WBJEE · Maths · Matrices
Let \(Q=\left(\begin{array}{cc}\cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right)\) and\(x=\left(\begin{array}{c}\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}}\end{array}\right)\) then \(Q^{3} x\) is equal to
- A \(\left(\begin{array}{l}0 \\ 1\end{array}\right) \quad\)
- B \(\left(\begin{array}{c}-\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}}\end{array}\right)\)
- C \(\left(\begin{array}{c}-1 \\ 0\end{array}\right)\)
- D \(\left(\begin{array}{c}-\frac{1}{\sqrt{2}} \\ -\frac{1}{\sqrt{2}}\end{array}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\begin{array}{c}-1 \\ 0\end{array}\right)\)
Step-by-step Solution
Detailed explanation
Given, \(Q=\left[\begin{array}{cc}\cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right]\) and \(x=\left[\begin{array}{c}\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}}\end{array}\right]\)…
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