MXB106 Linear Algebra
To view more information for this unit, select Unit Outline from the list below. Please note the teaching period for which the Unit Outline is relevant.
| Unit code: | MXB106 |
|---|---|
| Equivalent(s): | MAB112, MAB122, MAB132, PVB202 |
| Assumed Knowledge: | Specialist Mathematics or MXB100, or concurrently enrolled in MXB100. |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
| CSP student contribution | $592 |
| Domestic tuition unit fee | $3,816 |
| International unit fee | $4,872 |
Unit Outline: Semester 1 2026, Gardens Point, Internal
| Unit code: | MXB106 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB112, MAB122, MAB132, PVB202 |
| Assumed Knowledge: | Specialist Mathematics or MXB100, or concurrently enrolled in MXB100. |
| Coordinators: | Ravindra Pethiyagoda | ravindra.pethiyagoda@qut.edu.au Robyn Araujo | r.araujo@qut.edu.au Nicholas Buttle | n.buttle@qut.edu.au |
Overview
This is a foundational unit in linear algebra which introduces core algebraic concepts, as well as theoretical and practical tools, that will be of central importance to solving real-world problems in science and engineering by mathematical methods. Linear algebra is fundamental to most branches of mathematics, finding widespread applications in mathematical modelling, statistics, machine learning, finance, economics, information technology, operations research, and computational mathematics. This unit aims to cultivate a deep understanding of the basic mathematical structures of linear algebra, including vector spaces and linear combinations, matrix transformations, invariant subspaces and eigenvalue problems.
Learning Outcomes
On successful completion of this unit you will be able to:
- Interpret statements and concepts in linear algebra, both geometrically and algebraically.
- Recognise, construct and solve mathematical problems using the techniques of linear algebra.
- Critically select and apply appropriate tools of linear algebra to analyse and solve real world problems.
- Competently communicate mathematical arguments and results in written form.
Content
Vectors, algebra of vectors, geometric interpretation. Linear combinations, span, basis. Linear transformations and matrix representation, examples such as rotations, reflections and shears, composition of transformations. Determinants and inverse matrices. Linear systems, substitution, elimination. Rank, space, range, consistency. Underdetermined and overdetermined systems, general solutions of linear systems. Dot and cross products of vectors, angles and orthogonality. Change of basis, orthogonal and orthonormal bases. Eigenvalues, eigenvectors, diagonalisation, application to systems of linear, first-order ordinary differential equations.
Learning Approaches
As a first year unit your learning in this unit will be carefully scaffolded to support you to develop a solid understanding of the fundamental concepts relating to Linear Algebra.
In this unit, you will learn by engaging in the following:
- Weekly face to face lectures
- Online video resources
- Weekly workshops
This unit blends weekly face-to-face lectures and workshops with online videos. Theory and concepts will be presented in lectures and you will be exposed to the process required to solve problems. Supplementary videos will focus on the geometric intuitions of linear algebra, helping you to solidify the links between algebraic and geometric interpretations. In workshops you will capitalise on this enhanced learning by solving problems which will strengthen this deeper understanding.
The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios. The emphasis will be on learning by doing, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning.
You can expect to spend between 10 - 15 hours per week on average involved in preparing for and attending all scheduled classes, completing assessment tasks, and undertaking your own independent study to consolidate your learning.
Additional free support relating to this unit is available through the STIMulate peer program.
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Workbook
You will be required to solve specific problem sets assigned to you, and submit these for assessment and feedback throughout the semester. These will be hand-written or typeset solutions submitted in electronic form. Feedback provided will assist you by providing guidance for your ongoing learning.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
The ethical and responsible use of approved Generative AI tools is permitted for this assessment. The unit coordinator will provide guidance on their use - and any conditions that may apply - for this task. Please see the Assessment page on the canvas site for the unit for details.
