Show that L and {0} are the only subspaces of where V is a vector space over a field F and .
I don't know how to show they are the only subspaces of L and any help would be appreciated, thank you.
If is a subspace of , either it is equal to or it contains a non-zero vector . But if , there is a non-zero such that , hence , and as a consequence every scalar multiple of is in : and finally .