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.


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