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Linear Algebra - How to get matrix form Ax.

  1. Feb 22, 2012 #1
    1. The problem statement, all variables and given/known data
    I know the title is misleading but what I am asking is how I can get this matrix
    x1cosθ-x2sinθ
    x1sinθ+x2cosθ

    to the matrix multiplication form
    cosθ -sinθ | x1
    sinθ cosθ | x2


    where
    A=
    cosθ -sinθ
    sinθ cosθ
    x=
    x1
    x2


    Is there a good method to do this or do I have to find it by eye-balling it?
     
  2. jcsd
  3. Feb 22, 2012 #2

    Deveno

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    Science Advisor

    have you tried perfoming the matrix multiplication:

    [tex]\begin{bmatrix}\cos\theta&-\sin\theta\\ \sin\theta&\cos\theta\end{bmatrix}\begin{bmatrix}x_1\\x_2\end{bmatrix} = ?[/tex]

    and comparing that to what you want?
     
  4. Feb 22, 2012 #3

    vela

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    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    What's the usual way of finding the columns of the matrix representing a linear transformation? It should be mentioned in your book somewhere.
     
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