Terry D. Johnson
10.001 Fall 2000
 
 

We start with the augmented matrix below:
 
 

Step 1: Applying the Gaussian Elimination algorithm, we begin with the top row...
 
 

Step 2: PROBLEM! The algorithm tries to find a multiple of the 0 (circled) that will eliminate the 1 directly below it, and fails!

Solution: Row switching. Switch Row 2 with a row below it that doesn't have a zero in that position.

NEW Step 2: Switch Row 2 and Row 3
 
 

Now, continue with Gaussian Elimination.