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When you visit the NRICH site you may find some activities which are 'live'. This means we are inviting students to send us solutions, and we will publish a selection of them, along with each student's name and their school, a few weeks later. If you'd like to know more about what we're looking for, read this short article.
Explore a new way of multiplying with matrices.
Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.
What happens when you find the powers of this matrix?
Use matrices to find out how much cake I eat.
Explore the shape of a square after it is transformed by the action of a matrix.
Matrices and Complex Numbers combine to enable us to create four dimensional numbers.
Use matrices to model this popular party game.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the properties of matrix transformations with these 10 questions.
Take a look at these recently solved problems.
What is the remainder if you divide a square number by $8$?
Can you show that $n^5-n^3$ is always divisible by $24$?
Can you find the smallest integer which has exactly 426 proper factors?
Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?