%a=[0.012,0.01,0.167;1,0.8334,5.91;3200,1200,4.2];
%b=[0.6781,12.1,981]';
a=[1,-1,2,-1;2,-2,3,-3;1,1,1,0;1,-1,4,3];%系數矩陣a
b=[-8,-20,-2,4]';
%a=[0.003000,59.14;5.291,-6.130];%系數矩陣a1
%b=[59.17,46.78]';
L=[1,2,3,4];
n=length(b);
clu=[];
for k=1:n-1
    [p,q]=find(abs(a)==max(max(abs(a(k:n,k:n)))));
    
    if(p~=k|q~=k)
      t=a(k,:);
      a(k,:)=a(p,:);
      a(p,:)=t;
      r=a(:,k);
      a(:,k)=a(:,q);
      a(:,q)=r;
      t=L(k);L(k)=L(q);L(q)=t;
      u=b(k);
      b(k)=b(p);
      b(p)=u;
    end
    m(k+1:n,k)=a(k+1:n,k)./a(k,k);
    a(k+1:n,k:n)=a(k+1:n,k:n)-m(k+1:n,k)*a(k,k:n);
    b(k+1:n)=b(k+1:n)-m(k+1:n,k)*b(k);    
end


%%%%%%%%%%%%%回代%%%%%%%%%%%
y(n)=b(n)/a(n,n);
for i=n-1:-1:1
    sum=0;
    for j=i+1:n
        sum=sum+a(i,j)*y(j);
    end
    y(i)=(b(i)-sum)/a(i,i);
end

x(L(n))=y(n);
x(L(1:n-1))=y(1:n-1);
jie=x'