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