function []=hw4_2_13(n)

% find the condition number of the matrix in 2.10

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;

disp('numerical')
disp(cond(E))
disp('theoratical')
disp(4*n^2/pi^2)

% The relative error between the numerical and theoretical value decreases as
% n increases.