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| Module Availability |
| Semester 2 |
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| Assessment Pattern |
Assessment Pattern
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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1 class test
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25
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Exam, 2 hours
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75
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Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass the module.
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| Module Overview |
| This module is an introduction to the theory and methods of elementary Linear Algebra. |
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| Prerequisites/Co-requisites |
| MAT1031 Algebra |
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| Module Aims |
| The aim of this module is to extend students' knowledge of matrices and vectors and to introduce the abstract concepts of vector spaces, linear maps and inner products. |
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| Learning Outcomes |
At the end of the module the student should:
• Be able to solve systems of linear equations by Gaussian elimination.
• Know how to find eigenvalues and eigenvectors, and carry out matrix diagonalisation.
• Know and understand the terminology associated with vector spaces and subspaces
• Understand and be able to apply the relationship between linear maps and matrices.
• Recognise the equation of a conic, and know how to find its principal axes.
• Understand the concepts of inner product and orthogonality.
• Be familiar with vector spaces over the real numbers, complex numbers and finite fields.
• Be able to formulate simple proofs of results similar to those covered in the course.
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| Module Content |
• Solution of systems of linear equations by Gaussian elimination.
• Eigenvalues and eigenvectors. Matrix diagonalisation.
• Introduction to vector spaces. Subspaces, linear independence, basis, dimension.
• Linear transformations. Matrix representation. Kernel and image, rank and nullity.
• Quadratic forms. Orthogonal diagonalisation. Principal axes of conics.
• Bilinear forms and Inner products. Norms, orthogonality, the Gram-Schmidt process.
• Introduction to vector spaces over the complex numbers and finite fields
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| Methods of Teaching/Learning |
Teaching is by lectures, tutorials and tests: 4 hours per week for 11 weeks.
Learning takes place through lectures, tutorials, tests and exercise sheets.
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| Selected Texts/Journals |
Recommended:
David Poole, Linear Algebra – A Modern Introduction, Brooks Cole (2002), ISBN 0534341748.
Also useful:
J. Gilbert and C. Jordan (2002), Guide to Mathematical Methods, Palgrave Macmillan, ISBN 0333794443
H. Anton : Elementary Linear Algebra, Wiley (2000), ISBN 0471170550.
R.B.J.T. Allenby, Linear Algebra, Butterworth-Heinemann (1995), ISBN 0340610441
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| Last Updated |
| 21 April 2011 |
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