Линейна трансформация A->A'

[studentT]

Здравейте
Дадени са двете четворки:
A(1,0,1) B(-1,1,0) C(0,1,-1) D(1,2,0)
A'(2,1,1) B'(-1,2,3) C'(3,4,-1) D'(1,4,5)

Да се намери линейната трансформация Fi(t): A,B,C,D -> A',B',C',D'

Имам представяне:

[tex]ro * \left(\begin{array}{rrr} x' \\ y' \\ t' \\\end{array}\right) = \left(\begin{array}{rrr} t_{11} & t_{21} & t_{31} \\ t_{12} & t_{22} & t_{32} \\ t_{13} & t_{23} & t_{33} \\\end{array}\right)*\left(\begin{array}{rrr} x \\ y \\ t \\\end{array}\right)[/tex]

За А:
[tex]\left(\begin{array}{rrr} 2 \\ 1 \\ 1 \\\end{array}\right) = \left(\begin{array}{rrr} t_{11} & t_{21} & t_{31} \\ t_{12} & t_{22} & t_{32} \\ t_{13} & t_{23} & t_{33} \\\end{array}\right)*\left(\begin{array}{rrr} 1 \\ 0 \\ 1 \\\end{array}\right)[/tex]
[tex]t_{11} + t_{13} = 2 \\
t_{21} + t{23} = 1 \\
t_{31} + t_{33} = 1 \\[/tex]

За B:
[tex]\left(\begin{array}{rrr} -1 \\ 2 \\ 3 \\\end{array}\right) = \left(\begin{array}{rrr} t_{11} & t_{21} & t_{31} \\ t_{12} & t_{22} & t_{32} \\ t_{13} & t_{23} & t_{33} \\\end{array}\right)*\left(\begin{array}{rrr} -1 \\ 1 \\ 0 \\\end{array}\right)[/tex]
[tex]-t_{11} + t_{13} = -1 \\
-t_{21} + t{23} = 2 \\
-t_{31} + t_{33} = 3 \\[/tex]

За C:
[tex]\left(\begin{array}{rrr} 3 \\ 4 \\ -1 \\\end{array}\right) = \left(\begin{array}{rrr} t_{11} & t_{21} & t_{31} \\ t_{12} & t_{22} & t_{32} \\ t_{13} & t_{23} & t_{33} \\\end{array}\right)*\left(\begin{array}{rrr} 0 \\ 1 \\ -1 \\\end{array}\right)[/tex]
[tex]t_{12} - t_{13} = 3 \\
t_{22} - t{23} = 4 \\
t_{32} - t_{33} = -1 \\[/tex]

За D:
[tex]\left(\begin{array}{rrr} 1 \\ 4 \\ 5 \\\end{array}\right) = \left(\begin{array}{rrr} t_{11} & t_{21} & t_{31} \\ t_{12} & t_{22} & t_{32} \\ t_{13} & t_{23} & t_{33} \\\end{array}\right)*\left(\begin{array}{rrr} 1 \\ 2 \\ 0 \\\end{array}\right)[/tex]
[tex]t_{11} + 2t_{12} = 1 \\
t_{21} + 2t{22} = 4 \\
t_{31} + 2t_{32} = 5 \\[/tex]

Правя си система, която като реша отговорите не отговарят на всички уравнения, което ми подсказва, че явно това не е начинът. Някой може ли да даде упътване как да продължа или да каже къде съм сбъркал. Благодаря предварително

[garion]

[tex]ro * \left(\begin{array}{rrr} x' \\ y' \\ t' \\\end{array}\right) = \left(\begin{array}{rrr} t_{11} & t_{21} & t_{31} \\ t_{12} & t_{22} & t_{32} \\ t_{13} & t_{23} & t_{33} \\\end{array}\right)*\left(\begin{array}{rrr} x \\ y \\ t \\\end{array}\right)[/tex]

В пространството мисля че трябва да ползваш [tex]ro * \left(\begin{array}{rrrr} x' \\ y' \\ t' \\ 1 \\\end{array}\right) = \left(\begin{array}{rrrr} t_{11} & t_{21} & t_{31} & t_{41} \\ t_{12} & t_{22} & t_{32} & t_{42} \\ t_{13} & t_{23} & t_{33} & t_{43} \\\end{array}\right)*\left(\begin{array}{rrrr} x \\ y \\ t \\ 1 \\\end{array}\right)[/tex]