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Matrices — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMatrices1 Mark
Question
If $A=\left[\begin{array}{cc}0 & 2 \\ 3 & -4\end{array}\right]$ and $k A=\left[\begin{array}{cc}0 & 3 a \\ 2 b & 24\end{array}\right]$, then the values of $k, a$ and $b$ respectively are
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Answer

We have, $A=\left[\begin{array}{cc}0 & 2 \\ 3 & -4\end{array}\right] $
$\Rightarrow k A=\left[\begin{array}{cc}0 & 2 k \\ 3 k & -4 k\end{array}\right] $
$ \Rightarrow\left[\begin{array}{cc}0 & 3 a \\ 2 b & 24\end{array}\right]=\left[\begin{array}{cc}0 & 2 k \\ 3 k & -4 k\end{array}\right] \ ($Given$)$
$ \Rightarrow-4 k=24,3 a=2 k, 2 b=3 k $
$ \Rightarrow k=-6, a=-4, b=-9$

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