Answer
u is in Nul A because $Au=0$ is true.
Work Step by Step
For u to be in Nul A, $Au=0$ must be true.
$A=\begin{bmatrix}
-3&-2&0\\
0&2&-6\\
6&3&3
\end{bmatrix}
$ and $u=\begin{bmatrix}
-2\\
3\\
1
\end{bmatrix}
$
$\begin{bmatrix}
-3&-2&0\\
0&2&-6\\
6&3&3
\end{bmatrix}\begin{bmatrix}
-2\\
3\\
1
\end{bmatrix}=\begin{bmatrix}
0\\
0\\
0
\end{bmatrix}
$Therefore, u is in Nul A
