Use Exercise 28 to determine whether the given orthogonal matrix represents a rotation or a reflection. If
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Data From Exercise 28
(a) Prove that an orthogonal 2 Ã 2 matrix must have the form
where
is a unit vector.
(b) Using part (a), show that every orthogonal 2 Ã 2 matrix is of the form
where 0 ¤ u ¤ 2Ï.
(c) Show that every orthogonal 2 Ã 2 matrix corresponds to either a rotation or a reflection in 2.
(d) Show that an orthogonal 2 Ã 2 matrix Q corresponds to a rotation in R2 if det Q = 1 and a reflection in R2 if det Q = -1.
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