## MATH1060 Introductory Linear Algebra

### 10 creditsClass Size: 250

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2005/06

### Pre-requisites

A level Mathematics, or equivalent.

This module is approved as an Elective

### Objectives

A first introduction to Linear Algebra, and in particular to the use of matrices. Elementary row-operations are emphasised as a unifying theme. On completion of this module, students should be able to: (a) solve systems of linear equations; (b) perform elementary matrix algebra; (c) solve simple eigenvalue problems.

### Syllabus

Linear Algebra is the formal, detailed theory which covers the ideas involved in solving simultaneous equations, and using matrices and determinants. This course starts by treating simultaneous equations in full generality, and introduces the notions involved in matrices and vector spaces. These basic ideas will be used and expanded in a wide variety of further mathematics modules, and are essential for understanding much of numerical computing. Hence this (or an equivalent) is an essential module for all students of mathematics and many others. Topics covered include: 1. General systems of linear equations: Reduction by elementary row operations to echelon form; solution from echelon form by back substitution. 2. Matrices and matrix algebra: Elementary matrices and inverse of a matrix. 3. Determinants: Definition by expansion, effect of elementary operations, evaluation. Concrete vector spaces and subspaces: Definitions of span and linear combination; linear dependence. Basis and dimensions of a vector space. Rank. 4. Eigenvalues and eigenvectors: Characteristic polynomial for eigenvalues. Linear independence of eigenvectors for different eigenvalues. Use in solving linear differential equations and in computing powers.

### Teaching methods

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

Lectures (22 hours); tutorials (11 hours).

### Methods of assessment

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

2 hour written examination at end of semester (85%), coursework (15%).