Linear mapping/Composition/Fact

Let ${\displaystyle {}K}$ denote a field, and let ${\displaystyle {}U,V,W}$ denote vector spaces over ${\displaystyle {}K}$. Suppose that

${\displaystyle \varphi :U\longrightarrow V\,\,{\text{ and }}\,\,\psi :V\longrightarrow W}$

are linear mappings.