I’m 26 years out of high school, and I’ve used a lot of the algebra I’ve learned over the years at different jobs. This has allowed me to both appreciate and understand it better. But one thing I’ve never fully understood is Matrix Algebra. We spent a ridiculous amount of time on it in high school, but without ever receiving an explanation as to how we would end up using this in the future. Consequently, I’ve forgotten everything about it. I would also say I never really got it when they were teaching it to us, as I don’t do well on conceptual math versus practical math. So now I’m thinking back on the subject. Can anyone explain to me when matrix algebra comes in handy? And give an example of why it’s useful? thank you
***edited to matrix algebra, though couldn’t change title. Thought this was the plural of matrix…
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In: Mathematics
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You mean Matrix Algebra?
You can do a super neat trick if you want to solve a system of linear equations.
Take
3a-b+14c=7
2a+2b+3c=0
a-12b-18c=33
Now let’s split it up into 3 matrices, one is a square shaped one that has all the multipliers in it, then there is a single column one with the variables a, b and c in it. the last is another column, with the numbers on the right side. so:
|3 -1 14| | a | | 7 |
|2 2 3| × | b | = | 0 |
|1 -12 -18| | c | | 33 |
If you do a matrix multiplication on the two on the left you’ll get back the first form- try it if you want.
Anyway, let’s name them, in order, **A**, **x** and **b**
Now we can write the equation like this (pardon if the × and x look too similar – math works a *lot* better in LaTeX than reddit markdown.
**A** × **x** = **b**
Now, we want to know what the stuff in x is, right? those were our unknown variables after all! So let’s rearrange a bit so x is alone on the left side:
**x** = **A**^(-1) × **b**
That -1 in the corner means “A inverse”.
So, if we want to get **x**, we need to get **A inverse** and multiply it with **b**!
Now, I don’t feel like drawing another matrix by mashing spacebar, so you’ll have to believe me when I say that the result of A^(-1)×b is a column matrix that goes: 33/13, -900/403, -82/403. These three numbers correspond, in order top to bottom, to the variables in x. That is, the first is a, the second is b and the last is c.
Now, I’m not sure how much you meet linear equations on a daily basis but you are now immune to [facebook fruit math](https://www.google.com/search?q=facebook%20fruit%20math) – except in cases where you can’t fill out a square matrix and/or it isn’t invertable. In those cases the solution often doesn’t exist or there are infinite solutions anyway.
You can also use matrices to wrangle coordinates in 3D rendering/games and they are also used in a bunch of other places in computer science.
It’s used in calculations for rendering computer graphics. You can make a matrix that when you multiply a point by it, the resulting point does something specific such as translate or rotate it by a certain amount. You can also multiply a bunch of these matricies together to have a single matrix that does a bunch of operations all in one. This allows you to take a mesh of some model then take the points of that mesh and run it through the matrix multiplication to position the mesh where you want it in your rendered environment.
What is matrici algebra? You mean matrix/linear algebra?
If so; linear algebra is immensely important in all sorts of real-world computations, where you take complicated problems in physics and engineering and break them down into millions (if not billions) of smaller, simpler mathematical expressions that all need to be solved simultaneously, on a computer. Stress mechanics, fluid dynamics, anything that requires advanced computation overwhelmingly leans on linear algebra to actually solve these kinds of problems.
It’s great for engineering and systems of equations. I’m told computer science uses it in lots of things particularly graphics. For example I had a project last semester where we were given accelerometer data from a car in a 7×250,000 matrix and had to determine the rpm of the engine in 2 instances. I was told this is more common in load analysis of structures using strain gages.
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