messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, -1, -3, -2],\n [-2, -1, -3, 2],\n [-2, -4, -2, -1],\n [0, 1, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1051 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, 3, 2, 0],\n [2, -1, -1, -1],\n [-4, 1, -1, -2],\n [0, -3, -2, 1]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 1, 2, -1],\n [1, 0, -3, -2],\n [2, -3, 1, 2],\n [-1, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1273 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 4, 1, -1],\n [-1, -1, 2, -3],\n [-3, -2, 3, -2],\n [-3, 0, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -992 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 1, -1, -3],\n [3, 4, 4, 0],\n [0, 1, -4, -1],\n [4, 0, 2, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3854 | 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, -4],\n [3, 3, -2, -4],\n [1, -2, 0, 2],\n [-1, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4642 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[-1, -1, -2, -3],\n [-3, -3, -4, 4],\n [-4, -1, 3, 2],\n [-1, -3, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 344 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, -1, 0, 0],\n [-1, -2, 1, 4],\n [0, 1, 3, 0],\n [0, 4, 0, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 460 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -3, 0, -4],\n [-1, 3, -3, 2],\n [1, -4, 0, -3],\n [-2, 1, 0, 4]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1120 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, -1, 0, 1],\n [-1, 4, 0, 2],\n [4, 0, -2, -4],\n [-3, 2, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2048 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 2, -3, -2],\n [2, -3, 0, 2],\n [-3, 0, -1, 0],\n [-2, 2, 0, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[2, -4, 2, 2],\n [-3, 0, 2, 4],\n [2, -1, 4, -3],\n [-3, -1, -3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[-3, 0, 0, 4],\n [0, -2, -4, 0],\n [-4, 1, -2, 4],\n [1, -4, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, -3, 2, 1],\n [3, 1, 2, -2],\n [-1, 1, -1, -1],\n [-2, -4, 4, 4]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 0, -1, 2],\n [-4, 3, 2, -2],\n [4, 2, 4, 0],\n [3, -4, 0, 3]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 191 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -1, -2, 2],\n [3, -4, -3, -2],\n [0, -4, 4, 1],\n [-4, 3, -2, 0]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -139 | MATH |
[
{
"content": "What is the value at position (1, 2) of the matrix A^3 where A is:\n[[2, 2, 1, 4],\n [2, 3, 2, 0],\n [1, 2, 1, 0],\n [4, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 4, -4, -2],\n [-2, -2, -1, 1],\n [3, 0, 0, 4],\n [3, 3, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7201 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, -2, 1, -1],\n [-3, -4, 1, 3],\n [2, -2, 1, 4],\n [2, 2, -4, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2710 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, -4, -4, 4],\n [4, 2, 4, -3],\n [3, 3, 2, 2],\n [2, -1, -4, -4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -43 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, -1, -3, 0],\n [4, -1, -3, 1],\n [-1, 4, 2, -3],\n [-3, 2, -4, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1903 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[2, -3, 3, -2],\n [-3, 3, 1, 0],\n [3, 1, -2, 0],\n [-2, 0, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, -4, 2, -2],\n [-4, 0, 2, -4],\n [2, 2, -3, -3],\n [-2, -4, -3, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1339 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, -2, -1, -4],\n [-3, -2, -4, 4],\n [-1, 1, 4, -1],\n [-2, 3, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 858 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, -2, 3, 3],\n [2, 2, 1, 0],\n [-3, -1, -2, 0],\n [3, 3, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 3, 4, -1],\n [3, -1, 2, 3],\n [-2, -4, 1, 3],\n [2, 3, -2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1804 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, -2, 0, 2],\n [-2, -4, -2, -3],\n [0, -2, -1, 2],\n [2, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4347 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 1, 2, 3],\n [2, -3, -3, -1],\n [-2, -3, 3, -3],\n [0, -4, 3, 0]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 3th power of the matrix:\n[[2, -2, 1, 0],\n [-2, 0, -2, 1],\n [1, -2, 1, -2],\n [0, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 4, 1, 4],\n [3, 2, 0, 4],\n [2, -2, -4, -4],\n [0, 0, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 488 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, -3, -4, -3],\n [-3, 3, 0, 4],\n [-1, -2, 3, 3],\n [-2, 1, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19144 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -3, -2, 4],\n [1, 4, 4, -1],\n [-2, 1, 2, 2],\n [-1, -1, 4, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8930 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 4, 0, 2],\n [3, 1, 3, -4],\n [-1, 1, 0, 4],\n [-1, 0, -2, -2]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -184 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, 4, 4, -2],\n [4, 2, 2, -1],\n [4, 2, -3, 1],\n [-2, -1, 1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4903 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 0, -4, 0],\n [0, 0, 2, -2],\n [-4, 2, 1, -2],\n [0, -2, -2, 2]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -44 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, -1, -1, -3],\n [0, 0, 0, 1],\n [4, 2, 1, -4],\n [-1, -4, -1, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -317 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 2) of the result:\nA =\n[[0, 3, -1, -1],\n [-3, 0, -2, 1],\n [-4, 3, 4, 2],\n [-4, 1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-2, 4, 0, 3],\n [4, 0, -3, 0],\n [-3, 2, 0, 1],\n [-3, -4, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 666 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, -3, 1, -3],\n [3, -1, -1, -1],\n [4, -3, -1, 2],\n [1, 4, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 440 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 3, 1, 1],\n [1, 4, -1, -4],\n [2, -4, 2, -2],\n [-2, -2, -4, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8457 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 2, -4, 2],\n [3, 3, 0, 2],\n [3, -2, 3, -1],\n [2, -4, 1, -2]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 209 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[-2, -2, 2, 0],\n [-2, 2, 2, 0],\n [2, 2, -4, 2],\n [0, 0, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -384 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 3th power of the matrix:\n[[-1, -2, -4, 0],\n [1, 1, 2, 0],\n [4, 0, 4, -4],\n [-3, 0, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -23 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[4, -3, 3, -2],\n [-3, -2, 2, -2],\n [3, 2, 0, 1],\n [-2, -2, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3297 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-4, -2, -1, 0],\n [-2, -2, 0, 0],\n [-1, 0, 3, 0],\n [0, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1890 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[1, 2, 2, -4],\n [1, -3, 4, -1],\n [1, -4, -3, -2],\n [3, -1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 337 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -4, 2, 1],\n [0, 0, 1, -2],\n [2, -4, -3, 3],\n [4, -3, 1, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11939 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-1, 3, -4, -1],\n [4, 0, -3, -4],\n [2, 4, -4, 0],\n [-3, 0, 4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -150 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[4, 2, 2, -2],\n [2, 0, 0, 1],\n [2, 0, -2, 1],\n [-2, 1, 1, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 214 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-1, 0, 4, 0],\n [0, -4, -2, 2],\n [4, -2, -3, -2],\n [0, 2, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1762 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 4) of the result:\nA =\n[[-4, 0, 0, 2],\n [-1, -4, -2, -4],\n [3, -3, -4, -2],\n [-4, -3, -2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -282 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 2, 2, -1],\n [2, 4, -3, 2],\n [2, -3, 0, 0],\n [-1, 2, 0, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 194 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-4, 0, 0, 2],\n [0, 3, 0, 3],\n [0, 0, -4, 4],\n [2, 3, 4, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 344 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-4, 0, 2, 4],\n [0, -3, 2, 0],\n [2, 2, 2, 2],\n [4, 0, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1562 | MATH |
[
{
"content": "What is the value at position (4, 1) of the matrix A^3 where A is:\n[[1, 3, 0, 0],\n [2, -4, -1, 0],\n [4, -2, 2, 0],\n [2, 3, -4, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 2, -1, 0],\n [1, 1, -4, -1],\n [-4, 2, -4, 0],\n [0, -3, 1, -4]], determine the value at position (2, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -42 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 1, 2, 2],\n [1, 3, 0, 0],\n [2, 0, 4, 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"
}
] | 685 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 3, 0, 1],\n [3, -3, 4, 1],\n [0, 4, -2, 0],\n [1, 1, 0, 2]], determine the value at position (2, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 22 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-3, 2, 1, -2],\n [-2, 4, -1, 4],\n [2, 3, -2, -4],\n [1, -1, -1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -187 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, 1, 1, 2],\n [4, 1, 0, 2],\n [-3, 1, 4, 1],\n [1, -1, 1, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1032 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 2, 0, -4],\n [2, 1, 0, 2],\n [0, 0, 3, 2],\n [-4, 2, 2, 4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 644 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, 2, -2, 4],\n [2, -3, 0, 2],\n [-2, 0, -4, 0],\n [4, 2, 0, 2]], determine the value at position (1, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1852 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[4, -3, 3, -1],\n [2, -3, 2, 3],\n [2, 2, 4, -1],\n [-3, 4, -1, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1548 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[1, 1, -2, -4],\n [1, -2, -4, 4],\n [4, -3, 0, -3],\n [-1, -1, -1, 0]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, -1, 4, 0],\n [-1, -3, 1, 1],\n [4, 1, -4, -1],\n [0, 1, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6840 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[1, 0, -1, -1],\n [4, 0, -2, -2],\n [4, -4, 3, 1],\n [4, 2, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 261 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -3, -1, 3],\n [-4, -4, 1, 0],\n [-3, 1, 1, -1],\n [-1, -3, 2, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6030 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 1, 2, 0],\n [1, 2, 2, -1],\n [2, 2, 2, -3],\n [0, -1, -3, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6786 | MATH |
