Question

Determine if A is invertible. If it is, compute A⁻¹ by augmenting A with the identity matrix and converting the augmented matrix to reduced row echelon form. Show all work.

Answer 1

To determine if matrix A is invertible, check if the determinant of A is non-zero. If A is invertible, augment A with the identity matrix and convert the augmented matrix to reduced row echelon form to find A^(-1).

Step-by-step explanation:

To determine if matrix A is invertible, we need to check if the determinant of A is non-zero. If the determinant is non-zero, then A is invertible. If A is invertible, we can compute its inverse by augmenting A with the identity matrix and converting the augmented matrix to reduced row echelon form. Here's how:

1. Let A be the given matrix.
2. Create the augmented matrix [A | I], where I is the identity matrix of the same size as A.
3. Apply row operations to bring the augmented matrix to reduced row echelon form.
4. If the left side of the augmented matrix becomes the identity matrix, then the right side will be the inverse of A.

Note that the process of finding inverse only applies to square matrices.