Question

If $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right],B\left[\begin{array}{cc}3& 8\\ 7& 2\end{array}\right]$ and $2x+A=B$ then find $x$

Answer 1

$\begin{array}{c}A=\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right),B\left(\begin{array}{cc}3& 8\\ 7& 2\end{array}\right)\\ 2x=B-A\\ 2x=\left(\begin{array}{cc}3& 8\\ 7& 2\end{array}\right)-\left(\begin{array}{cc}1& 2\\ 3& 4\end{array}\right)\\ 2x=\left(\begin{array}{cc}2& 6\\ 4& -2\end{array}\right)\\ x=\frac{1}{2}\left(\begin{array}{cc}2& 6\\ 4& -2\end{array}\right)\to x=\left(\begin{array}{cc}1& 3\\ 2& -1\end{array}\right)\end{array}$