 clear all;
 close all;

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 A=[5 -3; -1 1];
 lamda=(3+sqrt(7));
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 randn(seed,129);
 x1=0.1+0.1*randn(1,8);
 randn(seed,131);
 x2=0.2+0.2*randn(1,8);

 rand(seed,3);
 ind=1+floor(8*rand(1,3));
 yy=(1/(1-lamda))*x1;

 x2(1,ind)=yy(1,ind);

 figure;plot(x1,x2,.,MarkerSize,14);

 %hold on;plot(x1(1,ind),x2(1,ind),r.,MarkerSize,14);
 grid on;axis([-1.5 1.6 -1 3.5]);


 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 lhs=A*[x1;x2];
 figure;plot(x1,x2,.,MarkerSize,14);
 hold on;plot(lhs(1,:),lhs(2,:),m.,MarkerSize,14);
 grid on;axis([-1.5 1.6 -1 3.5]);
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 rhs=lamda*[x1;x2];
 figure;plot(x1,x2,.,MarkerSize,14);
 hold on;plot(rhs(1,:),rhs(2,:),m.,MarkerSize,14);
 grid on;axis([-1.5 1.6 -1 3.5]);
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 figure;plot(lhs(1,:),lhs(2,:),.,MarkerSize,14);
 hold on;plot(rhs(1,:),rhs(2,:),r.,MarkerSize,14);
 grid on;axis([-1.5 1.6 -1 3.5]);

 ind1=find(abs(lhs(1,:)-rhs(1,:))<0.000001);
 hold on;plot(rhs(1,ind1),rhs(2,ind1),o,MarkerSize,10);
 grid on;axis([-1.5 1.6 -1 3.5]);
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 figure;plot(x1,x2,.,MarkerSize,14);grid on;
 hold on;plot(x1(ind1),x2(ind1),o,MarkerSize,10);
 axis([-1.5 1.6 -1 3.5]);

 figure;plot(x1,x2,.,MarkerSize,14);
 hold on;plot(x1(1,ind),x2(1,ind),r.,MarkerSize,14);
 grid on;axis([-1.5 1.6 -1 3.5]);