Let $\displaystyle \bold{A}$ be an $\displaystyle m \times n$ matrix and $\displaystyle f: \mathbb{R}^n \rightarrow \mathbb{R}^m $ :$\displaystyle \bold{x} \rightarrow \bold{A} \cdot \bold{x}$ What is a necessary and sufficient condition for f to be injective. And surjective?