Question

If $y=\left[\begin{array}{cc}1& 2\\ -1& 5\end{array}\right]$, find a matrix $X$ such that $2X+Y=\left[\begin{array}{cc}5& 0\\ -3& 3\end{array}\right]$

Answer 1

According to question,

$2X+Y=\left[\begin{array}{cc}5& 0\\ -3& 3\end{array}\right]$

$\Rightarrow$ $2X=\left[\begin{array}{cc}5& 0\\ -3& 3\end{array}\right]-Y$

$\Rightarrow$ $2X=\left[\begin{array}{cc}5& 0\\ -3& 3\end{array}\right]-\left[\begin{array}{cc}1& 2\\ -1& 5\end{array}\right]$

$\Rightarrow$ $X=\frac{1}{2}\left[\begin{array}{cc}4& -2\\ -2& -2\end{array}\right]$

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