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