Assessment: Project (applied)
The project will give you the opportunity to undertake the authentic task of applying the techniques of linear algebra to solve real-world problems, and to communicate your findings in writing. The problem specification will outline one or more real-world applications, providing you the necessary background information, to enable you to demonstrate your ability to apply learned techniques to new situations. You will submit hand-written or typeset solutions in electronic form.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
The ethical and responsible use of approved Generative AI tools is permitted for this assessment. The unit coordinator will provide guidance on their use - and any conditions that may apply - for this task. Please see the Assessment page on the canvas site for the unit for details.
Assessment: Examination (invigilated)
You will be required to complete this assessment where you will demonstrate your skills, techniques and problem solving abilities. This assessment may include short and long answer type questions.
The use of Generative AI tools is prohibited for this assessment. Please see the Assessment page on the canvas site for the unit for any further explanation.
The examination will require attendance at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide local testing centre information.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
All learning materials to support your learning in this unit are available in your Canvas unit site. We do have a recommended textbook for this unit, the details of which are listed below.
There are many reference texts for this unit, many of which can be located in the library and many online resources such as lecture notes and some e-books that can be found online.
Resource Materials
Recommended text(s)
Anton H. and Rorres C. Elementary Linear Algebra: Applications Version, Wiley
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp
Standards/Competencies
This unit is designed to support your development of the following standards\competencies.
Engineers Australia Stage 1 Competency Standard for Professional Engineer
1: Knowledge and Skill Base
Relates to: Workbook, Project (applied), Examination (invigilated)
2: Engineering Application Ability
Relates to: Project (applied)
Relates to: Project (applied), Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Workbook, Project (applied), Examination (invigilated)
Relates to: Project (applied)
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.DS01 Bachelor of Data Science
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the data science discipline, with depth of knowledge in at least one area developed through a major.
Relates to: Workbook, Project (applied), Examination (invigilated) - Use appropriate statistical, computational, modelling, data management, programming and generative artificial intelligence techniques to develop solutions for deriving insights from data.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem-solving skills, as well as adaptivity in applying learned techniques in new and unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Communicate effectively in a variety of modes, to expert and non-expert audiences, including in a professional context.
Relates to: Workbook, Project (applied), Examination (invigilated)
MS01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Workbook, Project (applied), Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Workbook, Project (applied), Examination (invigilated)
MV01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Workbook, Project (applied), Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Workbook, Project (applied), Examination (invigilated)
ST01 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Workbook, Project (applied), Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Workbook, Project (applied), Examination (invigilated)
SV02 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Workbook, Project (applied), Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Workbook, Project (applied), Examination (invigilated)
Unit Outline: Semester 1 2026, Online
| Unit code: | MXB106 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB112, MAB122, MAB132, PVB202 |
| Assumed Knowledge: | Specialist Mathematics or MXB100, or concurrently enrolled in MXB100. |
Overview
This is a foundational unit in linear algebra which introduces core algebraic concepts, as well as theoretical and practical tools, that will be of central importance to solving real-world problems in science and engineering by mathematical methods. Linear algebra is fundamental to most branches of mathematics, finding widespread applications in mathematical modelling, statistics, machine learning, finance, economics, information technology, operations research, and computational mathematics. This unit aims to cultivate a deep understanding of the basic mathematical structures of linear algebra, including vector spaces and linear combinations, matrix transformations, invariant subspaces and eigenvalue problems.
Learning Outcomes
On successful completion of this unit you will be able to:
- Interpret statements and concepts in linear algebra, both geometrically and algebraically.
- Recognise, construct and solve mathematical problems using the techniques of linear algebra.
- Critically select and apply appropriate tools of linear algebra to analyse and solve real world problems.
- Competently communicate mathematical arguments and results in written form.
Content
Vectors, algebra of vectors, geometric interpretation. Linear combinations, span, basis. Linear transformations and matrix representation, examples such as rotations, reflections and shears, composition of transformations. Determinants and inverse matrices. Linear systems, substitution, elimination. Rank, space, range, consistency. Underdetermined and overdetermined systems, general solutions of linear systems. Dot and cross products of vectors, angles and orthogonality. Change of basis, orthogonal and orthonormal bases. Eigenvalues, eigenvectors, diagonalisation, application to systems of linear, first-order ordinary differential equations.
