messages listlengths 1 1 | ground_truth stringlengths 1 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "For the matrix power A^3 where A =\n[[-4, 2, -4, -2],\n [0, 1, 1, -4],\n [1, 4, -4, 1],\n [-1, 0, 4, 2]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | 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, 2, -2],\n [0, 2, -2, 2],\n [2, -2, 2, -2],\n [-2, 2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6832 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[3, -1, 4, 0],\n [-1, 2, -3, 0],\n [4, -3, 4, -2],\n [0, 0, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 380 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[1, 1, 3, -2],\n [1, 2, 4, -2],\n [3, 4, -4, 2],\n [-2, -2, 2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 270 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-2, 4, 2, 0],\n [-4, 2, 1, -1],\n [0, 0, -3, -2],\n [2, 4, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2800 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, 4, -2, -1],\n [4, 4, 2, -1],\n [-2, 2, 0, 2],\n [-1, -1, 2, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1004 | 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, 0, -4],\n [0, 2, 0, 4],\n [0, 0, 2, 1],\n [-4, 4, 1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11266 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 1) of the result:\nA =\n[[1, -1, 2, 2],\n [-2, -3, 1, -2],\n [3, 1, 4, -3],\n [2, -4, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the value at position (1, 1) of the 4th power of the matrix:\n[[2, -4, 3, 0],\n [2, -4, -4, 1],\n [0, 3, 2, 4],\n [0, -2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, 1, -3, 3],\n [-2, -1, -4, -4],\n [-4, -1, 4, -2],\n [-2, -2, -3, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -638 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[3, 1, 3, 4],\n [4, 4, -3, 4],\n [-2, -3, -1, -2],\n [2, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1272 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, 0, -4, -2],\n [-3, 2, 1, 1],\n [-4, 1, -1, -1],\n [2, 1, -2, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1206 | 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, 0, 2],\n [-3, -3, 0, -4],\n [1, 3, 0, 4],\n [2, -1, -2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 496 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[1, 0, 4, 2],\n [0, -3, 2, 2],\n [4, 2, 4, 2],\n [2, 2, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1630 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-1, 0, 0, 0],\n [0, -3, -1, 2],\n [0, -1, 3, 0],\n [0, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 145 | MATH |
[
{
"content": "What is the value at position (4, 4) of the matrix A^4 where A is:\n[[-1, 2, 1, 3],\n [3, 3, 3, 1],\n [-4, 0, -4, -4],\n [0, 3, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 106 | MATH |
[
{
"content": "Find the value at position (3, 2) of the 4th power of the matrix:\n[[1, -2, 0, 0],\n [-2, 1, -2, 1],\n [0, -2, 0, -4],\n [0, 1, -4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -154 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 1, 3, -4],\n [-1, -3, 0, 4],\n [-2, -3, -4, 2],\n [0, 2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2917 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 2, 1, 4],\n [-1, 2, 0, -2],\n [-4, 0, 0, -1],\n [0, 3, -1, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -174 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[0, -1, 0, 0],\n [-4, -1, 1, -2],\n [0, 2, 3, -4],\n [-4, -3, -3, 3]], determine the value at position (3, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 408 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-3, -3, 3, -2],\n [-3, 1, 1, -2],\n [1, 1, -3, -2],\n [0, -1, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4929 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[0, -1, 0, 1],\n [-1, 2, -4, 0],\n [0, -4, -4, 0],\n [1, 0, 0, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -442 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 4) of the result:\nA =\n[[4, 2, 2, -1],\n [3, 1, 3, -3],\n [2, -1, -3, -3],\n [-4, -2, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1323 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-4, 4, 4, -1],\n [4, 0, -3, -1],\n [-4, 2, -1, -1],\n [-2, -1, 0, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 288 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, -2, -3, 4],\n [3, 1, -2, 4],\n [1, 3, -4, 3],\n [-4, -1, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1684 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 1, 0, 0],\n [1, 0, -1, 0],\n [0, -1, -2, 0],\n [0, 0, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 45 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 4) of the result:\nA =\n[[3, 0, -4, 1],\n [4, 0, 4, 2],\n [2, -2, -1, 0],\n [-2, -3, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-2, -1, -1, -2],\n [1, 1, -4, 3],\n [4, -1, -3, -2],\n [-1, -2, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -855 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, -4, -3, -3],\n [1, 2, -3, 2],\n [-2, -4, -4, -3],\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"
}
] | 1005 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 2, 2, 2],\n [2, -4, -2, 1],\n [2, -2, 0, -1],\n [2, 1, -1, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1521 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[0, 4, 3, 0],\n [4, 1, -2, -2],\n [3, -2, 1, 1],\n [0, -2, 1, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 178 | MATH |
[
{
"content": "Find the value at position (4, 3) of the 3th power of the matrix:\n[[1, -1, 4, 0],\n [-4, -2, 2, 1],\n [-4, -2, 4, -3],\n [-2, -4, -4, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 24 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-4, -2, -2, -3],\n [1, -2, -3, -3],\n [-3, -4, 4, -2],\n [-4, 0, -4, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15424 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-2, -3, 0, 0],\n [-3, 0, 0, 0],\n [0, 0, 2, 0],\n [0, 0, 0, 2]], determine the value at position (2, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -18 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[3, -1, 0, 0],\n [-1, 2, 0, -2],\n [0, 0, 1, 2],\n [0, -2, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1974 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 1, 2, 0],\n [1, 0, 2, -2],\n [2, 2, 0, 0],\n [0, -2, 0, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 270 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[0, 4, -1, 0],\n [4, 3, 0, -2],\n [-1, 0, -2, 2],\n [0, -2, 2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8403 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, 3, -2, -3],\n [-3, -1, 2, -2],\n [4, -3, -2, 1],\n [3, -3, 0, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 552 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 2, 4, 1],\n [-2, -3, -4, 0],\n [3, -4, -2, -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"
}
] | 1570 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[0, -2, -2, -3],\n [-2, 2, 0, 3],\n [-2, 0, 2, 4],\n [-3, 3, 4, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1722 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-3, -1, 0, -3],\n [-3, 0, -3, 2],\n [4, -2, -2, -1],\n [2, 3, 3, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 446 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, -1, -4, -4],\n [3, -4, 1, -2],\n [-1, -2, -3, -1],\n [4, -3, 3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3053 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, 1, -1, 0],\n [1, -3, 0, -2],\n [-1, 0, -1, 4],\n [0, -2, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9408 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[3, 0, 2, 2],\n [-2, -3, 1, -4],\n [1, -3, 4, 0],\n [0, 2, -2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 237 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -4, 0, -1],\n [3, 2, 0, -2],\n [-3, 0, 0, 3],\n [-4, -4, -4, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2551 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[2, -2, 0, 0],\n [-2, -2, 2, -1],\n [0, 2, -3, 0],\n [0, -1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -266 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[2, 1, 4, 2],\n [1, -2, 2, 1],\n [4, 2, 2, 0],\n [2, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8556 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[4, 1, -1, -1],\n [0, -2, -1, -3],\n [-3, -1, -4, 4],\n [4, 4, 4, 4]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, 2, -2, -2],\n [1, 0, 4, 3],\n [-3, -1, -1, 4],\n [-2, -4, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -222 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[0, -4, 0, -4],\n [-2, 0, -4, -3],\n [-3, -4, -2, 2],\n [-1, -4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1832 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[2, 3, 4, -3],\n [-4, 1, 1, 0],\n [-3, 1, 2, -3],\n [0, 4, 0, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1046 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (4, 4) of the result:\nA =\n[[3, 1, -1, 2],\n [1, -1, -1, 1],\n [-1, -1, 2, 0],\n [2, 1, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -1, 0, -4],\n [-3, -1, -3, 4],\n [0, -3, -4, 2],\n [-2, -1, 2, -4]], determine the value at position (1, 1).