Matrices

problem
Favourite

Limiting Probabilities

Age

16 to 18

Challenge level

3 out of 3

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.
problem
Favourite

8 Methods for Three by One

Age

14 to 18

Challenge level

2 out of 3

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?
problem

Rots and Refs

Age

16 to 18

Challenge level

1 out of 3

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

Stringing It Out

Age

14 to 16

Challenge level

1 out of 3

Explore the transformations and comment on what you find.
problem

Reflect Again

Age

16 to 18

Challenge level

3 out of 3

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.
problem

Flipping Twisty Matrices

Age

14 to 18

Challenge level

1 out of 3

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

The Matrix

Age

14 to 18

Challenge level

1 out of 3

Explore a new way of multiplying with matrices.
problem

A Powerful Matrix

Age

14 to 18

Challenge level

1 out of 3

What happens when you find the powers of this matrix?
problem

Markov Matrices

Age

14 to 18

Challenge level

1 out of 3

Use matrices to find out how much cake I eat.
problem

Square Pair

Age

14 to 18

Challenge level

2 out of 3

Explore the shape of a square after it is transformed by the action of a matrix.