Answer
$\left[\begin{array}{ccc}1 & 0 & -3 \\ 0 & 1 & 2 \\ 0 & 0 & 0\end{array}\right]$
Work Step by Step
Reduced echelon form of a matrix with first two pivot columns:
$\left[\begin{array}{lll}1 & 0 & a \\ 0 & 1 & b \\ 0 & 0 & 0\end{array}\right],$ where $a, b$ are scalars.
Write given problem using this matrix:
$\left[\begin{array}{lll}1 & 0 & a \\ 0 & 1 & b \\ 0 & 0 & 0\end{array}\right]\left[\begin{array}{c}3 \\ -2 \\ 1\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$
$3+a=0$
$a=-3$
$-2+b=0$
$b=2$
$\mathrm{So}, A=\left[\begin{array}{ccc}1 & 0 & -3 \\ 0 & 1 & 2 \\ 0 & 0 & 0\end{array}\right]$
