# Gauss method problem

• May 25th 2006, 06:14 PM
gotchy
Gauss 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 AM
CaptainBlack
$
\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:

$
\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:

$
\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:

$
\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 $w$ 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