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Problem 1: Iterative algorithm for the Jacobi and Gauss-Seidel methods applied to systems of linear and nonlinear equations (Modify the code from Pre-lab exercise 1) (1) Consider the following system of linear equations by the Jacobi iterative method 7x1 + 4x2 3x3 = 44 X1 + 5x2 + 2x3 = 22 -2x1 + x2 + 5x3 -2 (2) (3) a) Modify your codes from the pre-lab to perform the iterations until the relative approximate error is smaller than a maximum tolerance (maxtol) or the number of iterations has exceeded a maximum allowable number of iterations (maxitr). Define the error using the 2-norm. b) Test your codes with zero initial vector and maxtol=1e-4, maxitr=30. c) Modify the Gauss-Seidel code from Pre-lab exercise 1 and apply to the following system of equations Ax = b to observe convergence or divergence of the systems of equations. Note that these equations are the same but arranged in different order. Apply the iteration 10 times. [10 A=1 0 5 7 -6 -21 4 12] b= [10 A=0 1 5 -6 7 -21 12 4 b = 4 % 8x(1) + 2x(2) + 3x(3) = 51 % 2x(1) + 5x(2) + X(3) = 23 % - 3x(1) + x(2) + 6x(3) = 20 % n = 5; % Number of iterations X0 = zeros(1,3); % Initial guess vector (user-input) X = XO; % Initial guess vector %% Jacobi method fprintf(' Results from Jacobi method: ') for i=1:n xold = x; X(1) = (51-2*xold(2)-3* xold(3))/8; X(2) = (23-2*xold(1)-xold(3))/5; x(3) = (20+3* xold(1)-xold(2))/6; er(i)=norm(x-xold, 2)orm(x, 2); fprintf('i = %d, \txi = %3.49, \tx2 = %3.49, \tx3 = %3.4g ',i,x) end %% Gauss-Seidel method X = XO; fprintf(' Results from Gauss-Seidel method: ') for i=1:n xold = x; x(1) = (51-2*x(2)-3*x(3))/8; x(2) = (23-2**(1)-X(3))/5; x(3) = (20+3*x(1)-x(2))/6; er(i)=norm(x-xold, 2)orm(x, 2); fprintf('i = %d, \txi = %3.49, \tx2 = %3.4g, \tx3 = %3.4g ',i,x) end fprintf(' ')