Exactly two subspaces

Georgegr

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Joined
Nov 4, 2018
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Suppose that V is a vector space. How can I prove that dimV=1 if and only if V has exactly two subspaces?
 

pka

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Jan 29, 2005
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7,813
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 \(\displaystyle v\in V~\&~v\ne 0\) does \(\displaystyle span\{v\}=V~?\)
 
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