1. ## Exactly two subspaces

Suppose that V is a vector space. How can I prove that dimV=1 if and only if V has exactly two subspaces?

2. Originally Posted by Georgegr
Suppose that V is a vector space. How can I prove that dimV=1 if and only if V has exactly two subspaces?
For example: What are the two subspaces (some call them trivial) of any v-space?
If $v\in V~\&~v\ne 0$ does $span\{v\}=V~?$