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Math Help - Matrix Question

  1. #1
    Member alexgeek's Avatar
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    Matrix Question

    Having some problems with this question.

    The transformation T in the plane consists of an anticlockwise rotation through 90^{\circ} about the origin by a translation in which the point (x,y) is transformed to the point (x+1,y+2).

    (a) Show that the matrix representing T is

    \begin{bmatrix} 0 & -1 & 1 \\ 1 & 0 &2 \\ 0 & 0 & 1 \end{bmatrix}[/tex]
    It doesn't say in what plane the rotation is in.. 90 degrees in which direction?
    I assume its the yx plane but I tried that and my matrix was nothing like T.

    Thanks
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  2. #2
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    is that the whole question, unedited? your coordinates have 2 dimensions but your matrix has 3, which doesn't make sense to me

    (of course, i could be wrong!)
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  3. #3
    Member alexgeek's Avatar
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    I think z is just supposed to be invariant.. not sure. But that is the entire question
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  4. #4
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    I assume you mean he the proposition is that (x,y,z) maps to (x+1,y+2,z) under transformation T. You can check it is true by applying the transformation to the vector (x,y,z) and checking you get the required answer.

    Edit Dont see how the above could hold in general (it would be a shift, not a rotation) so the question must have meant something else. So, back to your original question. The question says "in the plane". that is not something a question would normally say without defining the plane first.
    Last edited by SpringFan25; October 1st 2010 at 12:05 PM.
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