
Can you make matrices which will fix one lucky vector and crush another to zero?
Two 18 year old students from Madras College St Andrews in Scotland produced eight different proofs of one result using (separately) Tan Angle Sum Formula, Sin Angle Sum Formula, Cosine Rule,. . . .

Explore the properties of matrix transformations with these 10 stimulating questions.
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.

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.

Investigate matrix models for complex numbers and quaternions.

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