# 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
$\displaystyle \begin{array}{cccccc} x&+3y&-2z&&=&-5\\ 2x&-y&-z&-w&=&-1\\ 3x&-2y&&+4w&=& 1\\ -x&+y&-3z&-w&=&-6 \end{array}$

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