If A= \begin{bmatrix} 0 &2 \\ 3& -4 \end{bmatrix}\: and\: \, kA= \begin{bmatrix} 0 & 3a\\ 2b&24 \end{bmatrix}, then find the values of k, a and b.

 

 

 

 
 
 
 
 

Answers (1)

Given:
A= \begin{bmatrix} 0 &2 \\ 3& -4 \end{bmatrix}\: kA= \begin{bmatrix} 0 & 3a\\ 2b&24 \end{bmatrix}---\left ( i \right )
kA=k \begin{bmatrix} 0 &2 \\ 3& -4 \end{bmatrix}\Rightarrow \begin{bmatrix} 0 &2k \\ 3k& -4k \end{bmatrix}---\left ( ii \right )
from equation (i) & (ii)
\begin{bmatrix} 0 &2k \\ 3k& -4k \end{bmatrix}= \begin{bmatrix} 0 &3a \\ 2b& 24 \end{bmatrix}
-4k= 24\: \: \Rightarrow k= -6
3a= 2k\Rightarrow a= -4
2b= 3k\Rightarrow b= -9

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