I'm not sure what you're allowed to use at this point, but do you have any results about a linear map and the dimension of its domain, image, and kernel?
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.