messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 4, 2, -2],\n [4, 4, 2, -2],\n [2, 2, 2, -4],\n [-2, -2, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26330 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 1, 2, -3],\n [0, -3, 2, 3],\n [1, -1, -4, 2],\n [1, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 228 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 3) of the result:\nA =\n[[-1, 3, 3, -2],\n [3, -3, 0, 3],\n [1, 1, -4, 4],\n [1, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2162 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -2, 0, 0],\n [-2, 2, -2, -4],\n [0, -2, 2, -1],\n [0, -4, -1, -4]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 412 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, 2, 3, 0],\n [2, -3, -4, -1],\n [3, -4, -3, 0],\n [0, -1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -700 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 1, 4, -3],\n [-4, 0, 4, -2],\n [3, -3, 1, -1],\n [2, -2, 0, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 658 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, -1, 3, 2],\n [-1, 4, -2, 0],\n [3, -2, -3, 0],\n [2, 0, 0, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1626 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, 0, 4, 1],\n [0, -4, 2, 2],\n [4, 2, 2, 0],\n [1, 2, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4462 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -4, 2, 4],\n [-4, 2, 0, 0],\n [2, 0, 1, 0],\n [4, 0, 0, -3]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 1) of the result:\nA =\n[[4, 3, 1, -1],\n [2, -2, -2, 4],\n [0, 3, -4, 2],\n [2, -3, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 152 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[-1, 1, 0, 0],\n [1, -4, -1, 0],\n [0, -1, -3, 0],\n [0, 0, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, 0, -2, 2],\n [0, 2, 0, 0],\n [-2, 0, -1, -2],\n [2, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 2, 2, 2],\n [2, -2, 0, 2],\n [2, 0, 2, -2],\n [2, 2, -2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4749 | MATH |
[
{
"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[-4, 4, -3, 1],\n [0, -2, -4, 0],\n [1, 2, -3, -1],\n [4, 1, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 2, -4, 3],\n [2, -4, 4, -1],\n [-4, -1, -3, 1],\n [1, 0, 1, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1321 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, 0, -2, 4],\n [4, 2, 0, 4],\n [4, -1, -4, 4],\n [1, 2, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1286 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^3 where A is:\n[[4, -4, 1, 2],\n [1, 4, 4, 4],\n [4, -2, 1, 3],\n [-3, -4, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[4, -1, -2, -4],\n [4, -1, 0, 4],\n [4, 0, 1, -4],\n [1, -2, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1565 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^4 where A is:\n[[-4, 0, 0, 4],\n [-1, -2, 1, 0],\n [-4, -4, -1, 4],\n [1, -3, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -324 | MATH |
[
{
"content": "What is the value at position (3, 2) of the matrix A^4 where A is:\n[[-1, 0, -3, 2],\n [4, 2, -3, -3],\n [3, 3, 3, -4],\n [3, -2, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -165 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 4th power of the matrix:\n[[-1, -4, -2, 1],\n [-3, 4, -3, -4],\n [1, 4, 2, -2],\n [1, 0, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[3, 2, 3, -4],\n [2, -2, 0, 0],\n [3, 0, 0, -2],\n [-4, 0, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 232 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 3th power of the matrix:\n[[4, -1, -4, 0],\n [-1, 1, 1, 0],\n [-4, 1, -3, -4],\n [0, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 161 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^3 where A is:\n[[-2, -4, -1, -3],\n [3, -4, 1, 2],\n [-3, 0, 4, -4],\n [-3, 4, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 4th power of the matrix:\n[[-3, 1, -3, -3],\n [1, -2, -2, 0],\n [-3, -2, -1, 0],\n [-3, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 386 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 0, 0, 3],\n [0, -2, -3, 3],\n [0, -3, 4, 2],\n [3, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2769 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, 3, -3, -1],\n [3, 1, 2, -4],\n [-1, -1, 3, 4],\n [-4, -1, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, -1, 4, 0],\n [-1, 3, -3, 0],\n [4, -3, 0, 2],\n [0, 0, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1460 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, -2, -1, 1],\n [-3, 2, 3, 0],\n [-3, -4, 0, 4],\n [4, -2, 2, -3]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -406 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, -4, -4, 2],\n [-1, 2, 4, -3],\n [-1, 1, 2, 2],\n [-4, 4, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 327 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 4, 1, 3],\n [4, 3, 0, -2],\n [1, 0, -3, -2],\n [3, -2, -2, 3]], determine the value at position (1, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[3, 2, 3, 1],\n [-4, -3, 2, -3],\n [-1, -4, -2, 3],\n [1, 2, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -537 | 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, 3],\n [4, -3, 3, -2],\n [-3, -4, 0, -3],\n [3, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5368 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 1, -3, 3],\n [4, -4, 2, 3],\n [-2, 3, 4, 4],\n [-2, -3, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1966 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 