Multilinear mapping/Vector space/Exercise

Let ${}K$ be a field, and let ${}V_{1},\ldots ,V_{n}$ and ${}W$ denote vector spaces over ${}K$. Show that the set of all multilinear mappings is, in a natural way, a vector space, denoted by ${}\operatorname {Mult} _{K}{\left(V_{1},\ldots ,V_{n};W\right)}$.

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