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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: monkeywantsabanana on April 16, 2011, 06:11:57 pm

Title: Just some basic matrices
Post by: monkeywantsabanana on April 16, 2011, 06:11:57 pm: Hey guys this is odd - check it out...

W= [2 -3]
[4 6]

and V = [4 0]
[3 -1]

find X such that WX=V...

so..

X = W^-1 times V
if i type that into calculator i get the right answer
but if i do it by hand i get a different answer - by hand my next step would be

det W = 24
W^-1 = 1/24 [6 3] [4 0]
[-4 2] [3 -1]

i type that into calculator I get a different answer, does anyone know why this is?

Sorry guys, idk how to do the math working out on the forum - it looks messy.

All replies appreciated.
Title: Re: Just some basic matrices
Post by: luffy on April 16, 2011, 07:07:55 pm: This is my working (by hand) - Sorry if I made any errors:

$W = \begin{bmatrix} 2 &-3 \\ 4 & 6 \end{bmatrix}$

$V = \begin{bmatrix} 4&0\\ 3 & -1 \end{bmatrix}$

$WX = V$

$X = W^{-1} V$

$X = \frac{1}{24}\begin{bmatrix} 6 &3 \\ -4 & 2 \end{bmatrix} \times \begin{bmatrix} 4&0\\ 3 & -1 \end{bmatrix}$

$\therefore X = \frac{1}{24} \begin{bmatrix} 24 + 9 & 0 - 3\\ -16 + 6 & 0 - 2 \end{bmatrix}$

$\therefore X = \frac{1}{24}\begin{bmatrix} 33 & - 3\\ -10 & - 2 \end{bmatrix}$

$\therefore X = \begin{bmatrix} \frac{11}{8} & -\frac{1}{8}\\ -\frac{5}{12} & -\frac{ 1}{12} \end{bmatrix}$

Hope I helped.
Title: Re: Just some basic matrices
Post by: monkeywantsabanana on April 16, 2011, 07:31:29 pm: I got that too!!

but - when you do that times by W you don't get V

Why is this ?
Title: Re: Just some basic matrices
Post by: BubbleWrapMan on April 16, 2011, 08:05:04 pm: It's different if you multiply it as WV or VW, maybe that's it?
Title: Re: Just some basic matrices
Post by: iNerd on April 16, 2011, 08:05:33 pm: Quote from: ClimbTooHigh on April 16, 2011, 08:05:04 pm
It's different if you multiply it as WV or VW, maybe that's it?
This. With matrices you multiply by order.
Title: Re: Just some basic matrices
Post by: monkeywantsabanana on April 16, 2011, 08:31:40 pm: Ah that's right.
Silly me...

THANK YOU ALL !!!

can some one teach me how to do the working out that 'luffy' did?
Title: Re: Just some basic matrices
Post by: pi on April 16, 2011, 08:34:30 pm: Do you mean $LaTeX$ or the actual mathematical process?
Title: Re: Just some basic matrices
Post by: monkeywantsabanana on April 16, 2011, 08:37:22 pm: not the process. how to do the process with that font. :O
Title: Re: Just some basic matrices
Post by: pi on April 16, 2011, 08:40:46 pm: Quote from: monkeywantsabanana on April 16, 2011, 08:37:22 pm
not the process. how to do the process with that font. :O

Its a long explanation :P

Firstly, you can use it through the 'TEX' button (when you hit 'reply', the button is under the 'change colour' dropdown box).

Then, try and experiment with some simple things here.

Some stuff not on there:
To create a matrix:
Code: [Select]
[tex] A = \begin{bmatrix} w & x \\ y & z \end{bmatrix} [/tex] $A = \begin{bmatrix} w & x \\ y & z \end{bmatrix}$

For fractions:
Code: [Select]
[tex]A = \frac{x}{y}[/tex] $A = \frac{x}{y}$

I'm still learning too! :)
Title: Re: Just some basic matrices
Post by: monkeywantsabanana on April 16, 2011, 08:53:57 pm: thanks !