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Reflect Again

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.

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Rots and Refs

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.

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The Matrix

Investigate the transfomations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0. -1 and +1.

Matrix Countdown

Age 16 to 18 Challenge Level:

Square matrices of the same dimension can be added, subtracted and multiplied. You can also convert a matrix into a scalar by taking the determinant. You can also multiply or divide a matrix by a scalar. Perfect for a game of matrix countdown!
 
 
We recommend that you take your time over a game of matrix countdown and suggest two possible scoring systems:
 
System 1: Good scores get small values for the determinant of the difference between your answer and the target matrix.
 
System 1: Good scores get small values of the sum of the absolute values of the components of the difference between your answer and the target matrix.
 
These two systems allow for different strategies. Perhaps you might like to think about this?