Hyperplane/Kernel of a linear form/Fact/Proof/Exercise

Let ${}V$ be an ${}n$-dimensional ${}K$-vector space, and let ${}U\subseteq V$ denote an ${}n-1$-dimensional linear subspace. Show that there exists a linear form ${}f\colon V\rightarrow K$ such that ${}U=\operatorname {kern} f$.

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