Learning Approaches
As a first year unit your learning in this unit will be carefully scaffolded to support you to develop a solid understanding of the fundamental concepts relating to Linear Algebra.
In this unit, you will learn by engaging in the following:
- Weekly face to face lectures
- Online video resources
- Weekly workshops
This unit blends weekly face-to-face lectures and workshops with online videos. Theory and concepts will be presented in lectures and you will be exposed to the process required to solve problems. Supplementary videos will focus on the geometric intuitions of linear algebra, helping you to solidify the links between algebraic and geometric interpretations. In workshops you will capitalise on this enhanced learning by solving problems which will strengthen this deeper understanding.
The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios. The emphasis will be on learning by doing, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning.
You can expect to spend between 10 - 15 hours per week on average involved in preparing for and attending all scheduled classes, completing assessment tasks, and undertaking your own independent study to consolidate your learning.
Additional free support relating to this unit is available through the STIMulate peer program.
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Workbook
You will be required to solve specific problem sets assigned to you, and submit these for assessment and feedback throughout the semester. These will be hand-written or typeset solutions submitted in electronic form. Feedback provided will assist you by providing guidance for your ongoing learning.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
The ethical and responsible use of approved Generative AI tools is permitted for this assessment. The unit coordinator will provide guidance on their use - and any conditions that may apply - for this task. Please see the Assessment page on the canvas site for the unit for details.
Assessment: Project (applied)
The project will give you the opportunity to undertake the authentic task of applying the techniques of linear algebra to solve real-world problems, and to communicate your findings in writing. The problem specification will outline one or more real-world applications, providing you the necessary background information, to enable you to demonstrate your ability to apply learned techniques to new situations. You will submit hand-written or typeset solutions in electronic form.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
The ethical and responsible use of approved Generative AI tools is permitted for this assessment. The unit coordinator will provide guidance on their use - and any conditions that may apply - for this task. Please see the Assessment page on the canvas site for the unit for details.
Assessment: Examination (invigilated)
You will be required to complete this assessment where you will demonstrate your skills, techniques and problem solving abilities. This assessment may include short and long answer type questions.
The use of Generative AI tools is prohibited for this assessment. Please see the Assessment page on the canvas site for the unit for any further explanation.
The examination will require attendance at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide local testing centre information.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
All learning materials to support your learning in this unit are available in your Canvas unit site. We do have a recommended textbook for this unit, the details of which are listed below.
There are many reference texts for this unit, many of which can be located in the library and many online resources such as lecture notes and some e-books that can be found online.
Resource Materials
Recommended text(s)
Anton H. and Rorres C. Elementary Linear Algebra: Applications Version, Wiley
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp
Standards/Competencies
This unit is designed to support your development of the following standards\competencies.
Engineers Australia Stage 1 Competency Standard for Professional Engineer
1: Knowledge and Skill Base
Relates to: Workbook, Project (applied), Examination (invigilated)
2: Engineering Application Ability
Relates to: Project (applied)
Relates to: Project (applied), Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Workbook, Project (applied), Examination (invigilated)
Relates to: Project (applied)
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.DS01 Bachelor of Data Science
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the data science discipline, with depth of knowledge in at least one area developed through a major.
Relates to: Workbook, Project (applied), Examination (invigilated) - Use appropriate statistical, computational, modelling, data management, programming and generative artificial intelligence techniques to develop solutions for deriving insights from data.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem-solving skills, as well as adaptivity in applying learned techniques in new and unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Communicate effectively in a variety of modes, to expert and non-expert audiences, including in a professional context.
