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Published byAnnabella Harrison Modified over 9 years ago
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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.
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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.
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Matrix multiplication
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This ‘structure’ can be helpful:
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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
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= = = Here are some examples – can you find the pattern? A A -1 = I = A -1 A
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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:
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Inverse of a 2 x 2 matrix What is the determinant of this matrix? Comments? singular
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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?
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In the context of transformations … has zero determinant
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In the context of transformations…
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