I have a work sheet on proofs but this is the first question and it would really help if I could be shown this one so I can attempt the last ones by myself. Thank you
Let $U, V, W$ be finite-dimensional vector spaces and let $P : U \to V$, and $Q : V \to W$ be linear maps. Prove that $null(Q \circ P) \le null(Q) + null(P)$.
Hint: it may help to consider the restriction of $P$ to $Ker(Q\circ P)$.
