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Question Bank [2022] — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsQuestion Bank [2022]1 Mark
Question
If $A=\left[\begin{array}{ccc}0 & 3 & 3 \\ -3 & 0 & -4 \\ -3 & 4 & 0\end{array}\right]$ and $B=\left[\begin{array}{l}x \\ y \\ z\end{array}\right]$, find the matrix $B^{\prime}(A B)$
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Answer

$AB =\left[\begin{array}{ccc}0 & 3 & 3 \\ -3 & 0 & -4 \\ -3 & 4 & 0\end{array}\right]\left[\begin{array}{l}x \\ z \\ y\end{array}\right]  =\left[\begin{array}{c}3 y+3 z \\ -3 x+4 z \\ -3 x+4 y\end{array}\right] $
$ B ^{\prime}( AB )=\left[\begin{array}{l}x \\ y \\ z\end{array}\right]\left[\begin{array}{c}3 y+3 z \\ -3 x-4 z \\ -3 x+4 y\end{array}\right] $
$ =\left[\begin{array}{lll}x & y & z\end{array}\right]\left[\begin{array}{c}3 y+3 z \\ -3 x-4 z \\ -3 x+4 y\end{array}\right] $
$=[3 x y+3 x z-3 x y-4 y z-3 x z+4 y z]$
$=[0]$

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