A matrix is said to be in reduced row echelon form or to be row-reduced if it satisfies the following properties:

P1. The first nonzero entry in each row (called the leading entry of that row) is a 1.
P2. The columns of the leading entries are clear (i.e., they contain zeros in all positions other than that of the leading entry).
P3. The leading entry in each row is to the right of the leading entry in the row above, and any rows of zeros are at the bottom.