, 1, 0],\n [0, 1, -4, 4, -4],\n [2, 1, 4, 3, -3],\n [-2, 0, -4, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -848 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -5, 1, -4, 1],\n [-5, 4, 4, 2, 4],\n [4, -4, -3, 2, -3],\n [-5, 3, 2, -2, 2],\n [-1, -3, -5, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 488339 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (2, 4) of the result:\nA =\n[[5, 0, -4, 0, 0],\n [0, -5, -2, -4, 0],\n [-4, -2, -4, -2, -3],\n [0, -4, -2, -2, 2],\n [0, 0, -3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -25828 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 5th power of the matrix:\n[[-1, -2, -2, 2, 0],\n [-2, -2, -2, -3, -1],\n [-2, -2, 1, 4, -1],\n [2, -3, 4, 5, -1],\n [0, -1, -1, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -257 | 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, 0],\n [-1, 3, -1, -3, 4],\n [2, -1, 2, 1, 0],\n [3, -3, 1, 0, -1],\n [0, 4, 0, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15835 | MATH |
[
{
"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[5, 4, -1, 4, 0],\n [4, -4, 0, -1, 2],\n [-1, 0, 2, -4, 3],\n [4, -1, -4, 3, 0],\n [0, 2, 3, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -54 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, 2, 2, 4, -3],\n [2, -2, -5, 2, 4],\n [2, -5, -2, 1, 2],\n [4, 2, 1, -4, 5],\n [-3, 4, 2, 5, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 654532 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-3, 0, 1, 2, 1],\n [0, 5, 0, 0, -2],\n [1, 0, 3, 2, 0],\n [2, 0, 2, 2, 4],\n [1, -2, 0, 4, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21994 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, 1, 0, 2, 0],\n [1, -2, 1, 1, 2],\n [0, 1, 2, 0, 0],\n [2, 1, 0, -3, 4],\n [0, 2, 0, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55710 | MATH |
[
{
"content": "Find the value at position (2, 5) of the 4th power of the matrix:\n[[-5, 3, -4, -4, 0],\n [3, -1, -3, 4, -4],\n [-4, -3, 0, -2, 2],\n [-4, 4, -2, 2, -2],\n [0, -4, 2, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 514 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[5, -5, -5, -4, -1],\n [3, 0, -2, -3, 2],\n [-3, -5, -2, 5, -1],\n [-1, -1, 2, 2, -2],\n [3, -5, -1, -1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7833 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 2, -2, 0, 0],\n [2, -3, -2, 0, -4],\n [-2, -2, -4, 3, -4],\n [0, 0, 3, -5, 0],\n [0, -4, -4, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8483 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 2, 2, 2, 0],\n [2, 2, -1, 2, -2],\n [2, -1, 1, 0, 2],\n [2, 2, 0, -4, 0],\n [0, -2, 2, 0, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1834 | MATH |
[
{
"content": "What is the value at position (5, 5) of the matrix A^4 where A is:\n[[-3, -1, -2, 0, 2],\n [-1, -4, -1, 0, -2],\n [-2, -1, 2, 2, -2],\n [0, 0, 2, 3, 2],\n [2, -2, -2, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 393 | 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, 0, -2, 0],\n [-2, -5, -2, -2, 1],\n [0, -2, -1, -2, -2],\n [-2, -2, -2, 1, 0],\n [0, 1, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75016 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 4th power of the matrix:\n[[2, 2, -1, -3, 0],\n [2, 0, 0, 2, -4],\n [-1, 0, 5, 2, -4],\n [-3, 2, 2, -5, 3],\n [0, -4, -4, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -756 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^5 where A is:\n[[4, -1, 0, 1, 1],\n [-1, 1, -2, 0, 0],\n [0, -2, -2, 1, 0],\n [1, 0, 1, 3, 0],\n [1, 0, 0, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1207 | 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, 2],\n [0, 2, 2, -4, 2],\n [-2, 2, 1, -2, 2],\n [2, -4, -2, 3, 2],\n [2, 2, 2, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 169287 | MATH |
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