edro@euler ~ $ octave
GNU Octave, version 2.9.17
Copyright (C) 2007 John W. Eaton and others.
This is free software; see the source code for copying conditions.
There is ABSOLUTELY NO WARRANTY; not even for MERCHANTIBILITY or
FITNESS FOR A PARTICULAR PURPOSE.  For details, type `warranty'.

Octave was configured for "x86_64-unknown-linux-gnu".

Additional information about Octave is available at 
http://www.octave.org.

Please contribute if you find this software useful.
For more information, visit http://www.octave.org/help-wanted.html

Report bugs to <bug@octave.org> (but first, please read
http://www.octave.org/bugs.html to learn how to write a helpful report).

For information about changes from previous versions, type `news'.

octave:1> tx = ty = linspace (-8, 8, 41)';
octave:2> [xx, yy] = meshgrid (tx, ty);
octave:3> r = sqrt (xx .^ 2 + yy .^ 2) + eps;
octave:4> tz = sin (r) ./ r;
octave:5> mesh (tx, ty, tz);

octave:6>
octave:6> axis off
octave:7> A=[1 2 1; -2 3 1]'
A =

   1  -2
   2   3
   1   1

octave:8> rank(A)
ans =  2
octave:9> A=[0 1 1; 0 1 -1]
A =

   0   1   1
   0   1  -1

octave:10> rank(A)
ans =  2
octave:11> null(A)
ans =

  -1.00000
   0.00000
   0.00000

octave:12> sol=null(A)
sol =

  -1.00000
   0.00000
   0.00000

octave:16> alfa=-3:0.5:3;
octave:17> plot3 (alfa,alfa*0,alfa*0)
Warning: empty cb range [-0:-0], adjusting to [-1:1]
octave:18> grid on
Warning: empty cb range [-0:-0], adjusting to [-1:1]
octave:19> xlabel ('x'); ylabel ('y'); zlabel ('z')
Warning: empty cb range [-0:-0], adjusting to [-1:1]
octave:20> A=[1 1 0]
A =

   1   1   0

octave:21> null(A)
ans =

  -0.70711   0.00000
   0.70711   0.00000
   0.00000   1.00000

octave:24> [Y,Z]=meshgrid (y,z);
octave:25> surf(-Y,Y,Z)
octave:26> xlabel ('x'); ylabel ('y'); zlabel ('z')
octave:27> axis([-3,3,-3,3,-3,3])
octave:28> A=[1 1 1 0;-1 1 0 1; 1 3 2 1; -3 1 -1 2]'
A =

   1  -1   1  -3
   1   1   3   1
   1   0   2  -1
   0   1   1   2

octave:29> rank(A)
ans =  2
octave:30> [l,V,p]=lu(A'); V'
ans =

  -3.00000   0.00000   0.00000   0.00000
   1.00000   3.33333   0.00000   0.00000
  -1.00000   1.66667   0.00000   0.00000
   2.00000   1.66667   0.00000   0.00000

octave:31> [l,U,p]=lu(A); U
U =

   1  -1   1  -3
   0   2   2   4
   0   0   0   0
   0   0   0   0

octave:32> clear
octave:33> A=[2 8 -2; 1 -17 6;9 6 1]'
A =

    2    1    9
    8  -17    6
   -2    6    1

octave:34> A=[2 8 -2; 1 -17 6;9 6 1]
A =

    2    8   -2
    1  -17    6
    9    6    1

octave:35> rank(A)
ans =  2
octave:36> [l,U,p]=lu(A); U
U =

    9.00000    6.00000    1.00000
    0.00000  -17.66667    5.88889
    0.00000    0.00000    0.00000

octave:37> [l,V,p]=lu(A'); V'
ans =

    8.00000    0.00000    0.00000
  -17.00000    5.25000    0.00000
    6.00000    7.50000    0.00000

octave:38> B=[3 -4 0 4;2 4 -2 0; 3 -2 4 -4]
B =

   3  -4   0   4
   2   4  -2   0
   3  -2   4  -4

octave:39> rank(B)
ans =  3
octave:40> [l,V,p]=lu(B'); V'
ans =

  -4.00000   0.00000   0.00000
   4.00000   5.00000   0.00000
  -2.00000   1.50000  -7.20000

octave:41> [l,U,p]=lu(B); U
U =

   3.00000  -4.00000   0.00000   4.00000
   0.00000   6.66667  -2.00000  -2.66667
   0.00000   0.00000   4.60000  -7.20000

octave:42>