Use homogeneous coordinates for all of the following problems 1) Construct the matrix that scales by (S1,s2,S3) relative to the point (C1,C2,C3) 2) Construct the matrix that magnifies the triangle (a,b,c) by the factor 3 while keeping vertex a fixed for a= (1,1,0), b= (2,2,0), and c = (4,-1,0). 3) Let R (a) denote the matrix that rotates (about the z axis) by R(a+b) and show that rotations R(a+b). angle a. Find an expression for commute; i.e., R(a)R(b) R(b)R(a) = = 4) Let A and B denote order-4 matrices, and let p be a point in matrix with last component equal multiplies required to compute no multiplies are required the last component of (B p). advantageous to combine transformations fact that case (a) requires homogeneous coordinates (4 by 1 to 1). Specify the number of (a) (A B)p and (b) A(B p) Note that to compute the last row of (A B) or Explain why it is usually before applying them (despite the more multiplications) 5) Show that translations and scalings commute among themselves T' T and S S' = S' S equal but not with each other; i.e., T T' but T s and S T are generally not