Intersection and Span Assume $S_{1}$ and $S_{2}$ are subsets of a vector space V.
It has already been proved that span $(S1 \cap S2)$ $\subseteq$ span $(S_{1}) \cap$ span $(S_{2})$ 
There seem to be many cases where span $(S1 \cap S2)$ $=$ span $(S_{1}) \cap$ span $(S_{2})$ but not many where span $(S1 \cap S2)$ $\not=$ span $(S_{1}) \cap$ span $(S_{2})$.
Please help me find an example.
Thanks.        

HINT: Let $S_1=\{v\}$, where $v$ is a non-zero vector, and let $S_2=\{2v\}$.
