messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "For the matrix power A^3 where A =\n[[1, 2, 1, -2],\n [2, -2, -2, 0],\n [1, -2, -2, 0],\n [-2, 0, 0, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 517 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[4, -1, -1, 2],\n [-1, 2, 0, -1],\n [-1, 0, -3, 1],\n [2, -1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1043 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 2, 2, 0],\n [1, 0, 0, 0],\n [-1, 3, 4, 1],\n [-1, 0, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1012 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, 3, 2, -4],\n [-2, 1, -3, 3],\n [1, 0, 3, -1],\n [-1, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, 1, -2, -1],\n [1, -3, 2, 1],\n [-2, 2, 1, 1],\n [-1, 1, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -54 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, -2, 3, 1],\n [-2, -3, 0, 1],\n [3, 0, 1, 3],\n [1, 1, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 328 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -2, 4, 3],\n [3, -4, -3, 4],\n [1, -2, 1, 2],\n [2, -2, -2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5766 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, 3, -2, 3],\n [1, -4, 2, -3],\n [-4, -1, -4, 4],\n [4, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1839 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -4, 2, -2],\n [0, -1, -3, 3],\n [-1, 0, 3, -4],\n [-2, 0, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-1, 0, 4, 2],\n [0, 1, -3, 3],\n [0, -4, -1, 2],\n [-4, 2, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 746 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, -1, 3, 0],\n [-1, -3, 1, 2],\n [3, 1, -3, 0],\n [0, 2, 0, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 79 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, -2, 0, 2],\n [-2, -3, -2, 1],\n [0, -2, 3, -2],\n [2, 1, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -142 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 0, 2, -2],\n [3, -3, -4, 0],\n [-3, -3, 3, -4],\n [-4, 1, 2, 2]], determine the value at position (2, 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[[0, -2, -3, 3],\n [-2, 0, 2, 2],\n [-3, 2, -3, -3],\n [3, 2, -3, -1]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 2) of the result:\nA =\n[[1, -1, -2, 0],\n [-2, 2, 3, 0],\n [4, -4, -4, -2],\n [-3, -4, -1, 3]]\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[[4, -3, 4, -4],\n [0, 2, 3, -2],\n [-2, 4, 1, 2],\n [-3, 4, 2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 842 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -4, -3, -1],\n [2, -1, 0, 4],\n [-1, -1, 4, 3],\n [-2, -2, 1, -4]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -96 | 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, 2],\n [2, 3, -2, -3],\n [-1, -2, -1, -4],\n [2, -3, -4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1772 | 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, -1, 0],\n [0, 0, -4, 0],\n [-1, -4, 4, -1],\n [0, 0, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6348 | 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, 0, 0],\n [-3, -1, -1, 0],\n [0, -1, -3, 1],\n [0, 0, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1675 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -1, -4, -2],\n [-1, 0, -2, -2],\n [-4, -2, -4, 2],\n [-2, -2, 2, -1]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 376 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 0, 4, 3],\n [-2, -1, -3, 0],\n [1, 1, 4, 4],\n [1, 2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 934 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[3, 0, 0, 4],\n [0, 2, -3, -1],\n [0, -3, 0, 2],\n [4, -1, 2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 633 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[2, -2, 2, 0],\n [-2, 2, 0, -2],\n [2, 0, -1, -2],\n [0, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 425 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, 0, 4, -4],\n [-4, -3, 1, 4],\n [-4, -4, -4, 1],\n [0, -4, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4985 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, 0, 3, -3],\n [-4, -4, -3, 4],\n [-3, 1, 4, 0],\n [3, 3, 4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1066 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, -3, 2, 2],\n [-3, 2, 4, 1],\n [2, 4, 4, 0],\n [2, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 816 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 1, -2, 1],\n [1, -3, -1, -4],\n [4, -1, 0, -2],\n [4, -1, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 702 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 0, 0, 0],\n [0, -2, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[3, -2, 3, 4],\n [-3, 0, -2, 1],\n [-2, -1, -3, 4],\n [0, -4, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1085 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 1) of the result:\nA =\n[[0, -4, 1, 2],\n [-4, 2, -2, 0],\n [1, -2, -4, 0],\n [2, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -112 | MATH |
[
{
