If $0<x<\pi$ and the matrix $\left[\begin{array}{cc}4 \sin x & -1 \\ -3 & \sin x\end{array}\right]$ is singular, then the values of x are :
Answer & explanation
Correct answer: option 1
Matrix is singular
⇒ $\left[\begin{array}{cc}4 \sin x & -1 \\ -3 & \sin x\end{array}\right] = 0$
⇒ 4 sin2x - 3 = 0
⇒ $\sin^2x = \frac{3}{4}$
⇒ $\sin x = \frac{\sqrt{3}}{2}, \frac{-\sqrt{3}}{2} \Rightarrow x = \frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}$ but as it is given $0<x<\pi$
so only first two values chosen
Option: 1