If A= [ cc 60^ & 90^ -3 45^ & 90^ ] and B= [ cc 0 & 45^ -2 & 3 90… - Vidyadip

Question

$ \text { If } A=\left[\begin{array}{cc} \sec 60^{\circ} & \cos 90^{\circ} \\ -3 \tan 45^{\circ} & \sin 90^{\circ} \end{array}\right]$ and $B=\left[\begin{array}{cc} 0 & \cos 45^{\circ} \\ -2 & 3 \sin 90^{\circ} \end{array}\right] $ Find $: BA$

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Answer

Given
$A=\left[\begin{array}{cc} \sec 60^{\circ} & \cos 90^{\circ} \\ -3 \tan 45^{\circ} & \sin 90^{\circ} \end{array}\right]$
and
$ B=\left[\begin{array}{cc} 0 & \cos 45^{\circ} \\ -2 & 3 \sin 90^{\circ} \end{array}\right]$
$\begin{aligned} & A=\left[\begin{array}{cc}\sec 60^{\circ} & \cos 90^{\circ} \\ -3 \tan 45^{\circ} & \sin 90^{\circ}\end{array}\right]=\left[\begin{array}{ll}2 & 0 \\ 3 & 1\end{array}\right] \ldots\left(\because \sec 60^{\circ}=2, \cos 90^{\circ}=0, \tan 45^{\circ}=1, \sin 90^{\circ}=1\right)\end{aligned} $
$ B=\left[\begin{array}{cc}0 & \cos 45^{\circ} \\ -2 & 3 \sin 90^{\circ}\end{array}\right]=\left[\begin{array}{cc}0 & 1 \\ -2 & 3\end{array}\right] \ldots\left(\because \cot 45^{\circ}=1\right)$
$\begin{aligned} & B A=\left[\begin{array}{cc}0 & 1 \\ -2 & 3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 3 & 1\end{array}\right] \end{aligned} $
$=\left[\begin{array}{cc}0-3 & 0+1 \\ -4-9 & 0+3\end{array}\right] $
$ =\left[\begin{array}{cc}-3 & 1 \\ -13 & 3\end{array}\right] .$

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