Answer
dim Col A=3 and dim Nul A=2
Work Step by Step
The basis for Col A include the pivot columns and the basis for Nul A include all other columns.
The basis for Col A is $\begin{bmatrix}
1\\
1\\
-2\\
4
\end{bmatrix}
$, $\begin{bmatrix}
-2\\
-1\\
0\\
1
\end{bmatrix}
$, and $\begin{bmatrix}
5\\
5\\
1\\
1
\end{bmatrix}
$
The basis for Nul A is $\begin{bmatrix}
9\\
6\\
-6\\
9
\end{bmatrix}
$ and $\begin{bmatrix}
4\\
-3\\
-2\\
-9
\end{bmatrix}
$
dim Col A=3 and dim Nul A=2
