| 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:No |
| Supplementary assessment is not available to students who gain a fail in this Unit. |
| Course Level: |
| Level of Unit in Course | AQF Level(s) of Course | | 5 | 6 | 7 | 8 | 9 | 10 | | Introductory | | |  | | | | | Intermediate | | | | | | | | Advanced | | | | | | |
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| Learning Outcomes: |
| Knowledge: |
| K1. | Classify the system of linear equations and demonstrate an understanding of methods for solving such systems. |
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| K2. | Explain and classify the fundamental structure of matrices and matrix arithmetic |
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| K3. | Demonstrate an understanding of inverses,determinants, eigenvalues and eigenvectors of matrices. |
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| K4. | Explain the nature of vectors. |
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| K5. | Recognise the basic techniques used for problems in linear programming |
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| Skills: |
| S1. | Express and solve systems of linear equations; |
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| S2. | Apply the operations of addition, multiplication, and transposition of matrices; |
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| S3. | Calculate the determinant and inverse of a matrix; |
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| S4. | Evaluate simple algebraic statements about vector addition, scalar multiplication and inner products; |
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| S5. | Apply vectors and operations involving vectors to solve problems involving lines and planes in 3-space; |
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| S6. | Calculate eigenvalues and eigenvectors of a matrix; |
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| S7. | Graphically explain linear programming problems in 2 dimensions; |
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| Application of knowledge and skills: |
| A1. | Apply appropriate algorithms to solve linear programming problems; |
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| A2. | Apply appropriate software packages to solve elementary problems of linear programming; |
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| 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% |
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