1. Suppose a linear transformation T : R2 -> R2 is formed by taking a rotation counterclockwise of
90 degrees, followed by a reflection in the x2-axis. Describe the points that will be moved back
to their original position by this transformation?
Solution
Let (x, y) be the general such point.
Hence rotating it by 90 deg. counterclockwise will give us (-y,x).
Reflecting (-y,x) on x axis gives us (-y,-x).
Hence if (x,y) = (-y,-x) then all ( x, y) where x = -y or x+y = 0 satisfy this condition.
Hence answer = All points on line x+y = 0