Hyperplane/Kernel of a linear form/Fact

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

Then there exists a

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

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