Affine mapping/One point suffices/Exercise

Let ${}K$ be a field, and let ${}E$ and ${}F$ denote affine spaces over the vector spaces ${}V$ and ${}W$, respectively. Let a mapping

$\psi \colon E\longrightarrow F,$

a linear mapping

$\varphi \colon V\longrightarrow W,$

and a point ${}P\in E$ be given such that

${}\psi (P+v)=\psi (P)+\varphi (v)\,$

holds for all ${}v\in V$. Show that ${}\psi$ is affine-linear.

Create a solution