A member in the robotic system rotates 53 about z-axis with a displacement of 2i + Oj + 4k. (A) Find the transformation matrix H of the homogeneous transformation. (B) If the point on the member is located at p= [1 3 2], find the corresponding position in another frame with the transformation matrix. (C) Find the inverse transformation matrix H1, and verify that the position derived from (B) can transfer back to its original vector. You need to show the numerical calculation of the inverse procedure. Credit will not be given to symbolic calculation.