I need to prove the following:
Let be a vector space over , such that .
Let be a linear transformation such that: .
Prove that for every : are linear independent.
This is what I tried so far:
suppose , I need to prove .
since is linear, and , then also , and then:
now since :
but now I'm not sure what conclusion should I draw from this...
I can really use some guidance here.
Thanks in advanced!