format compact
x=[-1 0 1];
A = [x;1 1 1]';
b = [1 0 2]'+[.5 -1 .5]';
p = ((A'*A)\A'*b);
y = A*p;

perp=[y';b'];

v1=[
    0.9235   -0.8870   -0.0000   -0.0182
    0.7777    0.2024    1.7976   -1.3888
    1.5945    0.4150   -0.8767   14.4336
    0         0         0    1.0000
    ];
v2 = [
    1.3252   -0.7490         0   -0.2881
    0.5611    0.2482    1.8544   -1.3319
    1.3888    0.6144   -0.7492   14.3730
         0         0         0    1.0000 ];
v3 = [
    1.6868   -0.5373   -0.0000   -0.5747
    0.2234    0.1754    1.9563   -1.1775
    1.0511    0.8250   -0.4158   14.2699
         0         0         0    1.0000 ];
grd=-2:.5:2;
grd=grd(grd~=0);
g2=[grd(1),grd(end)]
s1a=A*[0*grd+grd(1);grd]; % each col has one end point of a line to draw.
s1b=A*[0*grd+grd(end);grd]; % the other end points, varying the constant term.
s2a=A*[grd;0*grd+grd(1)]; % each col has one end point of a line to draw.
s2b=A*[grd;0*grd+grd(end)]; % the other end point, varying the slope.
zb=A*[0*g2;g2];  % the coordinate passing through the origin.
zm=A*[g2;0*g2];  % the coordinate passing through the origin.

figure(1);clf; hold off
tt=[g2(1):.05:g2(2)];
plot(x,b,'r*',tt,polyval(p,tt),'k-',[x;x],[y';b'],'r-');
axis equal
grid
hold on;
plot(x,[1,1,1],'b*');
plot(x,[-1,0,1],'mo');
hold off


figure(2);clf; hold off

plot3([s1a(1,:),s2a(1,:);s1b(1,:),s2b(1,:)], ...
      [s1a(2,:),s2a(2,:);s1b(2,:),s2b(2,:)], ...
      [s1a(3,:),s2a(3,:);s1b(3,:),s2b(3,:)], ...
      '-k',...
      0,0,0,'ko',...
      b(1),b(2),b(3),'r*',...
      perp(:,1),perp(:,2),perp(:,3),'r-');
axis equal
grid
view(v2);v=view;
hold on;
plot3(zb(1,:),zb(2,:),zb(3,:),'b-');
plot3(zm(1,:),zm(2,:),zm(3,:),'m-');
plot3(A(1,2),A(2,2),A(3,2),'b*');
plot3(A(1,1),A(2,1),A(3,1),'m*');
text(A(1,2),A(2,2),A(3,2),'1,1,1');
text(A(1,1),A(2,1),A(3,1),'-1,0,1');
h=text(b(1),b(2),b(3),'b');set(h,'color',[1 0 0]);
text(0,0,0,'origin')
plot3(y(1),y(2),y(3),'r*')
hold off
A
b
p
disp('A*p = ')
disp(A*p);