Question

If $2A+B=\left[\begin{array}{cc}3& -1\\ 2& 4\end{array}\right]$ and $B=\left[\begin{array}{cc}-1& -5\\ 0& 2\end{array}\right]$ , then find $A$.

Answer 1

$2A+B=\left[\begin{array}{cc}3& -1\\ 2& 4\end{array}\right]$

$B=\left[\begin{array}{cc}-1& -5\\ 0& 2\end{array}\right]$

$\therefore 2A=\left[\begin{array}{cc}3-(-1)& -1-(-5)\\ 2-0& 4-2\end{array}\right]$

$\therefore 2A=\left[\begin{array}{cc}4& 4\\ 2& 2\end{array}\right]$

$\Rightarrow A=\left[\begin{array}{cc}2& 2\\ 1& 1\end{array}\right]$