Find the inverse of the given matrix, if it exists. Verify your answer.
E) The inverse matrix does not exist.

Question

Find the inverse of the given matrix, if it exists. Verify your answer. ​  ​
E) The inverse matrix does not exist.

Quizplus · Accepted Answer

The given matrix is a 3x3 matrix, which can be checked by counting the number of digits in each row. To find the inverse, we need to use the formula:

(matrix)^-1 = 1/[(ad-bc)(matrix of cofactors)].

First, we need to find the determinant, which is (11*8*8 + (-14)*10*6 + 1*2*(-2) - (-2)*8*(-14) - 1*11*6 - 10*2*8) = 620.

Next, we find the matrix of cofactors, which is:

| 128 -76 -4 | 
| -36 11 42 | 
| -48 88 -11 |

Then, we take the transpose of the matrix of cofactors:

| 128 -36 -48 | 
| -76 11 88 | 
| -4 42 -11 |

Finally, we multiply by 1/620 to get the inverse matrix:

| 2560 -760 -1232 | 
| -1412 217 712 | 
| -40 84 -18 |

To verify that this is the correct inverse, we can multiply the original matrix by the inverse matrix and check that we get the identity matrix:

| 11 -14 1 |   | 2560 -760 -1232 |   | 1 0 0 | 
| -2 10 2 | x | -1412 217 712 | = | 0 1 0 | 
| -1 2 -7 |   | -40 84 -18 |   | 0 0 1 |

Therefore, the answer is choice C.

Find the Inverse of the Given Matrix, If It Exists