The Attempt at a Solution
The terminology in this question confuses me into what I am actually trying to solve. It seems to me that S-perp would naturally be a subspace of real column vectors based on the fact that we specify that S[tex]\neq[/tex]0. It goes on to mention that S-perp is nonempty which seems obvious in the fact that S is not empty and it asks to show that any scalar multiples of vectors within the subset of S-perp will continue to be elements of S-perp.
So i've reached the thought that either
1) This question is ridiculously simply that intends for me to re-state the obvious or
2) I've missed something completely and it actually requires a long proof. Any insights?