403/503 – HW4

Let $b\in\mathbb R^m$ and let $A$ be an $m\times n$ matrix with real entries. Set $C=\{x\in\mathbb R^n\mid Ax=b\}$, and suppose that $C\ne\emptyset$. Show that $C$ is an affine space.

(Due January 29 at the beginning of lecture.)