(%i2) M: matrix([0.6,0.1,0.2],[0.2,0.8,0.3],[0.2,0.1,0.5]);
                               [ 0.6  0.1  0.2 ]
                               [               ]
(%o2)                          [ 0.2  0.8  0.3 ]
                               [               ]
                               [ 0.2  0.1  0.5 ]

(%i3) "Vektor J"$

(%i4) J: transpose(matrix ([400.0,400.0,200.0]));
                                   [ 400.0 ]
                                   [       ]
(%o4)                              [ 400.0 ]
                                   [       ]
                                   [ 200.0 ]

(%i5) "a)"$

(%i6) "nach einem Jahr: M . J"$

(%i7) M . J;
                                   [ 320.0 ]
                                   [       ]
(%o7)                              [ 460.0 ]
                                   [       ]
                                   [ 220.0 ]

(%i8) "nach zwei Jahren: M . M . J = M^^2 . J"$

(%i9) M^^2 . J;
                             [ 282.0000000000001 ]
                             [                   ]
(%o9)                        [ 498.0000000000001 ]
                             [                   ]
                             [       220.0       ]

(%i10) "b) z. B. nach 12 Jahren"$

(%i11) M^^12 . J;
                             [ 241.4898347638001 ]
                             [                   ]
(%o11)                       [ 551.5455405892004 ]
                             [                   ]
                             [ 206.9646246470001 ]

(%i12) "z. B. nach 25 Jahren"$

(%i13) M^^25 . J;
                             [ 241.3793716705243 ]
                             [                   ]
(%o13)                       [ 551.7240387041518 ]
                             [                   ]
                             [ 206.8965896253251 ]

(%i14) "=> Kaum Veraenderung im Zustandsvektor J!"$

(%i15) "c)"$

(%i16) "Verwende statt der Matrix M die Matrix A . M mit A wie folgt:"$

(%i17) A: matrix([0.5,0.0,0.0],[0.0,0.5,0.0],[0.0,0.0,2.0]);
                               [ 0.5  0.0  0.0 ]
                               [               ]
(%o17)                         [ 0.0  0.5  0.0 ]
                               [               ]
                               [ 0.0  0.0  2.0 ]

(%i18) Mc : A . M;
                              [ 0.3  0.05  0.1  ]
                              [                 ]
(%o18)                        [ 0.1  0.4   0.15 ]
                              [                 ]
                              [ 0.4  0.2   1.0  ]

(%i19) Mc . J;
                                   [ 160.0 ]
                                   [       ]
(%o19)                             [ 230.0 ]
                                   [       ]
                                   [ 440.0 ]

(%i20) (Mc)^^2 . J;
                                   [ 103.5 ]
                                   [       ]
(%o20)                             [ 174.0 ]
                                   [       ]
                                   [ 550.0 ]