messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-4, -2, -2, 0],\n [0, 4, 1, 1],\n [0, -3, -2, 4],\n [2, -2, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -228 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[3, 1, 4, -3],\n [-2, -4, -4, 3],\n [-3, 0, 4, -1],\n [0, -4, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -276 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -2, 0, -3],\n [3, 1, -2, -2],\n [-1, -1, 1, -3],\n [1, 1, -1, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1185 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[3, -2, 0, 1],\n [-2, 0, 0, -3],\n [0, 0, 3, 0],\n [1, -3, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 423 | 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, -3, 0],\n [2, -1, 0, 2],\n [-3, 0, -1, 2],\n [0, 2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1818 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 2, -2, 1],\n [3, 0, -4, 4],\n [-2, 1, 3, 3],\n [3, 2, 3, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4794 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -1, 4, 3],\n [3, -3, -1, 4],\n [-3, 0, -3, 3],\n [3, 3, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8842 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, 0, -2, 2],\n [0, 3, -2, 2],\n [-2, -2, 0, 1],\n [2, 2, 1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 604 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, -2, 4, 3],\n [1, -1, -1, 0],\n [3, -2, 1, 1],\n [2, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3100 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-4, 0, -2, 0],\n [0, 0, 2, 2],\n [-2, 2, 0, 2],\n [0, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 0, 0, -1],\n [1, 0, -4, -2],\n [-1, 3, -2, -3],\n [-1, 1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3250 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 0, 0, 1],\n [0, 4, 3, 2],\n [0, 3, 3, -1],\n [1, 2, -1, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6039 | 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, 0, -2],\n [-2, -3, -2, 2],\n [0, -2, 1, -2],\n [-2, 2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-1, 3, -1, -1],\n [-2, -1, -1, -3],\n [3, -2, 2, -3],\n [4, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, 0, 2, 2],\n [0, 2, 0, 0],\n [2, 0, 3, 1],\n [2, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 296 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 1, 0, 0],\n [1, -4, -2, -2],\n [0, -2, -4, -2],\n [0, -2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6906 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, -2, -4, 4],\n [-2, 1, 2, -2],\n [-4, 2, -1, 0],\n [4, -2, 0, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -215 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, -3, -4, 4],\n [1, 3, -4, 1],\n [0, 2, 0, -4],\n [2, 2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3781 | 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, 2, 2],\n [-2, -4, -1, 0],\n [2, -1, 1, -2],\n [2, 0, -2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3886 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 2) of the result:\nA =\n[[-2, -3, 2, 2],\n [-3, 1, 3, 0],\n [2, 3, 3, -2],\n [2, 0, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, -1, 1, 1],\n [-1, -2, 2, 0],\n [1, 2, 3, -2],\n [1, 0, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 296 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, -2, -1, -4],\n [-2, -2, 0, 0],\n [-1, 0, 1, 0],\n [-4, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13853 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 1) of the result:\nA =\n[[1, 2, 1, 0],\n [2, -1, 0, -2],\n [1, 0, 1, 2],\n [0, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, 1, -2, -4],\n [1, 0, 0, 3],\n [-2, 0, -1, -3],\n [-4, 3, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -196 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 2, 1, 2],\n [2, 3, 0, 2],\n [1, 0, 1, 2],\n [2, 2, 2, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6486 | 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, 0, 1],\n [0, 0, 2, -1],\n [0, 2, -3, 0],\n [1, -1, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 193 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^4 where A is:\n[[4, 0, 2, 2],\n [3, 4, -4, -2],\n [4, 1, -2, 3],\n [-1, 3, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | 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, -4, 2],\n [-3, -3, -4, -2],\n [-2, -4, -4, 3],\n [2, 0, -3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26220 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 3) of the result:\nA =\n[[4, -3, 3, -2],\n [3, 3, 2, 3],\n [-3, 4, -4, -3],\n [3, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 4, 4, 1],\n [1, -4, 1, 4],\n [2, 2, 2, -4],\n [-1, -2, -4, 0]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -70 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 2, -2, 2],\n [2, -4, -3, 0],\n [-2, -3, 2, -3],\n [2, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8806 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -3, 2, 3],\n [0, -1, -4, 4],\n [0, -4, -1, 4],\n [4, 2, -2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4065 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[0, -3, -4, 2],\n [-3, 4, 0, 0],\n [-4, 0, -4, -1],\n [2, 0, -1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8051 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -3, -4, 3],\n [0, 4, 4, 1],\n [1, -4, 4, -2],\n [1, 0, 4, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1108 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 4th power of the matrix:\n[[3, -4, -1, 3],\n [-4, 2, 3, 2],\n [-1, 2, 0, -4],\n [1, 1, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -363 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 1, 0, -2],\n [1, 0, 1, 0],\n [0, 1, -1, 2],\n [-2, 0, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 517 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, 0, 2, 0],\n [0, -1, 4, -2],\n [2, 4, 4, -2],\n [0, -2, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 527 | MATH |
