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Solving a Matrix

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  1. Oct 31, 2014 #1
    Mod note: Moved from a technical section, so is missing the homework template.
    I am using matrix methods to do ray optics but my knowledge on matrices is behind.

    I found the system matrix to be
    \begin{bmatrix} \frac{-f_2}{f_1} & f_1 + f_2 \\ 0 & \frac{-f_1}{f_2} \end{bmatrix}

    I want to find [itex]y_2[/itex] (height of the emerging ray) and [itex]\alpha_2[/itex] (angle of emerging ray...which should equal zero) so I set up the system as follows:

    \begin{bmatrix} y_2 \\ \alpha_2 \end{bmatrix} = \begin{bmatrix} \frac{-f_2}{f_1} & f_1 + f_2 \\ 0 & \frac{-f_1}{f_2} \end{bmatrix} \begin{bmatrix} y_0 \\ \alpha_0 \end{bmatrix}

    (Apologies for the tex I couldn't figure out how to put it in one line)

    Is this the correct way to set it up in order to find [itex]y_2[/itex] and [itex]\alpha_2[/itex]? And how do I solve this system of matrices?
     
    Last edited by a moderator: Oct 31, 2014
  2. jcsd
  3. Oct 31, 2014 #2

    Mark44

    Staff: Mentor

    You don't "solve" the system - just do the indicated multiplication. If you're unclear about how to do that, do a web search for "matrix multiplication".
     
  4. Oct 31, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    For the tex: If you want
    [tex] \pmatrix{-f_2/f_1&f_1+f_2\\0&-f_1/f_2} \pmatrix{y_0\\0}[/tex]
    just put it all on one line. Right-click on the line above (and choose to display as tex) in order to see the commands used. Of course, you could use displayed fractions instead; try it and see.
     
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