We say that a matrix is in reduced row echelon form if the following properties are satisfied.
- Any rows in which all the entries are zero are at the bottom of the matrix.
- If we move across a row from left to right, the first nonzero entry we encounter is 1. We call this entry the leading entry in the row.
- The leading entry in one row is to the right of the leading entry in any row above.
- A leading entry is the only nonzero entry in its column.
We call a matrix in reduced row echelon form a reduced row echelon matrix.