For part (i), my matrix was K= 110110022 but I'm not sure how to prove the collineation is an affine transformation. How do i go about doing part (ii)?

b) In 50, the conic 1) whose equation is y2 2yz x2 = 0 contains the three noncollinear points (1:1:0), (1:1:0), (0:2:1). The conic xy = z2 is to be mapped to the conic Z) by a collineation WK : P > P satisfying the following conditions: K(1:0:0)=(l:1:0), wK(0:1:0)=(1:1:0), wK(1:1:1)=(0:2:l). i) Find a Isuitable matrix K for the collineation 90K. (You may use the fact that all points (s2 : 1 : s), VS 6 R, are mapped into D.) ii) Explain why 90K maps {'00 to itself. Hence show that when restricted to 8, the collineation is an a'lne transformation, and give its coordinate formula. iii) Find the homogeneous coordinates of K(O : O : 1)