Solving Matrices Using Gauss Jordan Elimination

Today we learned how to solve systems of equations using augmented matrices and two methods: Gaussian Elimination and Gauss Jordan Elimination.

I will explain the process for Gauss Jordan Elimination below, where the goal is to achieve a leading one in each row of the matrix while every other number in the matrix (except for the rightmost constants) is equal to zero.

To start, here are the problems from Step 1 of our assignment today; in these, I just solved for each variable as usual with systems of equations:

Now, I will demonstrate how to solve such problems using matrices and the Gauss Jordan Elimination method:

First, convert the system of equations into an augmented matrix. Next, perform any of the three elementary matrix operations on the augmented matrix: either switch rows, add rows, or multiply rows. Try to get a leading one in each row while making every other number a zero, except for the constant on the right. Also, it is recommended to work column-to-column from left to right.

Below, I have attached an image of two problems (#1 and #2) from Step 3 from our assignment today, which I have worked out. I also have listed the operation I performed on each matrix to produce it in the right margins.