Thread: find the matrix for the transformation

1. find the matrix for the transformation

the question is: Find the matrix for the transformation which first reflects across the main diagonal, then projects onto the line 2y+3^(1/2)=0 and then reflects about the line 3^(1/2)y=2x.

am i supposed to start by finding the reflection across the main diagonal then multiplying it by the projected first line then multiplying that by the reflected second line?

also, does anyone know how to reflect across the main diagonal in terms such as T(x,y) = (? , ?)o

help is appreciated

2. Re: find the matrix for the transformation

Originally Posted by bakinbacon
am i supposed to start by finding the reflection across the main diagonal then multiplying it by the projected first line then multiplying that by the reflected second line?
I think you have the right ideas, but your choice of terms is not quite right. What you want to do is to fix a basis (preferably the standard ones) and find the matrices associated with each linear transformation described above. Then you can compose all of these operations by multiplying the associated matrices.
also, does anyone know how to reflect across the main diagonal in terms such as T(x,y) = (? , ?)o
A linear transformation is determined by what it does to the basis. That said, I don't know what you mean by the main diagonal... is it the line $x=y$?