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Math Help - Gaussian Elimination, Am I correct?

  1. #1
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    Gaussian Elimination, Am I correct?

    I found this (solved) problem in my textbook:
    2x + y - 3z = 1
    5x + 2y - 6z = 5
    3x + y + 4z= 7
    This is a 3x3 system. I tried to solve it (using Gaussian elimination algorithm) and got this solution:
    z=0.8 y=-2.6 x=3

    But, the textbook said that the solution is:
    z=1 y=-2 x=3

    Which is correct? Me or the textbook?

    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by BanderHM
    I found this (solved) problem in my textbook:
    2x + y - 3z = 1
    5x + 2y - 6z = 5
    3x + y + 4z= 7
    This is a 3x3 system. I tried to solve it (using Gaussian elimination algorithm) and got this solution:
    z=0.8 y=-2.6 x=3

    But, the textbook said that the solution is:
    z=1 y=-2 x=3

    Which is correct? Me or the textbook?

    Thanks.
    Try this: substitute your solution back into the first of the
    equations and evaluate the LHS. Does this equal the RHS?

    The answer to this last question is no, try it with the answer
    from the text book. Now the RHS and LHS agree.

    So what do we conclude?

    1.Your answer is wrong.

    2. The text book could well be right.

    To confirm that the textbook is right substitute its solution
    into the other two equations and see if they hold.

    RonL
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  3. #3
    MHF Contributor
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    I get that you are both incorrect. I used matrices to solve the system and got that:

    x = 3
    y = -\frac{26}{7}
    z = \frac{3}{7}

    I also confirmed by plugging in the books answers into the system that it is incorrect and you can check your own answer by the same method.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Jameson
    I get that you are both incorrect. I used matrices to solve the system and got that:

    x = 3
    y = -\frac{26}{7}
    z = \frac{3}{7}

    I also confirmed by plugging in the books answers into the system that it is incorrect and you can check your own answer by the same method.
    A more likey explanation is that there has been a transcription error (either
    in composing the original question or in editing the textbook )and the last
    equation should be:

    <br />
3x-y-4z=7<br />

    RonL
    Last edited by CaptainBlack; March 8th 2006 at 06:04 AM.
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