Solutions and Hints to Selected Exercises

So, the matrix is not invertible when λ ∈ 1 2 5 + 3

2 5 ,3 .

(a) By direct calculation, we get det(R) = cos2θ + sin2θ = 1.

(b) The inverse is R−1 =

1 0 0

0 cosθ sinθ

0 − sinθ cosθ

.

(c) Observe that R−1 = RT.