Think about what it means to be a subspace.
You're notation is confusing. You should be dealing with an inner product, and show that when pairing with a linear combination of vectors in the orthogonal complement, that you still get 0.
Problem:
For a set of vectors { } show that the set of vectors that are orthogonal to each is a subspace of
Solution:
Alright, I'm thinking that since the set of vectors X is orthogonal to then I can say something like
{ } = 0
therefore,
= 0 , and = 0
so
+ = 0
Am I thinking this through properly?