"content": "What is the value at position (4, 3) of the matrix A^3 where A is:\n[[1, -1, 2, 3],\n [2, 3, 2, -2],\n [3, 0, -2, -1],\n [0, 0, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, -4, -2, -3],\n [0, 0, 0, 0],\n [-2, -3, 3, -3],\n [4, 4, -4, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 0, -4, 3],\n [-3, 2, 3, 2],\n [0, -1, 3, 1],\n [-3, -1, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 136 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 3th power of the matrix:\n[[2, 2, 1, -1],\n [2, -4, -2, 1],\n [1, -2, 4, 0],\n [-1, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 0, 4, 4],\n [2, -4, 0, 1],\n [4, -4, 3, -2],\n [4, 2, -3, -1]], 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, 1, -4, -2],\n [-3, 2, 2, -4],\n [-2, -2, 4, 1],\n [2, -3, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1427 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 4) of the result:\nA =\n[[3, -3, 1, -1],\n [3, 3, 1, 4],\n [3, -3, -4, -3],\n [-2, 1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -93 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 3, -4, 1],\n [-1, 1, -4, -4],\n [-1, 4, 1, 0],\n [1, 4, -4, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -305 | MATH |
[
{
"content": "What is the value at position (1, 1) of the matrix A^3 where A is:\n[[3, 2, 2, -3],\n [-4, 2, -2, 1],\n [2, 3, -1, -2],\n [0, -2, 3, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -91 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 4th power of the matrix:\n[[-1, -3, 1, -1],\n [0, 4, -4, -4],\n [2, 3, 3, 3],\n [3, 1, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -255 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-2, -1, 0, 0],\n [-1, 0, -2, 3],\n [1, 4, 4, -1],\n [-1, 0, -3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -152 | 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, 3],\n [0, 3, 4, 0],\n [-2, 2, 1, 2],\n [-1, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2862 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[3, -3, 0, -2],\n [-3, -4, 2, 2],\n [0, 2, -2, 0],\n [-2, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12 | 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, 1, 0],\n [0, 4, -1, 1],\n [1, -1, 3, 0],\n [0, 1, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 389 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 4, -3, 4],\n [3, 1, -1, 4],\n [2, 1, 4, -1],\n [-4, 2, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1081 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[1, -3, -4, -4],\n [1, 2, 4, -4],\n [0, 0, 1, -4],\n [-4, 1, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1433 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -4, -4, -2],\n [4, 0, 4, 2],\n [-3, 0, 4, -2],\n [-4, 3, 1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 1, -2, 0],\n [1, -1, 0, 0],\n [-2, 0, -1, 3],\n [0, 0, 3, 0]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, 0, 0, -1],\n [0, -3, 0, 1],\n [0, 0, 3, 0],\n [-1, 1, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, -2, -3, 0],\n [-2, 4, 0, 0],\n [-3, 0, 2, 0],\n [0, 0, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 562 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -4, 1, 2],\n [1, 0, 0, 3],\n [2, -1, 2, -2],\n [-4, 3, 0, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3907 | MATH |
[
{
"content": "Find the value at position (2, 1) of the 3th power of the matrix:\n[[0, -2, 2, 2],\n [-2, 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"
}
] | -20 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, 3, 2, -1],\n [-4, 3, -2, -4],\n [0, 1, -3, -4],\n [2, -2, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1064 | MATH |
[
{
"content": "What is the value at position (4, 2) of the matrix A^4 where A is:\n[[4, 0, 0, 2],\n [0, -4, -1, 2],\n [0, -1, 1, 2],\n [2, 2, 2, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the value at position (1, 4) of the 4th power of the matrix:\n[[3, -1, 0, 1],\n [-4, 3, -2, 0],\n [3, 2, -1, 2],\n [1, 3, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^4 where A is:\n[[-2, 0, -1, 0],\n [0, -4, 2, -2],\n [-1, 2, 1, 0],\n [0, -2, 0, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -64 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[4, 2, -1, -2],\n [0, 1, 4, -3],\n [4, 2, -2, 3],\n [3, 0, -3, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 513 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-4, -3, 3, -4],\n [1, -4, 0, -2],\n [-4, -1, 2, -1],\n [-4, -3, 2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1028 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 0, 2, 0],\n [0, 0, 2, 0],\n [2, 2, -1, 0],\n [0, 0, 0, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 3) of the result:\nA =\n[[1, -2, -4, 1],\n [4, 3, -4, 2],\n [2, -3, -1, -4],\n [-4, 0, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -55 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, 3, 0, -3],\n [2, 0, 3, -2],\n [3, 0, -4, 3],\n [1, -4, 1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 905 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, 2, 3, 2],\n [2, 3, -2, -4],\n [4, 3, 1, -2],\n [1, 0, 2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -82 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[1, 0, 1, 0],\n [0, -1, -2, -4],\n [1, -2, 3, 0],\n [0, -4, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 658 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-1, -2, 2, 0],\n [-2, -2, -3, 4],\n [-1, -2, 3, -4],\n [2, -1, 2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 595 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, 1, 2, -2],\n [1, -2, -2, -4],\n [2, -2, -2, -1],\n [-2, -4, -1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -468 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 0, 4, -2],\n [1, -4, -2, -1],\n [2, 