Relates to: Workbook, Project (applied), Examination (invigilated)
MS01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Workbook, Project (applied), Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Workbook, Project (applied), Examination (invigilated)
MV01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Workbook, Project (applied), Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Workbook, Project (applied), Examination (invigilated)
ST01 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Workbook, Project (applied), Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Workbook, Project (applied), Examination (invigilated)
SV02 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Workbook, Project (applied), Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Workbook, Project (applied), Examination (invigilated)
Unit Outline: Semester 2 2026, Gardens Point, Internal
| Unit code: | MXB106 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB112, MAB122, MAB132, PVB202 |
| Assumed Knowledge: | Specialist Mathematics or MXB100, or concurrently enrolled in MXB100. |
| Coordinators: | Matthew Adams | mp.adams@qut.edu.au |
Overview
This is a foundational unit in linear algebra which introduces core algebraic concepts, as well as theoretical and practical tools, that will be of central importance to solving real-world problems in science and engineering by mathematical methods. Linear algebra is fundamental to most branches of mathematics, finding widespread applications in mathematical modelling, statistics, machine learning, finance, economics, information technology, operations research, and computational mathematics. This unit aims to cultivate a deep understanding of the basic mathematical structures of linear algebra, including vector spaces and linear combinations, matrix transformations, invariant subspaces and eigenvalue problems.
Learning Outcomes
On successful completion of this unit you will be able to:
- Interpret statements and concepts in linear algebra, both geometrically and algebraically.
- Recognise, construct and solve mathematical problems using the techniques of linear algebra.
- Critically select and apply appropriate tools of linear algebra to analyse and solve real world problems.
- Competently communicate mathematical arguments and results in written form.
Content
Vectors, algebra of vectors, geometric interpretation. Linear combinations, span, basis. Linear transformations and matrix representation, examples such as rotations, reflections and shears, composition of transformations. Determinants and inverse matrices. Linear systems, substitution, elimination. Rank, space, range, consistency. Underdetermined and overdetermined systems, general solutions of linear systems. Dot and cross products of vectors, angles and orthogonality. Change of basis, orthogonal and orthonormal bases. Eigenvalues, eigenvectors, diagonalisation, application to systems of linear, first-order ordinary differential equations.
Learning Approaches
As a first year unit your learning in this unit will be carefully scaffolded to support you to develop a solid understanding of the fundamental concepts relating to Linear Algebra.
In this unit, you will learn by engaging in the following:
- Weekly face to face lectures
- Online video resources
- Weekly workshops
This unit blends weekly face-to-face lectures and workshops with online videos. Theory and concepts will be presented in lectures and you will be exposed to the process required to solve problems. Supplementary videos will focus on the geometric intuitions of linear algebra, helping you to solidify the links between algebraic and geometric interpretations. In workshops you will capitalise on this enhanced learning by solving problems which will strengthen this deeper understanding.
The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios. The emphasis will be on learning by doing, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning.
You can expect to spend between 10 - 15 hours per week on average involved in preparing for and attending all scheduled classes, completing assessment tasks, and undertaking your own independent study to consolidate your learning.
Additional free support relating to this unit is available through the STIMulate peer program.
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Workbook
You will be required to solve specific problem sets assigned to you, and submit these for assessment and feedback throughout the semester. These will be hand-written or typeset solutions submitted in electronic form. Feedback provided will assist you by providing guidance for your ongoing learning.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
The ethical and responsible use of approved Generative AI tools is permitted for this assessment. The unit coordinator will provide guidance on their use - and any conditions that may apply - for this task. Please see the Assessment page on the canvas site for the unit for details.
Assessment: Project (applied)
The project will give you the opportunity to undertake the authentic task of applying the techniques of linear algebra to solve real-world problems, and to communicate your findings in writing. The problem specification will outline one or more real-world applications, providing you the necessary background information, to enable you to demonstrate your ability to apply learned techniques to new situations. You will submit hand-written or typeset solutions in electronic form.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
The ethical and responsible use of approved Generative AI tools is permitted for this assessment. The unit coordinator will provide guidance on their use - and any conditions that may apply - for this task. Please see the Assessment page on the canvas site for the unit for details.
Assessment: Examination (invigilated)
You will be required to complete this assessment where you will demonstrate your skills, techniques and problem solving abilities. This assessment may include short and long answer type questions.
The use of Generative AI tools is prohibited for this assessment. Please see the Assessment page on the canvas site for the unit for any further explanation.
