Answer
See solution
Work Step by Step
Any vector x such that $x=\begin{bmatrix}
\frac{1}{3}\\
-\frac{5}{3}\\
1\\
\end{bmatrix}x_3
$ where $x_3$ is a free variables will be in Nul A.
One example is $\begin{bmatrix}
1\\
-5\\
3
\end{bmatrix}
$
Any x such that $x=\begin{bmatrix}
1\\
4\\
-5\\
2
\end{bmatrix}c_1+\begin{bmatrix}
2\\
5\\
-1\\
-7
\end{bmatrix}c_2+\begin{bmatrix}
3\\
7\\
0\\
11
\end{bmatrix}c_3
$ where $c_1,c_2,c_3$ are scalars is in Col A. One example is $\begin{bmatrix}
1\\
4\\
-5\\
2
\end{bmatrix}$
