###### 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*.