I have 2 problem to solve with the Gauss metohd an im a little lost in that. someone help ?

#1

x + 3y - 2z = -5

2x + -y - z - w = -1

3x - 2y +4w = 1

-x + y - 3z - w = -6

#2

5x + y - z =1

2x - y - z = 0

thanks

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- May 25th 2006, 06:14 PMgotchyGauss method problem
I have 2 problem to solve with the Gauss metohd an im a little lost in that. someone help ?

#1

x + 3y - 2z = -5

2x + -y - z - w = -1

3x - 2y +4w = 1

-x + y - 3z - w = -6

#2

5x + y - z =1

2x - y - z = 0

thanks - May 26th 2006, 09:31 AMCaptainBlack
$\displaystyle

\begin{array}{cccccc}

x&+3y&-2z&&=&-5\\

2x&-y&-z&-w&=&-1\\

3x&-2y&&+4w&=& 1\\

-x&+y&-3z&-w&=&-6

\end{array}

$

Now subtract twice the first row from the second, and

subtarct three times the first row from the third, and

add the first row to the fourth:

$\displaystyle

\begin{array}{cccccc}

x&+3y&-2z&&=&-5\\

&-7y&3z&-w&=& 9\\

&-11y&6z&+4w&=& 7\\

&4y&z&-w&=&-11

\end{array}

$

replace row three by row3+row4-row2, and row 4 by 11(2row4+row2)+row3:

$\displaystyle

\begin{array}{cccccc}

x&+3y&-2z&&=&-5\\

&-7y&3z&-w&=& 9\\

&&4z&+4w&=& -13\\

&&61z&-29w&=&-136

\end{array}

$

Now replace row 4 by 4row4-61row3:

$\displaystyle

\begin{array}{cccccc}

x&+3y&-2z&&=&-5\\

&-7y&3z&-w&=& 9\\

&&4z&+4w&=& -13\\

&&&-400w&=&244

\end{array}

$

Now you need to check the arithmetic as I'm not too careful about that.

Then solve starting from the last equation and $\displaystyle w$ for the

variables, using the values for the variables found at each step to

substitute into the next earlier equation to solve for the next variable.

RonL