Sunday, April 29, 2007


I have just uncovered a conspiracy theory. The mechanics homework questions are made funny to disguise how hard they are. The original question can be found here. My version of the question is as follows:

Beans is sitting in a 10th floor office. Whilst staring aimlessly out of the window beans hears a
scream, “I hate Mechanics!”, and sees a fellow bean plummet past to the pavement
below. Whilst contemplating whether or not to do as the other bean had done, beans denotes the distance from the bottom to the top of the window as h, and the time that the suicidal bean took to cross that distance as T. Beans estimates that h = 1m and T= 0.05s. What floor do you think the suicidal bean jumped from, if each floor is approximately 4m and the suicidal bean was initially at rest?

Relax- I bounce, if you've forgotten, so the whole idea of me doing the same thing is ridiculous. Obviously I didn't consider it, but I certainly did consider chucking other things out of my window (namely mechanics things!) just to vent my frustration. (Once again not really, but I my initial amusement at the question soon turned to horror.)

I also noticed the footer where it said that if we find that question easy we should hand in question 3! That must be another joke, but alas this time round I'm not amused. I've been circulating between my homeworks today, and have not been very successful. I started with the mechanics question, did hopefully the first bits and then became stuck. So then I moved onto Linear Algebra. Can I just say that some of the books I have are ridiculously silly as is Google. The question is as follows.
Now I understand that ker(T)= null(T). So I first started by writing the following:

This seemed right enough to me, however I can't help but feel that I'm missing the 'plot'. I didn't worry about this for too long, since I'd gone through all that effort(!) and didn't want to feel that it was wasted. So naturally I moved onto part (ii). If you've got your face buried in your hands after my first attempt at that question, then let me reassure you that although I did start the second question in the same manner, I soon realised that I had a big mess! So I once again consulted my notes, the books that I had and the Internet. (You've probably realised that I didn't find the range, well I got it as span( [1 0 1 0]^T, [0 1 0 1]^T) but that's not left me filled with much confidence!).

In the end for question two I did it as follows:

So ker(T) ={0}. I once again smelt a rat, but after deciding that the range was all possible nxn matrices over R I moved on. (Well that was the only possible range it could be, since the nullity of T is 0, so the rank has to be 4!).

I'm using this post as an excuse for writing matrices with LaTeX, so please bare with me. I must say the most enjoyable part of my day has been trying to get them matrices to work! I felt that things could only get better, so like a blind mouse I continued to part iii. This was 'nicer' or so I thought anyway. I did the same as question 3i and then got it down to the following:

Hmmm, you see typing this up has another benefit. I've just realised that it's when A equals it's transpose, so I can have anything were the zeroes are, since it doesn't really matter what they are! But then that'll change the nullity to 3!

Anyway, fun's over for me. The range stinks and so do these questions. I despaired for a moment, thinking who am I kidding! I can't do any of my homeworks, so what the heck can I do? You see whilst I'd become stuck with the linear algebra homework I'd jumped to sequence and series. I was doing ok until that became impossible, however I was more relaxed about this since I just added the problems to my standard list of questions. Now I was stuck- what shall I do? Thankfully the moment of despair didn't last for long, since it can be quite demoralizing. I decided to look towards the positives but what also didn't help me was that whilst flicking through the text books, in hope for help, I'd stumbled across other questions which I couldn't do. Me being panicky didn't help, but I'm all calm now.

I'm going to tackle the mechanics problem again. I've got such a cool diagram drawn out, however I can't seem to use my ideas to get some answers. Maybe I'll do question 2 first (not yet tried that) to get in the 'swing' of things. About three weeks left till the exams. Coming back to university has given me the false sense of security that I'm 'working' and 'revising'.

However on to less depressing things. I'm going to yet comment on the football proceedings, since I'm going to patiently wait for next weekend! (Go Arsenal :D). Today my other uncle came over and he brought his kids as well. Now the funny thing is that today as was sitting watching TV my auntie asked, 'Are you any good at maths?' (I was pretty annoyed at this moment since I'd not been able to do my homeworks). I laughed and said, 'I'm OK at it.' She then asked me to help her daughters with her maths homework. I breathed a sigh of relief. Although I'm not sure whether she was being funny, or whether she truly didn't know that I'm doing a maths degree. Whatever it is, I was in no mood to 'defend' why I do maths so I gladly escaped to help my cousin with her work. (She's in year 5 and boy did I have a good cry when I saw her homework sheet!). It seems that she doesn't like maths- and the reason being was that she liked English better. Fair enough I thought so didn't worry myself by trying to convince her otherwise. (Noddy ended up helping her in the end, since I hadn't been there when she was stuck).

Primary school seems so appealing at the moment! I mean during break time or lunch time all we did was play football, cricket, tig tig etc etc. Wednesday's was the chess club and some other other clubs were also ran. No stress whatsoever. You stressed about getting picked to play on F's team, since his team always won. You didn't run around during your lunch time trying to complete your matlab project. Excuse this garbage- it's just that being 'older' isn't appealing as it seems. As Milo comments, when we're small we always think 'woo we're going to be 18 one day', but once you're 18 you think what the heck is so special? (although since technically I'm six this doesn't apply to me :D)

BTW I think I may have offended you guys by asking whether the theorem was 'correct'. The answer, for anyone who like me never lets on when things aren't obvious is that the theorem is incorrect. This is because zero is a real number, but the square of zero is zero which is not a positive number. So the square of every real number is not positive. (This stupid little fact was what caused me to miss the answer from the multiple choice test- I'd assumed that 0 was positive. Anyway one learns from their mistakes right?)

Maybe it's because of the weight on my head, but this post seems duh duh! I didn't accomplish what I set out to do, but worry not got another few hours left to finish mechanics!

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