Answer
$ w\in$Nul A
Work Step by Step
By definition,
Nul A =$\{$x$: $ x$\in \mathbb{R}^{n}$ and Ax=0 $\}$.
---------
$Aw=\left[\begin{array}{lll}
3 & -5 & -3\\
6 & -2 & 0\\
-8 & 4 & 1
\end{array}\right]\left[\begin{array}{l}
1\\
3\\
-4
\end{array}\right]$
$=\left[\begin{array}{l}
3-15+12\\
6-6+0\\
-8+12-4
\end{array}\right]=\left[\begin{array}{l}
0\\
0\\
0
\end{array}\right]$
$Aw=0$, so $ w\in$Nul A
