- Homepage
- Key Information
- Students
- Taught programmes (UG / PGT)
- Computer Science
- Engineering
- Geology (CSM)
- Mathematics (Exeter)
- Mathematics (Penryn)
- Mining and Minerals Engineering (CSM)
- Physics and Astronomy
- Renewable Energy
- Natural Sciences
- CSM Student and Staff Handbook

- Student Services and Procedures
- Student Support
- Events and Colloquia
- International Students
- Students as Change Agents (SACA)
- Student Staff Liaison Committees (SSLC)
- The Exeter Award
- Peer Support
- Skills Development
- Equality and Diversity
- Athena SWAN
- Outreach
- Living Systems Institute Webpage
- Alumni
- Info points and hubs

- Taught programmes (UG / PGT)
- Staff
- PGR
- Health and Safety
- Computer Support
- National Student Survey (NSS)
- Intranet Help
- College Website

## ECM1701 - Vectors and Matrices (2015)

MODULE TITLE | Vectors and Matrices | CREDIT VALUE | 15 |
---|---|---|---|

MODULE CODE | ECM1701 | MODULE CONVENER | Dr Gihan Marasingha (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
---|---|---|---|

DURATION: WEEKS | 0 | 11 | 0 |

Number of Students Taking Module (anticipated) | 331 |
---|

Vectors essentially underlie all areas of pure and applied mathematics, computer science and engineering. They are the fundamental ways of describing multi-dimensional objects and the natural language of information retrieval systems, computer aided design, 3D graphics, and pattern recognition. Matrices are operators that act on vectors.

This introduction to vectors and matrices gives you an excellent foundation in and understanding of these concepts; aiming to familiarise you and build confidence in using and applying them to any computer science, mathematics and engineering theory and application. This foundation in the concepts of vectors and matrices, together with applications of geometry and the solution of systems of linear equations aims to prepare you for everything you are likely to encounter over the course of your chosen programme and discipline.

On completing this module you will be equipped with the skills to apply vectors and matrices to all areas of maths and computing, along with the ability to tackle a range of problems, and a sound understanding of the basic concepts of linear algebra. This course uses small tutorial-based group work (of up to 15 students per group) to encourage the practice of theory learned in large lectures.

Prerequisite module: ECM1706

The module aims to provide you with a foundation in the concepts of vectors and matrices, together with some applications both to geometry and to the solution of systems of linear equations. It is not essential to have previous knowledge of vectors and matrices. Lecturers will place an emphasis on both algorithmic aspects and theoretical development and will include proofs where appropriate.

On successful completion of this module, **you should be able to**:

**Module Specific Skills and Knowledge**:

1 perform accurate computations relating to matrices and column vectors with real or complex entries;

2 apply those concepts in tackling an appropriate range of problems;

3 discuss the abstract concepts of vector spaces, linear transformations, and other associated ideas;

4 apply the abstract concepts in 3 to concrete instances of vector spaces;

5 understand and be able to prove abstract theorems concerning vector spaces.

**Discipline Specific Skills and Knowledge:**

6 state and apply key definitions from this topic;

7 develop pure mathematical notions and skills including sets, functions, and mathematical proof.

**Personal and Key Transferable/ Employment Skills and Knowledge:**

8 reason using abstract ideas;

9 formulate and solve problems;

10 communicate reasoning and solutions effectively in writing;

11 use learning resources appropriately;

12 demonstrate self-management and time management skills;

- complex numbers, their arithmetic and geometry;

- extended example in two and three dimensions: vectors; matrices as linear transformations;

- eigenvalues and eigenvectors;

- systems of linear equations: matrix representation;

- elementary row operations;

- Gaussian elimination (including parameterisation of general solution);

- reduced echelon form;

- finding the inverse of a matrix by Gaussian elimination;

- criteria for invertibility of a matrix;

- matrices: addition/subtraction and multiplication of matrices;

- matrices as linear functions on sets of vectors; e.g. rotation and reflection matrices in two dimensions;

- algebra of matrices;

- transpose;

- symmetric matrices;

- inverse of a matrix;

- determinants: recursive definition of determinant;

- behaviour of determinants under elementary row/column operations;

- evaluation of determinants by Gaussian elimination;

- vectors: the notion of vector quantities;

- addition and scalar multiplication of vectors;

- simple geometric proofs;

- length of a vector;

- unit vectors, standard basis vectors;

- linear independence, bases and dimension;

- scalar product and vector product;

- triple products;

- eigenvectors and eigenvalues: definitions;

- characteristic polynomial;

- diagonalisation of matrices;

- examples in two and three dimensions (including cases with a repeated eigenvalue);

- abstract definition of vector space and linear maps with examples;

- the kernel and image of a linear map.

Scheduled Learning & Teaching Activities | 49.00 | Guided Independent Study | 101.00 | Placement / Study Abroad | 0.00 |
---|

Category | Hours of study time | Description |

Scheduled learning and teaching activities | 33 | Lectures |

Scheduled learning and teaching activities | 5 | Seminars |

Scheduled learning and teaching activities | 11 | Tutorials |

Guided independent study | 101 | Guided independent study |

Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|

Fortnightly exercise | One sheet of problems | 1-12 | Three questions marked by tutors. Feedback given on all questions during tutorials |

Mid-term test | 40 minutes | 1,2,6-12 | Students mark each other's work, based on answer sheet and feedback session. |

Coursework | 0 | Written Exams | 100 | Practical Exams | 0 |
---|

Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|---|

Written examination - closed book | 100 | 2 hours | 1-9 | Available on request |

Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-reassessment |
---|---|---|---|

All above | Written exam (100%) | All | August Ref/Def period |

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | Thomas, G, Weir, M, Hass, J | Thomas' Calculus | 12th | Pearson | 2010 | 978-0321643636 | [Library] |

Set | Lipschutz, S, Lipson, M | Schaum's outlines: linear algebra | 4th | Mc-Graw-Hill | 2008 | 978-0071543521 | [Library] |

Set | Finney R.L., Maurice D., Weir M and Giordano F.R. | Thomas' calculus based on the original work by George B. Thomas, Jr. | 10th or later | Addison-Wesley | 2003 | 000-0-321-11636-4 | [Library] |

Set | Allenby R.B. | Linear Algebra, Modular Mathematics | Arnold | 1995 | 000-0-340-61044-1 | [Library] | |

Set | Hamilton A.G. | Linear Algebra: an introduction with concurrent examples | Cambridge University Press | 1989 | 000-0-521-32517-X | [Library] | |

Extended | McGregor C., Nimmo J. & Stothers W. | Fundamentals of University Mathematics | 2nd | Horwood, Chichester | 2000 | 000-1-898-56310-1 | [Library] |

Extended | Stewart J. | Calculus | 5th | Brooks/Cole | 2003 | 000-0-534-27408-0 | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
---|---|---|---|

PRE-REQUISITE MODULES | ECM1706 |
---|---|

CO-REQUISITE MODULES |

NQF LEVEL (FHEQ) | 4 | AVAILABLE AS DISTANCE LEARNING | No |
---|---|---|---|

ORIGIN DATE | Friday 09 January 2015 | LAST REVISION DATE | Monday 12 January 2015 |

KEY WORDS SEARCH | Vectors; matrices; Gaussian elimination; determinants; geometry; linear algebra. |
---|