Linear subspace/Intersection/Dimension estimate/Fact

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}V}$ be a ${\displaystyle {}K}$-vector space of dimension ${\displaystyle {}n}$. Let ${\displaystyle {}U_{1},U_{2}\subseteq V}$ denote linear subspaces of dimensions ${\displaystyle {}\dim _{K}{\left(U_{1}\right)}=n-k_{1}}$ and ${\displaystyle {}\dim _{K}{\left(U_{2}\right)}=n-k_{2}}$.