# Thread: [Linear Algebra] Determine if a set is a basis

1. ## [Linear Algebra] Determine if a set is a basis

Determine if {v1,v2,...vn} is a basis of Rn and A is invertible n x n matrix, then {Av1,Av2...Avn} is a basis of Rn

So I got all the questions before this correct, but this one confusing me.
I'm not sure what a matrices invertibility has to do with any of this. I do know (i think I know) that if a matrix is invertible then it has linearly independent columns. It looks like {Av1,Av2...Avn} is supposed to be the basis of some matrix transformation but I'm lost on any of the rest of it.

2. ## Re: [Linear Algebra] Determine if a set is a basis

Show that $\displaystyle A v_1,A v_2,\text{...},A v_n$ are linearly independent