Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Introduction to Linear Algebra
Code MATH103
Coordinator Professor VV Goryunov
Mathematical Sciences
Victor.Goryunov@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2023-24 Level 4 FHEQ First Semester 15

Aims

• To develop techniques of complex numbers and linear algebra, including equation solving, matrix arithmetic and the computation of eigenvalues and eigenvectors.
• To develop geometrical intuition in 2 and 3 dimensions.
• To introduce students to the concept of subspace in a concrete situation.
• To provide a foundation for the study of linear problems both within mathematics and in other subjects

Learning Outcomes

(LO1) Manipulate complex numbers and solve simple equations involving them, solve arbitrary systems of linear equations.

(LO2) Understand and use matrix arithmetic, including the computation of matrix inverses.

(LO3) Compute and use determinants.

(LO4) Understand and use vector methods in the geometry of 2 and 3 dimensions.

(LO5) Calculate eigenvalues and eigenvectors.

(S1) Numeracy

Syllabus
 

Complex numbers: geometrical interpretation and algebraic manipulation. Equations involving complex numbers.

Vectors in 2 and 3 dimensions, dot and cross products, equations of lines and planes, intersections of planes, distance formulae. Linear independence.

Matrix algebra.  Solution of systems of linear equations.  Determinants: definition and basic properties. Eigenvalues and eigenvectors of matrices.

Similar matrices and diagonalisation. Further work on linear independence, basis of a subspace.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Final Assessment/Exam  120    65       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homework 1  0    10       
Homework 2  0    10       
Homework 3  150    15