The examination will require attendance at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide local testing centre information.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
All learning materials to support your learning in this unit are available in your Canvas unit site. We do have a recommended textbook for this unit, the details of which are listed below.
There are many reference texts for this unit, many of which can be located in the library and many online resources such as lecture notes and some e-books that can be found online.
Resource Materials
Recommended text(s)
Anton H. and Rorres C. Elementary Linear Algebra: Applications Version, Wiley
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp
Standards/Competencies
This unit is designed to support your development of the following standards\competencies.
Engineers Australia Stage 1 Competency Standard for Professional Engineer
1: Knowledge and Skill Base
Relates to: Workbook, Project (applied), Examination (invigilated)
2: Engineering Application Ability
Relates to: Project (applied)
Relates to: Project (applied), Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Workbook, Project (applied), Examination (invigilated)
Relates to: Project (applied)
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.DS01 Bachelor of Data Science
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the data science discipline, with depth of knowledge in at least one area developed through a major.
Relates to: Workbook, Project (applied), Examination (invigilated) - Use appropriate statistical, computational, modelling, data management, programming and generative artificial intelligence techniques to develop solutions for deriving insights from data.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem-solving skills, as well as adaptivity in applying learned techniques in new and unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Communicate effectively in a variety of modes, to expert and non-expert audiences, including in a professional context.
Relates to: Workbook, Project (applied), Examination (invigilated)
MS01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Workbook, Project (applied), Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Workbook, Project (applied), Examination (invigilated)
MV01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Workbook, Project (applied), Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Workbook, Project (applied), Examination (invigilated)
ST01 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Workbook, Project (applied), Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Workbook, Project (applied), Examination (invigilated)
SV02 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Workbook, Project (applied), Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Workbook, Project (applied), Examination (invigilated)
Unit Outline: Semester 2 2026, Online
| Unit code: | MXB106 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB112, MAB122, MAB132, PVB202 |
| Assumed Knowledge: | Specialist Mathematics or MXB100, or concurrently enrolled in MXB100. |
Overview
This is a foundational unit in linear algebra which introduces core algebraic concepts, as well as theoretical and practical tools, that will be of central importance to solving real-world problems in science and engineering by mathematical methods. Linear algebra is fundamental to most branches of mathematics, finding widespread applications in mathematical modelling, statistics, machine learning, finance, economics, information technology, operations research, and computational mathematics. This unit aims to cultivate a deep understanding of the basic mathematical structures of linear algebra, including vector spaces and linear combinations, matrix transformations, invariant subspaces and eigenvalue problems.
Learning Outcomes
On successful completion of this unit you will be able to:
- Interpret statements and concepts in linear algebra, both geometrically and algebraically.
- Recognise, construct and solve mathematical problems using the techniques of linear algebra.
- Critically select and apply appropriate tools of linear algebra to analyse and solve real world problems.
- Competently communicate mathematical arguments and results in written form.
Content
Vectors, algebra of vectors, geometric interpretation. Linear combinations, span, basis. Linear transformations and matrix representation, examples such as rotations, reflections and shears, composition of transformations. Determinants and inverse matrices. Linear systems, substitution, elimination. Rank, space, range, consistency. Underdetermined and overdetermined systems, general solutions of linear systems. Dot and cross products of vectors, angles and orthogonality. Change of basis, orthogonal and orthonormal bases. Eigenvalues, eigenvectors, diagonalisation, application to systems of linear, first-order ordinary differential equations.
Learning Approaches
As a first year unit your learning in this unit will be carefully scaffolded to support you to develop a solid understanding of the fundamental concepts relating to Linear Algebra.
In this unit, you will learn by engaging in the following:
- Weekly face to face lectures
- Online video resources
- Weekly workshops
This unit blends weekly face-to-face lectures and workshops with online videos. Theory and concepts will be presented in lectures and you will be exposed to the process required to solve problems. Supplementary videos will focus on the geometric intuitions of linear algebra, helping you to solidify the links between algebraic and geometric interpretations. In workshops you will capitalise on this enhanced learning by solving problems which will strengthen this deeper understanding.
