# Linear algebra/matlab: find vector when e2 is reflected over line B with x-axis

1. Mar 9, 2010

### RossH

1. The problem statement, all variables and given/known data
The assignment is to find a matrix, A, that multiplied by a matrix that represents a rectangle will reflect that rectangle about a line through the origin that is at and beta with the x axis. This is all in homogenous coordinates.

2. Relevant equations
Elementary vectors: e1 is <1,0, ... 0> e2 is <0,1,0 ...> etc.
No others.

3. The attempt at a solution
I thought that the matrix might be: (I hope this formats correctly)
cos(2B) sin(2B) 0
sin(2B) -cos(2B) 0
0 0 1
But when I use this in Matlab, it seems to rotate the rectangle represented by my first matrix in 3 dimensions, rather than reflect it in two dimensions. So right now I am left trying to remake the matrix.

I am trying to figure out the transformation applied to the elementary vectors. When the elementary vector e1 is reflected, that gives me the transformation vector <cos2B,sin2B>
but I am having a lot of trouble figuring out the same vector when e2 is reflected. Any ideas? Thank you.