Vector spaces/Evaluation mapping/Multilinearity/Exercise

Let ${}K$ be a field, and let ${}V$ and ${}W$ denote a ${}K$-vector space. Determine whether the mapping

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

is multilinear.

Create a solution