If A= [ cc 0 & 2 3 & -4 ] and k A= [ cc 0 & 3 a 2 b & 24 ], then … - Vidyadip

MCQ

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

A
$-6,-12,-18$
B
$-6,-4,-9$
C
$-6,4,9$
D
$-6,12,18$

✓

Answer

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

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