# 2008/09 Undergraduate Module Catalogue

## MATH1331 Linear Algebra with Applications

### 15 creditsClass Size: 250

**Module manager:** Dr D. Pauksztello**Email:** davidp@maths.leeds.ac.uk

**Taught:** Semester 2 (Jan to Jun) View Timetable

**Year running** 2008/09

### Pre-requisite qualifications

A-Level Mathematics or equivalent.### This module is mutually exclusive with

MATH1015 | Linear Algebra 1 |

MATH1060 | Introductory Linear Algebra |

**This module is not approved as an Elective**

### Module summary

The module covers a variety of topics in linear algebra and discrete mathematics, with an emphasis on their application to financial problems.### Objectives

On completion of this module students should be able to:(a) use Gaussian elimination to solve systems of linear equations;

(b) work with the basic concepts of linear algebra: linear independence, bases, dimension, linear independence;

(c) compute the product of matrices;

(d) compute the inverse of a specified invertible matrix; calculate the determinant of a square matrix, with numerical and algebraic entries;

(e) compute the eigenvalues and eigen vectors of a specified matrix; determine whether a specified matrix can be diagonalized;

(f) model and solve problems in linear programming;

(g) use stochastic matrices to determine the limiting behaviour of simple Markov processes.

### Syllabus

Linear equations: manipulation of inequalities, matrices, Gaussian elimination, linear independence, bases, dimension, linear transformations, matrix algebra, inverse matrices, determinants, eigenvalues and eigenvectors, diagonalisation.

Linear programming: feasible sets, slack resources, the simplex method, marginal analysis.

Theory of games: games and strategies, mixed strategies, determining optimal mixed strategies.

Markov processes: transition matrices, stochastic matrices, regular and absorbing stochastic matrices, convergence to stable states.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Delivery type | Number | Length hours | Student hours |

Lecture | 33 | 1.00 | 33.00 |

Tutorial | 11 | 1.00 | 11.00 |

Private study hours | 106.00 | ||

Total Contact hours | 44.00 | ||

Total hours (100hr per 10 credits) | 150.00 |

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

**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) | 3 hr 00 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 websiteLast updated: 20/11/2008

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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