1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Algebra- Matrix Linear Transformation

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the Matrix M which represents the reflection about the line L given by the equation y=(1/2)x. By two methods:

    a) By writing the composition as a composition of rotations and reflections about the x-axis. Note that the line L makes an angle of pi/6 with the x-axis

    b)By using projection onto the line L to compute M(1 0) and M (0 1)

    3. The attempt at a solution

    For part a: Multiply counterclockwise rotation by x-axis reflection, and multiply that by clockwise rotation to get the matrix product:

    \begin{equation}

    \left[
    \begin{array}{ccc}
    cos(2pi/6) & (sin2pi/6) \\
    sin(pi/6) & -cos(2pi/6)\\
    \end{array}
    \right]

    \end{equation}


    For part b: I used the formula RefL(x)=2projL(x)-x

    \begin{equation}

    \left[
    \begin{array}{ccc}
    3/5 & 4/5\\
    4/5 & -3/5\\
    \end{array}
    \right]

    \end{equation}

    Assuming my methods were correct(maybe a big assumption), I'm confused about why two different matrices yield the same transformation. Shouldn't I be getting the same matrix? Thanks for any help, I really do appreciate it.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Linear Algebra- Matrix Linear Transformation
Loading...