Question

F(x) = $\begin{bmatrix} \cos x & - \sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix}$and

G(x) = $\begin{bmatrix} \cos x & 0 & \sin x \ 0 & 1 & 0 \

• \sin x & 0 & \cos x \end{bmatrix}$, then [F(x) G(y)]^–1 is equal to –

• A. F(–x ) G (–y)
• B. F(x –1) G(y –1)
• C. G (–y) F(–x)
• D. G(y ^–1) F (x^–1)

Answer 1

Answer: (C)

G (–y) F(–x)

Answer 2

F(x) G(N)]^–1 [F(x)]^–1

[F(x)]^–1 = $\begin{bmatrix} \cos x & \sin x & 0 \

• \sin x & \cos x & 0 \ 0 & 0 & 1 \end{bmatrix}$= F(–x)

Similarly, [G(n)]^–1 –G(–y) F(–x)