Row echelon form VS Reduced row echelon form

A matrix is in row echelon form if

All nonzero rows (rows with at least one nonzero element) are above any rows of

all zeroes (all zero rows, if any, belong at the bottom of the matrix).

The leading coefficient (the first nonzero number from the left, also called the

pivot) of a nonzero row is always strictly to the right of the leading coefficient of

the row above it (some texts add the condition that the leading coefficient

must be 1).

All entries in a column below a leading entry are zeroes (implied by the first two

criteria)

This is an example of a 35 matrix in row echelon form:

A matrix is in reduced row echelon form if it satisfies the following conditions:

It is in row echelon form.

Every leading coefficient is 1 and is the only nonzero entry in its column.

This is an example of a 35 matrix in reduced row echelon form:

Row echelon form Reduced row echelon form

1 4 5 2 3

0 0 1 4 5

0 0 0 1 6

0 0 0 0 0

0

0

1 4 0 3

0 0 1 5

0 0 0 1 6

0 0 0 0 0