Answer
$x=\left( \frac{1}{2},-\frac{9}{2}, -\frac{9}{2}\right)$.
Work Step by Step
Assume that $x=(a,b,c)$, and $2 {x}-{u}+3 {v}+{w}={0}$, then we have
\begin{align*}
&\Longrightarrow 2 (a,b,c)-(1,-2,1)+3 (0,2,3)+(0,1,1)=(0,0,0)\\
&\Longrightarrow 2 (a,b,c)+(-1,2,-1)+ (0,6,9)+(0,1,1)=(0,0,0)\\
&\Longrightarrow (2a,2b,2c)+(-1,9,9)=(0,0,0)\\
&\Longrightarrow (2a,2b,2c)=(0,0,0)-(-1,9,9)\\
&\Longrightarrow (2a,2b,2c)=(1,-9,-9).
\end{align*}
Hence, $a=\frac{1}{2}$, $b=-\frac{9}{2}$, $c=-\frac{9}{2}$ and $x=\left( \frac{1}{2},-\frac{9}{2}, -\frac{9}{2}\right)$.
