# Linear mapping/Composition/Fact/Proof/Exercise

Let ${\displaystyle {}K}$ be a field and let ${\displaystyle {}U,V,W}$ be vector spaces over ${\displaystyle {}K}$. Let ${\displaystyle {}\varphi \colon U\rightarrow V}$ and ${\displaystyle {}\psi \colon V\rightarrow W}$ be linear maps. Prove that also the composite function
${\displaystyle \psi \circ \varphi \colon U\longrightarrow W}$