#OK to post homework
#Julian Herman, 10/11/21, Assignment 10

#2)
#i)
M := Matrix([[-16/3, 5], [-7, 13/2]]);
                          [       16     ]
                          [uminus0--   5 ]
                          [        3     ]
                     M := [              ]
                          [            13]
                          [&uminus0;7  --]
                          [            2 ]


A := Matrix([[0.3], [0.6]]);
                                [0.3]
                           A := [   ]
                                [0.6]

(M^1000) . A;
             [                       &uminus0;176]
             [6.07858099239567times10            ]
             [                                   ]
             [                       &uminus0;176]
             [7.29429719087481times10            ]
#The transformation applied to (0.3,0.6) maps back to the point ~(0,0)
#after many iterations, thus (0,0) is stable!

#ii)
M := Matrix([[92/3, -25], [35, (-57)/2]]);
                          [92             ]
                          [--  &uminus0;25]
                          [3              ]
                     M := [               ]
                          [            57 ]
                          [35   uminus0-- ]
                          [            2  ]

(M^1000) . A;
             [                                176]
             [&uminus0;8.88365229772445times10   ]
             [                                   ]
             [                                177]
             [&uminus0;1.03642610140118times10   ]
#The transformation applied to (0.3,0.6) goes off to a large value,
#and does NOT map to the (0,0) point after many iterations,
#therefore, it is UNSTABLE!


#iii)
M := Matrix([[-177/4, 75/2], [-105/2, 89/2]]);
                          [       177  75]
                          [uminus0---  --]
                          [        4   2 ]
                     M := [              ]
                          [       105  89]
                          [uminus0---  --]
                          [        2   2 ]

(M^1000) . A;
             [                       &uminus0;125]
             [8.63623905093621times10            ]
             [                                   ]
             [                       &uminus0;124]
             [1.03634868611234times10            ]
#The transformation applied to (0.3,0.6) maps back to the point ~(0,0)
#after many iterations, thus (0,0) is stable!