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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
If matrix $A = \left[ {\begin{array}{*{20}{c}}
{\sin \theta }&{\cos ec\theta }&1\\
{\cos ec\theta }&1&{\sin \theta }\\
1&{\sin \theta }&{\cos ec\theta }
\end{array}} \right]$ is a non invertible matrix, then possible value of $'\theta'$ is 

$($ where $n \in I)$

  • A
    $n\pi  + {( - 1)^n}\frac{\pi }{4}$
  • B
    $n\pi  + {( - 1)^n}\frac{\pi }{3}$
  • C
    $n\pi  + {( - 1)^n}\frac{\pi }{6}$
  • ✓
    $2n\pi+\frac{\pi}{2}$
✓

Answer

Correct option: D.
$2n\pi+\frac{\pi}{2}$
d
$|A|=0 \Rightarrow$  either  $\sin \theta  = \cos ec\theta  = 1$

$\Rightarrow \theta=2 n \pi+\frac{\pi}{2}$ or $\sin \theta  + \cos ec\theta  + 1 = 0$

Not possible.

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