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Math Help - gauss jordan elimination

  1. #1
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    gauss jordan elimination

    Hello i need help to solve this:

    Use gauss jordan elimination to solve for x' and y' in terms of x and y

    the matrix is:

    cos(theta) -sin(theta) x
    sin(theta) cos(theta) y

    thank you
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  2. #2
    MHF Contributor

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    So you have
    \left(\begin{array}{c}x' \\ y'\end{array}\right)= \left(\begin{array}{cc}cos(\theta) & -sin(\theta) \\ sin(\theta) & cos(\theta)\end{array}\right)\left(\begin{array}{c  } x \\ y\end{array}\right)

    The augmented matrix is
    \left(\begin{array}{ccc}cos(\theta) & -sin(\theta) & x' \\ sin(\theta) & cos(\theta) & y'\end{array}\right)
    Do you know how to row-reduce that?

    This is, by the way, the matrix corresponding to rotation through angle [itex]\theta[/itex]. It has an obvious, easy, inverse that you can use to check your answer.
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