Linear Transformation.

[kathw]

I need help for one of my homework question, thank you in advance!

Find the matrix in homogeneous coordinates that maps the rectangle with vertices (1,−2), (1, 2), (4, 2), (4,−2) onto the unit square.

I understand that unit square is (0,0), (1,0), (1,1), (0,1), but I'm lost after trying to compute the matrix.

My attempt is attached in this post.

 

[Steven G]

After your first matix multiplication you found that a=2b and c=2d but you did NOT use that in the 2nd matrix multiplication. The matrix is no longer a,b,c,d it is now 2b,b,2d,d.
Now try again.