I've been working on the following problem:
"Let be a finite-dimensional vector space over a field , and let be an ordered basis for . Let be an invertible matrix with entries from . Define for , and set . Prove that is a basis for and hence that is the change of coordinate matrix changing -coordinates into -coordinates."
Can someone point me in the right direction with this? Obviously I need to show that is linearly independent and spans . I know there are n vectors in so it only remains to show that its elements are linearly independent, correct? I can't seem to figure it out though.