Question

If $\left[\begin{array}{cc}x-y& z\\ 2x-y& \mathrm{\omega }\end{array}\right]=\left[\begin{array}{cc}-1& 4\\ 0& 5\end{array}\right]$, find x, y, z, ω.

Answer 1

$$\begin{gathered} \mathrm{Given}:\left[\begin{array}{cc}x-y& z\\ 2x-y& w\end{array}\right]=\left[\begin{array}{cc}-1& 4\\ 0& 5\end{array}\right] \\ \mathrm{Since}\mathrm{all}\mathrm{the}\mathrm{corresponding}\mathrm{elements}\mathrm{of}\mathrm{a}\mathrm{matrix}\mathrm{are}\mathrm{equal}, \\ x-y=-1 \\ \Rightarrow x=-1+y...\left(1\right) \\ 2x-y=0...\left(2\right) \\ z=4 \\ w=5 \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{in}\mathrm{eq}.\left(2\right),\mathrm{we}\mathrm{get} \\ 2\left(-1+y\right)-y=0 \\ \Rightarrow -2+2y-y=0 \\ \Rightarrow -2+y=0 \\ \Rightarrow y=2 \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}y\mathrm{in}\mathrm{eq}.\left(1\right),\mathrm{we}\mathrm{get} \\ x=-1+2 \\ \Rightarrow x=1 \end{gathered}$$