World Cup Matrix Multiplication….  Below is a league table for the group stage of the World Cup  The top 2 teams in each group progress through to the next round; scoring 3 points for a win, 1 point for a ‘draw’ and 0 points for a losing a match  Matrix multiplication can be used to calculate the final points and hence state who progressed through to the next round.

Solution  We can write the league table as a matrix.  Next we can write down the matrix that represents the points awarded.  Its important to make sure that the correct points line up with the appropriate column.

Matrix multiplication

This ‘structure’ can be helpful:

Inverse of a 2 x 2 matrix When a matrix is multiplied by its inverse, the answer is the identity A A -1 = I = A -1 A

= = = Here are some examples – can you find the pattern? A A -1 = I = A -1 A

The determinant and the Inverse of a 2 x 2 matrix e.g. Find the inverse of this matrix The determinant of A is ad - bc The inverse of A is:

Inverse of a 2 x 2 matrix What is the determinant of this matrix? Comments? singular

In the context of transformations … Use the transformations represented by the matrices below to find the image of the triangle above: What happens in each case?

In the context of transformations … has zero determinant

In the context of transformations…