EC133: Linear Algebra
Nicholas Jackson
Module Leader
Introduction
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 Aims
To give the students a clear understanding of some important topics in linear algebra. Students will acquire an understanding of systems of simultaneous linear equations, vectors and linear maps in two-, three- and higher-dimensional space, theory and applications of matrix diagonalisation, general vector spaces, and quadratic forms.
Principal Learning Outcomes
1. Reproduce definitions and examples of core concepts, perform standard calculations, and state and prove standard facts and results in linear algebra.
2. Interpret, generalize and apply a range of mathematical techniques, concepts and results to questions in linear algebra, and understand their relevance to economics.
3. Use existing concepts and theorems to construct illustrative examples and counterexamples and rigorously prove further mathematical results.
Syllabus
The module will typically cover the following topics: Vector and matrix algebra; Vector spaces and coordinate systems; 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, R2L5 - Year 1, R4LA - Year 1, R1L5 - Year 1, L1CA - Year 1
- Pre or Co-requisites
- A-level in Mathematics
Assessment
- Assessment Method
- Coursework (30%) + Centrally-timetabled examination (On-campus) (70%)
- Coursework Details
- Assessment 3: Quizzes (10%) , Centrally-timetabled examination (On-campus) (70%) , Problem Set 1 (10%) , Problem Set 2 (10%)
- Exam Timing
- Summer
Subject Specific Skills
- Abstraction
- Analytical reasoning
- Analytical thinking and communication
- Critical thinking
- Problem solving
Transferable Skills
- Numeracy and quantitative skills
- Mathematical, statistical and data-based research skills
- Oral communication
- Written communication
Exam Rubric
Time Allowed: 2 Hours
Read all instructions carefully - and read through the entire paper at least once before you start entering your answers.
A formula sheet is provided at the end of the exam paper.
There is ONE section in this paper. Answer THREE questions (25 marks each).
Use a GOLD booklet.
You must write the number(s) of the question(s) you have answered on the front cover of each booklet. Make sure the numbers are clearly visible and correspond to the questions you completed inside that booklet.
Do not submit answers to more than the required number of questions. If you do, only the first answers (in the order they appear) will be marked, up to the required number for each section.
Approved scientific (non-graphical) pocket calculators are allowed.
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.