Question

Write an advanced function (a program) in MATHCAD to perform Gauss-Jordan Elimination. Your program should be able to handle problems of any size. Remember that you MUST explain each and every line of code with comments. (Preferable with for loops)

Answer 1

A=0;
x=0;
n=input('How many variables=');
disp('Enter the coefficients along with constants For instance if x+y+3z=-5 then enter 1 1 3 -5 each number followed by an enter not space');
for i=1:n
    for j=1:n+1
        A(i,j)=input('');
    end
end
%pivoting
for i=1:n-1
    for j=i+1:n
        if abs(A(j,i))>abs(A(i,i))
            T=A(j,:);
            A(j,:)=A(i,:);
            A(i,:)=T;
        end
    end
end
disp('After pivoting');
disp(A);
for k=1:n-1
    for i=k+1:n
        m=A(i,k)/A(k,k);
        for j=k:n+1
            A(i,j)=A(i,j)-m*A(k,j);
        end
    end
end
disp('Triangularize Form ');
disp(A);
          
if A(n,n)==0
    disp('No unique solution');
end
    x(n)=A(n,n+1)/A(n,n);
    for j=n-1:-1:1
        sum=0;
    for i=1:n
        sprintf('x%.0f=%.10f',i,x(i))
    end
          for i=1:n-j
            sum=sum+A(j,n+1-i)*x(n+1-i);
        end
        x(j)=(A(j,n+1)-sum)/A(j,j);
    end