# EC133: Linear Algebra

### 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- and three-dimensional space, theory and applications of matrix diagonalisation, general vector spaces, and quadratic forms.

### Principal Learning Outcomes

By the end of the module the student should be able to 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) and understand formal mathematical definitions and theorems and apply them to solve problems in linear algebra.

### 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
- 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, L100 - Year 1, L116 - 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 (80%)
- Coursework Details
- Five problem sets (worth 4% each)
- Exam Timing
- May/June

### Exam Rubric

Time Allowed: 2 Hours.

Answer THREE questions. Each question is worth 25 marks.

Calculators are not needed and are not permitted in this examination.

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.