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Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices1 Mark
Question
If $A=\left[\begin{array}{ll}3 & 4 \\ 5 & 2\end{array}\right]$ and $2 A+B$ is a null matrix, then $B$ is equal to:
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Answer

Given, $A=\left[\begin{array}{ll}3 & 4 \\ 5 & 2\end{array}\right]$ and $2 A+B=O=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
Let $B=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right] $
$\Rightarrow 2\left[\begin{array}{ll}3 & 4 \\ 5 & 2\end{array}\right]+\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
On comparing, we get
$a+6=0 $
$\Rightarrow a=-6 ; b+8=0 $
$\Rightarrow b=-8$
$c+10=0$
$ \Rightarrow c=-10 $ and $ d+4=0 $
$\Rightarrow d=-4 . $
$ \therefore$  Required matrix, $ B=\left[\begin{array}{cc} -6 & -8 \\ -10 & -4 \end{array}\right]$

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