I almost think I should delete my last post about Matrix Algebra - it is probably just plain confusing, and years away for most of you, also I just wrote it out without thinking too much. Sorry if it was confusing.

Yes keep it! That was amazing I actually understand inverses a little more. I'm pretty sure we'll be introduced a little into matrix algebra this year. I hope anyway, it sounds uberly exciting

Roraborealis wrote:

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

The implications of such a post fathom the mind.

mathsyperson wrote:

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.