A rectangular matrix is in echelon form if:
- All zero rows (if any are present) are at the bottom.
- The first non-zero entry (or leading entry) of a row is to the right of any leading entries in the row above it (if any).
- All entries below a leading entry (if any) are zero.
A matrix in echelon form is in row reduced echelon form if:
- It is in echelon form
- All leading entries, if any, are equal to 1.
- Leading entries are the only nonzero entry in their respective column.
Each matrix is row equivalent to one and only one reduced echelon matrix.