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7 projection on a different axes question

  1. Oct 28, 2011 #1
    7)
    [tex]T:R^{2}->R^{2}[/tex] projection transformation on X-axes paralel to the
    line
    [tex]y=-\sqrt{3}x[/tex]
    find the representative matrices of T{*} by B=\{(1,0),(0,1)\} basis
    how i tried:
    i understood that the x axes stayed the same but the y axes turned
    into
    [tex]y=-\sqrt{3}x[/tex]
    our T takes some vector and returns only the new x part with respect
    to the new y axes.
    any guidanse?
     
  2. jcsd
  3. Oct 28, 2011 #2

    Mark44

    Staff: Mentor

    If I understand what you're trying to say, then
    [tex]T\begin{bmatrix}1 \\ 0\end{bmatrix} = \begin{bmatrix}1\\ 0\end{bmatrix}[/tex]
    and
    [tex]T\begin{bmatrix}0 \\ 1\end{bmatrix} = k\begin{bmatrix}1\\\sqrt{3}\end{bmatrix}[/tex]

    With a little trig you can figure out what k needs to be. What you know what a linear transformation does to a basis, you can write the matrix that represents the transformation.
     
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