## MATH1060 Introductory Linear Algebra

### 10 creditsClass Size: 250

Module manager: Dr A. Parker
Email: parker@maths.leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

### Pre-requisite qualifications

A good A-level Mathematics grade or equivalent.

### This module is mutually exclusive with

 MATH1015 Linear Algebra 1 MATH1331 Linear Algebra with Applications

This module is approved as an Elective

### Module summary

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.

### 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

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

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Tutorial 11 1.00 11.00 Private study hours 67.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 100.00

### 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) 2 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