Linear subspace/Realization as kernel of a linear mapping/Exercise

Let $K$ be a field, and let $V$ denote a finite-dimensional $K$-vector space. Let $U\subseteq V$ be a linear subspace. Show that there exists a $K$-vector space $W$ and a surjective $K$-linear mapping

$\phi :V⟶W$

such that $U=\mathrm{kern}\phi$ holds.

Create a solution