messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[1, -2, 5, 2, -1],\n [1, 4, -3, 1, 5],\n [5, 2, -1, -2, 2],\n [2, -3, 0, -1, -4],\n [2, 0, -4, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -169 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 0, 3, -5, 5],\n [5, 4, -3, 1, -2],\n [3, -3, -1, -3, 1],\n [-1, 3, 1, -4, -2],\n [3, -4, 4, 3, 4]], determine the value at position (5, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -146 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, -4, -2, 1, 2],\n [-3, -5, -2, -4, 2],\n [-2, -4, 0, 0, 4],\n [-2, 0, -4, 4, -4],\n [4, -2, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17280 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -1, -4, -1, 2],\n [4, 3, 3, -5, 3],\n [1, 3, 2, -5, 2],\n [2, 5, -3, -5, 2],\n [-3, -3, -5, 5, -1]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -381 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 5th power of the matrix:\n[[4, 1, 4, 3, 1],\n [3, 2, -4, -5, 1],\n [1, 2, -1, -3, 2],\n [0, 5, -3, -5, -3],\n [-1, -3, -5, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1417 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 2, 2, 0, 0],\n [2, -3, 0, -2, 1],\n [2, 0, 1, 3, 4],\n [0, -2, 3, -3, 0],\n [0, 1, 4, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40506 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-2, 5, 4, 1, 3],\n [1, -5, -5, 3, 5],\n [3, -2, 3, -3, 1],\n [0, 2, 5, 3, -1],\n [-5, -3, 4, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16426 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -2, 0, -4, -2],\n [-2, 4, -4, 3, -2],\n [0, -4, -1, -5, 0],\n [-4, 3, -5, -4, -4],\n [-2, -2, 0, -4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87766 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 5) of the result:\nA =\n[[-3, -2, 2, 1, -2],\n [-2, -2, -2, 0, 2],\n [2, -2, 0, 1, 2],\n [1, 0, 1, 0, 2],\n [-2, 2, 2, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -328 | MATH |
[
{
"content": "What is the value at position (3, 5) of the matrix A^4 where A is:\n[[-2, 1, 0, 0, 0],\n [1, -3, -4, -2, 0],\n [0, -4, 2, 3, 0],\n [0, -2, 3, 3, 0],\n [0, 0, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 3, -2, -5, -4],\n [-5, -1, -1, 5, 1],\n [3, 3, -3, -3, -3],\n [-2, 2, 0, 2, -5],\n [2, -2, 5, -5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -181 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 2, -1, -4, 0],\n [2, -3, 2, -3, -1],\n [-1, 2, -3, -1, 0],\n [-4, -3, -1, -1, -2],\n [0, -1, 0, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11824 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, 2, 0, -2, -1],\n [2, 0, 2, -4, -2],\n [0, 2, 5, -2, -3],\n [-2, -4, -2, -3, -2],\n [-1, -2, -3, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 186277 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, 3, -1, 2, -5],\n [-1, -3, -5, -2, -1],\n [1, -5, -3, -4, 3],\n [4, 0, 4, -3, 2],\n [2, -4, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 231834 | MATH |
[
{
"content": "Find the value at position (2, 5) of the 4th power of the matrix:\n[[5, 3, -2, 0, -1],\n [3, -5, 4, 4, -1],\n [-2, 4, 1, 3, -2],\n [0, 4, 3, 4, -2],\n [-1, -1, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1362 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-3, 1, -4, -4, 1],\n [0, -3, 3, 4, 0],\n [4, 4, 0, -5, -2],\n [4, 0, 0, 5, -1],\n [-5, 2, -1, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21726 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 0, -2, -3, 1],\n [2, -2, -4, 4, -3],\n [-5, 2, -3, 4, 1],\n [4, -1, 4, -1, 1],\n [3, -1, -5, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -15268 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, -4, 0, 3, 2],\n [-1, -5, 1, -1, 0],\n [1, -3, 4, -3, -1],\n [0, 3, -1, -5, -2],\n [-1, 4, 4, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104234 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -5, -1, 1, 4],\n [4, 0, -1, -2, -4],\n [-2, 4, 4, -3, 4],\n [-5, 2, -1, -2, 2],\n [1, -4, -5, 5, -2]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -118 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, -4, -4, -4, 0],\n [-4, 5, 0, -4, -2],\n [-4, 0, 4, 1, 0],\n [-4, -4, 1, 1, 0],\n [0, -2, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -17198 | MATH |
