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

$$\begin{gathered} \mathrm{Given}:\hspace{0.17em}2X+Y=\left[\begin{array}{cc}1& 0\\ -3& 2\end{array}\right] \\ \Rightarrow 2X+\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]=\left[\begin{array}{cc}1& 0\\ -3& 2\end{array}\right] \\ \Rightarrow 2X=\left[\begin{array}{cc}1& 0\\ -3& 2\end{array}\right]-\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right] \\ \Rightarrow 2X=\left[\begin{array}{cc}1-3& 0-2\\ -3-1& 2-4\end{array}\right] \\ \Rightarrow 2X=\left[\begin{array}{cc}-2& -2\\ -4& -2\end{array}\right] \\ \Rightarrow X=\frac{1}{2}\left[\begin{array}{cc}-2& -2\\ -4& -2\end{array}\right] \\ \Rightarrow X=\left[\begin{array}{cc}-1& -1\\ -2& -1\end{array}\right] \end{gathered}$$