Answer
As there are 3 pivot columns, the dimension of the subspace is 3.
Work Step by Step
Given Subspace:
$\begin{bmatrix}1\\-2\\0\end{bmatrix},\begin{bmatrix}-3\\4\\1\end{bmatrix},\begin{bmatrix}-8\\6\\5\end{bmatrix},\begin{bmatrix}-3\\0\\7\end{bmatrix}$
Let's write the given vectors in augmented matrix $\mathbf{M}$ form and row reduce to echelon form;
$\mathbf{M}=\begin{bmatrix}1&-3&-8&-3\\-2&4&6&0\\0&1&5&7\end{bmatrix}\sim\begin{bmatrix}1&0&7&0\\0&1&5&0\\0&0&0&1\end{bmatrix}$
As there are 3 pivot columns, the dimension of the subspace is 3.