❖ To solve a linear system of equations by Gauss Jordan elimination, we have to put the augmented matrix in Reduced Row Echelon Form which is called RREF.

❖ This Linear Algebra video tutorial provides a basic introduction to the Gauss-Jordan elimination which is a process that involves elementary row operations with \(3 \times 3\) matrices which allows you to solve a system of linear equations with \(3\) variables \((x, y, z)\).

So, to solve the example you need

1) Convert the system of linear equations into an augmented matrix \([ A | b ]\).

2) Convert the \(3 \times 3\) matrix into the RREF by using Elementary row operations.

You can easily determine the answers once you convert the augmented matrix to the RREF.

❖ We have solved the system \(Ax=b\) in the following way:

\([ A | b ]\) to \([ \text{REFF} | c ]\)

So,

\(b\) vector changed to \(c\) vector,

because we have done RREF for the augmented matrix \([ A | b ]\).