In Matlab Please

function [x,er,n_iter] = newtraph_vector(F,JF,x1,maxtol,maxitr)

if nargin

if nargin

if isrow(x1), x1=x1.'; end % or use x=x(:);

k = 0; % Initialize the iteration number

er = 1; % Initialize the relative approximate error

n = length(x1);

x = [x1, zeros(n,maxitr)]; % pre-allocate the solution matrix

% alternatively, initialize x = x1;

while er >= maxtol && k

k = k+1;

if norm(x(:,k+1)) >= eps

er = % define the relative approx error

else

warning('A close to zero solution is obtained for the current estimated solution; approximate error is evaluated instead')

er = norm((x(:,k+1)-x(:,k)));

end

end

% Examine the condition under which the loop terminates

if er>=maxtol && k==maxitr

warning('Maximum number of iterations is reached before convergence')

elseif er

fprintf(' The algorithm converges at the maximum number of iterations ')

end

n_iter = k;

disp(' ')

disp('The solution estimates are =')

disp(x(:,1:k+1)')

end

(Code Provided)

Problem 1: Newton's method for solving a system of nonlinear equations In the prelab, we applied the Newton's method to solve the following system of equations. 4x} xi = -28 (la) 3x} + 4x2 = 145 (1b) The above two equations can be compactly written in the vector form F(x) = 0, where F is the vector function of the system of equations. The Newton's Method can be used to determine the solution to a system of nonlinear equations where the algorithm iteratively updates the estimated solution using the following relationship: VF(xk) Xk+1 = VF(xx) XK F(xx) (2) where, Xk denotes the k-th estimate of the solution vector. Develop the numerical solver newtraph_vector to solve a set of nonlinear algebraic equations, based on the Newton's method to solve for a single algebraic equation. Test your code using x1=[1; 1], maxtol=1e-4, maxitr=20. = function(x, er, n_iter] newtraph_vector(F_system, Jacobian_system, x1, maxtol, maxitr) Note: Complete the function file newtraph_vector based on the programming logic of Newtonroot for solving a scalar equation. Problem 1: Newton's method for solving a system of nonlinear equations In the prelab, we applied the Newton's method to solve the following system of equations. 4x} xi = -28 (la) 3x} + 4x2 = 145 (1b) The above two equations can be compactly written in the vector form F(x) = 0, where F is the vector function of the system of equations. The Newton's Method can be used to determine the solution to a system of nonlinear equations where the algorithm iteratively updates the estimated solution using the following relationship: VF(xk) Xk+1 = VF(xx) XK F(xx) (2) where, Xk denotes the k-th estimate of the solution vector. Develop the numerical solver newtraph_vector to solve a set of nonlinear algebraic equations, based on the Newton's method to solve for a single algebraic equation. Test your code using x1=[1; 1], maxtol=1e-4, maxitr=20. = function(x, er, n_iter] newtraph_vector(F_system, Jacobian_system, x1, maxtol, maxitr) Note: Complete the function file newtraph_vector based on the programming logic of Newtonroot for solving a scalar equation