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 Rn
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.
Unnecessary- the problem says nothing about Rn