# Span and Subspace Question

• October 13th 2008, 09:55 AM
kbartlett
Span and Subspace Question
Let V be a vector space over a field F, and let $S\subset S'$ 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 $V = R^3$ and give an example to show that it is possible that Span(S) = Span (S') even though $S \subset S'$ and $S \neq S'$.

d) Let U,W be subspaces of V. Prove that U+W is also a subspace of V.
• October 13th 2008, 12:53 PM
Lipticboven
I think subspace is a set closed under addition and scalar multiplication, i dont know if thats any help thou.