Linear Algebra and Applications

Unit Outline (Higher Education)

Level of Unit in Course

AQF Level(s) of Course

Level of Unit in Course

Introductory

Intermediate

Effective Term:

2024/20

Institute / School :

Institute of Innovation, Science & Sustainability

Unit Title:

Linear Algebra and Applications

Unit ID:

MATHS1102

Credit Points:

15.00

Prerequisite(s):

Nil

Co-requisite(s):

Nil

Exclusion(s):

(MATHS1005)

ASCED:

010101

Other Change:

Brief description of the Unit

This unit aims to offer students from diverse backgrounds an introduction to the use of mathematical methods in finding optimal choices in business, industry, economics, and social, behavioural and biological sciences. It introduces students to linear algebra and linear programming that underlie applications in operations research.

Grade Scheme:

Graded (HD, D, C, P, MF, F, XF)

Work Experience Indicator:

No work experience

Placement Component:

Supplementary Assessment:Yes

Where supplementary assessment is available a student must have failed overall in the Unit but gained a final mark of 45 per cent or above, has completed all major assessment tasks (including all sub-components where a task has multiple parts) as specified in the Unit Description and is not eligible for any other form of supplementary assessment

Course Level:

Learning Outcomes:

This unit introduces students to the fundamentals of linear algebra and linear programming that underlie applications in operations research. After successfully completing this unit, students should be able to:

Knowledge:

K1.	Classify the system of linear equations and demonstrate an understanding of methods for solving such systems.

K2.	Explain and classify the fundamental structure of matrices and matrix arithmetic

K3.	Demonstrate an understanding of inverses,determinants, eigenvalues and eigenvectors of matrices.

K4.	Explain the nature of vectors.

K5.	Recognise the basic techniques used for problems in linear programming

Skills:

S1.	Express and solve systems of linear equations;

S2.	Apply the operations of addition, multiplication, and transposition of matrices;

S3.	Calculate the determinant and inverse of a matrix;

S4.	Evaluate simple algebraic statements about vector addition, scalar multiplication and inner products;

S5.	Apply vectors and operations involving vectors to solve problems involving lines and planes in 3-space;

S6.	Calculate eigenvalues and eigenvectors of a matrix;

S7.	Graphically explain linear programming problems in 2 dimensions;

Application of knowledge and skills:

A1.	Apply appropriate algorithms to solve linear programming problems;

A2.	Apply appropriate software packages to solve elementary problems of linear programming;

Unit Content:

Topics may include:
1. matrix representations of systems of linear equations;
2. methods for solving the sytem of linear equations
3. vectors and matrices and their algebraic properties;
4. determinants and inverses of matrices;
5. dot products and cross products of vectors;
6. lines and planes in 3-space;
7. vector spaces, linear independence, basis, dimension and rank of matrices;
8. inner products, orthonormal bases, orthogonal matrices;
9. diagonalization of matrices, eigenvalues and eigenvectors;
10. Linear Programming (LP) problems and the geometry of LP problems
11. the Simplex algorithm;
12. duality;
13. network flow problems;
14. applications of LP;
15. software packages for solving LP problems.

Graduate Attributes:

	Learning Outcomes Assessed	Assessment Tasks	Assessment Type	Weighting
1.	K1-2, S1-7, A1	Participate in Class Activities	Portfolio of completed work	10 - 20%
2.	K1-5, S1-7, A1, A2	Self Directed or Group Exploration	Projects	10 - 30%
3.	K1-5, S1-7, A1, A2	Self Directed or Group Exploration	Presentation	10 - 20%
4.	K1-5, S1-7, A1	Review and skills practice	Tests/Examination(s)	40 - 60%

Adopted Reference Style:

APA ()

Professional Standards / Competencies:

Standard / Competency

Threshold Learning Outcomes - Mathematics: Initial

Attribute			Assessed	Level
1 Understanding
	1.1 Demonstrate a coherent understanding of the mathematical sciences.
		1.1.1 Ability to construct logical, clearly presented and justified arguments incorporating deductive reasoning.	Yes	Introductory
		1.1.2 Understanding of the breadth of the discipline, its role in other fields, and the way other fields contribute to development of the mathematical sciences.	Yes	Introductory
2 Knowledge
	2.1 Exhibit depth and breadth of knowledge in the mathematical sciences.
		2.1.1 Knowledge of the principles and concepts of a broad range of fundamental areas in the mathematical sciences.	Yes	Introductory
		2.1.2 Well-developed knowledge in at least one sub-discipline of the mathematical sciences.	Yes	Introductory
3 Inquiry and Problem Solving
	3.1 Investigating and solving problems using mathematical and statistical methods.
		3.1.1 Ability to formulate and model practical and abstract problems in mathematical and / or statistical terms using a variety of methods.	Yes	Introductory
		3.1.2 Ability to apply mathematical and / or statistical principles, concepts, techniques and technology to solve practical and abstract problems and interpret results critically.	Yes	Introductory
4 Communication
	4.1 Communicate mathematical and statistical information, arguments, or results for a range of purposes using a variety of means.
		4.1.2 Appropriate presentation of information, reasoning and conclusions in a variety of modes, to diverse audiences (expert and non-expert).	Yes	Introductory
5 Responsibility
	5.1 Demonstrate personal, professional and social responsibility.
		5.1.1 Ability to self direct learning to extend their existing knowledge and that of others.	Yes	Introductory
		5.1.2 Ability to work effectively and responsibly in an individual or team context.	Yes	Introductory

Engineers Australia - Stage 1 (Professional): 2017 accreditation & AQF

Attribute

Assessed

Level