## 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