# Row Echelon Form

A matrix is in __row echelon form__ if...

- all zero rows (if any) are at the bottom
- Each leading entry of a row is to the
__right__of the leading entry in the row above - Below a leading entry, all entries are zero
- all pivots equal 1
- each pivot is the only non-zero entry in its column

Example matrix in row echelon form

A matrix is in __reduced row echelon form__ if it is in row echelon form and...

there is no pivot in the middle column with the 4, which can't be reduced to 1 without messing up the pivot in its row

## Row Reduction (to get RREF)

- from left to right, finding pivots 1 by 1 and eliminating terms below them
- from right to left, eliminate the terms above pivots

- along the way, scale pivots so each is 1

## Example 2

Which matrices are in RREF?

- NO, pivot isn't 1

- YES

- NO, zero row is not at the bottom