Module manager: Prof R. Hollerbach
Email: rh@maths.leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2010/11
A-level Mathematics or equivalent
| MATH1060 | Introductory Linear Algebra |
| MATH1331 | Linear Algebra with Applications |
This module is approved as an Elective
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.
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.
- 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.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 33 | 1 | 33 |
| Tutorial | 5 | 1 | 5 |
| Private study hours | 112 | ||
| Total Contact hours | 38 | ||
| Total hours (100hr per 10 credits) | 150 | ||
111 hours:
- 2 hours reading per lecture
- 30 hours completing 5 problems sheets
- 15 hours exam revision.
5 problems sheets at two week intervals.
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 15 |
| Total percentage (Assessment Coursework) | 15 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 30 Mins | 85 |
| Total percentage (Assessment Exams) | 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 4/1/2011
Errors, omissions, failed links etc should be notified to the Catalogue Team