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Are you ready to enter the matrix?
A matrix is a set of numbers arranged in rows and columns (they form what is called a rectangular array). They have many applications in maths, statistics, economics, physics, engineering etc. as well as computer graphics and web-search page ranking. One of the reasons they are so powerful is that we can use computers to solve large matrix problems relatively
easily.
In this feature you will discover how matrices can be multiplied, explore how they can be used to represent transformations, use them to model probability problems and explore four dimensional numbers.
problem
A powerful matrix
Age
14 to 18
Challenge level
What happens when you find the powers of this matrix?
problem
Flipping twisty matrices
Age
14 to 18
Challenge level
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
Square pair
Age
14 to 18
Challenge level
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
Matrices and Complex Numbers combine to enable us to create four dimensional numbers.
problem
Fix me or crush me
Age
16 to 18
Challenge level
Can you make matrices which will fix one lucky vector and crush another to zero?
problem
Matrix meaning
Age
16 to 18
Challenge level
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
problem
Transformations for 10
Age
16 to 18
Challenge level
Explore the properties of matrix transformations with these 10 questions.