Answer
See solution
Work Step by Step
The basis for the subspace include the pivot columns of matrix $\begin{bmatrix}
1&-3&2&-4\\
-3&9&-1&5\\
2&-6&4&-3\\
-4&12&2&7
\end{bmatrix}
$
After row reducing, we can see columns 1, 3, and 4 are pivot columns. The basis for the subspace 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}
$ and the dimension is 3.
