Let $V$ and $W$ be vector spaces over $F$ , let $f\in \operatorname[Hom]_F(V,W)$ and let $ \vec v_1 \ldots \vec v_k \in V$ . Prove that if the set ${f(\vec v_1), \ldots , f(\vec v_k )}$ is linearly independent then $ \vec v_1 \ldots \vec v_k $ must be linearly independent.
not sure how to go about this one