Suppose that is linearly independent oset of vectors in . Show that if A is an nxn nonsingular matrix then is also linearly independent.

So if the given set is linearlly independent that means that

and that

doesn't that mean that A must be 0?

can I use the theorem that if the larger set is linearally independent then it's subspace must be linearally independent? I'm not sure if I can use this becuse it's not like Av is part of the original set of vectors.