Comments from Trevor:

Question 1) This should be straightforward. Part (b) was meant to see if you understood how multiplication works. Part (c) was designed to make students anxious about saying two parts of a question couldn't be done.

Question 2) I found this one interesting. It tests transposes in two ways, both computing them and using transpose laws to see the relation in part (b).

Question 3) Part (a) is a warm-up for Part (c), which is much trickier. Part (a) had an obvious starting position, while Part (c) did not. You also had to know properties of inverses to get part (c) right. Part (b) exists to test whether or not you understand how linear systems and invertibility interact.

Question 4) Just follow the algorithm. This is your fun computation question that you shouldn't get wrong. (Although, I messed up the first time I did it).

Question 5) It's 8 points because it's long and requires you to do an if and only if proof. You're basically proving why Question 4 works the way it does, so the methods you used for Question 4 hopefully triggered an idea of how to tackle this question. Question 3(b) and 3(c) also contribute some properties needed to finish the proof. Make sure you can do these proofs. It was probably difficult if you weren't prepared.