Question

Solve for $A$ and $B,$ when $2A+B=\left[\begin{array}{cc}3& -4\\ 2& 7\end{array}\right]$ and $A-2B=\left[\begin{array}{cc}4& 3\\ 1& 1\end{array}\right].$

Answer 1

$2A+B=\left[\underset{2}{3}\underset{7}{-4}\right]$

$4A+2B=\left[\underset{4}{6}\underset{14}{-8}\right]$

$\underset{–}{A-2B=\left[\underset{1}{4}\underset{1}{3}\right]}$

$5A=\left[\underset{5}{10}\underset{15}{-5}\right]\Rightarrow A=\left[\underset{1}{2}\underset{3}{-1}\right]$

$B=\left[\underset{2}{3}\underset{7}{-4}\right]-2\left[\underset{1}{2}\underset{3}{-1}\right]$

$=\left[\underset{2}{3}\underset{7}{-4}\right]-\left[\underset{2}{4}\underset{6}{-2}\right]$

$B=\left[\underset{0}{-1}\underset{1}{-2}\right]$

$\therefore$ , $A=\left[\underset{1}{2}\underset{3}{-1}\right]B=\left[\underset{0}{-1}\underset{1}{-2}\right]$