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2010/11 Undergraduate Module Catalogue

MATH1015 Linear Algebra 1

15 creditsClass Size: 180

Module manager: Prof R. Hollerbach
Email: rh@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2010/11

Pre-requisite qualifications

A-level Mathematics or equivalent

This module is mutually exclusive with

MATH1060	Introductory Linear Algebra
MATH1331	Linear Algebra with Applications

This module is approved as an Elective

Module summary

Linear algebra provides a basis for wide areas of mathematics. This module (or an equivalent) is an essential foundation for most students who wish to study mathematics at higher levels.

Objectives

On completion of this module, students should be able to:

a) find the solution set of a system of linear equations using row reduction;
b) test specified sets of vectors to see if they form subspaces;
c) check specified sets of vectors to see if they form bases for given vector spaces;
d) write the equations of lines and planes in vector form;
e) calculate dot products of vectors and use them to evaluate angles between vectors;
f) calculate cross products of three dimensional vectors;
g) test specified mappings between vector spaces to determine if they are linear transformations;
h) work out the matrix representation of a specified linear transformation with respect to specified bases for the domain and co-domain;
i) determine whether the product of two specified matrices exists, and be able to evaluate the product where it does exist;
j) compute the inverse of a specified invertible matrix;
k) use the inverse of a matrix to solve systems of linear equations and to perform forward error analysis for these;
l) calculate the determinant of a square matrix, with numerical and algebraic entries;
m) compute the eigenvalues and eigenvectors of a specified matrix;
n) determine whether a specified matrix can be diagonalized;
o) orthogonally diagonalize symmetric matrices.

Syllabus

- Linear equations
- Use of matrix notation, systematic row reduction
- Cases of unique, infinitely many and no solutions
- Geometrical interpretation of these cases
- Vectors, vector equations of lines and planes
- Dot product
- Angles between vectors
- Cross product. Rn as a vector space
- Linear independence
- Spanning, basis and dimension
- Linear transformations
- Matrix representation of linear transformations
- Matrix multiplication
- Inverses of matrices
- Determinants
- Eigenvalues and eigenvectors
- Diagonalization of matrices
- Orthogonal diagonalization of symmetric matrices.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	33	1.00	33.00
Tutorial	5	1.00	5.00
Private study hours			112.00
Total Contact hours			38.00
Total hours (100hr per 10 credits)			150.00

Private study

111 hours:
- 2 hours reading per lecture
- 30 hours completing 5 problems sheets
- 15 hours exam revision.

Opportunities for Formative Feedback

5 problems sheets at two week intervals.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
Total percentage (Assessment Coursework)		15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	85.00
Total percentage (Assessment Exams)		85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 01/04/2011

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