MATH1902 - Linear Algebra (Advanced)
Semester 1, 2001

This page contains links to

  1. images of the overhead transparencies used in the 11am lectures given by Associate Professor Don Taylor in General Lecture Theatre N205.
  2. interactive quizzes on vectors and linear algebra

Back to the MATH1902 main page.

Each week's lectures will be available here as PDF files. To read PDF files you will need the (free) Adobe Acrobat Reader. This is available from within the University (Macintosh, Windows, Unix) or from Adobe's own site: Acrobat

Notes from the lectures

Week 1 Lecture 1
scalars, vectors, division of a line segment
Lecture 2
Cartesian coordinates
Week 2 Lecture 3
triangle inequality, vectors in 3-D, direction cosines
Lecture 4
geometry problems, linear dependence, scalar product
Week 3 Lecture 5
scalar product properties, projection
Lecture 6
resolution into components, vector product
Week 4 Lecture 7
area of triangle, scalar triple product, volume of parallelepiped, shortest distance calculations
Lecture 8
various forms of the equation of a line
Week 5 Lecture 9
various forms of the equation of a plane
Lecture 10
simultaneous linear equations, Gaussian elimination, row operations
Week 6 Lecture 11
row echelon form, back substitution, reduced row echelon form, consistency of equations
Lecture 12
row and column vectors, matrix notation
Week 7 Lecture 13
matrix algebra: associative law, distributive law. matrix multiplication and substitution of variables
Lecture 14
the identity matrix, Kronecker delta notation, inverses
Easter No lecture No lecture
Week 8 Lecture 15
calculating the inverse, elementary matrices
Lecture 16
proofs of properties of elementary matrices and inverses
Week 9 Lecture 17
rank of a matrix, uniqueness of the reduced row echelon form. Introduction to permutations
Lecture 18
properties of permutations
Week 10 Lecture 19
determinants, minors, cofactors, the transpose, adjoints
Lecture 20
fundamental properties of determinants: the effect of row operations
Week 11 Lecture 21
determinants and permutations: the standard definition; transpositions and row swaps
Lecture 22
determinant of a product; introduction to eigenvalues
Week 12 Lecture 23
eigenvalues, eigenvectors and the characteristic equation
Lecture 24
linear combinations, linear independence, diagonalization of matrices
Week 13 Lecture 25
applications of eigenvalues and eigenvectors: powers of matrices, recurrence relations, population models; transformations of the plane
Lecture 26
rotations and reflections

From time to time there are reports that not all characters in the PDF documents are displayed and that there are problems when printing. Unfortunately this seems to depend on the individual system being used and it is therefore hard to debug.

However, for printing, there is the following advice in the Acrobat 4.0 Reader help file: "If Acrobat Reader fails to print a file correctly, try selecting the Print as Image option in Acrobat Reader's Print dialogue."

Tools

Quizzes

Quiz 1 Quiz 2
Quiz 3 Quiz 4
Quiz 5 Quiz 6


Last major change: 29 May 2001
Don Taylor