Question

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

(sin3q) x – y + z = 0,

(cos2q) 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, p, $\frac{\pi}{6}$, $\frac{5\pi}{6}$
• C. 0, $\frac{\pi}{6}$, $\frac{5\pi}{6}$
• D. None

Answer 1

Answer: (B)

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

Answer 2

The system has non-trivial solution is

D = $\left| \begin{matrix} \sin 3\theta & –1 & 1 \\ \cos 2\theta & 4 & 3 \\ 2 & 7 & 7 \end{matrix} \right|$ = 0 Ž sin3q + 2cos2q = 2

Ž sinq = 0, 1/2 sinq ¹ –3/2

Interval [0, p], 0 = 0, p, p/6, 5p/6