# Exactly two subspaces

#### Georgegr

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

#### pka

##### Elite Member
Suppose that V is a vector space. How can I prove that dimV=1 if and only if V has exactly two subspaces?
If $$\displaystyle v\in V~\&~v\ne 0$$ does $$\displaystyle span\{v\}=V~?$$