4) of the result:\nA =\n[[2, 2, -1, -2],\n [0, -3, 1, -3],\n [2, -3, -4, -1],\n [0, 2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 0, 0, 0],\n [0, 0, 1, -2],\n [0, 1, -3, 0],\n [0, -2, 0, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 863 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 4, 4, 3],\n [-1, -2, 1, -2],\n [3, 1, -2, 4],\n [0, 3, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1830 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, -1, -2, -1],\n [-2, 2, 2, 3],\n [-1, 3, 0, 2],\n [4, 4, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5328 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[3, 2, 4, 3],\n [2, 0, -2, 3],\n [4, -2, 1, -1],\n [3, 3, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 596 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[0, -4, 1, 2],\n [-4, 2, -2, 2],\n [1, -2, 1, 0],\n [2, 2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 928 | MATH |
[
{
"content": "What is the value at position (1, 2) of the matrix A^4 where A is:\n[[1, -2, -4, -3],\n [-1, -4, -1, -2],\n [4, 3, 1, 2],\n [-1, 2, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 92 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 1, -2, 0],\n [1, -3, -3, -1],\n [-2, -3, 0, 3],\n [0, -1, 3, 0]], determine the value at position (4, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -292 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^3 where A is:\n[[2, 2, -2, 0],\n [2, 3, 1, 0],\n [-2, 1, -2, -2],\n [0, 0, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 4, -4, -4],\n [0, -1, 1, 4],\n [1, -1, 1, -3],\n [3, 2, 4, 2]], determine the value at position (3, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -50 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, -2, 2, -2],\n [-2, -4, 2, -4],\n [2, 2, -2, 0],\n [-2, -4, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5813 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[4, 2, 3, 4],\n [2, -4, -4, 4],\n [0, -2, -3, 3],\n [4, -1, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1966 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, 3, -2, -4],\n [-1, 2, -2, 3],\n [-4, -1, -1, -1],\n [4, -4, 3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1317 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[1, 2, 4, -1],\n [-4, -4, 2, -1],\n [0, -1, 0, 3],\n [-4, 1, -3, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3336 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -3, 1, 1],\n [4, 1, -1, 4],\n [-1, -1, -4, 1],\n [-1, 2, 2, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3381 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, -4, 2, -4],\n [-2, 2, -2, 2],\n [3, 3, -4, -4],\n [4, 1, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12957 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, -2, -2, -2],\n [-2, 3, 0, 2],\n [-2, 0, -3, -2],\n [-2, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1155 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 0, 1, -2],\n [0, -4, 0, 2],\n [1, 0, 1, 3],\n [-2, 2, 3, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 573 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-4, -4, 2, 4],\n [-4, -1, 0, 0],\n [2, 0, -2, 4],\n [4, 0, 4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2281 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -1, 0, -2],\n [-1, 2, 3, 2],\n [0, -4, -4, 4],\n [-1, 2, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2311 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, -2, -2],\n [0, -2, 0, -1],\n [-2, 0, 2, 1],\n [-2, -1, 1, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 364 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, -2, -2, 0],\n [-2, -3, -2, 0],\n [-2, -2, -4, -2],\n [0, 0, -2, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1902 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 2, 0, 0],\n [2, -1, 2, 0],\n [0, 2, 0, 0],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1194 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -2, 0, 1],\n [-2, -4, 1, 0],\n [0, 1, -4, 0],\n [1, 0, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4123 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 4, -1, 2],\n [4, -1, -2, 4],\n [4, 2, 4, -1],\n [2, 1, 0, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-4, 0, 2, -2],\n [0, -1, 2, -2],\n [2, 2, -4, 2],\n [-2, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1553 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[-3, 2, -3, -1],\n [-1, 2, 4, 2],\n [3, 3, 2, -3],\n [2, 2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 396 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, 4, -4, -4],\n [-3, -4, 4, -1],\n [-4, -4, -2, -2],\n [0, -3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5261 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, 0, 1, 4],\n [-4, 0, -4, 0],\n [-3, -4, 4, 2],\n [2, -3, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2243 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, -2, -4, -3],\n [0, -3, 2, 3],\n [1, 1, 2, -2],\n [0, -3, -3, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -88 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[3, 1, 3, -3],\n [3, -3, 2, -3],\n [-2, 0, 3, 0],\n [3, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -369 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, 2, 0, -4],\n [-1, -2, -2, 2],\n [3, 2, -2, 0],\n [2, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 250 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 3, 0, 3],\n [3, -3, 0, -1],\n [0, 0, -2, 0],\n [3, -1, 0, 1]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 618 