Linear mapping/Composition/Fact/Proof/Exercise

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

$\psi \circ \varphi \colon U\longrightarrow W$

is a linear map.

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