I hope this question hasnt been posted before.
Let A(3, 2, 3), B(5, 2, 3), C(3, 5, 3) and D(6, 5, 5) be a pyramid. Find all affine transformations that map the pyramid back to itself.
So find all affine transformations t so that for each x in the pyramid t(x) also lies in the pyramid.
What is the strategy when solving these kind of tasks. You dont have to give me the solution, just a hint would be nice :) thank you
I have written the pyramid as P = A + t1*(B-A)+t2*(C-A)+t3*(D-A) and I know that every affine transformation can be written as t(x) = Mx + s, where M is a semilinear matrix and s a vector. But that does not help a lot.