Matrices

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

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.

Explore the transformations and comment on what you find.

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.

Matrices and Complex Numbers combine to enable us to create four dimensional numbers.

Can you make matrices which will fix one lucky vector and crush another to zero?