Question

Find the value of x from the following: $\left[\begin{array}{cc}2x-y& 5\\ 3& y\end{array}\right]=\left[\begin{array}{cc}6& 5\\ 3& -2\end{array}\right]$

Answer 1

The corresponding elements of two equal matrices are equal.

$$\begin{gathered} \mathrm{Given}:\left[\begin{array}{cc}2x-y& 5\\ 3& y\end{array}\right]=\left[\begin{array}{cc}6& 5\\ 3& -2\end{array}\right] \\ 2x-y=6...\left(1\right) \\ y=-2 \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}y\mathrm{in}\mathrm{eq}.\left(1\right) \\ 2x-\left(-2\right)=6 \\ \Rightarrow 2x+2=6 \\ \Rightarrow 2x=6-2 \\ \Rightarrow 2x=4 \\ \Rightarrow x=\frac{4}{2}=2 \\ \therefore x=2 \end{gathered}$$