Find if & [ c ] [ lll & & ]=[17] - Vidyadip

Question

Find if $\begin{aligned} &\left[\begin{array}{c}\sin \theta \\ \cos \theta \\ \theta\end{array}\right]\left[\begin{array}{lll}\sin \theta & \cos \theta & \theta\end{array}\right]=[17] \end{aligned}$

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Answer

Let $\left[\begin{array}{c}\sin \theta \\ \cos \theta \\ \theta\end{array}\right]\left[\begin{array}{lll}\sin \theta & \cos \theta & \theta\end{array}\right]=[17],$
$\therefore\left[\sin ^2 \theta+\cos ^2 \theta+\theta^2\right]=[17]$
$\therefore$ By definition of equality of matries
$ \therefore 1+\theta=17 $
$\therefore \theta=17-1 $
$\therefore \theta^2=16,$
$\therefore \theta= \pm 4$

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