> A3:=matrix(3,3,[1,0,0,0,1,0,0,0,0]);

                              [1  0  0]


                              [       ]


                        A3 := [0  1  0]


                              [       ]


                              [0  0  0]

>         A4 := matrix(3, 3, [1, 0, 0, 0, 1, 0, 0, 0, 0])

                              [1  0  0]


                              [       ]


                        A4 := [0  1  0]


                              [       ]


                              [0  0  0]



Com t'expliques que tinguin la mateixa forma?

Tenen la mateixa forma perquè utilitzen la mateixa base en l'arribada que en la sortida i perquè la imatge del tercer vector, que coincideix amb el vector llum, sempre serà (0,0,0).

La matriu A3 és la del pla1 (pla paret) i la base de sortida i d'arribada és {(1,0,0),(0,0,1),(2,4,3)}.

La matriu A4 és la del pla2 (pla terra) i la base de sortida i d'arribada és {(1,0,0),(0,1,0),(2,4,3)}.



Com quedarien ara les matrius de canvi de base?



> C1:=matrix(3,3,[1,0,2,0,0,4,0,1,3]);

                              [1  0  2]


                              [       ]


                        C1 := [0  0  4]


                              [       ]


                              [0  1  3]

> B1:=inverse(matrix(3,3,[1,0,2,0,0,4,0,1,3]));

                              [   -1   ]


                              [1  --  0]


                              [   2    ]


                              [        ]


                              [   -3   ]


                        B1 := [0  --  1]


                              [   4    ]


                              [        ]


                              [    1   ]


                              [0   -  0]


                              [    4   ]

> C2:=matrix(3,3,[1,0,2,0,1,4,0,0,3]);

                              [1  0  2]


                              [       ]


                        C2 := [0  1  4]


                              [       ]


                              [0  0  3]

> B2:=inverse(matrix(3,3,[1,0,2,0,1,4,0,0,3]));

                              [      -2]


                              [1  0  --]


                              [      3 ]


                              [        ]


                              [      -4]


                        B2 := [0  1  --]


                              [      3 ]


                              [        ]


                              [       1]


                              [0  0   -]


                              [       3]