# 2021/22 Undergraduate Module Catalogue

## MATH1331 Linear Algebra with Applications

### 15 creditsClass Size: 130

**Module manager:** Eleonore Faber; Paul Martin**Email:** e.m.faber@leeds.ac.uk; p.p.martin@leeds.ac.uk

**Taught:** Semester 1 (Sep to Jan) View Timetable

**Year running** 2021/22

### Pre-requisite qualifications

Grade B in A-level Mathematics or equivalent.### This module is mutually exclusive with

MATH1005 | Core Mathematics |

MATH1010 | Mathematics 1 |

MATH1012 | Mathematics 2 |

MATH1060 | Introductory Linear Algebra |

**This module is not approved as a discovery module**

### 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 | 11 | 1.00 | 11.00 |

Tutorial | 5 | 1.00 | 5.00 |

Private study hours | 134.00 | ||

Total Contact hours | 16.00 | ||

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

### Private study

Studying and revising of course material.Completing of assignments and assessments.

### Opportunities for Formative Feedback

Regular problem solving assignments!!! In order to pass the module, students must pass the examination. !!!

### 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 |

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

**Exams**

Exam type | Exam duration | % of formal assessment |

Open Book exam | 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 websiteLast updated: 12/11/2021

## Browse Other Catalogues

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

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