lesson_2_ex_3_19_20_GaussNaive

#Save the following function as GaussNaive.m file

function x = GaussNaive(A,b)
% GaussNaive: naive Gauss elimination
% x = GaussNaive(A,b): Gauss elimination without pivoting.
% input:
% A = coefficient matrix
% b = right hand side vector
% output:
% x = solution vector
    [m,n] = size(A);
    if m~=n, error('Matrix A must be square'); end
    nb = n+1;
    Aug = [A b];
% forward elimination
    for k = 1:n-1
        for i = k+1:n
            factor = Aug(i,k)/Aug(k,k);
           Aug(i,k:nb) = Aug(i,k:nb)-factor*Aug(k,k:nb);
        end
    end
% back substitution
    x = zeros(n,1);
    x(n) = Aug(n,nb)/Aug(n,n);
    for i = n-1:-1:1
        x(i) = (Aug(i,nb)-Aug(i,i+1:n)*x(i+1:n))/Aug(i,i);
    end