function []=hw3_2_6()

% solve tridiagonal systems Ax=v of different sizes as full and sparse matrices
a=2;
b=1;
timetable=[];

% I used larger values than they suggest because if n=50 it take virtually no
% time to solve the system
for n=400:40:800
    
    % set up A and v
    u1=a*ones(1,n);
    u2=b*ones(1,n-1);
    A=diag(u2,-1)+diag(u1)+diag(u2,1);
    v=ones(n,1);
    
    % time the full method
    tic
    fullx=A\v;
    t1=toc;
    
    % convert A to a sparse matrix and time the sparse method
    spA=sparse(A);
    tic
    spx=spA\v;
    t2=toc;
    
    % append rows onto timetable
    timetable=[timetable;[n, t1, t2]];
end

format short g
disp('           n      full time    sparse time')
disp('           -      ---------    -----------')
disp(timetable)
format short