Question: Let u R3 be a unit vector. (a) Explain why the elementary reflection matrix R = I - 2uuT represents a reflection through the

Let u ˆˆ R3 be a unit vector.
(a) Explain why the elementary reflection matrix R = I - 2uuT represents a reflection through the plane orthogonal to u.
(b) Prove that R is an orthogonal matrix. Is it proper or improper?
(c) Write out R when u =

(d) Give a geometrical explanation why Qn = - R represents the rotation of Exercise 7.2.20.

(i) (3.0,-/ (ii) (iii) ( -**)" (4 .-12)" 13' 13"13

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