Answer
The matrix is in the row-echelon form. It is also in the reduced row echelon form.
Work Step by Step
The matrix $$
\left[\begin{array}{rrrr}{1} & {2} & {-3} & {0} \\ {0} & {0} & {0} & {1} \\ {0} & {0} & {0} & {0}\end{array}\right]
$$
is in the row-echelon form. It is also in the reduced row echelon form.