Solve this

Solution:

Since all the corresponding elements of a matrix are equal,

$\left[\begin{array}{cc}x & 3 x-y \\ 2 x+z & 3 y-w\end{array}\right]=\left[\begin{array}{ll}3 & 2 \\ 4 & 7\end{array}\right]$

$x=3$                 .....(1)

$3 x-y=2$           ....(2)

Putting the value of $x$ in eq. (2), we get

$3(3)-y=2$

$\Rightarrow 9-y=2$

$\Rightarrow-y=-7$

$\Rightarrow y=7$

 

$2 x+z=4$              ....(3)

Putting the value of $x$ in eq. (3), we get

$2(3)+z=4$

$\Rightarrow 6+z=4$

$\Rightarrow z=4-6$

$\Rightarrow z=-2$

 

$3 y-w=7$             ....(4)

Putting the value of $y$ in eq. (4), we get

$3(7)-w=7$

$\Rightarrow 21-w=7$

$\Rightarrow 21-7=w$

 

$\Rightarrow w=14$

$\therefore x=3, y=7, z=-2$ and $w=14$