It is given that

$\left[\begin{array}{lll}2& 2& 3\\ 7& 1& 1\\ 0& 6& 5\end{array}\right]\left[\begin{array}{l}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}3y+11\\ 6z-1\\ 5y+11\end{array}\right]+\left[\begin{array}{c}x\\ x\\ 4z\end{array}\right]+\left[\begin{array}{c}z\\ 3x\\ 4y\end{array}\right]$

Solve the above matrix

$\left[\begin{array}{c}2x+2y+3z\\ 7x+y+z\\ 6y+5z\end{array}\right]=\left[\begin{array}{c}3y+x+z+11\\ 3x+x+6z-1\\ 5y+4y+4z+11\end{array}\right]$

$\left[\begin{array}{c}2x+2y+3z\\ 7x+y+z\\ 6y+5z\end{array}\right]=\left[\begin{array}{c}x+3y+z+11\\ 4x+6z-1\\ 9y+4z+11\end{array}\right]$

On comparing
$x-y+2 z=11$

$\Rightarrow 3x+y-5z=-1$

$\Rightarrow -3 y+z=11$

From the above three equations

$x=4, y=-3, z=2$