EXERCISES FOR WEEK 3
week3-1

Multiply the following matrices (if possible):

  • [A] * [B] where [A] = [ 2 1 4
                        3 7 -2
                        1 0 5  ]

and [B] = [ 2
           4
           6]

  • [B] * [A], where A and B are as given above
week3-2

What is the homogeneous scaling matrix MS if you wish to make the object twice as wide as it is now?

 
week3-3

What is the homogeneous scaling matrix MS if you wish to make the object one-third as tall as it now is?

 
week3-4

What is the homogeneous rotation matrix if you wish to rotate the object 60 degrees CCW (counter clock wise) with respect to the origin? Round off all numbers to 3 decimal places.

 
week3-5

Assume P= (2,7). What will be the new point Q' if P is

  • rotated 60 degrees CCW with respect to the origin?

What will THEN be the new point if this resulting point Q is

  • now scaled by a factor of 2 units in the x-direction and 3 units in the y-direction?

 
week3-6

What is the homogeneous rotation matrix if you wish to rotate the object 60 degrees CCW with respect to the point (10,25)? Round to 3 decimal places.

 
week3-7

What is the homogeneous translation matrix MT if you wish to move the object 5 units to the right and down 12 units?

 
week3-8

What is the homogeneous transformation matrix M if you wish to

  • rotate CCW 90 degrees with respect to the z axis
  • scale by a factor of 2 in the x direction, 0.1 in the y direction, and 0.5 in the z direction
  • translate 5 units in the x direction, -2 units in the y direction, and 4 units in the z direction

 
week3-9

Assume P = (4,5,2). What will be the new point if the transformation matrix in the previous problem is applied to P?