First Loop

I may be forgetting my circuit diagrams, but isn't the voltage drop across $V$ the opposite sign of the drop across $E$ in the first loop? In which case the first equation would be $V-E=i_1$. If so, this means the rest of the questions for 3 must be redone.

Hi Alistair,

You're right about the first equation, but there is no need to redo the problem- I just made a typo in that equation. You can see that the matrix equation described below is correct.

Also, I'm pretty sure the answers to parts (b) and (c) are correct because I checked them with an online tool.