[
{
"content": "Find the value at position (2, 4) of the 3th power of the matrix:\n[[-1, -1, 1, 0],\n [1, -2, -2, 1],\n [-3, -1, -2, -2],\n [-3, -1, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[3, 2, 0, -2],\n [2, -2, 0, 0],\n [0, 0, -3, 0],\n [-2, 0, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 254 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 3th power of the matrix:\n[[1, -3, -2, 4],\n [2, -3, -2, 3],\n [-4, -1, 2, 4],\n [3, 4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 88 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -4, -4, 4],\n [-3, 4, -3, -3],\n [3, 1, 0, 3],\n [2, -4, 3, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4531 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 3th power of the matrix:\n[[1, 4, -2, 1],\n [4, -4, -2, -2],\n [-2, -2, -1, 2],\n [1, -2, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 164 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 4, 0, 0],\n [4, 1, 0, -3],\n [0, 0, 2, 2],\n [0, -3, 2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3912 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 3th power of the matrix:\n[[1, -3, 4, 3],\n [-2, 3, 1, 3],\n [-2, -3, 4, 2],\n [-4, 1, 3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -24 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 1, -4, -3],\n [-3, 4, 1, 4],\n [1, -2, 2, -3],\n [-3, -1, -4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4918 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 0, -1, 0],\n [0, -2, 0, 2],\n [-1, 0, 3, 1],\n [0, 2, 1, 1]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, -2, 0, -2],\n [-2, -2, -2, 3],\n [0, -2, 4, 2],\n [-2, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1526 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^4 where A is:\n[[-1, 0, 2, 2],\n [4, -2, 0, 2],\n [-4, 3, -4, 1],\n [0, 0, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 135 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[3, 0, 0, 0],\n [0, 4, 0, -3],\n [0, 0, 2, 2],\n [0, -3, 2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 557 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-4, 4, 0, -2],\n [4, 3, 2, -2],\n [0, 2, 4, 0],\n [-2, -2, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 354 | 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, -2, 2],\n [-1, 1, -3, 1],\n [4, 3, 0, -4],\n [3, 4, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 726 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[0, 1, -2, 1],\n [1, 1, 3, 0],\n [-2, 3, 3, 0],\n [1, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 459 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 3, -1, -2],\n [3, 2, 1, -4],\n [2, 4, 2, 1],\n [-1, 3, -1, 3]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -675 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[-4, -1, -2, 2],\n [-1, -2, 0, -4],\n [-2, 0, 3, 0],\n [2, -4, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 733 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 4) of the result:\nA =\n[[-2, -3, -4, -2],\n [3, -1, -1, -1],\n [1, 2, -4, -4],\n [-4, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -51 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, 0, 2, 3],\n [2, 0, -4, 3],\n [2, 1, -1, 4],\n [-1, 3, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3293 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 0, -3, 4],\n [2, 0, -2, 2],\n [3, -1, -3, -1],\n [0, -3, 4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -423 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[4, -4, 2, 0],\n [-4, -3, 0, -2],\n [2, 0, 2, -3],\n [0, -2, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1277 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 1, 2, 4],\n [1, -4, 1, -2],\n [2, 4, -2, -1],\n [-1, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3536 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 0, 1, 4],\n [0, 3, 3, -1],\n [1, 0, 2, -2],\n [0, 1, -3, -1]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[0, -2, 1, 0],\n [-2, 2, 1, 2],\n [1, 1, -2, -2],\n [0, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3113 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[0, 0, 0, -1],\n [3, 0, 3, 4],\n [0, 3, -4, -2],\n [0, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -84 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 4) of the result:\nA =\n[[1, -2, -3, 1],\n [-2, -1, -3, 0],\n [-3, -3, 0, 1],\n [1, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, -3, 2, 4],\n [1, 1, -3, 4],\n [4, 0, 0, 2],\n [0, -4, 1, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 771 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 0, 0, 2],\n [0, -2, 0, 4],\n [0, 0, -1, 2],\n [2, 4, 2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 555 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 2, 2, -4],\n [-4, 1, 3, -1],\n [0, -1, -4, 3],\n [3, -3, -2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -65 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, 1, 4, 0],\n [-4, 