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 675 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, 3, -4, -2],\n [3, 3, 0, -2],\n [-4, 0, -3, 0],\n [-2, -2, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4410 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-4, -1, -1, 2],\n [0, -2, 4, -3],\n [2, 0, -4, -3],\n [-2, 4, -1, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 931 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of all entries of the result:\nA =\n[[-3, 0, -2, 2],\n [0, -4, 4, 4],\n [-2, 4, 1, 0],\n [2, 4, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 239 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-4, 2, 4, 1],\n [3, 0, 2, 1],\n [3, -4, 2, 0],\n [3, -2, 1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1019 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, -2, 1, 4],\n [-2, 2, 2, 0],\n [1, 2, 2, 2],\n [4, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2478 | MATH |
[
{
"content": "What is the value at position (1, 4) of the matrix A^3 where A is:\n[[2, 3, 3, -3],\n [4, 4, -4, 1],\n [-1, -1, -1, 1],\n [-2, 1, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -51 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 0, 2, 0],\n [0, -2, 4, 0],\n [2, 4, -1, 0],\n [0, 0, 0, 2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2906 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[-4, 0, 0, 0],\n [0, -2, 0, -2],\n [0, 0, 3, -2],\n [0, -2, -2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 363 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -2, 2, 4],\n [-2, 1, -1, -2],\n [2, -1, -4, 0],\n [4, -2, 0, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6209 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-3, 3, 3, 2],\n [-3, -3, -2, -2],\n [-4, -4, -4, -1],\n [4, -4, -1, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1066 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-3, 3, 3, 0],\n [0, 2, 3, 4],\n [-4, -1, -4, -1],\n [0, 0, 3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 589 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^3 where A is:\n[[-2, -2, -2, -2],\n [-2, -3, 2, 2],\n [-2, 2, -4, 1],\n [-2, 2, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 787 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[-2, -2, -4, 0],\n [2, -2, -2, 1],\n [-3, 1, -1, -4],\n [-1, 1, -2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4079 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (1, 1) of the result:\nA =\n[[4, -2, 4, -2],\n [1, 4, -4, -4],\n [1, 2, 2, -3],\n [0, 3, -3, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 572 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -2, -2, -3],\n [2, 1, 0, 2],\n [-1, -1, 3, -3],\n [0, -1, -1, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 431 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, 2, 0, -4],\n [2, -3, 2, -2],\n [0, 2, 3, 2],\n [-4, -2, 2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8404 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, 2, -2, 4],\n [4, -4, 3, 3],\n [3, -3, 2, 3],\n [2, 4, 3, -4]], determine the value at position (4, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-3, -4, 0, 0],\n [-4, 1, 2, 4],\n [0, 2, 2, -3],\n [0, 4, -3, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1322 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[0, 0, 0, 0],\n [0, -3, 0, 0],\n [0, 0, -3, 2],\n [0, 0, 2, -1]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 1, -2, -4],\n [1, -1, 1, 2],\n [-2, 1, 3, 0],\n [-4, 2, 0, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6271 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, 0, 0, -3],\n [0, 2, 1, 2],\n [0, 1, 3, 0],\n [-3, 2, 0, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2878 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 0, -2, 2],\n [0, 0, 0, -3],\n [-2, 0, -2, -2],\n [2, -3, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1018 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -1, 3, 3],\n [0, 4, -1, 