Question

Find $X$, if $Y=\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]$ and $2X+Y=\left[\begin{array}{cc}1& 0\\ -3& 2\end{array}\right]$.

Answer 1

$Y=\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]$

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

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

$\Rightarrow$ $2X=\left[\begin{array}{cc}1& 0\\ -3& 2\end{array}\right]-\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]$

$\Rightarrow$ $2X=\left[\begin{array}{cc}1-3& 0-2\\ -3-1& 2-4\end{array}\right]$

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

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

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