(%i1) "Cornelsen, S. 207, Übung 2"$

(%i2) "a)"$

(%i3) A: matrix([2.0,3.0,-1.0],[4.0,-2.0,1.0]);
                             [ 2.0   3.0   - 1.0 ]
(%o3)                        [                   ]
                             [ 4.0  - 2.0   1.0  ]

(%i4) B: matrix([1.0,2.0,-2.0,3.0],[-1.0,3.0,2.0,0.0],[2.0,0.0,4.0,1.0]);
                          [  1.0   2.0  - 2.0  3.0 ]
                          [                        ]
(%o4)                     [ - 1.0  3.0   2.0   0.0 ]
                          [                        ]
                          [  2.0   0.0   4.0   1.0 ]

(%i5) A . B;
                         [ - 3.0  13.0  - 2.0  5.0  ]
(%o5)                    [                          ]
                         [  8.0   2.0   - 8.0  13.0 ]

(%i6) "b)"$


(%i7) "c_23 => 2. Zeile von A mit 3. Spalte von B"$


(%i8) "c)"$


(%i9) A1: matrix([1.0,2.0,0.0],[2.0,3.0,0.0],[3.0,4.0,1.0]);
                               [ 1.0  2.0  0.0 ]
                               [               ]
(%o9)                          [ 2.0  3.0  0.0 ]
                               [               ]
                               [ 3.0  4.0  1.0 ]

(%i10) B1: matrix([-3.0,2.0,0.0],[2.0,-1.0,0.0],[1.0,-2.0,1.0]);
                             [ - 3.0   2.0   0.0 ]
                             [                   ]
(%o10)                       [  2.0   - 1.0  0.0 ]
                             [                   ]
                             [  1.0   - 2.0  1.0 ]

(%i11) A1 . B1;
                               [ 1.0  0.0  0.0 ]
                               [               ]
(%o11)                         [ 0.0  1.0  0.0 ]
                               [               ]
                               [ 0.0  0.0  1.0 ]

(%i12) "D. h.: B = A^(-1)  (→ inverse Matrix!)"$