[
{
"content": "What is the value at position (3, 4) of the matrix A^3 where A is:\n[[-3, 4, -3, 4],\n [-1, -3, 4, 3],\n [-4, 2, -1, -2],\n [1, 1, 4, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -98 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^3 where A is:\n[[-2, 1, 0, 2],\n [1, 0, 2, 2],\n [0, 2, -3, -2],\n [2, 2, -2, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[4, 3, 0, -2],\n [0, 1, 0, 2],\n [2, 0, -4, 1],\n [0, -2, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 122 | MATH |
[
{
"content": "What is the value at position (2, 4) of the matrix A^3 where A is:\n[[-1, -4, 2, 4],\n [1, 4, 3, 0],\n [2, 0, 4, 1],\n [-2, 1, 3, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[0, -2, -3, -3],\n [-4, 2, -4, -4],\n [-3, -2, -2, 4],\n [0, 4, -1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -39 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -2, 4, 3],\n [4, -4, 1, 0],\n [-1, 2, -2, 3],\n [-3, 3, 3, 3]], determine the value at position (4, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -54 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -4, 0, -3],\n [-3, 3, 3, 1],\n [0, -3, 4, -3],\n [-3, 4, -2, 4]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -52 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 2, 1, -3],\n [4, 1, -3, 1],\n [4, -4, 4, -2],\n [4, 4, -3, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -106 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, 2, -2],\n [0, 0, 0, -1],\n [2, 0, -1, -2],\n [-2, -1, -2, -3]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-4, -2, 0, 2],\n [-2, -1, 0, 0],\n [0, 0, 3, 2],\n [2, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 453 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, 2, 1, 2],\n [4, 3, 3, -1],\n [-1, 1, -4, 2],\n [-2, 4, 4, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5434 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[1, 0, 0, 0],\n [0, -4, 0, -2],\n [0, 0, -1, 0],\n [0, -2, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1127 | MATH |
[
{
"content": "Find the value at position (1, 3) of the 4th power of the matrix:\n[[3, -2, 1, 0],\n [-2, -3, -1, 2],\n [1, -1, 2, 2],\n [0, 2, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 149 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 0, 3, 1],\n [3, 0, 3, 4],\n [2, -1, 0, 1],\n [-2, -2, -1, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[0, 1, 0, 0],\n [1, -1, 0, -1],\n [0, 0, 2, 0],\n [0, -1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[1, -1, 0, -2],\n [-1, -3, 1, 4],\n [0, 1, 4, 2],\n [-2, 4, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 991 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 3, -2, -1],\n [4, 0, 1, -3],\n [-4, 2, 3, 0],\n [-1, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6971 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-4, 3, 3, -2],\n [2, -4, 3, 1],\n [-4, 1, -3, -2],\n [-3, -1, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1638 | 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, -2, 0],\n [0, -2, -4, 0],\n [1, 0, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -109 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[4, -2, 1, 1],\n [-2, 4, 1, 2],\n [1, 1, 1, 1],\n [1, 2, 1, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 694 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 3th power of the matrix:\n[[-3, 3, 3, 3],\n [-1, -3, 0, 4],\n [1, -4, 2, 0],\n [2, 2, -4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[-1, -1, -4, -1],\n [0, 4, 4, -2],\n [-2, -1, 0, -2],\n [-2, 0, -1, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -255 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, -3, -2, -2],\n [-3, -1, 3, 0],\n [-2, 3, -2, 4],\n [-2, 0, 4, -4]], determine the value at position (1, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -93 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 0, -2, 0],\n [0, -1, 2, -3],\n [-2, 2, 1, 2],\n [0, -3, 2, 1]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -86 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -4, -2, 2],\n [3, 3, -2, 1],\n [-4, -1, 2, -1],\n [-2, -4, 4, 3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13213 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 3) of the result:\nA =\n[[3, 3, -2, 1],\n [3, 0, -2, 0],\n [-2, -2, 1, -2],\n [1, 0, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -692 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 2) of the result:\nA =\n[[-1, 0, 4, -2],\n [1, 1, -1, 4],\n [-2, -4, 0, 3],\n [-1, -4, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 4, -1, 2],\n [-3, 4, 4, -3],\n [-2, -2, 4, 3],\n [-3, 3, -4, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -29 | MATH |
[
{
"content": "Find the value at position (4, 1) of the 3th power of the matrix:\n[[2, -2, 0, 0],\n [-2, 0, 4, -1],\n [0, 4, -2, -1],\n [0, -1, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 0, 0, -4],\n [0, -3, 2, 0],\n [0, 2, 1, 3],\n [-4, 0, 3, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -247 | 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, -1],\n [2, 4, 4, 2],\n [-3, -3, 0, 2],\n [-1, -2, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 506 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, 2, 1, -2],\n [3, -3, 3, -2],\n [4, -2, -4, 1],\n [4, -3, 3, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 238 | MATH |
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