## MATH1060 Introductory Linear Algebra

### 10 creditsClass Size: 185

Module manager: Bethany Marsh
Email: B.R.Marsh@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) 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 MATH1331 Linear Algebra with Applications

This module is approved as a discovery module

### 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.

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.
4. Concrete vector spaces and subspaces: Definitions of span and linear combination; linear dependence. Basis and dimensions of a vector space. Rank. Linear maps.
4. Eigenvalues and eigenvectors: Characteristic polynomial for eigenvalues. Eigenvalues adn eigenvectors of symmetric matrices. Classification of critical points of multivariate maps.

### 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 84.00 Total Contact hours 16.00 Total hours (100hr per 10 credits) 100.00

### Private study

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

### Opportunities for Formative Feedback

Regular example sheets.

!!! 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 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