### 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.

### 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    10
Homework 2    10
Homework 3  150    15