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a=[1,2,3;2,5,2;3,1,5]; 
b=[14,18,20]; 
n=size(a,1); 
u=zeros(size(a)); 
l=zeros(size(a)); 
u(1,:)=a(1,:); 
for i=2:n 
l(i,1)=a(i,1)/u(1,1); 
end 
for r=2:n 
    for i=r:1:n 
        sum1=0; 
        for k=1:r-1 
           sum1=sum1+l(r,k)*u(k,i); 
       end 
       u(r,i)=a(r,i)-sum1; 
   end 
   for i=r+1:n 
       sum2=0; 
       for k=1:r-1 
           sum2=sum2+l(i,k)*u(k,r); 
       end 
       l(i,r)=(a(i,r)-sum2)/u(r,r); 
   end 
end 
for i=1:n 
    l(i,i)=1; 
end 
y(1)=b(1);  
for i=2:n 
    sum3=0; 
    for k=1:i-1 
        sum3=sum3+l(i,k)*y(k); 
    end 
    y(i)=b(i)-sum3; 
end 
y 
x(n)=y(n)/u(n,n); 
for i=n-1:-1:1 
    sum4=0; 
    for k=i+1:n 
        sum4=sum4+u(i,k)*x(k); 
    end 
    x(i)=(y(i)-sum4)/u(i,i); 
end 
x