Pasted

box% octave
GNU Octave, version 5.2.0
Copyright (C) 2020 John W. Eaton and others.
This is free software; see the source code for copying conditions.
There is ABSOLUTELY NO WARRANTY; not even for MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  For details, type 'warranty'.
 Octave was configured for "x86_64-pc-linux-gnu".
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 octave:1> A=[1;1]; B=[3;-1]; C=[4;3]; P=[5;-7]; Q=[7;-2]; R=[2;-1];
octave:2> homo = @(v) [v;1];
octave:3> T1 = [homo(A) homo(B) homo(C)]
T1 =
    1   3   4
   1  -1   3
   1   1   1
 octave:4> T2 = [homo(P) homo(Q) homo(R)]
T2 =
    5   7   2
  -7  -2  -1
   1   1   1
 octave:5> aff = @(v) v(1:2)/v(3);
octave:6> aff((T2/T1) * homo(A))
ans =
    5.0000
  -7.0000
 octave:7>