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Math Help - Gauss method

  1. #1
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    Gauss method

    Please HELP!
    I have a problem to solve with the Gauss metohd.

    { X1 + X2 + 3X3 + 2X4 + 2X5 = 3
    { X1 + X2 + X3 + 2X4 = 1
    { X1 + X2 - X3 + 2X4 - 2X5 = -1
    { -X1 + X2 + X3 = 1

    Thanks!
    You are THE BEST
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Aiviekste92 View Post
    Please HELP!
    I have a problem to solve with the Gauss metohd.

    { X1 + X2 + 3X3 + 2X4 + 2X5 = 3
    { X1 + X2 + X3 + 2X4 = 1
    { X1 + X2 - X3 + 2X4 - 2X5 = -1
    { -X1 + X2 + X3 = 1

    Thanks!
    You are THE BEST
    The augmented matrix is:

     <br />
\left[ <br />
\begin{array}{ccccc}<br />
1&1&3&2&3\\<br />
1&1&1&2&1\\<br />
1&1&-1&2&-1\\<br />
-1&1&1&0&1<br />
\end{array}<br />
\right]<br />

    Now subtract the first row from the second and third rows and add it to the third row to get:

     <br />
\left[ <br />
\begin{array}{ccccc}<br />
1&1&3&2&3\\<br />
0&0&-2&0&-2\\<br />
0&0&-4&0&-4\\<br />
0&2&4&2&4<br />
\end{array}<br />
\right]<br />

    Now interchange the last row with the second row:

     <br />
\left[ <br />
\begin{array}{ccccc}<br />
1&1&3&2&3\\<br />
0&2&4&2&4\\<br />
0&0&-4&0&-4\\<br />
0&0&-2&0&-2<br />
\end{array}<br />
\right]<br />

    Now because the last two rows are identical it means that one of the variables will be indeterminate, and we might as well let this be x_4. We also observe that the last two rows mean that x_3=1.

    Now substituting into the equation corresponding to our second row:

    2x_2+4+2x_4=4

    so:

     <br />
x_2=-x_4<br />

    Now substituting into the equation corresponding to our first row:

    x_1-x_4+3+2x_4=3

    so:

     <br />
x_1=-x_4<br />

    CB
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  3. #3
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    thank you ever so much
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