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[3, 3, -4, 2],\n [-4, -4, -3, -4],\n [-3, -4, -3, 2],\n [-3, 0, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7718 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^4 where A is:\n[[4, 1, -1, 3],\n [-1, -1, -3, -3],\n [0, -1, 0, 1],\n [3, -2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -273 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 2) of the result:\nA =\n[[-1, -1, 1, -3],\n [3, -2, 0, 3],\n [-4, -3, -2, 0],\n [1, 0, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -31 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 2, 0, -4],\n [2, 3, 0, 2],\n [0, 0, -1, -1],\n [-4, 2, -1, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2395 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-3, 2, 4, 2],\n [2, -3, 1, 4],\n [4, 1, -1, 2],\n [2, 4, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1542 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, 2, -1, 4],\n [3, 2, -3, -3],\n [-4, 3, 4, 2],\n [1, -2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2986 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -1, -1, 1],\n [-1, -3, -4, 1],\n [-1, -4, -3, -2],\n [1, 1, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1212 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -2, -2, -2],\n [-2, 2, 2, 0],\n [-2, 2, 3, -1],\n [-2, 0, -1, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1129 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[4, -3, 0, -1],\n [-3, 3, 0, 0],\n [0, 0, -3, 0],\n [-1, 0, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 693 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -4, 1, 2],\n [3, 3, 2, 4],\n [-3, -3, 3, -1],\n [-1, 1, -2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5472 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -4, 4, 3],\n [4, -3, -1, 2],\n [-1, 1, 2, 4],\n [0, 2, 4, -3]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, 0, -1, 1],\n [0, -1, -1, -2],\n [-1, -1, -3, 0],\n [1, -2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1098 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -2, 2, 1],\n [-3, -4, -4, -3],\n [4, -2, -4, -2],\n [-2, -1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1190 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 4th power of the matrix:\n[[4, 1, 1, -2],\n [-1, -1, -4, -1],\n [-4, -3, -4, 3],\n [-4, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -1, -4, 1],\n [0, 2, -4, 1],\n [-3, -4, -3, -1],\n [-2, 0, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5827 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[0, -3, 1, -4],\n [2, 1, 4, -2],\n [0, 3, 0, -2],\n [-2, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 750 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 1, -2, -1],\n [0, -1, 3, 0],\n [-4, 3, 3, -2],\n [1, 3, 1, -3]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 143 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 0, 0, 0],\n [0, -4, 3, -1],\n [0, 3, -2, 1],\n [0, -1, 1, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4345 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 2, 2, -1],\n [2, -2, 0, 2],\n [2, 0, 4, 0],\n [-1, 2, 0, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 821 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-2, 3, 0, 0],\n [3, 1, 2, 4],\n [0, 2, 4, 0],\n [0, 4, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 694 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-4, -2, 1, 3],\n [1, -3, 3, 4],\n [-4, 0, -1, -3],\n [-1, -3, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -847 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -1, -2, 2],\n [-1, 3, 2, 2],\n [-2, 2, 4, -2],\n [2, 2, -2, 2]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, -2, -3, 2],\n [4, 4, 1, 0],\n [-4, 1, 3, -4],\n [4, -1, -3, -1]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1261 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 0, 0, -1],\n [0, 1, 4, 0],\n [0, 4, -2, -1],\n [-1, 0, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 509 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[-1, 3, 2, 2],\n [3, -4, 0, 3],\n [2, 0, 2, 3],\n [2, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 876 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -2, -1, 0],\n [-2, -1, 1, 3],\n [-3, 3, 1, -1],\n [4, 0, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 532 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 1, -1, -1],\n [1, 0, 0, 2],\n [-1, 0, 2, 0],\n [-1, 2, 0, 2]], determine the value at position (3, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-4, 0, 0, -3],\n [0, 2, 0, 0],\n [0, 0, -2, -2],\n [-3, 0, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -510 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 3, 3, -4],\n [-1, 1, 4, 0],\n [-4, 0, -4, 2],\n [-2, -3, -4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -165 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[0, 2, -1, -3],\n [-2, -1, -1, -4],\n [-2, 3, 0, 4],\n [0, -1, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 521 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[-4, -4, 2, -2],\n [3, 4, 3, 4],\n [3, -1, 2, 3],\n [-4, -2, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -130 | 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, -2, -3],\n [-2, -3, -2, -2],\n [-2, -2, 3, -2],\n [-3, -2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18995 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, 2, -2, -2],\n [2, 4, 0, -1],\n [-2, 0, -2, 0],\n [-2, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -364 | MATH |
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