# 2008/09 Undergraduate Module Catalogue

## MATH1015 Linear Algebra 1

### 15 creditsClass Size: 250

**Module manager:** Dr R. Hollerbach**Email:** rh@maths.leeds.ac.uk

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

**Year running** 2008/09

### Pre-requisite qualifications

A-level Mathematics or equivalent### This module is mutually exclusive with

MATH1060 | Introductory Linear Algebra |

MATH1331 | Linear Algebra with Applications |

Module replaces

MATH1011**This module is approved as an Elective**

### Module summary

Linear algebra provides a basis for wide areas of mathematics. This module (or an equivalent) is an essential foundation for most students who wish to study mathematics at higher levels.### Objectives

On completion of this module, students should be able to:a) find the solution set of a system of linear equations using row reduction;

b) test specified sets of vectors to see if they form subspaces;

c) check specified sets of vectors to see if they form bases for given vector spaces;

d) write the equations of lines and planes in vector form;

e) calculate dot products of vectors and use them to evaluate angles between vectors;

f) calculate cross products of three dimensional vectors;

g) test specified mappings between vector spaces to determine if they are linear transformations;

h) work out the matrix representation of a specified linear transformation with respect to specified bases for the domain and co-domain;

i) determine whether the product of two specified matrices exists, and be able to evaluate the product where it does exist;

j) compute the inverse of a specified invertible matrix;

k) use the inverse of a matrix to solve systems of linear equations and to perform forward error analysis for these;

l) calculate the determinant of a square matrix, with numerical and algebraic entries;

m) compute the eigenvalues and eigenvectors of a specified matrix;

n) determine whether a specified matrix can be diagonalized;

o) orthogonally diagonalize symmetric matrices.

### Syllabus

Linear equations; use of matrix notation, systematic row reduction; cases of unique, infinitely many and no solutions; geometrical interpretation of these cases. Vectors, vector equations of lines and planes; dot product; angles between vectors; cross product. Rn as a vector space; linear independence; spanning, basis and dimension. Linear transformations; matrix representation of linear transformations; matrix multiplication; inverses of matrices. Determinants; eigenvalues and eigenvectors; diagonalization of matrices; orthogonal diagonalization of symmetric matrices.

### 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 | 6 | 1.00 | 6.00 |

Private study hours | 111.00 | ||

Total Contact hours | 39.00 | ||

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

### Private study

111 hours: 2 hours reading per lecture; 30 hours completing 5 problems sheets; 15 hours exam revision.### Opportunities for Formative Feedback

5 problems sheets at two week intervals.### 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) | 3 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

### Reading list

The reading list is available from the Library websiteLast updated: 24/05/2010

## Browse Other Catalogues

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

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