Solve the minimization problem

$mi{n}_{x}f(x),$

where $x=[x_1,x_2],f(x)-=\frac{1}{2}{F}^T(x)F(x)$ and $F(x)=\left[\begin{array}{c}3x_1^2+2x_1{x}_2-1\\ -3x_2+5x_1{x}_2-4\\ e^{x_1}-sin(x_2)+1\end{array}\right],$ by the Gauss$-$

Newton method without line search.

$($a$).(20$ marks$)$ Implement the evaluation of $F(x)$ and evaluate the Jacobian matrix of $F(x)$

by the finite difference method with $x_i=0\mathrm{.}01,i=1,2$ in Matlab. The head of the

function for the Matlab code is $"[F,J]=$pfun$(x)",$ where $F$ is the function value of $x$

and $J$ is the Jacobian matrix.