7. Matrix by vector multiplication step-by-step

• Multiplying a point (represented by a vector) by a matrix (representing a transformation) yields a new transformed point (another vector.)

• Points are always stored with a 1 for the 4th element of the vector.

• Suppose we want to rotate point [1 0 0] around z axis by 90 degrees:

  | cos(90) -sin(90) 0 0 |     | 1 |     | ? |
  | sin(90)  cos(90) 0 0 |  .  | 0 |  =  | ? |
  |   0         0    1 0 |     | 0 |     | ? |
  |   0         0    0 1 |     | 1 |     | ? |