F18XR - Mathematics 3

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Syllabus

1.1 Introduces: Matrices Matrix Operations, Special Matrices, Elementary Matrices, Matrix Transformations and Linear Equations Systems of Linear Equations, Row Echelon Form, Gaussian Elimination, Applications of Linear Equations.

2.1 Introduces: Linear Algebra concepts, theories, and methods Vectors, vector spaces, Linear independence, Basis and dimension, Subspaces, Null space, Column space, Linear Transformations, Kernel and Range

3.1 Introduces: Determinants Definition, Properties, Cofactor Expansion, Applications; Eigenvalues and Eigenvectors Eigenvalues and Eigenvectors; Characteristic Polynomial; Diagonalization; Applications and Quadratic Forms Definition; Matrix Representation; Diagonalization; Positive Definite Quadratic Forms

Learning outcomes

By the end of the course, students should be able to do the following:

• apply matrix operations to solve systems of linear equations
• analyse vector spaces and linear transformations using their properties and definitions
• analyse eigenvalues and eigenvectors using matrix diagonalization techniques
• utilise determinants to solve linear algebra problems
• model real-world problems using linear algebra concepts

Further details

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SCQF Level: 8

Credits: 15