Computer Graphics

1) Write out (as the product of exact matrices) the transformation matrix that results from a rotation of 45 degrees about the Y axis, followed by a translation by the vector [1,2,2,0]', followed by a rotation of 30 degrees around the Z-axis. 2)We defined an instance transformation as the product of a translation, a rotation, and a scaling. Can we accomplish the same effect by applying these three types of transformations in a different order? 3) Show that the sum P=α_1 P_1+ α_2 P_2+⋯+α_n P_n Is defined if and only if α_1+ α_2+⋯+α_n=1 Hint: Start with the first two terms and write them as P=α_1 P_1+ α_2 P_2+⋯= α_1 P_1+ 〖(α〗_2+α_1-α_1) P_2+⋯= α_1 〖(P〗_1-P_2)+(α_1+α_2)P_2+⋯ and proceed inductively.