If A= 0&2 3&-4 and kA= 0&3a 2b&24 , then the values of k, a, b, a… - Vidyadip

MCQ

If $\text{A}=\begin{bmatrix}0&2\\3&-4\end{bmatrix}$ and $\text{kA}=\begin{bmatrix}0&3\text{a}\\2\text{b}&24\end{bmatrix},$ then the values of $k, a, b,$ are respectively

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

✓

Answer

Correct option: C.

$-6, -4, -9$

$\text{A}=\begin{bmatrix}0&2\\3&-4\end{bmatrix}$
$\text{kA}=\begin{bmatrix}0&3\text{a}\\2\text{b}&24\end{bmatrix}$
$\Rightarrow\begin{bmatrix}0&2\text{k}\\3\text{k}&-4\text{k}\end{bmatrix}=\begin{bmatrix}0&3\text{a}\\2\text{b}&24\end{bmatrix}$
$\Rightarrow-4\text{k}=24$
$\Rightarrow\text{k}=-6$
$2\text{k}=3\text {a}$
$\Rightarrow\text{a}=-4$
$3\text{k}=2\text{b}$
$\Rightarrow\text{b}=-9$

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