Hi guys.

I had the following statement to prove:

Let be a linear transformation, and a set of vectors.

If are linear independent, and is one-to-one, then are also linear independent.

that's how I proved it:

are linear independent, so if:

then:

now, since is a linear transformation, it holds that , therefore:

and since we know that , then are linear independent.

my question here is:why should I care that is one-to-one?

any help would be greatly appreciated.