Hey guys, I've been trying this question but never get the same result as the answer sheet. It doesn't go into much, if any detail at all about it's methods so I was wondering if anybody can help me with it.

I know what rank and nullity are, and also the properties of linear mapping. But I just can't even figure out where to start.

Please could someone give me some hints, or maybe even just a step by step.

This is much appriciated - Thank you.