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Online Session 1 Session 1

Unit Summary

Unit type

UG Coursework Unit

Credit points

12

AQF level

7

Level of learning

Intermediate

School/College

School of Education

Unit aim

Introduces students to the theory, techniques and applications of linear algebra. Topics include matrices and determinants, vectors, vector and inner product spaces, linear transformations.

Unit content

Topics 1 and 2: Matrices and determinants – Matrix definitions and operations – Inverse matrices – Determinants, evaluation and properties – Diagonal, triangular and symmetric matrices.

Topics 3 and 4: Vectors Definitions – Basic operations and algebra of vectors.

Topics 5 to 8: Vector spaces Euclidean and general vector spaces and subspaces – Linear independence – Basis and dimension – Linear transformations.

Topic 9: Inner product spaces – Inner product – Orthonormal bases.

Topic 10: Eigenvalues and eigenvectors – Eigenvalues and eigenvectors – Diagonalisation and orthogonal diagonalisation.

Learning outcomes

Unit Learning Outcomes express learning achievement in terms of what a student should know, understand and be able to do on completion of a unit. These outcomes are aligned with the graduate attributes. The unit learning outcomes and graduate attributes are also the basis of evaluating prior learning.

GA1: Intellectual rigour, GA2: Creativity, GA3: Ethical practice, GA4: Knowledge of a discipline, GA5: Lifelong learning, GA6: Communication and social skills, GA7: Cultural competence
On completion of this unit, students should be able to: GA1 GA2 GA3 GA4 GA5 GA6 GA7
1 demonstrate a sound knowledge and understanding of the concepts of linear algebra Intellectual rigour Knowledge of a discipline Communication and social skills
2 demonstrate a proficiency in applying techniques from linear algebra Intellectual rigour Knowledge of a discipline Communication and social skills
3 apply appropriate techniques from linear algebra to 'real world' problems Intellectual rigour Knowledge of a discipline Communication and social skills
4 communicate mathematical ideas, processes and results effectively at different levels of formality. Intellectual rigour Knowledge of a discipline Communication and social skills

On completion of this unit, students should be able to:

  1. demonstrate a sound knowledge and understanding of the concepts of linear algebra
    • GA1: Intellectual rigour
    • GA4: Knowledge of a discipline
    • GA6: Communication and social skills
  2. demonstrate a proficiency in applying techniques from linear algebra
    • GA1: Intellectual rigour
    • GA4: Knowledge of a discipline
    • GA6: Communication and social skills
  3. apply appropriate techniques from linear algebra to 'real world' problems
    • GA1: Intellectual rigour
    • GA4: Knowledge of a discipline
    • GA6: Communication and social skills
  4. communicate mathematical ideas, processes and results effectively at different levels of formality.
    • GA1: Intellectual rigour
    • GA4: Knowledge of a discipline
    • GA6: Communication and social skills

Prescribed texts

  • Anton, H & Rorres, C, 2014, Elementary linear algebra with applications, 11th edn, Wiley, Hoboken, NJ.
Prescribed texts may change in future study periods.