Linear subspaces/Same dimension/Automorphism/Exercise

Let ${}V$ be a finite-dimensional ${}K$-vector space, and let ${}U_{1},U_{2}\subseteq V$ denote linear subspaces of the same dimension. Show that there exists an ${}K$-automorphism

$\varphi \colon V\longrightarrow V$

such that

${}\varphi (U_{1})=U_{2}\,.$

Create a solution