Row Eschelon Form

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

1. All zero rows (consisting only of zeros) are at the bottom.
2. Each leading entry is to the right of all leading entries in the row above it.
3. All entries below a leading entry are zero.

Broken examples

$$\left[\begin{array}{ccc}1& 0& 3\\ 0& 2& 1\\ 0& 0& 0\end{array}\right]$$

Invalid b/c it violates rule 2 above in row 2.

$$\left[\begin{array}{ccc}1& 0& 3\\ 0& 1& 2\\ 0& 1& 0\end{array}\right]$$

Violates rule 3 above in row 3.

$$\left[\begin{array}{ccc}1& 0& 3\\ 0& 0& 0\\ 0& 0& 0\end{array}\right]$$

Violates rule 1 in row 2.

Good examples

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