AP EAMCET · Maths · Matrices
Let \(G(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]\). If \(x+y=0\), then \(G(x) G(y)=\)
- A null Matrix
- B skew-symmetric Matrix
- C identity Matrix
- D symmetric Matrix
Answer & Solution
Correct Answer
(C) identity Matrix
Step-by-step Solution
Detailed explanation
Here, \(G(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]\) \(G(y)=\left[\begin{array}{ccc}\cos y & -\sin y & 0 \\ \sin y & \cos y & 0 \\ 0 & 0 & 1\end{array}\right]\) So, \(x+y=0 \Rightarrow y=(-x)\) Now,…
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