## Tables and Matrices

Tables of values may often be naturally represented as matrices, and operations performed on them.

The table below shows the results achieved by four teams in twelve events of an athletics match. In each event, 1st place scores 5 points, 2nd place scores 3 points, 3rd place scores 2 points and 4th place scores 1 point.

We may use one matrix to represent the results:

and another matrix to represent the point awarded to each place:

Then the total number of points awarded to each team is given by the product of the two matrices:

This is possible because the places in the table occupy the columns and the place values in the column vectors occupy the rows. When we multiply as above we sum the total points for each team.

This method is applicable to a wide variety of situations and suitable for calculation by computers. It is widely used in spreadsheets.