2, 3, 2],\n [2, 0, -3, -3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1306 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 3th power of the matrix:\n[[-2, 4, 1, -1],\n [-2, -4, 0, 4],\n [-4, 3, 0, 0],\n [0, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, -1, 2, -2],\n [-2, 2, 3, 0],\n [2, -2, 2, 3],\n [3, 1, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1436 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, 3, 0, 1],\n [1, -2, -3, 3],\n [0, -3, 4, 3],\n [4, -3, -4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -159 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, 0, -1, 0],\n [0, 4, 2, 0],\n [-1, 2, -4, -1],\n [0, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2064 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 2) of the result:\nA =\n[[-1, -2, 0, 0],\n [-1, 1, -1, 0],\n [-4, 4, 1, 0],\n [-4, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, -2, -4, 0],\n [-2, 4, 2, 0],\n [-4, 2, 1, -4],\n [0, 0, -4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11254 | MATH |
[
{
"content": "What is the value at position (1, 2) of the matrix A^3 where A is:\n[[-3, -3, 3, 0],\n [-3, 2, -4, -4],\n [-2, 4, 4, 0],\n [-4, -3, 2, -3]]?\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 (3, 4) of the result:\nA =\n[[-3, 4, -3, 3],\n [3, 2, 1, -3],\n [0, 2, 3, -4],\n [3, -2, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -108 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, -2, 0, -2],\n [-2, 4, 0, 1],\n [0, 0, 3, -1],\n [-2, 1, -1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -108 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[4, 3, -4, -4],\n [1, -4, -3, -1],\n [-3, 1, -4, -2],\n [1, -4, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^3 where A is:\n[[-1, 0, 0, 0],\n [0, -1, 0, -1],\n [0, 0, 2, 0],\n [0, -1, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, 2, 0, 2],\n [2, 3, 2, 0],\n [0, 2, -4, 0],\n [2, 0, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 1, 2, 3],\n [1, -2, 1, -1],\n [2, 1, 0, -2],\n [3, -1, -2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9884 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^3 where A is:\n[[-1, -3, 3, -3],\n [0, 0, -2, -3],\n [3, 4, 3, -3],\n [-2, 0, 3, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69 | MATH |
[
{
"content": "Find the value at position (3, 3) of the 4th power of the matrix:\n[[3, 0, 2, -2],\n [0, 4, -2, -1],\n [2, -2, 4, -2],\n [-2, -1, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1404 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -2, 2, -2],\n [-2, -3, 0, -2],\n [2, 0, -2, -2],\n [-2, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4649 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 4th power of the matrix:\n[[-3, -4, 1, 0],\n [1, 1, -1, 3],\n [0, -3, -2, -2],\n [-4, -1, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 147 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, -1, -1, 0],\n [-1, -1, -2, -1],\n [-1, -2, -1, 0],\n [0, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 241 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 4, -1, -4],\n [3, -4, -2, 0],\n [3, 1, -3, -3],\n [2, 2, 2, 3]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -200 | MATH |
[
{
"content": "Find the value at position (3, 1) of the 3th power of the matrix:\n[[1, 4, -2, 0],\n [3, -4, 2, -4],\n [2, -4, 1, -2],\n [0, 2, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[0, -4, 3, 1],\n [1, 3, -3, -3],\n [0, -1, 0, -2],\n [-4, 0, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -362 | 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, -3, 2],\n [-3, 4, -1, -1],\n [3, 3, 0, -2],\n [4, 0, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3128 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 4, 2, -4],\n [1, -2, -1, 3],\n [-1, 3, -1, -4],\n [-2, 3, -3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16740 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[4, -3, 1, 3],\n [2, -2, 2, 0],\n [1, -3, -1, -3],\n [1, 1, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 150 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[2, 0, 1, 0],\n [0, -4, -2, 0],\n [1, -2, 1, 0],\n [0, 0, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -190 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 1, 4, -1],\n [3, 2, 4, -1],\n [-3, -3, -1, 2],\n [0, -1, -3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 831 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 2, 0, -2],\n [2, 3, 0, -2],\n [0, 0, -1, 1],\n [-2, -2, 1, -4]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[2, 2, -2, -1],\n [2, -1, -3, -1],\n [-2, 4, -3, 4],\n [1, 2, 0, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 2, 1, 0],\n [2, 2, 2, 4],\n [1, 2, 2, 1],\n [0, 4, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8480 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, 3, -2, -4],\n [-2, -4, 0, -3],\n [0, -1, -2, -3],\n [2, -2, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -398 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[3, 0, 0, 0],\n [0, 1, -2, 2],\n [0, -2, -3, 3],\n [0, 2, 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[[-1, 0, 2, 2],\n [3, 2, 3, -2],\n [3, 0, -2, 0],\n [4, -2, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, -1, 2, -4],\n [-3, 0, -2, -3],\n [-2, 3, -1, 4],\n [3, -2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 592 | MATH |
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