What is the use of reduced row echelon form (not a row echelon form)?

There is raw echelon form and reduced raw echelon form: https://en.wikipedia.org/wiki/Row_echelon_form https://en.wikipedia.org/wiki/Row_echelon_form#Reduced_row_echelon_form

The row echelon form is used to solved the system of linear equations. What is the practical use of reduced raw echelon form?

Previous question in the forum was related to row echelon form (and not to reduced row echelon form): Is reducing a matrix to row echelon form useful at all?

Thanks

• @amWhy This question was marked as duplicate in error. – Yves Daoust Aug 19 '17 at 13:28
• Can you use please remove the "duplicate" from the subject? – student Aug 19 '17 at 13:45

For the resolution of linear systems, Gaussian elimination is preferred over Gauss-Jordan (these parallel the echelon and reduced echelon forms) as the former involves less operations (roughly $n^3/3$ vs $n^3/2$), for a similar numerical stability.