Question

Find the inverse of the matrix if it exists. [ 4 2 3 ] [ 3 3 2 ] [ 1 0 1 ]

Answer 1

To find the inverse of a matrix, calculate its determinant, check if the determinant is not zero, find the adjugate, and divide each element by the determinant.

Step-by-step explanation:

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

1. Calculate the determinant of the matrix.
2. If the determinant is not equal to zero, proceed to the next step.
3. Find the adjugate of the matrix by taking the transpose of the matrix of cofactors.
4. Divide each element of the adjugate matrix by the determinant.

In this case, the given matrix:

[4 2 3]

[3 3 2]

[1 0 1]

has a determinant of 13. Since the determinant is not zero, we can proceed to find the adjugate matrix:

[3 -2 3]

[-3 4 -3]

[6 -6 4]

Finally, divide each element of the adjugate matrix by the determinant:

[3/13 -2/13 3/13]

[-3/13 4/13 -3/13]

[6/13 -6/13 4/13]

Therefore, the inverse of the given matrix is:

[3/13 -2/13 3/13]

[-3/13 4/13 -3/13]

[6/13 -6/13 4/13]