Solution to Exercise 3.21.
Mathematics is a lot like eating steak; you've got to cut it into little pieces or you'll choke.
—Jeff Lewis (1995)

Exercise 3.21. Given three points P(0, 0, 1), Q(1, 0, 1), and R(2, 1, 1), and an affine transformation T.
(a)  Find the points P' = T(P), Q' = T(Q), and R' = T(R) where the matrix of the transformation is  
, , and
(b)  Sketch triangle PQR and triangle P'Q'R'.  
Triangle PQR is blue and triangle P'Q'R' is brown.
      
(c)  Describe how the transformation moved and changed the triangle PQR.

The triangle PQR is rotated, translated, and the sides are lengthened. PQ = 1 &   &  Q'R' = 3, and  &