The resilt of 9 matches played by 4 football teams can be shown in a table or stored in a matrix.

Question

Team                 wins           draws        losses

  A                         3                6              0

  B                         2                1              6

  C                         4                4              1

  D                         1                5              3

 

Three points are awarded for a win , 1 for a draw and zero for a loss. Give this information in a 3×1 matrix. Use matrix multiplication to find out which of A, B, C, or D has;

 

1) most points

 

2)fewest points after the 9 matches?

Answer 1

The column matrix is [ 3  1  0 ] 

 

The matrix multiplication of a 4 by 3 matrix with a 3 by 1 matrix results in a 4 by 1 column matrix 

 

A     3*3 + 6*1 + 0*0 = 15

B     2*3 + 1*1 + 6*0 = 7

C     4*3 + 4*1 + 1*0 = 16

D     1*3 + 5*1 + 3*0 = 8 

 

So C has the most points and B has the fewest