Question

Find the value of y, if$\left[\begin{array}{cc}x-y& 2\\ x& 5\end{array}\right]=\left[\begin{array}{cc}2& 2\\ 3& 5\end{array}\right]$

Answer 1

$$\begin{gathered} \mathrm{Given}:\left[\begin{array}{cc}x-y& 2\\ x& 5\end{array}\right]=\left[\begin{array}{cc}2& 2\\ 3& 5\end{array}\right] \\ \mathrm{The}\mathrm{corresponding}\mathrm{elements}\mathrm{of}\mathrm{two}\mathrm{equal}\mathrm{matrices}\mathrm{are}\mathrm{equal}. \\ \therefore x-y=2...\left(1\right) \\ \mathrm{and}x=3 \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{in}\mathrm{eq}.\left(1\right) \\ 3-y=2 \\ \Rightarrow 3-2=y \\ \therefore y=1 \end{gathered}$$