I.e. it is a singleton.
I've already showed that it is a subspace of (hopefully you'll agree that it is indeed a vector space).
But the problem is:
How can I find a basis for it?!
A basis must span the set S, but it must also be a linearly independent set!
So if I understand correctly, spans S, but it is not linearly independent (since any singleton set containing just the 0 vector is linearly dependent).
What am I to do?