Linear mapping/Sum/Exercise

Let ${}V$ and ${}W$ be vector spaces over a field ${}K$, and let ${}\varphi ,\psi \colon V\rightarrow W$ be linear mappings. Show that the mapping, defined by

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

is also linear.

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