First slide

System of linear equations

Question

The system of equations $(\sin 3 θ) x - y + z = 0, (\cos 2 θ) x + 4 y + 3 z = 0, 2 x + 7 y + 7 z = 0$ has a non-trivial solution if

Moderate

A

$\sin 3 θ + 2 \cos 2 θ = 2$
B

$\sin 3 θ - 2 \cos 2 θ = 2$
C

$\sin 3 θ - 2 \cos 2 θ = 1$
D

$\sin 3 θ + 2 \cos 2 θ = 1$

Solution

Given equations have a non-zero solution $\Rightarrow |\begin{matrix} \sin 3 θ & - 1 & 1 \\ \cos 2 θ & 4 & 3 \\ 2 & 7 & 7 \end{matrix}| = 0$
$\Rightarrow \sin 3 θ (28 - 21) + 1 (7 \cos 2 θ - 6) + 1 (7 \cos 2 θ - 8) = 0$
$\Rightarrow 7 \sin 3 θ + 14 \cos 2 θ - 14 = 0 \Rightarrow \sin 3 θ + 2 \cos 2 θ = 2$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App