tau = .0001;
nprob = 10000;
jfig = 0;
delta = .002;
iexample=2;
A = [1+delta,delta-1;delta-1,1+delta];
b = [2;-2];
xval=[-5,5];
yval = (b(1) - A(1,1)*xval)./A(1,2);
xtrue = A \ b;

for i=1:nprob,
      E = tau*randn(2,2);
      x = (A+E)\b;
      forward(i,:) = (x-xtrue)';
      backward(i,:) = (b - A * x)';
end

jfig = jfig + 1;
figure(jfig)
plot(forward(:,1),forward(:,2),'*')
title(sprintf('Changes in x for Linear System %d',iexample))
xlabel('\delta x_1')
ylabel('\delta x_2')