messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[2, -4, 1, -4],\n [2, -1, 4, -3],\n [-4, 0, -1, 1],\n [0, 2, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2648 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 4, 2, -4],\n [4, 1, 0, -4],\n [2, 0, -3, 0],\n [-4, -4, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 254 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 1) of the result:\nA =\n[[-2, 1, -2, 2],\n [1, 0, 0, 0],\n [-2, 0, 0, -2],\n [2, 0, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 1) of the result:\nA =\n[[-2, -2, 1, -2],\n [-2, 4, -4, -2],\n [1, -4, 4, 1],\n [-2, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -21 | MATH |
[
{
"content": "What is the value at position (3, 2) of the matrix A^3 where A is:\n[[-2, 1, 1, -3],\n [1, 1, 3, 4],\n [0, -1, 1, -3],\n [3, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 3th power of the matrix:\n[[-4, 3, 3, 0],\n [3, 2, -2, -1],\n [3, -2, -2, -2],\n [0, -1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -100 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 4, 0, 1],\n [-3, 2, -3, 4],\n [3, 3, -2, 3],\n [-1, -2, 3, -1]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 193 | MATH |
[
{
"content": "Find the value at position (1, 2) of the 3th power of the matrix:\n[[-2, -1, 0, -2],\n [-1, 1, 0, 0],\n [0, 0, 2, 0],\n [-2, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -2, 0, 2],\n [-2, 2, -2, 2],\n [0, -2, 3, 0],\n [2, 2, 0, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 4) of the result:\nA =\n[[-3, -2, -3, -1],\n [-3, -1, -1, 3],\n [1, 2, -1, 1],\n [1, 2, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 267 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[4, 4, -2, -4],\n [2, 4, 1, -1],\n [-2, 0, 0, -2],\n [4, 2, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 256 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[0, 0, 0, 0],\n [0, 2, 0, 0],\n [0, 0, -3, 0],\n [0, 0, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 99 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -4, 0, 4],\n [-4, -4, 0, 0],\n [0, 0, -1, 4],\n [4, 0, 4, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2033 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, 0, 0, 2],\n [0, -2, 2, 2],\n [0, 2, -4, 0],\n [2, 2, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 2, 4, -1],\n [2, 4, -4, 4],\n [3, -4, -3, -4],\n [-1, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3139 | MATH |
[
{
"content": "What is the value at position (1, 2) of the matrix A^3 where A is:\n[[0, -4, -3, 2],\n [0, 4, 3, -2],\n [-3, -4, 2, 0],\n [4, -4, 1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -76 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 3th power of the matrix:\n[[-3, 4, -4, -2],\n [4, 0, -4, 2],\n [-1, -1, -3, -1],\n [-2, 3, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 172 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 1) of the result:\nA =\n[[1, 2, 4, -3],\n [-2, 4, -4, -3],\n [-4, -4, 4, 1],\n [-3, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -46 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, 3, 3, -1],\n [-2, 3, -4, 2],\n [3, 0, -1, 1],\n [-4, 0, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 988 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, -1, 2, 0],\n [-1, 3, -1, 4],\n [2, -1, 3, -1],\n [0, 4, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 890 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[0, 4, 1, -1],\n [0, 1, 0, 2],\n [4, -1, -2, 1],\n [3, 4, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 83 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 0, 0, 2],\n [0, 0, 4, 0],\n [0, 4, -1, -4],\n [2, 0, -4, -3]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 132 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 2, -4, 4],\n [0, -3, 1, 1],\n [2, 3, -1, 4],\n [2, 2, 3, 1]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 166 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, 1, 1, 0],\n [1, -4, -4, -1],\n [1, -4, -4, 0],\n [0, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7330 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-1, -2, 0, -2],\n [-2, 1, 2, 2],\n [0, 2, -4, 2],\n [-2, 2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 204 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 1, 4, -3],\n [-3, -1, -3, -1],\n [-3, 1, -2, 0],\n [2, -1, 3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3748 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 3th power of the matrix:\n[[4, 2, -4, 4],\n [1, 3, 2, -2],\n [4, 2, -4, 1],\n [4, 2, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 2, 0, -1],\n [2, 3, 0, 2],\n [0, 0, 2, -3],\n [-1, 2, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2622 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 0, -2, 2],\n [0, 0, -4, 0],\n [-2, -4, 4, 0],\n [2, 0, 0, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5958 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^3 where A is:\n[[3, 2, -4, 3],\n [4, 4, -4, 2],\n [-1, -1, 2, 3],\n [4, 1, -4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 239 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, 4, -2, -4],\n [1, 2, -4, 0],\n [0, -4, 2, -2],\n [1, 4, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 785 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, 1, 3, -2],\n [1, 3, 0, 0],\n [3, 0, 0, 0],\n [-2, 0, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1719 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[2, -1, 0, -4],\n [-1, 2, 4, 3],\n [0, 4, 4, 0],\n [-4, 3, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1600 | 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, -2],\n [-1, -1, 4, -4],\n [0, -4, 2, 0],\n [-2, -1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2528 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, 2, 0, -2],\n [2, 3, 4, 3],\n [-3, -2, 3, -1],\n [-1, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4311 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 2, 2, 2],\n [1, 2, 2, -1],\n [-4, 2, 3, -4],\n [-4, -1, 0, -1]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -58 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, 0, 0, 4],\n [0, -2, 0, 0],\n [0, 0, -3, 0],\n [4, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 299 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -4, 0, -1],\n [4, 0, 2, 1],\n [-1, -2, 3, 1],\n [4, 4, 0, 0]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -162 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 0, 0, 2],\n [0, -1, 0, -4],\n [0, 0, -4, -2],\n [2, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2423 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 0, 0, -4],\n [0, 0, -1, 1],\n [0, -1, 4, -2],\n [-4, 1, -2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6244 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[3, -2, 3, -4],\n [-3, 3, -4, -4],\n [-3, 1, 2, -3],\n [3, -4, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11824 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[-4, 3, 0, 0],\n [0, -3, 2, -2],\n [-1, -1, 3, -3],\n [-1, 1, -3, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, 0, -2, 2],\n [0, -1, 2, 2],\n [-2, 2, 3, 0],\n [2, 2, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1146 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, -1, 4, -2],\n [-1, -4, 0, 1],\n [4, 0, -1, -3],\n [-2, 1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1154 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 0, 3, 1],\n [0, 3, -2, -2],\n [3, -2, 3, -2],\n [1, -2, -2, 2]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -70 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 3, 4, 4],\n [-2, 2, 1, 1],\n [0, -1, 0, -2],\n [3, 2, -3, -4]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[2, 2, 0, -4],\n [2, 0, 0, -2],\n [0, 0, -1, -2],\n [-4, -2, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -400 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 0, 4, 3],\n [-4, -2, 3, 2],\n [2, -3, -3, -3],\n [1, 1, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4544 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[0, -2, 3, -2],\n [-2, -2, -2, 2],\n [3, -2, -3, 0],\n [-2, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 261 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 2, 2, -3],\n [2, -3, 0, -2],\n [2, 0, -1, 0],\n [-3, -2, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 359 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, 0, 1, -4],\n [1, 2, 2, 2],\n [2, -1, 0, -4],\n [2, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 475 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 3th power of the matrix:\n[[0, 0, 2, 0],\n [0, 4, 2, -4],\n [2, 1, -1, 3],\n [1, 0, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the value at position (2, 4) of the 4th power of the matrix:\n[[2, 0, -3, -2],\n [0, -3, -1, 2],\n [-3, -1, -4, 2],\n [-2, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -442 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 3, 2, 1],\n [3, 0, 3, 4],\n [2, 3, 2, 3],\n [1, 4, 3, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21738 | MATH |
[
{
"content": "What is the value at position (4, 3) of the matrix A^4 where A is:\n[[-4, 1, -3, -1],\n [-4, -4, 0, -1],\n [2, -2, 4, 3],\n [-4, 2, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 2, 2, 1],\n [2, 0, 2, -1],\n [2, 2, -1, -3],\n [1, -1, -3, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 704 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, 4, -2, 2],\n [0, -4, 0, 1],\n [3, 4, 0, -3],\n [-4, 0, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1276 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 3) of the result:\nA =\n[[-2, -4, 3, 1],\n [-2, -2, -2, 0],\n [-2, -4, 2, -1],\n [4, 1, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -2, 2, 0],\n [-2, -3, 2, 2],\n [2, 2, 3, -2],\n [0, 2, -2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 803 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, 0, 2, -2],\n [0, 4, -3, 2],\n [2, -3, 4, -2],\n [-2, 2, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 3, 2, 4],\n [4, -3, 1, -2],\n [-4, 0, -4, 3],\n [-1, -1, -3, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 263 | MATH |
[
{
"content": "Find the value at position (4, 2) of the 4th power of the matrix:\n[[1, -1, -2, 1],\n [0, -1, 0, 3],\n [0, -3, -4, 1],\n [1, 3, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 427 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 2, -4, -2],\n [2, 1, 2, 1],\n [-4, 2, 3, -1],\n [-2, 1, -1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4545 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 4, 3, -3],\n [4, 1, 0, -2],\n [3, 0, -3, 4],\n [-3, -2, 4, 4]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -289 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 4, 4, 0],\n [4, -4, -3, 3],\n [4, -3, 2, -2],\n [0, 3, -2, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3764 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[3, 1, 2, 2],\n [1, -2, 0, 2],\n [2, 0, -4, 0],\n [2, 2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 703 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, -1, -1, -2],\n [-1, -2, -2, -1],\n [-1, -2, 