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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
The system of equations : $2x\, \cos^2\theta + y\, \sin2\theta - 2\sin\theta = 0$ $x\, \sin2\theta + 2y\, \sin^2\theta = - 2\, \cos\theta$ $x\, \sin\theta - y \cos\theta = 0$ , for all values of $\theta$ , can
  • A
    have a unique non - trivial solution
  • ✓
    not have a solution
  • C
    have infinite solutions
  • D
    have a trivial solution
✓

Answer

Correct option: B.
not have a solution
b
slope of $(1)$ and $(2)$ is $\cot \theta$

$\Rightarrow$ $(1)$ and $(2)$ are parallel and slope of $(3)$ is $\tan\theta$ 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 $4$

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