Linear algebra exam...with theory?

I will just go straight into this - I have not taken any mathematics examination with theory elements. Applying theory doesn't count. Until to this day. There was a glorious page of true/false questions on my linear algebra mid terms. Worth 25 marks in total, a simple true or false guess can give you 3 marks or take away from it. Wonderful.

Source

I once thought that handwriting programs is already nonsense enough (that changed since that post), but okay apparently having the need to memorize theory for something related to mathematics is a little more hilarious. You don't normally write "b^2 - 4ac > 0 means the equation has two separate real roots" on mathematics exams, you apply them, and knowing to use it or not is a little more important. But apparently linear algebra is a little different.

First of all, it is not as trivial as normal mathematics - it is just different. You will be dealing with brackets that group bunches of numbers together, performing arithmetic stuff on them, meet more brackets, and of course, more brackets. And, these brackets have different interpretations to different people - they either see it as data (computer science students), arrow lines where the projectile flies (physic students), or just a bunch of numbers (me, although I am studying computer science). But there is one thing in common - they make sense when you plot them up in a graph, or 3D space emulated in a computer. In fact, it is just matrices - you learnt that in secondary school, I suppose. Everything in linear algebra can be represented in geometry terms (unless it's a matrix with 4 dimensions or more, but we don't get them all the time anyway, in fact, you only see them in questions, there is literally no real life value of having 4 or more dimensions in a matrix), and everything makes sense when you see their geometry representations. Determinants, scaling, arithmetic operations, etc. Everything. If you are a student and you are struggling with this subject for whatever reason, like you don't get a thing in class or your lecturer just sucks, I highly suggest you to watch this 3Blue1Brown's playlist. Probably after the first two videos you will already have your mind blown and found a whole new world of maths.

To be honest, after watching what I need in the playlist, most things in linear algebra seems pretty trivial. But why we still need the theory?

Because, your brain is actually pretty bad at imagining things accurately - it does if you are extremely intelligent, but that's not me. If you are really intelligent enough, you won't need to remember if the determinant of a matrix is the same with the determinant of its inverse or not - you can just visualize it in the mind. Of course, you will need to be extremely intelligent, which I can say again, not me. With the theories, you can just slot in rule 1 rule 2 rule 63 theorem 54 theorem 32 and whatever that you can apply and bam, there's the solution.

So, that's why we have a totally crazy amount of theorem throughout the textbook - like (AB)C = A(BC), and don't ask for the rest because apparently I didn't memorize any of them. In those true or false questions I just go "well okay so I'll construct a matrix equation based on what you said, substitute random numbers into it, and see if it turns out to be true or not". It's the very first time I'm using the calculator for matrices. The Casio 570MS has functions on matrices, and it works for all arithmetic stuff, including finding the inverse, calculating determinant, etc. Not the best tool I have (Wolfram beats them all, you can't defeat Wolfram if you pay them, and I didn't), but it's really the best tool I have in the exam hall :)

There are two lecturers that set the question paper together - one of them is our lecturer, another one is someone who teaches for maths competitions. You know what is going to happen here. "Explain why this is the only matrix possible for this situation" and stuff like that. Mind blown. I was not expecting that, I forgot what I have wrote, but it might be some nonsense I created on the spot...like really, who studies these when the quizzes does not focus on them.

Whatever, I guess I won't do too badly? Idk, probably I will. I don't know, but there's no use thinking over it since I submitted the paper a few hours before this. Now probably I should go ham and play things, then care about assignment during the holidays. WiFi at house sucks, so you probably know why.

Right, see you next time.

--Lilacse