MTH2021 - Linear algebra with applications - 2018

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.



Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

Associate Professor Tim Garoni


Associate Professor Tim Garoni

Unit guides



  • First semester 2018 (On-campus)


MTH1030, MTH1035, ENG1005 or equivalent




Vector spaces, linear transformations. Determinants, eigenvalue problems. Inner products, symmetric matrices, quadratic forms. LU-decomposition, least squares approximation, power method. Applications to coding, economics, networks, graph theory, geometry, dynamical systems, Markov chains, differential equations.


On completion of this unit students will be able to:

  1. Understand basic concepts related to vector spaces, including subspace, span, linear independence and basis;
  2. Understand basic properties of linear transformations and identify their kernel and range;
  3. Diagonalize real matrices by computing their eigenvalues and finding their eigenspaces;
  4. Understand basic concepts related to inner product spaces and apply these to problems such as least-squares data fitting;
  5. Apply tools from linear algebra in a wide variety of relevant situations;
  6. Understand and apply relevant numerical methods and demonstrate computational skills in linear algebra;
  7. Present clear mathematical arguments in both written and oral forms.


Examination (3 hours): 60% (Hurdle)

Assignments and tests: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Workload requirements

Three 1-hour lectures and one 2-hour support class per week

See also Unit timetable information

This unit applies to the following area(s) of study