Introductory Linear Algebra
Taught Semester 2, Year running 2006/07
Pre-requisites: A level Mathematics, or equivalent.
A first introduction to Linear Algebra, and in particular to the use
of matrices. Elementary row-operations are emphasised as a unifying
theme. On completion of this module, students should be able to: (a)
solve systems of linear equations; (b) perform elementary matrix
algebra; (c) solve simple eigenvalue problems.
Linear Algebra is the formal, detailed theory which covers the ideas
involved in solving simultaneous equations, and using matrices and
determinants. This course starts by treating simultaneous equations in
full generality, and introduces the notions involved in matrices and
vector spaces. These basic ideas will be used and expanded in a wide
variety of further mathematics modules, and are essential for
understanding much of numerical computing. Hence this (or an
equivalent) is an essential module for all students of mathematics and
Topics covered include:
Form of teaching:
Lectures (22 hours); tutorials (11 hours).
Form of assessment:
2 hour written examination at end of semester (85%), coursework (15%).
- General systems of linear equations: Reduction by elementary row
operations to echelon form; solution from echelon form by back
- Matrices and matrix algebra: Elementary matrices and inverse of
- Determinants: Definition by expansion, effect of elementary
operations, evaluation. Concrete vector spaces and subspaces:
Definitions of span and linear combination; linear dependence. Basis
and dimensions of a vector space. Rank.
- Eigenvalues and eigenvectors: Characteristic polynomial for
eigenvalues. Linear independence of eigenvectors for different
eigenvalues. Use in solving linear differential equations and in
R. B. J. T. Allenby.
Edward Arnold, 1995.
H. Anton and C. Rorres.
Elementary Linear Algebra: applications version.
Wiley, sixth edition, 1991.
You could download handouts in Gzipped
PostScript format for printing,
or view it on screen as a PDF
Homework assignments are also available for downloading
as PostScript or PDF
If you cannot view/print the above files please ask
ISS Help Desk
for an assistance.
- Lectures: on Wed at 12am (RSLT 25); on Thu
11am ( RSLT 18).
- Lecturer: Dr Vladimir V Kisil, room 8.18L (Math).
- Classes: run on even weeks (i.e., second,
fourth, ...) Thu at 3pm
(RSLT 19). They are dedicated to homework and exams
Classes on even weeks are shared by MATH1410 and MATH1610.
- Attendance: will be collected during the lectures and
A fact: absent from > 35% lectures
have 64% failure rate, in opposite to missing
< 15% lecture with only 9%!
- Homework: 6 assignments during the
semester, contribute 15% toward the final mark.
- Tutorials: (mainly) on Tuesdays 2pm, run by tutors by groups.
- Office hours: Wed 1pm-2pm; Thu noon-2pm.
- Web page:
- Handouts contain some intended omission, which are
supposed to be filled down by students during the lectures. Watch
- Booklist: almost any book about "Linear Algebra" is
suitable, the handouts should not replace reading a book!
Do not forget to write your name, group, and your
tutor's name before submitting the homework!
1.1 Seventh Homework
The Seventh Homework is NOT to be
submitted for an assessment. Solutions to this homework will be
distributed due to time.
Figure 1: Graphic representations
of linear systems.
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