Results 1 to 3 of 3

Thread: Gauss method

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    2

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5
    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:

    $\displaystyle
    \left[
    \begin{array}{ccccc}
    1&1&3&2&3\\
    1&1&1&2&1\\
    1&1&-1&2&-1\\
    -1&1&1&0&1
    \end{array}
    \right]
    $

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

    $\displaystyle
    \left[
    \begin{array}{ccccc}
    1&1&3&2&3\\
    0&0&-2&0&-2\\
    0&0&-4&0&-4\\
    0&2&4&2&4
    \end{array}
    \right]
    $

    Now interchange the last row with the second row:

    $\displaystyle
    \left[
    \begin{array}{ccccc}
    1&1&3&2&3\\
    0&2&4&2&4\\
    0&0&-4&0&-4\\
    0&0&-2&0&-2
    \end{array}
    \right]
    $

    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 $\displaystyle x_4$. We also observe that the last two rows mean that $\displaystyle x_3=1$.

    Now substituting into the equation corresponding to our second row:

    $\displaystyle 2x_2+4+2x_4=4$

    so:

    $\displaystyle
    x_2=-x_4
    $

    Now substituting into the equation corresponding to our first row:

    $\displaystyle x_1-x_4+3+2x_4=3$

    so:

    $\displaystyle
    x_1=-x_4
    $

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    2
    thank you ever so much
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Gauss' Method Proof
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Nov 9th 2009, 02:03 AM
  2. Method of the Gauss-Jordan
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Sep 22nd 2008, 06:19 AM
  3. Gauss Seidal method
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Sep 1st 2007, 10:15 PM
  4. Replies: 0
    Last Post: Jan 4th 2007, 01:29 PM
  5. Gauss method problem
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: May 26th 2006, 09:31 AM

Search Tags


/mathhelpforum @mathhelpforum