>> N=6; A=tril(-0.99*ones(N),-1)+diag(ones(N,1)); A(:,N)=ones(N,1), [L,U]=lu(A)
A =

           1           0           0           0           0           1
       -0.99           1           0           0           0           1
       -0.99       -0.99           1           0           0           1
       -0.99       -0.99       -0.99           1           0           1
       -0.99       -0.99       -0.99       -0.99           1           1
       -0.99       -0.99       -0.99       -0.99       -0.99           1

L =

           1           0           0           0           0           0
       -0.99           1           0           0           0           0
       -0.99       -0.99           1           0           0           0
       -0.99       -0.99       -0.99           1           0           0
       -0.99       -0.99       -0.99       -0.99           1           0
       -0.99       -0.99       -0.99       -0.99       -0.99           1

U =

           1           0           0           0           0           1
           0           1           0           0           0        1.99
           0           0           1           0           0      3.9601
           0           0           0           1           0      7.8806
           0           0           0           0           1      15.682
           0           0           0           0           0      31.208

>> N=6; A=tril(-0.99*ones(N),-1)+diag(ones(N,1)); A(:,N)=ones(N,1); [L,U]=lu(A); [norm(L) norm(U)]
ans =

      3.2336      36.095

>> N=60; A=tril(-0.99*ones(N),-1)+diag(ones(N,1)); A(:,N)=ones(N,1); [L,U]=lu(A); [norm(L) norm(U)]
ans =

      36.892  4.9606e+17

>> x=rand(N,1); b=A*x; y=A\b; norm(x-y)/norm(x)
ans =    0.12653

>> B=randn(N,N); bB=B*x; yB=B\bB; norm(x-yB)/norm(x)
ans = 6.6591e-14