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Investigations. Vectors. Biology. Mathematical modelling. Physics. Graph sketching. Estimating and approximating. Maths Supporting SET. Trigonometric functions and graphs. Trial and improvement.There are 13 results
Broad Topics > Vectors and Matrices > Matrices
Transformations for 10
Age 16 to 18 Challenge Level:
Explore the properties of matrix transformations with these 10 stimulating questions.
Square Pair
Age 16 to 18 Challenge Level:
Explore the shape of a square after it is transformed by the action of a matrix.
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?
Matrix Meaning
Age 16 to 18 Challenge Level:
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Two and Four Dimensional Numbers
Age 16 to 18 Challenge Level:
Investigate matrix models for complex numbers and quaternions.
Rots and Refs
Age 16 to 18 Challenge Level:
Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.
Reflect Again
Age 16 to 18 Challenge Level:
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.
8 Methods for Three by One
Age 14 to 18 Challenge Level:
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?. . . .
Limiting Probabilities
Age 16 to 18 Challenge Level:
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.
The Matrix
Age 16 to 18 Challenge Level:
Investigate the transfomations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0. -1 and +1.
Stringing it Out
Age 14 to 16 Challenge Level:
Explore the transformations and comment on what you find.
The Golden Ratio, Fibonacci Numbers and Continued Fractions.
Age 14 to 16
An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.
NRICH is part of the family of activities in the Millennium Mathematics Project.