Proving Basis of Av with Invertible A Matrix

[Chris Rorres]

If A is an invertible matrix and vectors (v₁,v₂,...,v_n) is a basis for Rⁿ, prove that (Av₁,Av₂,...,Av_n) is also a basis for Rⁿ.

 

[tiny-tim]

Hi Chris!

Show us how far you get, and where you're stuck, and then we'll know how to help!

 

[ilia1987]

why don't threads like this get moved to homework?

 

[HallsofIvy]

Just lazy mentors!

 

[Chris Rorres]

I need to prove that (Av1,Av2,...,Avn) spans and that it is linearly independent but this proof is so confusing to me that i don't even know where to start doing that.

 

[Quantumpencil]

You need to show that b* A(v_1) + ... b_n A(v_n) = 0 implies b_1 ... b_n equals zero, right? Well, you know since A is invertible, what is it's kernal?