Reduced row-eschelon form

A row-eschelon matrix is said to be in reduced row-eschelon form if in addition it satisfies the following conditions:

1. Must be in Row Eschelon Form
2. Each leading 1 is the only nonzero entry in its column
3. The first non-zero entry from the left in each non-zero row is a 1. This is called a leading one for that row.

Good examples

$$\left[\begin{array}{ccc}1& \ast & 0\\ 0& 0& 1\end{array}\right]$$ $$\left[\begin{array}{cccc}0& 1& 0& \ast \\ 0& 0& 1& \ast \\ 0& 0& 0& 0\end{array}\right]$$ $$\left[\begin{array}{cccc}1& 0& \ast & 0\\ 0& 1& \ast & 0\\ 0& 0& 0& 0\end{array}\right]$$ $$\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$$

Pivots

Once a matrix is in Reduced row-eschelon form, the leading 1’s are called pivots and the column that contains them are called pivot columns.