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This programme tests to see if the matrices, representing the linear transformations describing the symmetry group of a triangle, themselves form a group. It then tests to see if all 2 x 2 matrices... form a group.
Metadata describing this Open University video programme
Module code and title: M203, Introduction to pure mathematics
Item code: M203; 07
First transmission date: 27-03-1980
Published: 1980
Rights Statement:
Restrictions on use:
Duration: 00:25:00
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Producer: David Saunders
Contributors: Norman Gowar; Robin Wilson
Publisher: BBC Open University
Keyword(s): Symmetries; Transformations; Triangles
Subject terms: Algebra, Abstract; Matrices; Symmetric matrices
Footage description: Norman Gowar describes the symmetry group of a triangle. He argues that each of the six symmetries can be thought of as linear transformations of the plane, these in turn can be represented by matrices. These matrices may form a group. Robin Wilson works out the matrices for the symmetries of the triangle. He explains the importance of matrices for making calculations and for expressing the coordinates of the image vector. Again he works through some examples to demonstrate this. Norman Gowar argues that as symmetries can be combined so also matrices must have a corresponding method of combination. Working through an example he derives a law of combination for these matrices. Robin Wilson works through some examples to show this general rule. Norman Gowar argues that this last finding, combined with the other properties of matrices allows us to state that these matrices form a group. He extends this to ask if all 2 by 2 matrices form a group. He examines the group axioms. He works out that not all matrices have inverses. Robin Wilson works through some examples to find a test of whether or not a matrix has an inverse. He explains this test both geometrically and algebraically. Norman Gowar now poses the question, does the set of all invertible 2 by 2 matrices form a group? The closure axiom presents some difficulties, but the student is asked to sort these out after the programme.
Master spool number: 6HT/72871
Production number: 00525_4287
Videofinder number: 839
Available to public: no