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clear all 
%a1=[1,-1,2,-1;2,-2,3,-3;1,1,1,0;1,-1,4,3];%系数矩阵a1 
%b=[-8,-20,-2,4]'; 
%a1=[0.012,0.01,0.167;1,0.8334,5.91;3200,1200,4.2]; 
%b=[0.6781,12.1,981]'; 
a1=[2,-2,5;2,3,1;-1,4,1]; 
b=[6,13,3]'; 
n=length(b);%方程组大小为n 
a=zeros(n,n+1); 
a(:,1:n)=a1; 
a(1:n,n+1)=b;%增广矩阵 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%消元过程%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
for i=1:n-1 
    if(a(i:n,i)==0) 
       error('方程组没有唯一解');  
    end 
    for p=i:n 
        if(a(p,i)~=0) 
            p;%找到a的第i列第一个不是0的行号 
            break; 
        end 
    end  
    if(p~=i)  %如果p不等于i，则交换第p和第i行 
      t=a(i,:); 
      a(i,:)=a(p,:); 
      a(p,:)=t; 
    end 
    for j=i+1:n 
        a(j,i)=a(j,i)/a(i,i);%为节省存储空间，将比例因子存于a的下三角处 
        a(j,:)=a(j,:)-a(j,i)*a(i,:); 
    end 
end 
if (a(n,n)==0) 
     error('方程组没有唯一解'); 
end 
b=a(:,n+1); 
%%%%%%%%%%%%%%%%%%%%%%%%%%%回代过程%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
x(n)=b(n)/a(n,n); 
for i=n-1:-1:1 
    sum=0; 
    for j=i+1:n 
        sum=sum+a(i,j)*x(j); 
    end 
    x(i)=(b(i)-sum)/a(i,i); 
end 
jie=x'