Also, could you explain how you inversed the matrices?

The only drawback of Matrices is the amount of number-crunching, and that is why it is good to use a computer program to calculate the inverse.

To find **A^-1** (the inverse of Matrix A) you want the answer to

A * **A^-1** = I

"I" is called the "Identity Matrix" and is really just the number 1 as a matrix !

For a 2x2 matrix I = [ 1 0 ]

[ 0 1 ]

For a 3x3 matrix I = [ 1 0 0 ]

[ 0 1 0 ]

[ 0 0 1 ]

(Now don't get confused, this is just like normal maths, it is just like saying you are trying to find the inverse of 7 by answering 7 * 7^-1 = 1)

In the case of the 2x2 matrix it is pretty easy, and you can do a bit of "voodoo" that gets you th right answer, like this:

Start with:

[ a b ]

[ c d ]

1) flip it around the "/" diagonal:

[ d b ]

[ c a ]

2) Apply negatives in a checkerboard fashion

[ d -b ]

[-c a ]

3) divide all be (ad-bc)

So, I did this:

(ad-bc) = 3*2 - 1*1 = 5

flip minuses divide

[3 1] ==> [2 1] ==> [ 2 -1] ==> [ 2/5 -1/5]

[1 2] [1 3] [-1 3] [-1/5 3/5]

[Would someone like to check to see if multiplying the original with this inverse does actually produce the identity matrix "I" mentioned above, it would prove that we have the right inverse]

For larger matrices there are different techniques to calculate the inverse, most of which burn up your calculator keys. People have been refining computer programs for years now that can do inversion pretty quick.

But note: *it may be impossible to invert a matrix!*. First of all it has to be square (2x2, 3x3 ...), and what happens if (ad-bc)=0? You can't divide by zero, and so if (ad-bc)=0, then you can't do it. Just like you couldn't solve 0a=1.

Or it just has different meanings in different places (most likely explanation!), because I **know** Rora would not intentionally be rude - I mean, she has corrected US often enough.

(I know it CAN mean to "cheat or defeat someone through trickery or deceit", what does it mean in Geordie?)

Anyway, best left out.

]]>No! No! Keep it, or I will ? !

The implications of such a post fathom the mind.

]]>No! No! Keep it, or I will ? !

I would agree with the first half of that.

Also, could you explain how you inversed the 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

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

Such is my ambition.

]]>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.

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