Gauss Elimination Algorithm

For example, in the following sequence of row operations (where multiple elementary operations might be done at each step), the third and fourth matrix are the ones in row echelon form, and the final matrix is the unique reduced row echelon form. 

Use row operations to convert a matrix into reduced row echelon form is sometimes named gauss – Jordan elimination. Some writers use the term Gaussian elimination to refer only to the procedure until the matrix is in echelon form, and use the term gauss – Jordan elimination to refer to the procedure which ends in reduced echelon form. The name is used because it is a variation of Gaussian elimination as described by Wilhelm Jordan in 1888.

Gauss Elimination source code, pseudocode and analysis