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

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.
problem

Two and Four Dimensional Numbers

Age

16 to 18

Challenge level

1 out of 3

Matrices and Complex Numbers combine to enable us to create four dimensional numbers.