Let L ⊂ R2 be a line through the origin in the direction of the unit vector u.
(a) Prove that the matrix representative of reflection through L is R = 2uuT - 1.
(b) Find the corresponding formula for reflection through a line in the direction of a general nonzero vector v ≠ 0.
(c) Determine the matrix representative for reflection through the line in the direction
(i) (1, 0)T
(ii) (3/5, -4/5)T
(iii) (1, 1)T
(iv) (2, -3)T