I think subspace is a set closed under addition and scalar multiplication, i dont know if thats any help thou.
Let V be a vector space over a field F, and let be subsets of V.
a) Show that span(S) is a subspace of V.
b) Show that span(S) is a subset of Span(S').
c) Take and give an example to show that it is possible that Span(S) = Span (S') even though and .
d) Let U,W be subspaces of V. Prove that U+W is also a subspace of V.