function [A]=hw6_2_17(n)
% notice the pattern in A
A=zeros(n);
for i=1:n
    for j=1:n
        A(i,j)=n-max(i,j)+1;
    end
end
evals=sort(eig(A));

% the book really messed up here these are the WRONG eigenvalues for this matrix!
% $20 to the first person who can find an exact formula for them!
i=[1:n]';
lambda=sort(.5*(1-cos((2*i-1)*pi/(2*n+1))));

disp('smallest evals, numerical then exact')
disp(evals(1))
disp(lambda(1))
disp('largest evals, numerical then exact')
disp(evals(n))
disp(lambda(n))