Linear Algebra and Applications
84 hours
One Semester or equivalent
Hawthorn
Available to incoming Study Abroad and Exchange students
Overview
This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies.
Requisites
Teaching Periods
Location
Start and end dates
Last self-enrolment date
Census date
Last withdraw without fail date
Results released date
Semester 1
Location
Hawthorn
Start and end dates
26-February-2024
26-May-2024
26-May-2024
Last self-enrolment date
10-March-2024
Census date
31-March-2024
Last withdraw without fail date
12-April-2024
Results released date
02-July-2024
Learning outcomes
Students who successfully complete this unit will be able to:
- Perform simple operations involving determinants, the rank of a matrix and its null space (K2)
- Perform operations with vectors and have a working understanding of vector spaces. Use vectors to calculate scalar and vector products, determine linear (in)dependence of vectors (K2, S1)
- Use the methods of Gaussian elimination, Cramer’s rule and inverse matrices to solve systems of linear equations and apply them to relevant examples (K2, S1)
- Describe straight lines and planes in three dimensions and the relationships between them (K2, S1)
- Use curvilinear coordinates, linear transformations and conversions with parametric forms to solve simple problems. Determine the curvature and radius of curvature for a curve, angular velocity and torque (K2, S1)
- Use complex numbers to solve equations, describe graphically complex numbers in the Argand plane (K2)
Teaching methods
Hawthorn
| Type | Hours per week | Number of weeks | Total (number of hours) |
|---|---|---|---|
| Live Online Lecture | 2.00 | 12 weeks | 24 |
| On-campus Class | 2.00 | 12 weeks | 24 |
| On-campus Class | 2.00 | 12 weeks | 24 |
| Online Directed Online Learning and Independent Learning | 1.00 | 12 weeks | 12 |
| Unspecified Activities Independent Learning | 5.50 | 12 weeks | 66 |
| TOTAL | 150 |
Assessment
| Type | Task | Weighting | ULO's |
|---|---|---|---|
| Examination | Individual | 40 - 50% | 1,2,3,4,5,6 |
| Online Assignment | Individual | 20 - 30% | 1,2,3,4,5,6 |
| Test | Individual | 10 - 20% | 1,2,3,4 |
| Tutorial Exercises | Individual | 10 - 20% | 1,2,3,4,5,6 |
Hurdle
As the minimum requirements of assessment to pass a unit and meet all ULOs to a minimum standard, an undergraduate student must have achieved:
(i) an aggregate mark of 50% or more, and(ii) at least 40% in the final exam.Students who do not successfully achieve hurdle requirement (ii) will receive a maximum of 45% as the total mark for the unit.
Content
- Matrices. Matrix algebra operations, determinants, rank, nullity, basis, linear independence
- Vectors. Direction, magnitude, vector spaces, sub-spaces spanning and bases, scalar product and vector product
- Systems of linear equations. Elementary row operations, augmented matrix, row-echelon form, Gaussian elimination, Cramer’s rule, inversion
- Elements of linear geometry & differential geometry. Equation of straight lines and planes, intersection & distance between points, lines and planes. curvilinear coordinates, curvature, velocity and acceleration
- Linear transformations. Matrix of linear transformations, rotations, inversions and projections
- Complex numbers and their properties. Imaginary numbers, Argand plane in Cartesian and polar forms, roots of complex numbers, complex exponential form and applications
Study resources
Reading materials
A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.