Quote by JonF
I would show that any S could be extended to be a basis for V, then show that a basis for V can be extended to be a basis for R^{n}.

Sorry, but this makes no sense to me. The problem
was to show that any such S could be extended to a basis for V and there is no mention of R
^{n}.
Let B be a basis for S, what would the minimal subset of B look like that spans V?

This also makes no sense. S is a set of vectors, not a vector space and so has
no "basis". Even if S were a subspace of V, any basis for V would have to be a
superset of a basis for S, not a subset.
Ask your self a similar question to go from V to R^{n}

Unnecessary the problem says nothing about R
^{n}.