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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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    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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    Staff Emeritus
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    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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