Question Number 212159 by boblosh last updated on 04/Oct/24
Answered by Rasheed.Sindhi last updated on 04/Oct/24
![[(( 2),( 3)),((−1),(−1)) ]+a [(2,1),(0,4) ]= [(8,b),(c,d) ] [((2a+2),(a+3)),((0a−1),(4a−1)) ]= [(8,b),(c,d) ] 2a+2=8⇒a=3 c=−1 b=a+3=3+3=6 d=4a−1=4(3)−1=11](https://www.tinkutara.com/question/Q212165.png)
$$\begin{bmatrix}{\:\:\:\:\:\mathrm{2}}&{\:\:\:\:\mathrm{3}}\\{−\mathrm{1}}&{−\mathrm{1}}\end{bmatrix}+{a}\begin{bmatrix}{\mathrm{2}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{4}}\end{bmatrix}=\begin{bmatrix}{\mathrm{8}}&{{b}}\\{{c}}&{{d}}\end{bmatrix} \\ $$$$\begin{bmatrix}{\mathrm{2}{a}+\mathrm{2}}&{{a}+\mathrm{3}}\\{\mathrm{0}{a}−\mathrm{1}}&{\mathrm{4}{a}−\mathrm{1}}\end{bmatrix}=\begin{bmatrix}{\mathrm{8}}&{{b}}\\{{c}}&{{d}}\end{bmatrix} \\ $$$$\mathrm{2}{a}+\mathrm{2}=\mathrm{8}\Rightarrow{a}=\mathrm{3} \\ $$$${c}=−\mathrm{1} \\ $$$${b}={a}+\mathrm{3}=\mathrm{3}+\mathrm{3}=\mathrm{6} \\ $$$${d}=\mathrm{4}{a}−\mathrm{1}=\mathrm{4}\left(\mathrm{3}\right)−\mathrm{1}=\mathrm{11} \\ $$