## MATH1331 Linear Algebra with Applications

### 15 creditsClass Size: 110

Module manager: Prof. Robert Marsh
Email: r.j.marsh@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2019/20

### Pre-requisite qualifications

A-Level Mathematics or equivalent.

### This module is mutually exclusive with

 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 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

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 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