[
{
"content": "What is the value at position (5, 5) of the matrix A^4 where A is:\n[[-4, -3, 3, 1, -2],\n [4, -1, -4, 5, 2],\n [-2, 3, -1, 3, -2],\n [4, -1, 3, 2, -3],\n [-5, -3, -2, -4, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1310 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 2, -2, 2, -4],\n [2, 1, -1, -3, 3],\n [-2, -1, -2, -1, 0],\n [2, -3, -1, -2, 0],\n [-4, 3, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 129051 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[4, -1, -1, -3, 3],\n [-2, 5, -1, -2, -1],\n [1, 3, 1, -1, 4],\n [4, 1, 4, -1, -3],\n [1, 5, 5, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -27395 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 4) of the result:\nA =\n[[4, 4, -5, 0, 1],\n [2, 4, 3, -4, 5],\n [4, -4, -1, -1, 0],\n [-3, 2, -5, 0, -2],\n [-5, 1, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 33 | MATH |
[
{
"content": "What is the value at position (4, 5) of the matrix A^5 where A is:\n[[0, 0, -2, 1, 4],\n [0, 4, 0, -2, 0],\n [-2, 0, -2, 0, -1],\n [1, -2, 0, 3, -2],\n [4, 0, -1, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1722 | MATH |
[
{
"content": "What is the value at position (5, 3) of the matrix A^4 where A is:\n[[0, 4, -1, 0, -1],\n [5, -1, -2, -3, -3],\n [-2, 3, -4, 3, -5],\n [-5, -1, 0, 0, -3],\n [1, 3, 5, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 777 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[0, 2, -1, 2, 4],\n [-2, 4, 2, 4, -4],\n [-1, 3, -2, 5, 0],\n [-5, 3, -5, -1, -2],\n [-3, 0, -4, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 162635 | MATH |
[
{
"content": "Find the value at position (3, 5) of the 4th power of the matrix:\n[[3, 0, 2, 0, 0],\n [0, -1, -2, 3, -5],\n [2, -2, -4, -1, 0],\n [0, 3, -1, 0, 0],\n [0, -5, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 550 | MATH |
[
{
"content": "Find the value at position (5, 5) of the 5th power of the matrix:\n[[-3, -5, -1, 1, 0],\n [-5, -1, -1, 0, -3],\n [-1, 1, -1, -1, -1],\n [4, 4, -3, -5, -1],\n [3, -5, -3, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12637 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, 2, -4, 2, 1],\n [4, 4, -4, 0, 0],\n [-3, 5, -4, -5, 0],\n [-1, 5, 3, -5, 1],\n [-1, -1, -4, 5, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -33319 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[1, -2, -3, 0, -3],\n [-2, -4, 4, 0, 0],\n [-3, 4, 0, -4, 2],\n [0, 0, -4, -5, -3],\n [-3, 0, 2, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -39824 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-5, -1, 4, 2, -3],\n [-1, -1, -4, 2, 4],\n [4, -4, 3, 2, 2],\n [2, 2, 2, -2, 0],\n [-3, 4, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11634 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, -4, 4, -3, -3],\n [-1, -1, -4, 4, 0],\n [-1, 0, -5, -1, 3],\n [4, -4, -5, 4, 5],\n [3, 4, 3, 3, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3849 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 5, -5, 4, -2],\n [-5, 2, -5, -3, -2],\n [2, 0, 4, 1, 2],\n [-4, 4, 5, 2, -3],\n [1, -3, 1, 5, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3766 | MATH |
[
{
"content": "Find the value at position (5, 4) of the 5th power of the matrix:\n[[4, 0, -3, -3, 3],\n [1, -1, 4, 1, 3],\n [-5, 1, 0, 4, 3],\n [-5, -2, 3, -2, 4],\n [-3, 3, -4, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1028 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-4, 2, 2, -5, -3],\n [4, 3, -1, 0, -2],\n [4, -4, 5, 2, 5],\n [0, -1, 3, -5, -1],\n [0, -1, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 176518 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-2, 3, 0, 3, 2],\n [3, -3, 0, 0, 0],\n [0, 0, 0, -2, -2],\n [3, 0, -2, 0, -1],\n [2, 0, -2, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23648 | 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, -3, -1],\n [0, 4, 0, -2, -3],\n [-2, -5, -2, -5, -5],\n [4, 0, -1, 5, -2],\n [5, -3, -5, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47886 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 4, -1, 1, 4],\n [-4, 2, -4, -2, -5],\n [-1, 3, -5, 3, 5],\n [2, 0, 1, -3, -5],\n [-1, -4, -1, 2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1735 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, -4, -3, -3, -5],\n [2, 0, 2, 5, 3],\n [-1, -3, -1, -1, -1],\n [-3, 5, 4, -2, 3],\n [4, 3, -4, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3467 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 2, -1, -2, -4],\n [2, -5, 0, -2, -2],\n [-1, 0, -1, 0, 0],\n [-2, -2, 0, 0, 1],\n [-4, -2, 0, 1, 4]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -102 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -5, -2, 1, 5],\n [-2, 0, 3, -5, -1],\n [5, 1, -5, -2, 0],\n [-4, 4, -1, 5, 4],\n [-5, 0, 0, -2, 2]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 485 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-2, 2, 2, -1, -2],\n [-4, 5, -3, -3, -2],\n [-2, 4, 5, 5, -1],\n [-2, 5, 4, 2, 0],\n [0, 2, 1, 4, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 275262 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 2, -4, 3, -5],\n [2, 5, -2, -2, -1],\n [2, -1, 2, 4, -5],\n [4, 3, 0, -3, 2],\n [3, 0, 5, 1, -5]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -53 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 1) of the result:\nA =\n[[-1, 0, 0, 0, 2],\n [0, 3, -2, 2, 2],\n [0, -2, -1, 0, -2],\n [0, 2, 0, 3, -2],\n [2, 2, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 375 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, 0, 2, -1, 0],\n [0, 5, 0, 4, -2],\n [2, 0, 5, -1, -2],\n [-1, 4, -1, -2, -2],\n [0, -2, -2, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29756 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 4, -4, -1, -5],\n [1, -5, -2, 3, -5],\n [-2, 0, 0, 2, -5],\n [1, -5, 1, -3, 5],\n [2, -3, -5, 2, -3]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 722 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-4, -5, -3, -4, -4],\n [0, -5, -4, 0, -3],\n [-2, -5, 2, 1, 1],\n [-3, 4, 4, -3, -4],\n [-5, 1, 1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 548900 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 1) of the result:\nA =\n[[2, -5, 3, 1, -3],\n [2, 1, 5, 2, 0],\n [3, -1, -3, -3, -5],\n [2, -4, -3, 2, 2],\n [5, -2, -2, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4447 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 1, -4, 1, 4],\n [1, -5, 1, -1, -3],\n [-3, -2, -4, -4, -5],\n [-1, -2, 5, 4, -4],\n [-3, 1, 1, -2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1708 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, -2, -1, -4, 0],\n [-2, -2, 4, -2, -1],\n [-1, 4, 2, 1, 2],\n [-4, -2, 1, -5, 2],\n [0, -1, 2, 2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -103429 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 0, 5, -2, 4],\n [4, -4, 1, -1, 5],\n [0, -4, -1, 4, -2],\n [3, 0, -4, -5, -1],\n [3, 0, 4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12635 | 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, -1],\n [0, 5, 2, 0, 0],\n [-1, 2, 4, -4, 2],\n [2, 0, -4, 0, 2],\n [-1, 0, 2, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 165721 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[4, -2, 1, 1, 4],\n [-2, -5, 2, 0, 0],\n [1, 2, -4, 0, 0],\n [1, 0, 0, 2, -4],\n [4, 0, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1440 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-2, 0, -1, 4, 3],\n [0, 3, 4, 0, -2],\n [-1, 4, 2, -2, -4],\n [4, 0, -2, 4, 0],\n [3, -2, -4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2574 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 2, 0, 0, 0],\n [2, 5, -2, -3, 2],\n [0, -2, -5, -2, 0],\n [0, -3, -2, 1, 1],\n [0, 2, 0, 1, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3904 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[3, 5, 4, 3, 4],\n [4, 1, -5, 1, 4],\n [-1, 0, 4, 1, -1],\n [1, 3, -3, 2, -4],\n [5, 1, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3154 | 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, 5, 4, 1],\n [-5, 2, -3, -4, -3],\n [-1, 5, 2, 4, 1],\n [1, 1, 2, -5, -2],\n [0, 3, -4, -5, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21109 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-4, 1, -3, 4, -4],\n [5, 1, -4, -3, 5],\n [1, -2, -5, -1, 3],\n [2, 3, 4, 3, 1],\n [-2, -1, -5, -5, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 104 | MATH |
[
{
