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Math Help - Difficult Matrix Equation

  1. #1
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    Difficult Matrix Equation

    Hi

    I'm supposed to solve this matrix equation by GaussJordan elimination and I find it very difficult to see and carry out the row operations mainly because of the z's. If someone is able to help me I would truly appreciate it.

    zx1 + x2 + x3 = 1

    x1 + zx2 + x3 = 1

    x1 + x2 + zx3 = 1


    z has a real value.
    Last edited by Tala; October 5th 2012 at 06:51 AM.
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  2. #2
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    Re: Difficult Matrix Equation

    Do you have to use elimination?

    Can you see that x1=x2=x3?
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  3. #3
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    Re: Difficult Matrix Equation

    Yes I have to use the Gauss Jordan elimination method.
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  4. #4
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    Re: Difficult Matrix Equation

    The fact that it is "z" rather than a number is just means you have to use algebra rather than arithmetic.
    \begin{bmatrix}z & 1 & 1 & 1 \\ 1 & z & 1 & 1 \\ 1 & 1 & z & 1\end{bmatrix}

    The first thing I would do, to simplify the algebra, is swap the first and third rows:
    \begin{bmatrix}1 & 1 & z & 1 \\ 1 & z & 1 & 1 \\ z & 1 & 1 & 1 \end{bmatrix}

    Then "clear" the first column by subtracting the first row from the second and subtracting z times the first row from the third:
    \begin{bmatrix}1 & 1 & z & 1 \\ 0 & z- 1 & 1- z & 0 \\ 0 & 1- z & 1- z^2 & 1- z\end{bmatrix}

    Now divide the second row by z-1 to get
    \begin{bmatrix}0 & 1 & -1 & 0\end{bmatrix}

    and clear the second row by subtracting the second row from the first and subtracting 1- z times the second row from the third.

    You try to finish it.
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