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Math Help - Help with solving a linear system

  1. #1
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    Help with solving a linear system

    Hi,

    I need to answer the question as to what the pivot columns are for the following matrix representing a linear system of equations as well as whether the system is consistent or inconsistent.

    The augmented matrix for the system is:

    -2 0 3 1 | -1
    0 -1 1 1 | 2
    2 0 -1 -1 | 1
    -2 -1 4 2 | 0

    I performed row reduction using the following operations:

    R1/-2
    R3+R4-->R3
    2R1+R4-->R4
    R2/-1
    R2+R3-->R3
    R2+R4-->R4
    R3/2
    R2+R3-->R2
    3/2R3+R1-->R1

    I end with the following augmented matrix:

    1 0 0 -11/4 | -3/4
    0 1 0 -5/2 | -5/2
    0 0 1 -3/2 | -1/2
    0 0 0 0 | -1

    Based on this I conclude that the system is inconsistent because of the last row we have 0=-1. I also conclude that the pivot columns are columns 1,2, and 3.



    Can someone please check to see if I conducted the problem correctly and ended up with the correct matrix?

    Thank you
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Help with solving a linear system

    The system is indeed inconsistent, I did some other row operations and my last row was also 0 0 0 0 | -1 thus there's no solution.
    Thanks from dumbledore
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  3. #3
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    Re: Help with solving a linear system

    Thank you! Any ideas on the pivot columns?
    Last edited by dumbledore; September 24th 2012 at 05:35 AM.
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