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
Which matrices are in RREF?
- NO, pivot isn't 1
- NO, zero row is not at the bottom