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Math Help - Gauss method problem

  1. #1
    gotchy
    Guest

    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
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  2. #2
    Grand Panjandrum
    Joined
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    4
    <br />
\begin{array}{cccccc}<br />
x&+3y&-2z&&=&-5\\<br />
2x&-y&-z&-w&=&-1\\<br />
3x&-2y&&+4w&=& 1\\<br />
-x&+y&-3z&-w&=&-6<br />
\end{array}<br />

    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:

    <br />
\begin{array}{cccccc}<br />
x&+3y&-2z&&=&-5\\<br />
&-7y&3z&-w&=& 9\\<br />
&-11y&6z&+4w&=& 7\\<br />
&4y&z&-w&=&-11<br />
\end{array}<br />

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

    <br />
\begin{array}{cccccc}<br />
x&+3y&-2z&&=&-5\\<br />
&-7y&3z&-w&=& 9\\<br />
&&4z&+4w&=& -13\\<br />
&&61z&-29w&=&-136<br />
\end{array}<br />

    Now replace row 4 by 4row4-61row3:

    <br />
\begin{array}{cccccc}<br />
x&+3y&-2z&&=&-5\\<br />
&-7y&3z&-w&=& 9\\<br />
&&4z&+4w&=& -13\\<br />
&&&-400w&=&244<br />
\end{array}<br />

    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
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