units

MTH2021

Faculty of Science

# Undergraduate - UnitMTH2021 - Linear algebra with applications

This unit entry is for students who completed this unit in 2013 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

## 6 points, SCA Band 2, 0.125 EFTSL

To find units available for enrolment in the current year, you must make sure you use the indexes and browse unit tool in the current edition of the Handbook.

 Level Undergraduate Faculty Faculty of Science Organisational Unit School of Mathematical Sciences Offered Clayton First semester 2013 (Day) Coordinator(s) Dr Tim Garoni

### Synopsis

Vector spaces, linear transformations. Determinants, eigenvalue problems. Inner products, symmetric matrices, quadratic forms. Jacobi iteration, Gauss-Seidel iteration, least squares approximation, power method. Applications to coding, computer graphics, geometry, dynamical systems, Markov chains, differential equations.

### Outcomes

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;

1. Understand basic properties of linear transformations and identify their kernel and range;

1. Diagonalize real matrices by computing their eigenvalues and finding their eigenspaces;

1. Understand basic concepts related to inner product spaces and apply these to problems such as least-squares data fitting;

1. Apply tools from linear algebra in a wide variety of relevant situations;

1. Understand and apply relevant numerical methods and demonstrate computational skills in linear algebra;

1. Present clear mathematical arguments in both written and oral forms.

### Assessment

Examination (3 hours): 70%
Assignments: 20%
Laboratory work: 10%.

### Contact hours

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

### Prerequisites

MAT1841, MTH1030, MTH1035, or equivalent

MAT2912