# Thread: Exactly two subspaces

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?
Please post what you understand about this question.
For example: What are the two subspaces (some call them trivial) of any v-space?
If $v\in V~\&~v\ne 0$ does $span\{v\}=V~?$

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