### Linear Algebra MA106 Exam Reflection

This year’s exam was written by a different person (Daan Krammer) to the previous years’ and so naturally it differed. In particular, the last question wasn’t a series of true/false, which I preferred for easy marks and occasional interesting point (and nice tricks – an identity map is not always an identity matrix, for one).

As before, I did past paper questions, got bored quickly, and flipped through the markschemes the morning of the exam. I did find a much better (shorter) “ranks are equivalent” proof than the one I’d previously learnt, so it wasn’t a complete waste of time.

The first question was standard fare even for previous papers. One question was awkwardly phrased, so I decided to take it literally. The second dealt with surjectivity and injectivity – a new topic for exams, but one I’m pretty sure was dealt with in assignments. The third contained a matrix proof where I couldn’t be bothered to memorise the subscripts involved, in the hope it wouldn’t come up – ah well. The fourth contained a horrible “find this 5×5 matrix determinant” that I got terribly wrong. The last part of four was an interesting original proof in which I used parts of my old rank-equivalent proof, mostly relating to bases of row spaces and the like. The fifth, which I didn’t do, was full of questions that would be easy to work backwards. I was turned off by the hint to the second part, which I couldn’t comprehend in the time limit.

Overall I think I did pretty well, but I may have got large swathes of it incorrect. Nonetheless, it was a more interesting exam than the previous ones – original proof questions are very fun if you get them.

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