Definition 1.2.3

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.