# EC133: Linear Algebra

### Principal Aims

This module allows students to develop a fluency with the algebra of matrices and vectors, and an understanding of topics related to linear transformations, in particular eigenvalues and eigenvectors, coordinate transformations, and matrix diagonalisation and its applications. This provides students with a deeper understanding of techniques used in mathematical economics and econometrics.

### Principal Learning Outcomes

Subject knowledge and understanding: … demonstrate an understanding of symbolic logic, basic properties of number systems, vectors and matrices in R2, R3 and Rn, vector spaces, linear maps, quadratic forms and their applications to certain sorts of problems (solving systems of simultaneous equations, long-term behaviour of coupled recurrence relations, etc).The teaching and learning methods that enable students to achieve this learning outcome are: Lectures, tutorials, problem sheets and independent study.The summative assessment methods that measure the achievement of this learning outcome are: Problem sheets and unseen examination. Key skills: …understand formal mathematical definitions and theorems, and apply them to solve problems in linear algebra. The teaching and learning methods that enable students to achieve this learning outcome are: Lectures, tutorials, problem sheets and independent study.The summative assessment methods that measure the achievement of this learning outcome are: Problem sheets and unseen examination.

### Syllabus

The module will typically cover the following topics: Set theory; Number systems; Symbolic logic; Vectors and vector spaces; Linear transformations; Eigenvalues and eigenvectors; Simultaneous equations; Matrix diagonalisation; Inner products; Symmetric matrices; Quadratic forms.

### Context

- Optional Module
- L100 - Year 1, L116 - Year 1, LM1D (LLD2) - Year 1, V7ML - Year 1, L1L8 - Year 1, LA99 - Year 1, R9L1 - Year 1, R3L4 - Year 1, R4L1 - Year 1, R2L4 - Year 1, R1L4 - Year 1
- Pre or Co-requisites
- A-level Mathematics
- Part-year Availability for Visiting Students
- Available in the Spring term only (5 problem sets - 12 CATS) and in the Spring and Summer terms together (5 problem sets and 1 x 2 hour exam - 15 CATS)

### Assessment

- Assessment Method
- Coursework (20%) + 2 hour exam (summer) (80%)
- Coursework Details
- Problem Set 3 (4%), Problem Set 5 (4%), Problem Set 1 (4%), Problem Set 2 (4%), Problem Set 4 (4%), 2 hour exam (summer) (80%)
- Exam Timing
- Summer

### Exam Rubric

Time Allowed: 2 Hours.

Answer THREE questions. Each question is worth 25 marks.

Approved pocket calculators are allowed.

A formula sheet is provided at the end of the exam paper.

Read carefully the instructions on the answer book provided and make sure that the particulars required are entered on each answer book. If you answer more questions than are required and do not indicate which answers should be ignored, we will mark the requisite number of answers in the order in which they appear in the answer book(s): answers beyond that number will not be considered.

Previous exam papers can be found in the University’s past papers archive. Please note that previous exam papers may not have operated under the same exam rubric or assessment weightings as those for the current academic year. The content of past papers may also be different.