First slide

Introduction to Determinants

Question

$If A = [\begin{array}{ccc} 1 + \cos^{2} θ & \sin^{2} θ & 4 \cos 6 θ \\ \cos^{2} θ & 1 + \sin^{2} θ & 4 \cos 6 θ \\ \cos^{2} θ & \sin^{2} θ & 1 + 4 \cos 6 θ \end{array}] is a singular matrix and 3 θ \in (0, π) then θ =$

Moderate

A

$\frac{π}{9}$
B

$\frac{π}{18}$
C

$\frac{π}{6}$
D

$\frac{π}{12}$

Solution

$| A | = 0 \Rightarrow 2 + 4 \cos 6 θ = 0 \Rightarrow \cos 6 θ = - \frac{1}{2} \Rightarrow 6 θ = \frac{2 π}{3} \Rightarrow θ = \frac{π}{9}$

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