4],\n [-3, 0, -3, 4],\n [-1, -2, 2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 485 | 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, -2, 0],\n [0, 1, 0, 4],\n [-2, 0, -3, 0],\n [0, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 903 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^3 where A is:\n[[2, 1, 0, -4],\n [-2, 4, 1, 3],\n [3, -3, 3, -1],\n [4, -3, 3, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -377 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 4) of the result:\nA =\n[[0, -2, -4, 4],\n [0, -1, 3, 4],\n [-1, 1, -2, -3],\n [2, 0, 1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (3, 4) of the result:\nA =\n[[4, 2, -4, 0],\n [2, -2, 0, 0],\n [-4, 0, -3, 2],\n [0, 0, 2, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 1, 0, -4],\n [-4, -1, -1, -2],\n [4, -4, 0, -4],\n [-2, 0, -3, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10552 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, -4, 2, -2],\n [-3, 0, -1, 2],\n [3, 3, -2, -1],\n [-3, 0, 1, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4065 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[2, -2, -1, 4],\n [-2, 3, -1, 1],\n [-1, -1, 2, 0],\n [4, 1, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 97 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[2, 1, 2, -2],\n [1, 0, 1, 0],\n [2, 1, -2, -1],\n [-2, 0, -1, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, -4, -1, 2],\n [-4, -3, 0, -2],\n [-1, 0, -1, -1],\n [2, -2, -1, -3]], determine the sum of absolute values of all entries.\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[[-2, -2, -1, 3],\n [-2, -1, 0, 3],\n [-1, 0, -4, 2],\n [3, 3, 2, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -191 | MATH |
[
{
"content": "For the matrix power A^3 where A =\n[[-1, 3, 1, 3],\n [1, -3, 3, -1],\n [3, 3, -2, 3],\n [-4, 3, 2, -3]], determine the value at position (2, 3).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 131 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 3th power of the matrix:\n[[4, 1, 4, -2],\n [-3, 4, 2, -3],\n [-4, 3, -1, 1],\n [-3, -3, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1026 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[0, 1, 0, 0],\n [1, 2, 2, 4],\n [0, 2, 1, 0],\n [0, 4, 0, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5227 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[1, -2, 2, 4],\n [-2, 1, 1, 2],\n [2, 1, 1, 0],\n [4, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1985 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (1, 1) of the result:\nA =\n[[-1, 1, -1, 0],\n [-2, 4, -3, -3],\n [-2, 3, 1, 4],\n [-2, 4, -1, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, 2, 3, 4],\n [-1, 4, -1, 0],\n [3, 1, 3, 0],\n [-3, 1, 1, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2438 | MATH |
[
{
"content": "Find the sum of all entries of the 3th power of the matrix:\n[[-1, 4, 4, -1],\n [-4, 2, -4, 0],\n [3, 1, 2, -3],\n [-4, 3, 3, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -64 | MATH |
[
{
"content": "Find the value at position (3, 4) of the 4th power of the matrix:\n[[-3, 4, 1, -1],\n [4, -4, 0, -2],\n [-2, 3, -4, 3],\n [2, -3, 2, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -708 | MATH |
[
{
"content": "Calculate the matrix power A^3 and find the value at position (2, 3) of the result:\nA =\n[[3, -2, 0, 0],\n [-2, 1, -3, 0],\n [0, -3, -2, 4],\n [0, 0, 4, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -96 | MATH |
[
{
"content": "Find the value at position (2, 3) of the 3th power of the matrix:\n[[2, 0, -1, 4],\n [1, -3, -4, 0],\n [-4, -3, 4, -1],\n [-2, -1, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -119 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[4, -3, -1, -3],\n [3, 3, 4, -4],\n [2, -2, 3, -3],\n [1, 3, 4, -1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13750 | 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, 0],\n [2, -4, -3, -1],\n [2, -3, -1, -2],\n [0, -1, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12582 | MATH |
[
{
"content": "What is the value at position (3, 3) of the matrix A^3 where A is:\n[[3, -2, 2, -3],\n [-2, 1, 4, -3],\n [0, 2, 0, -2],\n [-1, 1, 0, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-2, 2, 3, -1],\n [-2, 0, 1, -1],\n [-3, 1, 0, -1],\n [3, 4, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 731 | MATH |
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