(a) Prove that an orthogonal 2 Ã 2 matrix must have the form where is a unit...
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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.
Transcribed Image Text:
or [b -a a b.
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a is a unit vector Now all we have left to show is d a and c b or d a and c b F...View the full answer
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