The following problem is an unsolved practice problem from a textbook which is assigned at the end of the chapter. So, I need hints on how to start solving the problem below:
Show that if $U$, $V$, $W$ are finite dimensional vector spaces, and $f\in \mathrm{Hom}\left ( U,V \right )$, $g\in \mathrm{Hom}\left ( V,W \right )$, then: $\dim \mathrm{Ker}\left ( gf \right )\leqslant \dim \mathrm{Ker}(f) + \dim \mathrm{Ker}(g)$