figure(1) 
plot([0 2],[0 1],'k','linewidth',2)
 %text(1.1,3,'x','fontsize',14)
 hold on
 plot([0 4],[0 2],'k','linewidth',1)
 text(2,0.6,'a_1','fontsize',14)
 text(4.3,1.9,'2a_1','fontsize',14)
 plot([0 3],[0 4],'k','linewidth',2)
 plot([0 9],[0 12],'k','linewidth',1)
 text(2.3,4.4,'a_2','fontsize',14)
 text(7.9,12.2,'3a_2','fontsize',14)
 plot([0 13],[0 14],'k','linewidth',1)
 text(12,14.4,'2a_1+3a_2','fontsize',14)
 %text(3.95,1.15,'y','fontsize',14)
 %text(0.25,0.25,'\theta','fontsize',14)
 plot([4 13],[2 14],'k--','linewidth',1)
 plot([9 13],[12 14],'k--','linewidth',1) 
 
 %axis([0 4.1 0 3.1])
 %axis equal
 hold off
 box off
 
 figure(2)
 A = [2 3; 1 4];
 for t=0:.1:2*pi,
     x = [cos(t); sin(t)];
     y = A*x;
     plot(x(1),x(2),'k.')
     hold on
     plot(y(1),y(2),'k*')
 end
 hold off
 axis equal
 axis tight
