function []=hw3_2_10(n)
% solve a linear system Ex=b by \ and by LU
% note: the answer should be [0,0,0... n+1]
% set up E, but don't use C that's an extra matrix to store
E=zeros(n);
for i=1:n
    for j=1:n
        if (i==j)
            E(i,j)=i*(n-i+1);
        elseif (j>i)
            E(i,j)=E(i,j-1)-i;
        else
            E(i,j)=E(j,i);
        end
    end
end
E=1/(n+1)*E;
b=[1:n]';

% \ method
x1=E\b;
 
% LU method
[L,U]=lu(E);
y=L\b;
x2=U\y;

% print x1,x2 as rows to save space
disp('x1 from the \ method')
x1'
disp('x2 from the LU method')
x2'

% cond(E)