Homomorphism space/K to W/Example/Exercise

Let ${}W$ be a ${}K$-vector space over the field ${}K$. Show that the mapping

$\operatorname {Hom} _{K}{\left(K,W\right)}\longrightarrow W,\varphi \longmapsto \varphi (1),$

is an isomorphism of vector spaces.

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