Write a MATLAB program to calculate the homogeneous transformation matrix AT when the user enters Z-Y-X Euler angles a--y and the position vector PB. Test for two examples: i) a = 10, B= 20, y = 30, and Pg = {1 2 3 1. ii) For = 20 ( =y=0), P = (3 0 1}. Define AT to be the result from (a)(i) and 27 to be the result from (a)(ii). i) Calculate 7, and show the relationship via a transform graph. Do the same for CT. ii) Given T and T from (d)(i)-assume you don't know 4T, calculate it, and compare your result with the answer you know. iii) Given 47 and 47 from (d)(i)-assume you don't know T, calculate it, and compare your result with the answer you know.