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Q.
If $A =\begin{bmatrix}0&2\\ 3&-4\end{bmatrix}$ and $kA =\begin{bmatrix}0&3a\\ 2b&24\end{bmatrix}$, then the values of $k , a , b$ are respectively.
Matrices
Solution:
The given matrix is $A =\begin{bmatrix}0&2\\ 3&-4\end{bmatrix}$
Now, $k\,A=k \begin{bmatrix}0&2\\ 3&-4\end{bmatrix} = \begin{bmatrix}0&2k\\ 3k&-4k\end{bmatrix}$
Also, it is given that $kA=\begin{bmatrix}0&3a\\ 2b&24\end{bmatrix}$
$\therefore \begin{bmatrix}0&2k\\ 3k&-4k\end{bmatrix} =\begin{bmatrix}0&3a\\ 2b&24\end{bmatrix}$
On equating corresponding elements, we get
$2 k =3 a,\, 3 k =2 b$ and $-4 k =24$
$\Rightarrow k =-6,\, a =-4,\, b =-9$