MTH2021 - Linear algebra with applications - 2017

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


Associate Professor Tim Garoni

Unit guides



  • First semester 2017 (Day)


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): 70% + Assignments and tests: 30%

Workload requirements

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

See also Unit timetable information

Chief examiner(s)

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


MTH1030, MTH1035, ENG1005 or equivalent