Matrices

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?

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.

Use matrices to find out how much cake I eat.

Use matrices to model this popular party game.

What happens when you find the powers of this matrix?

Explore a new way of multiplying with matrices.

Explore the properties of matrix transformations with these 10 questions.

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

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.

Explore the transformations and comment on what you find.