### 8 Methods for Three by One

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?

### 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.

### 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.

# 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.