Answer
p is not in Nul A because $Ap=0$ is not true
Work Step by Step
For p to be in Nul A, $Ap=0$ must be true.
However, $\begin{bmatrix}
2&-3&-4\\
-8&8&6\\
6&-7&-7
\end{bmatrix}
$$\begin{bmatrix}
6\\
-10\\
11
\end{bmatrix}
$=$\begin{bmatrix}
-2\\
-62\\
29
\end{bmatrix}
$, so p is not a solution to the homogenous equation and is not in Nul A.
