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Homework Help: Transformation problem

  1. Aug 7, 2008 #1
    Please help me solve this question:
    Question: Find the images of the lines r = i - j + n(i + j + k) under transformation
    M (matrix 3 x 3) =
    (2 1 4)
    (3 5 1)
    (1 2 0)
    in vector form.
     
  2. jcsd
  3. Aug 7, 2008 #2

    HallsofIvy

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    Science Advisor

    The image under the transformation is just that matrix times the vector? But what is n? My first thought was that it was the parameter but then that is just a single line. If that is correct then r= i- j+ n(i+ j+ k)= (n+1)i+ (n-1)j+ nk and its image is
    [tex]\left[\begin{array}{ccc}2 & 1 & 4 \\ 3 & 5 & 1 \\ 1 & 2 & 0\end{array}\right]\left[\begin{array}{c} n+1 \\ n-1 \\ n\end{array}\right][/tex]
     
  4. Aug 7, 2008 #3
    Thank you. There is some confusion here. I am confuse when to use inverse matrix to find transformation. Can you explain this. Example : 1. Find the images under the transformation
     
    Last edited: Aug 7, 2008
  5. Aug 7, 2008 #4

    HallsofIvy

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    Science Advisor

    I have no idea what you mean by that. You use the inverse matrix in order to find an "inverse image": x such that Mx= y. Given a matrix M, the image of x is, by definition Mx.
     
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