write a code for a linear system of equations with one matrix using the gauss-seidel iteration solver in matlab

Here is the sample code for solving a linear system of equations using Gauss-Seidel iteration method in MATLAB:

main.m
A = [4,-1,0; 2,-5,2; 0,1,4]; % matrix of the system
b = [8;-4;11]; % column matrix of constants
D = diag(diag(A)); % diagonal matrix
L = tril(A) - D; % lower triangular matrix
U = triu(A) - D; % upper triangular matrix
x0 = [0;0;0]; % initial approximation
tol = 10^-4; % tolerance
maxit = 1000; % maximum number of iterations

% Gauss-Seidel iteration
for i = 1:maxit
    x = (D+L)\(-U*x0+b);
    if norm(x-x0)/norm(x) < tol % checking for convergence
        fprintf('Solution converged after %d iterations\n',i);
        break
    end
    x0 = x;
end
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In this code, the matrix of the system is stored in variable A and the column matrix of constants is stored in variable b. The diagonal, lower triangular, and upper triangular matrices are calculated and stored in variables D, L, and U, respectively. The initial approximation is stored in variable x0 and the tolerance level is stored in variable tol. The maximum number of iterations is stored in variable maxit. In the for loop, Gauss-Seidel iteration is performed until the solution converges or the maximum number of iterations is reached. The result is stored in variable x.

Note: Convergence is not guaranteed for all matrices.