Let $U$ and $W$ be subspaces of $V$ with $U \subseteq W$. Show that there is a subspace $W^\prime$ of $V$ such that $W \cap W^\prime = U$ and $W + W^\prime = V$.
I'm not quite sure where to begin with this. I've considered using the dimension formula that $\dim(W+W^\prime) = \dim(W) + \dim(W^\prime) - \dim(W \cap W^\prime)$, but am not entirely sure. Any help would be appreciated