G Georgegr New member Joined Nov 4, 2018 Messages 6 Jan 11, 2019 #1 Suppose that V is a vector space. How can I prove that dimV=1 if and only if V has 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?

pka Elite Member Joined Jan 29, 2005 Messages 8,099 Jan 11, 2019 #2 Georgegr said: Suppose that V is a vector space. How can I prove that dimV=1 if and only if V has exactly two subspaces? Click to expand... 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 \(\displaystyle span\{v\}=V~?\)

Georgegr said: Suppose that V is a vector space. How can I prove that dimV=1 if and only if V has exactly two subspaces? Click to expand... 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 \(\displaystyle span\{v\}=V~?\)