Question: 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

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

Let e be a line through the origin in R2,

cos 2 sin2 Fx)

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