entry of every row above.

Some texts add the condition that the leading coefficient must be 1 while others require this only in reduced row echelon form.

These two conditions imply that all entries in a column below a leading coefficient are zeros.

The following is an example of a matrix in row echelon form, but not in reduced row echelon form:
:

Many properties of matrices may be easily deduced from their row echelon form, such as the rank and the kernel.