Question

Use the inversion algorithm to find the inverse of the given matrix, if the inverse exists.

2 6 6 2 7 6 2 7 7

Answer 1

To find the inverse of a matrix using the inversion algorithm, follow these steps: Write down the given matrix. Find the determinant. Transpose the matrix. Multiply each element by the reciprocal of the determinant.

Step-by-step explanation:

To find the inverse of a matrix using the inversion algorithm, follow these steps:

1. Write down the given matrix.
2. Find the determinant of the matrix.
3. If the determinant is non-zero, proceed to the next step. If the determinant is zero, the matrix does not have an inverse.
4. Transpose the matrix by swapping its rows with columns.
5. Multiply each element of the transposed matrix by the reciprocal of the determinant.

In the case of the given matrix, the determinant is -29, which is non-zero. Therefore, the inverse exists. Transposing the matrix gives the following result:

2 7 7
6 2 7
6 6 2

Multiplying each element by the reciprocal of the determinant (-1/29) gives the inverse matrix:

-2/29 -7/29 -7/29
6/29 2/29 -7/29
6/29 6/29 2/29

So, the inverse of the given matrix is:

-2/29 -7/29 -7/29
6/29 2/29 -7/29
6/29 6/29 2/29