1, 0],\n [-2, -1, 0, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -333 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 2, -3, -3],\n [-3, -4, 2, -1],\n [0, -2, 0, 4],\n [2, 1, -2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3418 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 4, 0, 2],\n [4, -1, -3, -4],\n [2, -4, -2, 1],\n [3, -4, 3, 1]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -960 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, -4, 4, 4],\n [4, -1, 4, 0],\n [-2, -4, 4, 0],\n [4, 1, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1179 | 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, -2, 0],\n [2, 4, 2, -2],\n [-2, 2, -4, 0],\n [0, -2, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 857 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 0, 1, 0],\n [2, -4, 0, 1],\n [2, -3, 4, -3],\n [0, -1, -4, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 3, 4, -2],\n [0, -4, -4, 0],\n [3, 4, -1, -4],\n [-3, 3, -3, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1942 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 1) of the result:\nA =\n[[3, 3, -2, 4],\n [-4, 0, 0, -3],\n [0, -4, -1, 3],\n [1, -4, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -496 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 0, 0, -2],\n [0, -4, -2, 0],\n [0, -2, 2, -2],\n [-2, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 889 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -2, 2, 2],\n [-2, 2, 0, -2],\n [2, 0, -3, 1],\n [2, -2, 1, -1]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "What is the value at position (3, 3) of the matrix A^3 where A is:\n[[3, -2, -2, -2],\n [4, -1, -2, 1],\n [-4, 0, -3, 2],\n [-1, -3, -3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -51 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, -3, -3, 4],\n [-3, -4, -3, -3],\n [2, -2, 3, -4],\n [-3, 2, -1, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4408 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-1, 0, 0, 0],\n [0, 4, -2, 0],\n [0, -2, -3, 1],\n [0, 0, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 2, 0, -1],\n [-4, 0, 1, -1],\n [2, 3, 4, -3],\n [0, -1, -3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 2, -1, 0],\n [2, 0, 0, 2],\n [-1, 0, -4, -1],\n [0, 2, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 610 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 4th power of the matrix:\n[[-1, 0, 0, 4],\n [0, -3, -1, 0],\n [0, -1, -3, 0],\n [4, 0, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[1, -2, 1, -4],\n [2, 2, 3, 1],\n [-1, -2, -1, 1],\n [4, -4, -4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -236 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[-1, 0, -4, 3],\n [0, -1, 2, 0],\n [-4, 2, 0, -1],\n [3, 0, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -87 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 2, 1, 1],\n [2, 0, 4, -1],\n [1, 4, 4, 0],\n [1, -1, 0, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1064 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[4, -1, 0, -2],\n [1, -1, 0, 3],\n [4, 2, -4, -3],\n [-4, 1, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -128 | 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, -2, 0, 0],\n [4, 0, -2, 0],\n [2, 0, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 776 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 3, 2, -3],\n [2, 0, 3, -1],\n [-1, 0, 0, -3],\n [2, -4, 2, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 181 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-1, 0, -1, -2],\n [0, -1, 3, 2],\n [-1, 3, 3, -2],\n [-2, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2567 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, 4, -1, 1],\n [4, -1, 0, 3],\n [1, 1, -2, -3],\n [-2, 0, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3994 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 1) of the result:\nA =\n[[2, 0, -1, 2],\n [0, -4, 3, -3],\n [-1, 3, -1, 1],\n [2, -3, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | MATH |
[
{
"content": "Find the value at position (2, 4) of the 3th power of the matrix:\n[[2, 0, 0, -2],\n [0, 4, 2, 0],\n [0, 2, 1, 3],\n [-2, 0, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[-1, 4, -1, -4],\n [-2, 4, 3, -2],\n [-4, 3, -4, -1],\n [-3, 2, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -69 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[2, 0, -3, 3],\n [0, 3, 0, 0],\n [-3, 0, -3, -2],\n [3, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 677 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, 2, -3, -2],\n [-1, 4, -2, -3],\n [1, 4, 4, 1],\n [3, -3, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6520 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, 0, 0],\n [0, 2, 2, 0],\n [0, 2, -1, 0],\n [0, 0, 0, 0]], determine the value at position (4, 4).\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[[1, -3, -3, -4],\n [2, 0, -1, 1],\n [2, -3, -2, -3],\n [2, 4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 646 | MATH |
[
{
"content": "What is the value at position (4, 4) of the matrix A^3 where A is:\n[[-3, -3, 0, 0],\n [1, -3, 4, 4],\n [0, 1, -4, 3],\n [-1, -1, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, 1, 3, 3],\n [3, -2, 2, -4],\n [-2, 0, -4, -3],\n [-2, -1, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2333 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 2, 2, 2],\n [2, -2, -2, -3],\n [2, -2, -3, -2],\n [2, -3, -2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24780 | MATH |
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