Hi guys.

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:

Let .

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!