Evaluate [ cc 45^ & 30^ 2 0^ & 0^ ] [ ll 45^ & 90^ 90^ & 45^ ] - Vidyadip

Question

Evaluate $\left[\begin{array}{cc}\cos 45^{\circ} & \sin 30^{\circ} \\ \sqrt{2} \cos 0^{\circ} & \sin 0^{\circ}\end{array}\right]\left[\begin{array}{ll}\sin 45^{\circ} & \cos 90^{\circ} \\ \sin 90^{\circ} & \cot 45^{\circ}\end{array}\right]$

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Answer

$\left[\begin{array}{cc}\cos 45^{\circ} & \sin 30^{\circ} \\ \sqrt{2} \cos 0^{\circ} & \sin 0^{\circ}\end{array}\right]\left[\begin{array}{ll}\sin 45^{\circ} & \cos 90^{\circ} \\ \sin 90^{\circ} & \cot 45^{\circ}\end{array}\right]$
$\begin{array}{l}=\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & \frac{1}{2} \\ \sqrt{2} & 0\end{array}\right]\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & 0 \\ 1 & 1\end{array}\right] \end{array} $
$ =\left[\begin{array}{cc}\frac{1}{2}+\frac{1}{2} & 0+\frac{1}{2} \\ 1+0 & 0+0\end{array}\right] $
$ =\left[\begin{array}{cc}1 & 0.5 \\ 1 & 0\end{array}\right]$

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