(%i1) "Einf. Determinante"$

(%i2) M1: matrix([1.0,0.0,1.0],[0.0,1.0,1.0],[0.0,0.0,1.0]);
                               [ 1.0  0.0  1.0 ]
                               [               ]
(%o2)                          [ 0.0  1.0  1.0 ]
                               [               ]
                               [ 0.0  0.0  1.0 ]

(%i3) determinant(M1);
(%o3)                                 1.0

(%i4) M3: matrix([1.0,3.0,1.0],[2.0,6.0,1.0],[0.0,0.0,1.0]);
                               [ 1.0  3.0  1.0 ]
                               [               ]
(%o4)                          [ 2.0  6.0  1.0 ]
                               [               ]
                               [ 0.0  0.0  1.0 ]

(%i5) determinant(M3);
(%o5)                                 0.0

(%i6) M4: matrix([1.0,3.0,1.0],[2.0,4.0,1.0],[0.0,0.0,0.0]);
                               [ 1.0  3.0  1.0 ]
                               [               ]
(%o6)                          [ 2.0  4.0  1.0 ]
                               [               ]
                               [ 0.0  0.0  0.0 ]

(%i7) determinant(M4);
(%o7)                                 0.0

(%i8) M2: matrix([1.0,3.0,1.0],[2.0,1.0,1.0],[0.0,2.0,1.0]);
                               [ 1.0  3.0  1.0 ]
                               [               ]
(%o8)                          [ 2.0  1.0  1.0 ]
                               [               ]
                               [ 0.0  2.0  1.0 ]

(%i9) determinant(M2);
(%o9)                                - 3.0

(%i10) M2a: matrix([1.0,3.0],[2.0,1.0]);
                                 [ 1.0  3.0 ]
(%o10)                           [          ]
                                 [ 2.0  1.0 ]

(%i11) determinant(M2a);
(%o11)                               - 5.0

(%i12) M2b: matrix([1.0,3.0],[0.0,2.0]);
                                 [ 1.0  3.0 ]
(%o12)                           [          ]
                                 [ 0.0  2.0 ]

(%i13) determinant(M2b);
(%o13)                                2.0

(%i14) M2c: matrix([2.0,1.0],[0.0,2.0]);
                                 [ 2.0  1.0 ]
(%o14)                           [          ]
                                 [ 0.0  2.0 ]

(%i15) determinant(M2c);
(%o15)                                4.0

(%i16) determinant(M2a) - determinant(M2b) + determinant(M2c);
(%o16)                               - 3.0

(%i17) "Aufbau des Normalenvektors"$


(%i18) "( det(M2c) , -det(M2b) , det(M2a) )^T "$

                                   [   det(M2c) ]
                                   [            ]
                                   [ - det(M2b) ]
                                   [            ]
                                   [   det(M2a) ]

(%i19) "Normalenvektor Vektor n1"$

(%i20) n1: transpose(matrix ([4.0,-2.0,-5.0]));
                                   [  4.0  ]
                                   [       ]
(%o20)                             [ - 2.0 ]
                                   [       ]
                                   [ - 5.0 ]

(%i21) "Vektor a"$

(%i22) a: transpose(matrix ([1.0,2.0,0.0]));
                                    [ 1.0 ]
                                    [     ]
(%o22)                              [ 2.0 ]
                                    [     ]
                                    [ 0.0 ]

(%i23) "Vektor b"$

(%i24) b: transpose(matrix ([3.0,1.0,2.0]));
                                    [ 3.0 ]
                                    [     ]
(%o24)                              [ 1.0 ]
                                    [     ]
                                    [ 2.0 ]

(%i25) "Skalarprodukt zwischen den Vektoren : <a,n1> = 0.0"$


(%i26) "Skalarprodukt zwischen den Vektoren : <b,n1> = 0.0"$


(%i27) "Kreuzprodukt a x b"$


(%i28) a_b : transpose(matrix ([4.0,-2.0,-5.0]));
                                   [  4.0  ]
                                   [       ]
(%o28)                             [ - 2.0 ]
                                   [       ]
                                   [ - 5.0 ]