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

Given $2X+A=B$ , which implies $2X=B-A=\left[\begin{array}{cc}3& 8\\ 7& 2\end{array}\right]-\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]=\left[\begin{array}{cc}3-1& 8-2\\ 7-3& 2-4\end{array}\right]=\left[\begin{array}{cc}2& 6\\ 4& -2\end{array}\right]=2\left[\begin{array}{cc}1& 3\\ 2& -1\end{array}\right]$

Therefore $X=\left[\begin{array}{cc}1& 3\\ 2& -1\end{array}\right]$