Linear algebra help: Linear independence

[epkid08]

Homework Statement

Let A be an m x n matrix of rank n. Suppose v_1, v_2, ..., v_k \in \mathbb{R}^n and \{v_1, v_2, ..., v_k\} is linearly independent. Prove that \{Av_1, Av_2, ..., Av_k\} is likewise linearly independent.

Homework Equations

The Attempt at a Solution

It says I need to use rank(A) = n, but I'm not sure how to use that info.

 

[Dick]

Rank n tells you that if you have a basis e_1, e_2, ..., e_n of \mathbb{R}^n then A(e_1), A(e_2), ..., A(e_n) are linearly independent. I.e. A takes R^n into an n-dimensional subspace of R^m.

 

[Deveno]

have you proven a subset of a linearly independent set is also linearly independent?

if so, extend the v's to a basis.