Echelon form

Definition

We say that a matrix is in row echelon form if

• The first non-zero entry of each row is $1$. (All zeroes are allowed)
• All entries which are directly below a leading $1$ are $0$.
• If $i<j$ then the leading $1$ on row $i$ must be be to the left of the leading $1$ of the row $j$.
• If there are $k$ rows of $0$‘s in the matrix, then these must be the last $k$ rows.

$$\left[\begin{array}{ccc}1& 1& 2\\ 0& 1& 0\end{array}\right]$$

is an example.