Like your avatar.

Welcome Kate!
Hooray! I'm not the only girl anymore!

There are one or two people here who MAY be girls, but they aren't saying.

"MathsIsFun " just a quick question, are you a mathmatician? I have no idea of your age.. but judging from your other posts I've read it seems as if you have the knowledge of university math. Haha if you're only a teenager or something then congratulations on your insane brain ;P

katecaroline wrote:

But I'll just keep a suspicion about Roraborealis then hehe.

What? I am a girl, and I follow in the footstpes of George Washington.

Ummmm, I thought you weren't.

i don't know nuffin bout no matrix algebra. what is matrix algebra?

I'm going to uni when I'm older and 'm gong to study maths!

Roraborealis wrote:

I'm going to uni when I'm older and 'm gong to study maths!

Good on you! I did my maths as part of an engineering degree - we already had to do a lot of maths, and then I took extra maths units as electives.

Oh, yes, I remember you saying you wanted to teach at Uni. Is that right? Or do you want to teach school kids?

MathsIsFun wrote:

Oh, yes, I remember you saying you wanted to teach at Uni.

Such is my ambition.

Yes, quite right. There are special rules for Matrices.

(Hold on to your hat, now, and I will try to explain a little - this may help you guys later ...)

For example you can't divide by a Matrix, but you can (sometimes) "Invert" a Matrix and Multiplying by an Inverse is the same as dividing.

So, let us say you know Matrices A and B, but don't know Matrix X in the following:

AX = B

Then, how do you find out Matrix X?

If you can invert Matrix A to become A^-1 (that is supposed to be an A with a neat little "-1" in the corner), then you can multiply both sides by A^-1:

A^-1 * AX = A^-1 * B

And A^-1 * A cancel each other out (just like 1/7 times 7 would), so you get:

X = A^-1 B

How Is This Useful ?

It can let Engineers, Scientists, Economists, etc play with large sets of equations. If you can figure out how to use matrices to express a problem, then you can get a program to crunch the sums for you.

Here is a really simple problem - we could solve it ourselves, but you could imagine that instead of 2 equations there were 200 to solve together:

3x + y = 7
x + 2y = 4

In Matrix form this would be:

[ 3  1 ] [x]  =  [7]
[ 1  2 ] [y]      [4]

The Inverse of  [ 3  1 ] is  [ 2/5  -1/5 ] (Just believe me, OK? There is a standard pattern to follow to get there)
                       [ 1  2 ]     [-1/5   3/5 ]

So the answer is:

[x]  =  [ 2/5  -1/5 ][7]
[y]      [-1/5   3/5 ][4]

Multiplying matrices follows a standard pattern, too. In this case I will write it out longhand:

x =  2/5 * 7  +  -1/5 * 4
y = -1/5 * 7  +   3/5 * 4

Calculating, the answer becomes:

x = 14/5 - 4/5 = 10/5 = 2
y = -7/5 + 12/5 = 5/5 = 1

As you can see, there is a fair amount of calculation involved, but that is what computers are for. So a program could handle a problem that had hundreds or thousands of equations for you.

So, YOU, the designer would work out the "Matrix Algebra" needed to solve your problem, then just tell the program "Invert A, multiply it by B ... " etc