### 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.

### Limiting Probabilities

Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.

# Matrix Countdown

##### Stage: 5 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!

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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.