# Homework Help: Linear Algebra- Matrix Linear Transformation

1. Sep 27, 2012

### bcahmel

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:

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

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

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

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.