Question

The system of equations :
$2 x \cos ^2 \theta+y \sin 2 \theta-2 \sin \theta=0 $
$x \sin 2 \theta+2 y \sin ^2 \theta=-2 \cos \theta$
$x \sin \theta-y \cos \theta=0$, for all values of $\theta$, can

• A. have a unique non - trivial solution
• B. not have a solution
• C. have infinite solutions
• D. have a trivial solution

Answer 1

Answer: (B)

slope of (1) and (2) is $\cot \theta \Rightarrow(1)$ and (2) are parallel and slope of (3) is $\tan \theta$
$\Rightarrow $ no solution.
Using $R_2 \rightarrow R_2-(2 \cos \theta) R_3$ and $R_1 \rightarrow R_1+(2 \sin \theta) R_3$, the value of determinat is 4