Answer
$dim\ Col\ A=3$ and $dim\ Nul\ A=1$
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\\
-3\\
2\\
-4
\end{bmatrix}
$, $\begin{bmatrix}
2\\
-1\\
4\\
2
\end{bmatrix}
$, and $\begin{bmatrix}
-4\\
5\\
-3\\
7
\end{bmatrix}
$
The basis for Nul A is $\begin{bmatrix}
-3\\
9\\
-6\\
12
\end{bmatrix}
$
dim Col A=3 and dim Nul A=1