If matrix $A = left[ {begin{array}{*{20}{c}} {sin θ }&{cos ecθ }&1 {cos ecθ }&1&{

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3 and 4 .Determinants and Matrices

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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

$n\pi + {( - 1)^n}\frac{\pi }{6}$

D

$2n\pi+\frac{\pi}{2}$

Solution

$|A|=0 \Rightarrow$ 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.

Standard 12

Mathematics

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(KVPY-2018)