Question

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 

पर्याय

•  −6, −12, −18 

•  −6, 4, 9

• −6, −4, −9

• −6, 12, 18

Answer 1

 −6, −4, −9 

\[Given: A = \begin{bmatrix}0 & 2 \\ 3 & - 4\end{bmatrix}\]

\[Here, \]

\[kA = \begin{bmatrix}0 & 3a \\ 2b & 24\end{bmatrix}\]

\[ \Rightarrow k\begin{bmatrix}0 & 2 \\ 3 & - 4\end{bmatrix} = \begin{bmatrix}0 & 3a \\ 2b & 24\end{bmatrix}\]

\[ \Rightarrow \begin{bmatrix}0 & 2k \\ 3k & - 4k\end{bmatrix} = \begin{bmatrix}0 & 3a \\ 2b & 24\end{bmatrix}\]

`"The corresponding elements of two equal matrices are equal ."`

\[ \Rightarrow 2k = 3a, 3k = \text{2b and - 4k} = 24 \]

\[Now, \]

\[ - 4k = 24 \]

\[ \Rightarrow k = - 6\]

\[Also, \]

\[2k = \text{3a and 3k }= 2b\]

⇒ 2(-6) = 3a and 3(-6) = 2b                       [using k = -6]

\[ \Rightarrow - 12 = \text{3a and - 18 }= 2b\]

\[ \therefore a = \text{- 4 and b} = - 9\]