"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[2, 0, 0, -2, 0],\n [0, -5, 0, 1, -2],\n [0, 0, -2, 5, 4],\n [-2, 1, 5, 0, -2],\n [0, -2, 4, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -199 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^4 where A is:\n[[1, -2, 2, 0, 0],\n [-2, 0, -2, 0, 2],\n [2, -2, 3, 0, 2],\n [0, 0, 0, 2, 0],\n [0, 2, 2, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -3, -2, 4, -5],\n [5, 4, -3, -4, -4],\n [-5, 2, -3, -3, 0],\n [2, 3, 3, -2, -1],\n [-4, 5, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21955 | MATH |
[
{
"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[5, 3, -3, 3, -4],\n [4, 3, 2, 3, -1],\n [5, 5, -4, 2, 0],\n [2, 5, -1, 4, -4],\n [0, -1, -1, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4089 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, -3, 4, -3, 2],\n [2, -4, 2, 5, -5],\n [0, 2, -3, 2, -5],\n [5, 5, 3, 5, 3],\n [-1, 4, -2, 5, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19722 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (3, 5) of the result:\nA =\n[[1, -1, 5, 4, 3],\n [-3, 1, 4, 4, 5],\n [-1, 1, -4, -2, -4],\n [1, -4, 5, -5, 3],\n [-5, 2, -4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2678 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -4, 0, 2, 2],\n [-4, -1, -2, -4, 1],\n [0, -2, -2, 4, -2],\n [2, -4, 4, 0, 0],\n [2, 1, -2, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3957 | MATH |
[
{
"content": "What is the value at position (5, 2) of the matrix A^4 where A is:\n[[-4, -2, 5, -3, -2],\n [1, 5, -5, 0, -3],\n [5, 4, 1, 4, -4],\n [-4, -2, -5, -3, 3],\n [1, 1, 5, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -186 | MATH |
[
{
"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[-2, -2, 2, 1, -4],\n [-2, 2, 0, 2, 1],\n [2, 0, -3, -1, -3],\n [1, 2, -1, 4, 2],\n [-4, 1, -3, 2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -498 | 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, 2, 1, -3, -2],\n [2, 1, -1, 2, 4],\n [0, -3, 2, 1, -2],\n [-4, -2, 4, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -31389 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[0, 1, -1, 1, 0],\n [1, 2, 0, -5, 1],\n [-1, 0, -4, 0, 1],\n [1, -5, 0, 3, 2],\n [0, 1, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2895 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-5, -1, -2, -1, -1],\n [-1, 4, -2, 0, -2],\n [-2, -2, -5, 2, 0],\n [-1, 0, 2, 1, 0],\n [-1, -2, 0, 0, -4]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 412 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 4, 0, -2, 2],\n [4, -3, 4, 1, 4],\n [0, 4, 1, 0, -3],\n [-2, 1, 0, -2, 2],\n [2, 4, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4950 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 0, 4, -3, 3],\n [4, 5, -4, 0, 1],\n [3, -3, 4, -3, 1],\n [-2, 2, 1, -1, 1],\n [-3, -4, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20031 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -2, -2, 2, 4],\n [-2, 4, -1, -2, -2],\n [-2, -1, -5, -1, 0],\n [2, -2, -1, -2, -2],\n [4, -2, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4704 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 0, 2, -4, -2],\n [0, -4, -2, -2, 2],\n [2, -2, -3, 3, 1],\n [-4, -2, 3, -1, -4],\n [-2, 2, 1, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38211 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -4, 1, -1, -1],\n [0, 3, 0, 2, 1],\n [3, -2, -4, 1, 0],\n [-5, 5, 3, 3, -4],\n [-3, -1, -1, -5, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24451 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -2, 1, 5, 4],\n [-3, 0, 4, 4, 3],\n [-5, -1, -2, 2, 5],\n [-5, 3, 0, -2, 3],\n [5, -1, -1, -1, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 0, 0, 0, 0],\n [0, -4, 0, 1, -3],\n [0, 0, -5, 0, -3],\n [0, 1, 0, 5, 2],\n [0, -3, -3, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11873 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, -4, 2, 2, 3],\n [-4, 3, 0, 2, 2],\n [2, 0, -4, 0, -2],\n [2, 2, 0, -4, 2],\n [3, 2, -2, 2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30377 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[1, 2, 0, -1, 0],\n [-4, -5, 1, 1, 4],\n [5, 4, -4, -4, -5],\n [4, 2, 2, -5, 5],\n [2, 3, -2, -5, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13843 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -1, -1, 3, 4],\n [-4, -4, 0, 