Mathematical Studies
MA203: Linear Algebra (5 ECTS)
An introduction to the theory and application of linear algebra.
Taught in Semester(s) 2?. Examined in Semester(s) 2?.
Workload: 126 hours (24 Lecture hours, 12 Tutorial hours, 90 Self study hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Draw diagrams that illustrate the basic operations of vector algebra in two and three dimensions;
- Recognise the equations of lines and planes in two and three dimensions;
- Perform the matrix computations outlined in the syllabus description below;
- Solve a linear system using Gaussian elimination;
- Compute the inverse of an invertible matrix;
- Find the orthogonal projection of a vector onto a hyperplane;
- Compute the determinant of a square matrix;
- Compute the characteristic equation of a matrix;
- Find the eigenvectors corresponding to a given eigenvalue;
- Diagonalise a diagonalisable matrix;
- Apply the theory to some real world problem.
Indicative Content
- Algebra and geometry of $\mathbb{R}^n$. Vector addition, scalar multiplication. Lines and planes in 2 and 3 dimensions. Parametric equations of lines and planes. (3 lectures)
- Matrix algebra. Addition, scalar multiplication, matrix product, transpose. Matrix inverses. (3 lectures)
- Systems of Linear Equations and Gaussian Elimination. Elementary operations, echelon form, over and underdetermined systems, homogeneous systems. Computing matrix inverses. (4 lectures)
- Dot product on $\mathbb{R}^n$. Perpendicular and parallel components, distance, angle, orthogonal matrices. (4 lectures)
- Determinants. Minors and cofactors, area and volume. Properties of determinants. Matrix inverses. (3 lectures)
- Eigenvalues and Eigenvectors. Characteristic equation, eigenvalues, eigenvectors, diagonalisation. Orthogonal diagonalisation of symmetric matrices. (4 lectures)
- Applications. (3 lectures)
Module Resources
- "Linear Algebra" (4th ed.) by Lipschuz and Lipson (McGraw-Hill)
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