A good answer might be:

a   =   ( 1, 2 )T
b   =   ( 3, 4 )T
b · a   =   3*1 + 4*2   =   1*3 + 2*4  =   a · b

Same Properties

The dot product between column matrices has the same properties as the dot product between vectors. Here is another example:

  1. p  =  ( -2, 5 )T
  2. q  =  ( 3, -1 )T
  3. then p · q   =   (-2)*3 + 5*( -1)   =   -6 + -5  =  -11

Here is a more realistic example:

  1. s  =  ( 1.082, -3.224 )T
  2. t  =  ( 2.381, 7.009 )T
  3. then s · t  = 1.082*2.381 + -3.224*7.009   =   2.576242 + -22.597016   =  -20.020774

In all cases the dot product takes two column matrix operands and yields one scalar value.

QUESTION 10:

Form the dot product of: ( -1, 3)T and (2, 4)T.

Form the dot product of: (2, 4)T and ( -1, 3)T.