Question

Consider the system of linear equation in x, y and z

(sin 3q)x – y + z = 0

(cos 2q)x + 4y + 3z = 0

2x + 7y + 7z = 0

if the system has non trivial solution, then qĪ[0, p] are

• A. 0, p, $\frac{\pi}{6}$
• B. 0, $\frac{\pi}{6}$, $\frac{5\pi}{6}$
• C. 0, p, $\frac{\pi}{6}$, $\frac{5\pi}{6}$
• D. None of these

Answer 1

Answer: (C)

0, p, $\frac{\pi}{6}$, $\frac{5\pi}{6}$

Answer 2

The system has a non trivial solution if

D = $\left| \begin{matrix} \sin 3\theta & - 1 & 1 \\ \cos 2\theta & 4 & 3 \\ 2 & 7 & 7 \end{matrix} \right|$ = 0

Ž 7 sin 3q + 7 cos 2q – 6 + 7 cos 2q – 8 = 0

Ž sin 3q + 2 cos 2q = 2 Ž 3 sinq – 4 sin³q + 2 – 2 sin²q = 2 Ž sinq (4 sin²q + 2 sinq – 3) = 0

Ž sinq (2 sinq + 3) (2 sinq – 1) = 0

Ž sin q = 0, $\frac{1}{2}$ since sinq ¹ –$\frac{3}{2}$

\ Int [0, p] q = 0, p, $\frac{\pi}{6}$, $\frac{5\pi}{6}$