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## Homework Statement

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