hello. my question is this:

2x-y+3=1

-x-3y+2z=-4

-3x+y+7z=-2

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- Sep 24th 2007, 09:09 PMjay123matrices
hello. my question is this:

2x-y+3=1

-x-3y+2z=-4

-3x+y+7z=-2 - Sep 24th 2007, 09:13 PMJhevon
- Sep 24th 2007, 09:16 PMjay123
Row of operation to an Augmented Matrix

- Sep 24th 2007, 09:47 PMjay123
is there any way you can help me.

I know there is a system to solving these equations. such as add the 1st two roles to get the 1st row but i cant remember the rest. - Sep 25th 2007, 03:46 AMWWTL@WHL
Are you talking about echelon form?

The most common way (I think) of doing this is finding the inverse of the matrix. Have you learned how to do that? - Sep 25th 2007, 07:39 AMJhevon
yes, that's what he's talking about. i will go all the way to reduced row echelon, i like doing that.

ok, here goes. i will not type what i did to get from one step to another, so if you don't understand something, just ask.

The augmented matrix is:

...$\displaystyle x$.....$\displaystyle y$....$\displaystyle z$

$\displaystyle \left| \begin {array}{ccc|c} 2 & {-1} & 3& 1 \\ {-1}&{-3} & 2& {-4} \\ {-3}&1 &7 &{-2} \end {array} \right|$

$\displaystyle \left| \begin {array}{ccc|c} 1& 3& {-2}& 4\\ 0& -7& 7&-7 \\ 0& 10&1 &10 \end {array} \right|$

$\displaystyle \left| \begin {array}{ccc|c} 1& 3& -2&4 \\ 0& 1& -1&1 \\ 0& 10& 1&10 \end {array} \right|$

$\displaystyle \left| \begin {array}{ccc|c} 1& 0& 1&1 \\ 0& 1& -1&1 \\ 0& 0& 11& 0\end {array} \right|$

$\displaystyle \left| \begin {array}{ccc|c} 1& 0& 1&1 \\ 0&1 &0 &1 \\ 0& 0& 1& 0\end {array} \right|$

$\displaystyle \left| \begin {array}{ccc|c} 1& 0& 0&1 \\ 0& 1&0 &1 \\ 0& 0& 1& 0\end {array} \right|$

now read off your solutions...