Play countdown with matrices
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
Explore the properties of matrix transformations with these 10 stimulating questions.
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?. . . .
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore how matrices can fix vectors and vector directions.
Can you make matrices which will fix one lucky vector and crush another to zero?
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.
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.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore the transformations and comment on what you find.