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# MATH1060 Introductory Linear Algebra

### Taught Semester 2, Year running 2006/07

Pre-requisites: A level Mathematics, or equivalent.
Co-requisites: None
Objectives
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.
Syllabus
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 many others.
Topics covered include:
1. General systems of linear equations: Reduction by elementary row operations to echelon form; solution from echelon form by back substitution.
2. Matrices and matrix algebra: Elementary matrices and inverse of a matrix.
3. 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.
4. Eigenvalues and eigenvectors: Characteristic polynomial for eigenvalues. Linear independence of eigenvectors for different eigenvalues. Use in solving linear differential equations and in computing powers.
Form of teaching: Lectures (22 hours); tutorials (11 hours).
Form of assessment: 2 hour written examination at end of semester (85%), coursework (15%).

## Booklist:

[1]
R. B. J. T. Allenby. Linear Algebra. Edward Arnold, 1995.
[2]
H. Anton and C. Rorres. Elementary Linear Algebra: applications version. Wiley, sixth edition, 1991.

## Useful Information

• 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 questions. Classes on even weeks are shared by MATH1410 and MATH1610.
• Attendance: will be collected during the lectures and classes.
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: http://maths.leeds.ac.uk/~kisilv/courses/math1060.html
• Handouts contain some intended omission, which are supposed to be filled down by students during the lectures. Watch out!
• Booklist: almost any book about "Linear Algebra" is suitable, the handouts should not replace reading a book!
You could download handouts in Gzipped PostScript format for printing, or view it on screen as a PDF presentation. Homework assignments are also available for downloading as PostScript or PDF file.
If you cannot view/print the above files please ask ISS Help Desk for an assistance.
Lecturer:
 (Dr.) Vladimir V. Kisil Email: kisilv@maths.leeds.ac.uk Room 8.18L, School of Mathematics. Telephone (0113) 343 5173.

## 1  Homeworks

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.