The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios. The emphasis will be on learning by doing, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning.
You can expect to spend between 10 - 15 hours per week on average involved in preparing for and attending all scheduled classes, completing assessment tasks, and undertaking your own independent study to consolidate your learning.
Additional free support relating to this unit is available through the STIMulate peer program.
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Workbook
You will be required to solve specific problem sets assigned to you, and submit these for assessment and feedback throughout the semester. These will be hand-written or typeset solutions submitted in electronic form. Feedback provided will assist you by providing guidance for your ongoing learning.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
The ethical and responsible use of approved Generative AI tools is permitted for this assessment. The unit coordinator will provide guidance on their use - and any conditions that may apply - for this task. Please see the Assessment page on the canvas site for the unit for details.
Assessment: Project (applied)
The project will give you the opportunity to undertake the authentic task of applying the techniques of linear algebra to solve real-world problems, and to communicate your findings in writing. The problem specification will outline one or more real-world applications, providing you the necessary background information, to enable you to demonstrate your ability to apply learned techniques to new situations. You will submit hand-written or typeset solutions in electronic form.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
The ethical and responsible use of approved Generative AI tools is permitted for this assessment. The unit coordinator will provide guidance on their use - and any conditions that may apply - for this task. Please see the Assessment page on the canvas site for the unit for details.
Assessment: Examination (invigilated)
You will be required to complete this assessment where you will demonstrate your skills, techniques and problem solving abilities. This assessment may include short and long answer type questions.
The use of Generative AI tools is prohibited for this assessment. Please see the Assessment page on the canvas site for the unit for any further explanation.
The examination will require attendance at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide local testing centre information.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
All learning materials to support your learning in this unit are available in your Canvas unit site. We do have a recommended textbook for this unit, the details of which are listed below.
There are many reference texts for this unit, many of which can be located in the library and many online resources such as lecture notes and some e-books that can be found online.
Resource Materials
Recommended text(s)
Anton H. and Rorres C. Elementary Linear Algebra: Applications Version, Wiley
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp
Standards/Competencies
This unit is designed to support your development of the following standards\competencies.
Engineers Australia Stage 1 Competency Standard for Professional Engineer
1: Knowledge and Skill Base
Relates to: Workbook, Project (applied), Examination (invigilated)
2: Engineering Application Ability
Relates to: Project (applied)
Relates to: Project (applied), Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Workbook, Project (applied), Examination (invigilated)
Relates to: Project (applied)
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.DS01 Bachelor of Data Science
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the data science discipline, with depth of knowledge in at least one area developed through a major.
Relates to: Workbook, Project (applied), Examination (invigilated) - Use appropriate statistical, computational, modelling, data management, programming and generative artificial intelligence techniques to develop solutions for deriving insights from data.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem-solving skills, as well as adaptivity in applying learned techniques in new and unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Communicate effectively in a variety of modes, to expert and non-expert audiences, including in a professional context.
Relates to: Workbook, Project (applied), Examination (invigilated)
MS01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Workbook, Project (applied), Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Workbook, Project (applied), Examination (invigilated)
MV01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Workbook, Project (applied), Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Workbook, Project (applied), Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Workbook, Project (applied), Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Workbook, Project (applied), Examination (invigilated)
ST01 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Workbook, Project (applied), Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Workbook, Project (applied), Examination (invigilated)
SV02 Bachelor of Science
- Develop a broad, multidisciplinary understanding of science and a specialised, in-depth knowledge of at least one discipline.
Relates to: ULO1, Workbook, Project (applied), Examination (invigilated) - Use higher order thinking skills to design, plan, and conduct investigations and evaluate data to address scientific questions and challenges.
Relates to: ULO1, ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Develop and demonstrate key competencies in scientific practices and relevant technologies.
Relates to: ULO2, ULO3, Workbook, Project (applied), Examination (invigilated) - Communicate scientific findings, concepts and evidence-based reasoning to diverse audiences using a variety of methods.
Relates to: ULO4, Workbook, Project (applied), Examination (invigilated)