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Math Help - Rotation matrix

  1. #1
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    Rotation matrix

    Find the rotation matrix that C that transforms the matrix
    |0| into |3|
    |5| |4|

    (the first matrix is 0 5 and the second has 3 4, each vertical)
    Last edited by noles2188; September 15th 2009 at 08:43 PM. Reason: Clear up matrix
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Hint : look at the vectors (0,5) and (3,4) in the (x,y) plane. What is the angle between them? That's the angle you're looking for; then just find the corresponding rotation matrix.
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  3. #3
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    Another way to do this: Any "rotation" matrix in the plane is of the form
    \begin{bmatrix}a & -b \\ b & a\end{bmatrix}
    with a^2+ b^2= 1.
    \begin{bmatrix}a & -b \\ b & a\end{bmatrix}\begin{bmatrix}0 \\ 5\end{bmatrix}=\begin{bmatrix}-5b \\ 5a\end{bmatrix}=  \begin{bmatrix}3 \\ 4\end{bmatrix}
    gives you two equations to solve for a and b. Since the lengths of the two vectors, <0, 5> and <3, 5> are the same, a^2+ b^2= 1 will automatically be satisfied.
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