Jacobian Matrix set-up: J=[∂F∂x∂F∂y∂G∂x∂G∂y]J=\begin{bmatrix} \dfrac{\partial F}{\partial x} & \dfrac{\partial F}{\partial y} \\ \dfrac{\partial G}{\partial x} & \dfrac{\partial G}{\partial y}\end{bmatrix} , where JJ is the coefficient of linearized equations. For this example let’s take the two equations F(x,y)=x+y−2y2=4F(x,y)=x+y-2y^2=4 and G(x,y)=x2+y2=8G(x,y)=x^2+y^2=8. (Use x0=1x_0=1 and y0=1y_0=1 for initial approximations.) Let’s do the partial derivative calculate to plug into…