WBJEE · Maths · Matrices
If \(A=\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right)\) and \(\theta=\frac{2 \pi}{7}\), then \(A^{100}=A \times A \times \ldots .(100\) times \()\) is equal to
- A \(\left(\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right)\)
- B \(\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right)\)
- C \(\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)\)
- D \(\left(\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\begin{array}{cc}\cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta\end{array}\right)\)
Step-by-step Solution
Detailed explanation
Hint : \(\because A^{100}=\left[\begin{array}{cc}\cos 100 \theta & -\cos 100 \theta \\ \sin 100 \theta & \cos 100 \theta\end{array}\right]\) As \(\theta=\frac{2 \pi}{7}\)…
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