Homomorphism space/Linear subspace/Mapping space/Exercise

Let ${}K$ be a field, and let ${}V$ and ${}W$ be ${}K$-vector spaces. Show that the homomorphism space

$\operatorname {Hom} _{K}{\left(V,W\right)}$

is a linear subspace of the mapping space ${}\operatorname {Map} \,{\left(V,W\right)}$.

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