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Math Help - Gaussian elimination with back subbing

  1. #1
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    Gaussian elimination with back subbing

    Hi, I need help with a question -

    I need to use Gaussian elimination and back substitution to solve the following system:

    0 + 4x2 3x3 = 3
    -x1 + 7x2 5x3 = 4
    -x1 + 8x2 - 6x3 = 5

    Since the first pivotal position is 0, I interchange rows one and two before eliminating numbers below the pivot. I'm not sure what to do after that.


    Thanks for any help.
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  2. #2
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    Quote Originally Posted by Kenny12345 View Post
    Hi, I need help with a question -

    I need to use Gaussian elimination and back substitution to solve the following system:

    0 + 4x2 – 3x3 = 3
    -x1 + 7x2 – 5x3 = 4
    -x1 + 8x2 - 6x3 = 5

    Since the first pivotal position is 0, I interchange rows one and two before eliminating numbers below the pivot. I'm not sure what to do after that.


    Thanks for any help.
    interchange first and last equation:

    -x1 + 8x2 - 6x3 = 5
    -x1 + 7x2 – 5x3 = 4
    0 + 4x2 – 3x3 = 3

    Subtract equation 1 from 2:

    -x1 + 8x2 - 6x3 = 5
    0 - 1x2 + x3 = -1
    0 + 4x2 – 3x3 = 3

    Add 4 times the second to the last:

    -x1 + 8x2 - 6x3 = 5
    0 - 1x2 + x3 = -1
    0 + 0 + 1x3 = -1

    Now start the back substitution with x3=-1, put this into the second to find x2, etc..

    .
    Last edited by Constatine11; January 8th 2009 at 09:46 AM.
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  3. #3
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    The solution in my book said the answer is (1,0,-1) - it doesn't offer an explanation though. Also, why did you interchange the first and last equations instead of the first and second equations?
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  4. #4
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    Quote Originally Posted by Kenny12345 View Post
    The solution in my book said the answer is (1,0,-1) - it doesn't offer an explanation though. Also, why did you interchange the first and last equations instead of the first and second equations?
    Arithmetic error corrected.

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  5. #5
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    Thanks for the help , but I still wonder why you would exchanged the 1st equation with the 3rd equation instead of exchanging the 1st and 2nd?
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