Exercise 6.11.4

Answers

1.
Compute that
det ⁡ (A) = −cos ⁡ 2ϕ − sin ⁡ 2ϕ = −1.

By Theorem 6.45, it’s a reflection.

2.
Find the subspace {x : Ax = x}. That is, find the null space of A − I. Hence the axis is
span ⁡ {(sin ⁡ ϕ,1 − cos ⁡ ϕ)}.
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2011-06-27 00:00
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