Factorization Method

**zorro** · December 15th 2009, 05:10 PM

Question : Solve the equations
2x + 3y+z=9
x+2y+3z=6
3x+y+2z=8
by factorization method

**pickslides** · December 15th 2009, 05:16 PM

I don't know of the method you are speaking of but you can solve it as follows

$ \left[ \begin{array}{c} x\\ y\\ z\end{array}\right]=\left[ \begin{array}{ccc} 2 & 3 & 1 \\ 1 & 2 & 3 \\ 3 & 1 & 2 \end{array} \right]^{-1} \left[ \begin{array}{c} 9\\ 6\\ 8\end{array}\right] $

**zorro** · December 15th 2009, 07:19 PM

Originally Posted by pickslides

I don't know of the method you are speaking of but you can solve it as follows

$ \left[ \begin{array}{c} x\\ y\\ z\end{array}\right]=\left[ \begin{array}{ccc} 2 & 3 & 1 \\ 1 & 2 & 3 \\ 3 & 1 & 2 \end{array} \right]^{-1} \left[ \begin{array}{c} 9\\ 6\\ 8\end{array}\right] $

Thanks Pickslides but i dont know what should i do next with that the method u posted does it have a method which i could sees on how to solve that problem ...

**pickslides** · December 15th 2009, 07:33 PM

To finish with the method posted you need to find this

$ \left[ \begin{array}{ccc} 2 & 3 & 1 \\ 1 & 2 & 3 \\ 3 & 1 & 2 \end{array} \right]^{-1} $

which is the inverse of a $3\times 3$ matrix, read this
Cramer's rule - Wikipedia, the free encyclopedia

the result needs to be mulitplied by

$\left[ \begin{array}{c} 9\\ 6\\ 8\end{array}\right]$

do you know how to multiply matrices?

Read this, Matrix multiplication - Wikipedia, the free encyclopedia

or try this Matrix Multiplying Calculator

Good luck!

**zorro** · December 16th 2009, 07:38 PM

Originally Posted by pickslides

To finish with the method posted you need to find this

$ \left[ \begin{array}{ccc} 2 & 3 & 1 \\ 1 & 2 & 3 \\ 3 & 1 & 2 \end{array} \right]^{-1} $

which is the inverse of a $3\times 3$ matrix, read this
Cramer's rule - Wikipedia, the free encyclopedia

the result needs to be mulitplied by

$\left[ \begin{array}{c} 9\\ 6\\ 8\end{array}\right]$

do you know how to multiply matrices?

Read this, Matrix multiplication - Wikipedia, the free encyclopedia

or try this Matrix Multiplying Calculator

Good luck!

Thanks mate for helping me with this one ..............

cheers mate

**pickslides** · December 17th 2009, 12:13 PM

Originally Posted by zorro

**zorro** · December 18th 2009, 07:20 PM

Originally Posted by pickslides

**Bacterius** · December 19th 2009, 02:59 AM

Just couldn't resist

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Thanks but what should i do next ????

Thanks mate........

Cheers mite

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