Gauss Jordan vs Gauss Elimination

Gauss Jordan and Gauss Elimination methods are quite similar. The elimination step is almost the same. In Gauss Jordan method, we eliminate the pivot from all the rows while in Gauss Elimination we eliminate from only the lower rows. We can tweak code of Gauss Elimination method slightly to work it as Gauss Jordan method. Similarly, both methods require pivoting when the pivot element is zero.

Despite these similarities there are lots of differences between these method. We can outline the differences as follows:

Gauss Jordan	Gauss Elimination
1. Pivot element is eliminated from all the rows	1. Pivot element is eliminated from only the lower rows.
2. Normalization is done after elimination	2. Back substitution is done after elimination
3. Coefficient matrix becomes diagonal matrix after elimination and identity matrix after normalization	3. Coefficient matrix becomes upper triangular matrix after elimination.
4. It is slower method as it requires 50% more step than Gauss Elimination method.	4. It is faster method.
5. Implementation is easier as back substitution is not required.	5. Implementation is harder as back substitution is required.