0, -3, -4],\n [0, -1, 4, 4],\n [1, -3, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7502 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 1) of the result:\nA =\n[[0, -3, -2, -4],\n [-3, -3, 0, -2],\n [-2, 0, 3, 2],\n [-4, -2, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -95 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 3th power of the matrix:\n[[4, 2, 0, 2],\n [2, -4, 0, -1],\n [0, 0, -1, 4],\n [2, -1, 4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -55 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 0, -3, 0],\n [0, 4, 0, 3],\n [-3, 0, 2, 0],\n [0, 3, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4060 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 3th power of the matrix:\n[[-1, 2, -1, 4],\n [2, 4, 4, 3],\n [-2, -2, -1, -3],\n [0, -1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 0, -1, -2],\n [0, -4, -2, 0],\n [-1, -2, -1, -2],\n [-2, 0, -2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4872 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 1, -4, 3],\n [0, -2, 0, 0],\n [2, 3, -1, 2],\n [-2, 1, -2, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1228 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^3 where A is:\n[[4, 0, 0, 0],\n [0, 3, 2, 0],\n [0, 2, -4, -2],\n [0, 0, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[3, -3, 4, -3],\n [4, -3, -2, 3],\n [4, 2, -1, 2],\n [-3, -2, -3, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 606 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 0, -4, -4],\n [4, 1, -1, 0],\n [1, 4, -2, -2],\n [3, 1, 4, 3]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -77 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 3) of the result:\nA =\n[[-2, 0, 0, 2],\n [0, 2, 2, -2],\n [0, 2, -1, 0],\n [2, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 4th power of the matrix:\n[[0, -1, 4, -4],\n [2, -4, 0, -4],\n [-3, -4, 4, -2],\n [1, 2, -3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 3, -4, 2],\n [3, 2, 4, 3],\n [3, 1, 0, 0],\n [-3, 2, 1, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2153 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-1, 0, -3, -1],\n [4, 2, -1, -1],\n [-4, 2, -4, 3],\n [-1, -3, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1216 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-4, 1, 0, 0],\n [1, 2, 1, 0],\n [0, 1, -2, 0],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 581 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 0, 2, 2],\n [0, -4, 1, -3],\n [2, 1, -2, 2],\n [2, -3, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7428 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -1, -1, 4],\n [2, -3, 2, -1],\n [3, 4, 1, 1],\n [4, 1, 0, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, 2, -2, -2],\n [2, -1, 2, -2],\n [-2, 2, -4, -1],\n [-2, -2, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 800 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 0, -2, 2],\n [0, -2, 0, 0],\n [-2, 0, -3, 0],\n [2, 0, 0, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -69 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-2, 2, -1, -1],\n [2, 2, 0, 2],\n [-1, 0, 3, -2],\n [-1, 2, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 462 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[-4, 3, -3, -2],\n [0, 2, 1, -4],\n [2, 4, 1, -3],\n [-3, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, -4, 2, -2],\n [-4, 4, 0, -3],\n [2, 0, 0, 2],\n [-2, -3, 2, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -459 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 3, -2, -4],\n [-3, 4, 0, 2],\n [-2, -4, 0, 0],\n [-2, 0, 1, -2]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -87 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-1, 0, 4, 0],\n [0, -3, 0, 0],\n [4, 0, -4, -2],\n [0, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -215 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[2, -1, 0, 0],\n [-1, -3, -3, 0],\n [0, -3, 3, 0],\n [0, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -104 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 4, 2, 1],\n [4, 1, -3, -4],\n [1, 4, -1, 3],\n [-2, -2, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 225 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 3th power of the matrix:\n[[-1, -3, 2, 2],\n [-3, 2, 0, -4],\n [2, 0, 3, 0],\n [2, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^3 where A is:\n[[-3, -2, 4, 1],\n [-2, 2, -2, -2],\n [4, -2, 4, -4],\n [1, -2, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, -4, -4, -2],\n [-4, 3, 0, 3],\n [-4, 0, -2, -2],\n [-2, 3, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1553 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, -2, 4, 3],\n [-2, 0, 2, 4],\n [-1, 1, 0, 1],\n [0, 0, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 142 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -4, 2, 3],\n [3, -1, 0, 4],\n [2, -2, -4, -4],\n [0, 3, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5096 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-3, -4, -2, 2],\n [-2, -4, -2, 0],\n [-4, 2, 4, -2],\n [-1, 2, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1392 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, 0, 2, 0],\n [0, -2, 2, -3],\n [2, 2, -2, 2],\n [0, -3, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1301 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 2, 0, 3],\n [-1, 4, 4, -1],\n [2, 3, 0, 2],\n [1, 2, 0, -2]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
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