Big noise playing in the street

Gaah, I've spent the entire day on the same "mechanical" question. I should heed my own advice more often - labelling a problem "mechanical" is akin to calling it "easy", which I swore never to do again.

My first two attacks on this problem resulted in incorrect eigenvalues after I kept making silly errors while simplifying the characteristic polynomial. After I'd finally figured out that there was only one eigenvalue, I then tried to be clever in finding the invertible matrix Q with the property that A=QBQ^-1. Cleverness got me nowhere fast, and after an hour of abortive attempts and checking, I finally had to slow down and come at the thing systematically. It was only then that I realised I had an insoluble system on my hands. After a bit more checking of every stage of my workings I arrived at the conclusion that something funny was going on. The only thing left to do was flick a despairing email to Chris, which I did as quickly as possible.

Chris, being a terrific lecturer and extremely available even on weekend afternoons, replied promptly with a small novel's worth of explanation and elaboration. I've worked over it a bit, but more work is in order. And those two proofs still need to be done. And I haven't written up yet. And the assignment is due in 17 hours. Suddenly I'm glad I already got so far ahead on the test...