Question

Find a matrix $X$ such that $2A+B+X=O,$ where $A=\left[\begin{array}{cc}-1& 2\\ 3& 4\end{array}\right]$ $B=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]$

Answer 1

$X=-2A-B$
$=-2\left[\begin{array}{cc}-1& 2\\ 3& 4\end{array}\right]-\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]$
$=\left[\begin{array}{cc}2& -4\\ -6& -8\end{array}\right]-\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]$
$=\left[\begin{array}{cc}-1& -2\\ -7& -13\end{array}\right]$