[[Linear equations MOC]]
# Gauß-Jordan elimination
**Gauß-Jordan elimination** is a modified form of [[Gaußian elimination]]
by which a [[system of linear equations]] may be manipulated into [[Row echelon form#Reduced row echelon form|reduced row echelon form]]
through [[Elementary row operation|elementary row operations]].
It modifies Gaußian elimination as follows:

- All nonzero leading entries are set to $1$ by scaling the row.
- Entries both above and below a pivot entry are set to $0$ instead of just below.
  The same method of adding multiples of the pivot row is used.


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