Let e be a line through the origin in R2, Pl the linear transformation that projects a vector onto l, and Fl the transformation that reflects a vector in l.
(a) Draw diagrams to show that Fl is linear.
(b) Figure 3.14 suggests a way to find the matrix of Fe, using the fact that the diagonals of a parallelogram bisect each other. Prove that Fl(x) = 2Pl(x) - x, and use this result to show that the standard matrix of Fl is

(Where the direction vector of e is

(c) If the angle between e and the positive x-axis is θ, show that the matrix of Fl is

Transcribed Image Text:

cos 2θ sin2θ Fx)