Hyperplane/Kernel of a linear form/Fact

Let ${}V$ be an ${}n$-dimensional ${}K$-vector space, and let ${}U\subseteq V$ denote an ${}n-1$-dimensional linear subspace.

Then there exists a

linear form ${}f\colon V\rightarrow K$ such that

${}U=\operatorname {kern} f$.

Proof, Write another proof