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  • Choose the correct answer in the Exercises 11 and 12. If A = and A + A′ = I, then the value of alpha is (A) pi/6 (B) pi/3 (C) pi (D) 3 pi/2

Choose the correct answer in the Exercises 11 and 12.

Q12.    If A = \begin{bmatrix} \cos\alpha & -\sin\alpha\\ \sin\alpha& \cos\alpha \end{bmatrix} and A+A' =I, then the value of \alpha is

            (A)    \frac{\pi}{6}

            (B)    \frac{\pi}{3}

            (C)    \pi

            (D)    \frac{3\pi}{2}

Answers (1)

best_answer

A = \begin{bmatrix} \cos\alpha & -\sin\alpha\\ \sin\alpha& \cos\alpha \end{bmatrix}

A' = \begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha& \cos\alpha \end{bmatrix}

A+A' = \begin{bmatrix} \cos\alpha & -\sin\alpha\\ \sin\alpha& \cos\alpha \end{bmatrix}+ \begin{bmatrix} \cos\alpha & \sin\alpha\\ -\sin\alpha& \cos\alpha \end{bmatrix}= \begin{bmatrix} 1& 0\\ 0 & 1 \end{bmatrix}

A+A' = \begin{bmatrix} 2\cos\alpha & 0\\ 0 & 2\cos\alpha \end{bmatrix}= \begin{bmatrix} 1& 0\\ 0 & 1 \end{bmatrix}

2 cos \alpha=1 

cos \alpha=\frac{1}{2}

\alpha=\frac{\pi}{3}

Option B is correct.

 

 

Posted by

seema garhwal

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