> 
> read("/afs/eos.ncsu.edu/users/k/kaltofen/www/courses/LinAlgebra/Maple/
> initlib.mpl");

  libname := /afs/eos.ncsu.edu/users/k/kaltofen/www/courses/LinAlg\

        ebra/Maple, "/afs/bp.ncsu.edu/dist/maple551/update",

        "/afs/bp.ncsu.edu/dist/maple551/lib"

> with(refpkg);

       [E_I, E_II, E_III, mydet, myinverse, mysolve, ref, xref]

> rnd := rand(-10..10);

  rnd := proc()
local t;
global _seed;
    _seed := irem(427419669081*_seed, 999999999989);
    t := _seed;
    irem(t, 21) - 10
end

> v1 := matrix(4,1,[rnd(),rnd(),rnd(),rnd()]);

                                    [-4]
                                    [  ]
                                    [ 7]
                              v1 := [  ]
                                    [ 8]
                                    [  ]
                                    [10]

> v2 := matrix(4,1,[rnd(),rnd(),rnd(),rnd()]);

                                    [-6]
                                    [  ]
                                    [-8]
                              v2 := [  ]
                                    [-5]
                                    [  ]
                                    [ 7]

> v3 := matrix(4,1,[rnd(),rnd(),rnd(),rnd()]);

                                    [ 6]
                                    [  ]
                                    [-6]
                              v3 := [  ]
                                    [ 0]
                                    [  ]
                                    [ 5]

> v4:=evalm(rnd()*v1+rnd()*v2+rnd()*v3);

                                   [ 40]
                                   [   ]
                                   [-84]
                             v4 := [   ]
                                   [-85]
                                   [   ]
                                   [-88]

> v5 :=evalm(rnd()*v1+rnd()*v2+rnd()*v3);

                                   [102]
                                   [   ]
                                   [ 29]
                             v5 := [   ]
                                   [ 26]
                                   [   ]
                                   [-75]

> with(linalg):
> A := blockmatrix(1,5,[v5,v1,v4,v2,v3]);

                      [102    -4     40    -6     6]
                      [                            ]
                      [ 29     7    -84    -8    -6]
                 A := [                            ]
                      [ 26     8    -85    -5     0]
                      [                            ]
                      [-75    10    -88     7     5]

> rank(A);

                                  3

> ref(A);

                [102    -4      40       -6      6  ]
                [                                   ]
                [       415    -4864    -107    -131]
                [  0    ---    -----    ----    ----]
                [       51      51       17      17 ]
                [                                   ]
                [               873     291     582 ]
                [  0     0      ---     ---     --- ]
                [               83      83      83  ]
                [                                   ]
                [  0     0       0       0       0  ]

> B:=transpose(A);

                        [102     29     26    -75]
                        [                        ]
                        [ -4      7      8     10]
                        [                        ]
                   B := [ 40    -84    -85    -88]
                        [                        ]
                        [ -6     -8     -5      7]
                        [                        ]
                        [  6     -6      0      5]

> ref(B);

                     [102    29     26     -75 ]
                     [                         ]
                     [       415    460    120 ]
                     [  0    ---    ---    --- ]
                     [       51     51     17  ]
                     [                         ]
                     [              873    2004]
                     [  0     0     ---    ----]
                     [              83      83 ]
                     [                         ]
                     [  0     0      0      0  ]
                     [                         ]
                     [  0     0      0      0  ]

>