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Finding Variables within Matricies Question

  1. Jun 12, 2006 #1
    :confused: Hi There!!
    I have a quick question and I would really appreciate some guidence!

    I have three matrix multiplied together like so

    (horizontal matrix 1 k)(2x2 matrix 3 4 -2 1)(vertical matrix 1 k) equals 11

    I'm asked to find two values for k.
    I've tried multiplying them out but i end up with something like the vertical matrix 3-2k 4k+k^2 equals 11. Not sure what to do from there... Any ideas
    !!
    Thanks for your replies
     
  2. jcsd
  3. Jun 12, 2006 #2

    matt grime

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    Try mulitplying them out again: you should have a 1x1 matrix at the end (ie a scalar): you are multiplying 1x2, 2x2, 2x1 matrices, so the answer is 1x1.
     
  4. Jun 12, 2006 #3

    HallsofIvy

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    Just for reference, is the product
    [tex]\left(\begin{array}{cc}1&k\end{array}\right)\left(\begin{array}{cc}3 & 4 \\ -2 & 1\end{array}\right)\left(\begin{array}{c}1 \\ k\end{array}\right)= 11[/tex]?

    If so, as matt grime says, go ahead and multiply it out. The first product
    [tex]\left(\begin{array}{cc}3 & 4 \\ -2 & 1\end{array}\right)\left(\begin{array}{c}1 \\ k\end{array}\right)[/tex]
    will be a vertical 1x2 matrix and then the product of horizontal and vertical matrices is a number (technically, a 1 by 1 matrix).
    You will get a quadratic equation for k.
     
  5. Jun 12, 2006 #4
    Hi

    Ya that's the one!
    Thanks guys!!!
    Much appreciated!
     
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