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World Cup Matrix Multiplication….

World Cup Matrix Multiplication…. Below is a league table for the group stage of the World Cup 2010. 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

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World Cup Matrix Multiplication….

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  1. World Cup Matrix Multiplication…. • Below is a league table for the group stage of the World Cup 2010. • 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.

  2. 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.

  3. Matrix multiplication

  4. This ‘structure’ can be helpful:

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

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

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

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

  9. 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?

  10. In the context of transformations … has zero determinant

  11. In the context of transformations…

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