> v1 := matrix(4,1,[2,0,1,-1]);

                                    [ 2]
                                    [  ]
                                    [ 0]
                              v1 := [  ]
                                    [ 1]
                                    [  ]
                                    [-1]

> v2 := matrix(4,1,[4,0,2,-2]);

                                    [ 4]
                                    [  ]
                                    [ 0]
                              v2 := [  ]
                                    [ 2]
                                    [  ]
                                    [-2]

> v3 := matrix(4,1,[1,1,0,0]);

                                    [1]
                                    [ ]
                                    [1]
                              v3 := [ ]
                                    [0]
                                    [ ]
                                    [0]

> v4 := evalm(2*v1 -3*v2);

                                    [ 1]
                                    [  ]
                                    [-3]
                              v4 := [  ]
                                    [ 2]
                                    [  ]
                                    [-2]

> read("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); with(linalg):

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

Warning, new definition for norm
Warning, new definition for trace
> A := blockmatrix(1,4,[v1,v2,v3,v4]);

                           [ 2     4    1     1]
                           [                   ]
                           [ 0     0    1    -3]
                      A := [                   ]
                           [ 1     2    0     2]
                           [                   ]
                           [-1    -2    0    -2]

> ref(A);

                         [2    4    1     1]
                         [                 ]
                         [0    0    1    -3]
                         [                 ]
                         [0    0    0     0]
                         [                 ]
                         [0    0    0     0]

> B := array(identity,1..4,1..4);

               B := array(identity, 1 .. 4, 1 .. 4, [])

> print(B);

                          [1    0    0    0]
                          [                ]
                          [0    1    0    0]
                          [                ]
                          [0    0    1    0]
                          [                ]
                          [0    0    0    1]

> C := blockmatrix(1,3,[v1,v3,B]);

                       [ 2    1    1    0    0    0]
                       [                           ]
                       [ 0    1    0    1    0    0]
                  C := [                           ]
                       [ 1    0    0    0    1    0]
                       [                           ]
                       [-1    0    0    0    0    1]

> ref(C);

                  [2    1     1       0     0    0]
                  [                               ]
                  [0    1     0       1     0    0]
                  [                               ]
                  [0    0    -1/2    1/2    1    0]
                  [                               ]
                  [0    0     0       0     1    1]

>