Question Number 25623 by Sunilll last updated on 12/Dec/17
![solve for A and B if 2A+B [((6 3)),((6 −2)) ] and 3A+2B [((1 0)),((0 5)) ]](https://www.tinkutara.com/question/Q25623.png)
$${solve}\:{for}\:{A}\:{and}\:{B}\:{if}\:\mathrm{2}{A}+{B}\:\begin{bmatrix}{\mathrm{6}\:\:\:\mathrm{3}}\\{\mathrm{6}\:\:−\mathrm{2}}\end{bmatrix} \\ $$$${and}\:\mathrm{3}{A}+\mathrm{2}{B}\:\begin{bmatrix}{\mathrm{1}\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\mathrm{5}}\end{bmatrix} \\ $$
Answered by mrW1 last updated on 12/Dec/17
![2A+B=C ...(i) 3A+2B=D ...(ii) 2(i)−(ii): ⇒A=2C−D= [((11),6),((12),(−9)) ] ⇒B=C−2A= [((−16),(−9)),((−18),(16)) ]](https://www.tinkutara.com/question/Q25629.png)
$$\mathrm{2}{A}+{B}={C}\:\:…\left({i}\right) \\ $$$$\mathrm{3}{A}+\mathrm{2}{B}={D}\:\:…\left({ii}\right) \\ $$$$\mathrm{2}\left({i}\right)−\left({ii}\right): \\ $$$$\Rightarrow{A}=\mathrm{2}{C}−{D}=\begin{bmatrix}{\mathrm{11}}&{\mathrm{6}}\\{\mathrm{12}}&{−\mathrm{9}}\end{bmatrix} \\ $$$$\Rightarrow{B}={C}−\mathrm{2}{A}=\begin{bmatrix}{−\mathrm{16}}&{−\mathrm{9}}\\{−\mathrm{18}}&{\mathrm{16}}\end{bmatrix} \\ $$