problem 1: Prove that the multiplication of the 3X3 matrices in 2-D geometry in each of the given operations is commutative, that is, independent of the order of execution:
a) Two successive rotations
b) Two successive translations
c) Two successive scaling
problem 2: In brief describe the concept of the 2D graphics.
problem 3: What are inverse geometric transformations?
problem 4: Show that the order in which transformations are performed is significant by the transformation of triangle A(1, 0), B(0, 1), C(1, 1) by (a) rotating 45° regarding the origin and then translating in the direction of vector I, and (b) translating and then rotating.
problem 5: An object point P(x, y) is translated in the direction v = aI + bJ and concurrently an observer moves in the direction v. Show that there is no apparent motion (from the view-point of the observer) of the object point.