8. Matrix by vector multiplication step-by-step

• We could take 4 steps to find the solution:

  | cos(90) -sin(90) 0 0 |     | 1 |     | 0 |    cos(90)*1 + -sin(90)*0 + 0*0 + 0*1
  | sin(90)  cos(90) 0 0 |  .  | 0 |  =  | ? |
  |   0         0    1 0 |     | 0 |     | ? |
  |   0         0    0 1 |     | 1 |     | ? |
  
  | cos(90) -sin(90) 0 0 |     | 1 |     | 0 |
  | sin(90)  cos(90) 0 0 |  .  | 0 |  =  | 1 |     sin(90)*1 + cos(90)*0 + 0*0 + 0*1
  |   0         0    1 0 |     | 0 |     | ? |
  |   0         0    0 1 |     | 1 |     | ? |
  
  | cos(90) -sin(90) 0 0 |     | 1 |     | 0 |
  | sin(90)  cos(90) 0 0 |  .  | 0 |  =  | 1 |
  |   0         0    1 0 |     | 0 |     | 0 |     0*1 + 0*0 + 1*0 + 0*1
  |   0         0    0 1 |     | 1 |     | ? |
  
  | cos(90) -sin(90) 0 0 |     | 1 |     | 0 |
  | sin(90)  cos(90) 0 0 |  .  | 0 |  =  | 1 |
  |   0         0    1 0 |     | 0 |     | 0 |
  |   0         0    0 1 |     | 1 |     | 1 |     0*1 + 0*0 + 0*0 + 1*1
  
  Answer:
  | cos(90) -sin(90) 0 0 |     | 1 |     | 0 |
  | sin(90)  cos(90) 0 0 |  .  | 0 |  =  | 1 |
  |   0         0    1 0 |     | 0 |     | 0 |
  |   0         0    0 1 |     | 1 |     | 1 |