3, -5],\n [3, 3, 3, -1, 3],\n [5, -2, -4, 0, -2],\n [0, -3, 0, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26783 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, 2, -4, 4, -2],\n [2, 0, 2, -1, 2],\n [-4, 2, 1, -3, 1],\n [4, -1, -3, -5, -3],\n [-2, 2, 1, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4187 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, -4, 3, -3, -1],\n [4, 2, -4, 0, -1],\n [4, 3, -1, -4, -1],\n [-2, 5, 1, 0, -4],\n [5, 5, -1, 1, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 127712 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[1, -1, 3, -2, 5],\n [-3, -2, -1, 0, -3],\n [-4, -2, -1, -2, 5],\n [-3, 2, 4, -2, -4],\n [-4, -5, -2, 4, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60306 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[5, 2, 1, 0, 1],\n [2, -5, 1, 0, 1],\n [1, 1, -2, 1, 0],\n [0, 0, 1, 4, 2],\n [1, 1, 0, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5110 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, 4, 3, 4, 2],\n [4, 3, 4, 2, 2],\n [-5, 4, 5, -1, -2],\n [-4, 2, -3, -2, 1],\n [4, 3, -4, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88816 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (3, 4) of the result:\nA =\n[[4, -5, 0, -2, 1],\n [-5, -3, -4, 0, -2],\n [0, -4, 0, 2, -3],\n [-2, 0, 2, 3, 2],\n [1, -2, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2608 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 0, 0, 0, 0],\n [0, -5, 2, 0, 0],\n [0, 2, 4, 1, 4],\n [0, 0, 1, -1, -2],\n [0, 0, 4, -2, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10903 | MATH |
[
{
"content": "What is the value at position (5, 2) of the matrix A^4 where A is:\n[[5, -2, 2, 0, -3],\n [-2, -4, 0, 4, 0],\n [2, 0, 2, -4, -4],\n [0, 4, -4, 0, 0],\n [-3, 0, -4, 0, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 156 | MATH |
[
{
"content": "What is the value at position (3, 5) of the matrix A^4 where A is:\n[[-3, -2, 1, 0, 2],\n [-2, 4, 1, -2, 2],\n [1, 1, 3, -1, -3],\n [0, -2, -1, 1, -2],\n [2, 2, -3, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -333 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^5 where A is:\n[[2, -5, 3, -1, -2],\n [0, 0, -4, 2, 1],\n [-5, -1, 0, -2, -4],\n [-2, -5, 1, -4, -4],\n [3, -1, -4, 5, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 876 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, -2, 2, -2, -1],\n [-2, 4, -2, -3, -2],\n [2, -2, 0, 4, -2],\n [-2, -3, 4, -5, 3],\n [-1, -2, -2, 3, 4]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16319 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -2, -1, 0, 0],\n [-2, -3, -4, 0, -4],\n [-1, -4, -2, 0, 2],\n [0, 0, 0, 0, -4],\n [0, -4, 2, -4, -3]], determine the value at position (5, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 608 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-3, 3, 0, 3, -1],\n [-4, 2, -1, -4, -2],\n [3, -2, -2, -4, 0],\n [5, -4, 1, -3, -3],\n [-1, -3, -4, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107166 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-4, 3, 0, 0, 2],\n [3, -3, 0, -1, -2],\n [0, 0, 1, -2, -2],\n [0, -1, -2, -5, -2],\n [2, -2, -2, -2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 205156 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[1, -2, 0, -2, -1],\n [-2, 5, 0, 0, 2],\n [0, 0, 1, -2, 4],\n [-2, 0, -2, -1, 2],\n [-1, 2, 4, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-5, -1, 0, -2, -2],\n [-1, -4, -3, -2, -4],\n [0, -3, 5, 2, 0],\n [-2, -2, 2, -2, -4],\n [-2, -4, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -343701 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, -2, 4, -2, 2],\n [-2, 3, -5, 3, 0],\n [4, -5, -4, -2, 3],\n [-2, 3, -2, -1, 5],\n [2, 0, 3, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5414 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -5, -5, 1, 2],\n [-3, -1, -5, 1, -1],\n [2, 2, 3, 1, 5],\n [-5, -3, 2, -3, 2],\n [-5, -1, -2, -1, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2573 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, -2, 5, -2, -3],\n [1, -3, -3, 5, 4],\n [-1, -1, 0, 2, 4],\n [0, -5, 2, 2, 3],\n [3, -4, -4, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 195664 | MATH |
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