Answer
reduced row-echelon form
Work Step by Step
A matrix is in row-echelon form if the first non-zero (leading) entry in each row is $1$ and the leading entry is to the right of the leading entry of the row above. Also, all rows consisting only of zeros are at the bottom of the matrix. Furthermore, the matrix is in reduced row-echelon form if a column that contains a leading entry has all other entries as zero.
Here the matrix is:
$\left[\begin{array}{c c} 1& 0&0&3\\ 0&1&0&-2\\ 0&0&1&3/2\end{array} \right]$
Thus, according to the criteria above, this matrix is in reduced row-echelon form.