Question

Find the inverse of the given matrix, if it exists, using the algorithm for row reducing?

Answer 1

To find the inverse of a given matrix using row reduction, follow these steps: Write the given matrix and an identity matrix of the same size side by side. Perform row operations on the given matrix and identity matrix simultaneously until the given matrix is transformed into the identity matrix. If the given matrix can be transformed into the identity matrix, then the corresponding transformed identity matrix is the inverse of the given matrix.

Step-by-step explanation:

To find the inverse of a given matrix using row reduction, follow these steps:

1. Write the given matrix and an identity matrix of the same size side by side.
2. Perform row operations on the given matrix and identity matrix simultaneously until the given matrix is transformed into the identity matrix.
3. If the given matrix can be transformed into the identity matrix, then the corresponding transformed identity matrix is the inverse of the given matrix.

For example, let's say we have the matrix:

[3 4][1 2]

We can write the matrix and the identity matrix as:

[3 4 | 1 0][1 2 | 0 1]

Performing row operations, we can transform the given matrix into:

[1 0 | -2 1][0 1 | 1 -1]

Therefore, the inverse of the given matrix is:

[-2 1][1 -1]