Answer
$ w\in $ Nul A
Work Step by Step
By definition,
Nul A =$\{$x$: $ x$\in \mathbb{R}^{n}$ and Ax=0 $\}$.
---------
$Aw=\left[\begin{array}{lll}
5 & 21 & 19\\
13 & 23 & 2\\
8 & 14 & 1
\end{array}\right]\left[\begin{array}{l}
5\\
-3\\
2
\end{array}\right]$
$=\left[\begin{array}{l}
25-63+38\\
65-69+4\\
40-42+2
\end{array}\right]=\left[\begin{array}{l}
0\\
0\\
0
\end{array}\right]$
$Aw=0$, so $ w\in$Nul A
