Gauss-Jordan Elimination and Reduced-Row Echelon Form

Also a method of solving linear equations. Done by transforming the system's augmented matrix into Reduced-Row Echelon form by the use of Elementary Row Operations. 

*Named for Carl Friedrich Gauss and Wilhelm Jordan. Started as Gaussian Elimination and improved by Wilhelm Jordan. 

Reduced-Row Echelon Form: 
The following are the conditions that your matrix is in RREF: 
1. When it satisfies all the conditions in Row-Echelon Form.