# Show that the affine transformation of a polyhedron is a polyhedron.

Let $$P=\{x \in \mathbb{R}^n \mid Ax \geq b\}$$ be a nonempty polyhedron for a matrix $$A \in \mathbb{R}^{m \times n}$$ and $$b \in \mathbb{R}^{m}$$.

Let $$F:\mathbb{R}^m \rightarrow \mathbb{R}^n$$ be an affine transformation defined by $$F(x)=Tx+c$$, where $$T \in \mathbb{R}^{m \times n}$$ and $$c \in \mathbb{R}^m$$.

Show that the set $$F(P) \subseteq \mathbb{R}^m$$ is polyhedron.

Probably, this can be shown by the Minkowski-Weyl theorem.