function [A,xinitial] = genmatrix1(n)
% GENMATRIX1 : Create sample data for Homework 1
%
% [A,xinitial] = genmatrix1(n)
%
% This returns an n-by-n matrix whose largest eigenvalue
% is known, for testing CS240A problem 1.  It also returns
% a randomly chosen n-vector to start the power iteration.
%
% John R. Gilbert    13 Jan 2006

A = ones(n,n) / sqrt(n);
A = A + diag(2*sqrt(n)*ones(1,n));
A = A - diag(sqrt(n)*ones(1,n-1),-1);
A = A - diag(sqrt(n)*ones(1,n-1),1);
A(1,n) = A(1,n) - sqrt(n);
A(n,1) = A(n,1) - sqrt(n);

xinitial = randn(n,1);