Question
Evaluate $:\left[\begin{array}{c}4 \sin 30^{\circ}, 2 \cos 60^{\circ} \\ \sin 90^{\circ}, 2 \cos 0^{\circ}\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$
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Answer
$\left[\begin{array}{c}4 \sin 30^{\circ}, 2 \cos 60^{\circ} \\ \sin 90^{\circ}, 2 \cos 0^{\circ}\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$
$=\left[\begin{array}{cc}4 \times \frac{1}{2} & 2 \times \frac{1}{2} \\ 1 & 2 \times 1\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$
$ =\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$
$=\left[\begin{array}{cc}8+5 & 10+4 \\ 4+10 & 5+8\end{array}\right] $
$ =\left[\begin{array}{ll}13 & 14 \\ 14 & 13\end{array}\right]$
$=\left[\begin{array}{cc}4 \times \frac{1}{2} & 2 \times \frac{1}{2} \\ 1 & 2 \times 1\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$
$ =\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]\left[\begin{array}{ll}4 & 5 \\ 5 & 4\end{array}\right]$
$=\left[\begin{array}{cc}8+5 & 10+4 \\ 4+10 & 5+8\end{array}\right] $
$ =\left[\begin{array}{ll}13 & 14 \\ 14 & 13\end{array}\right]$
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