Linear maps on vector spaces are the basis for a large area of mathematics, in particular linear equations and linear differential equations, which form the basic language of the physical sciences.
This module restricts itself to the vector space R^n to build an intuitive understanding of the concepts of linear algebra and tools for calculations. We begin with the geometry of lines and planes in R^3 and R^n looking at the intuitive concept of vectors on the one hand, and with systems of linear equations on the other. This leads us to matrix algebra, and in particular the inversion of matrices.
One of the pre-requisites for MATH1049, MATH1057, MATH1058, MATH1060, MATH2013, MATH2045, MATH3087, MATH3033 and MATH3090
Aims and Objectives
Having successfully completed this module you will be able to:
- Find eigenvalues/eigenvectors of square matrices; diagonalize symmetric matrices
- Calculate the determinants, invert and perform basic operations with matrices
- Solve systems of linear equations and apply this to other questions from Linear Algebra
- Work with linear transformations of R^n and their matrices.
- Apply Linear Algebra methods to geometric problems in R^3 and R^n.
- Complex arithmetic
- Vectors in R^n: examples from R³, equations of lines and planes in R³.
- Systems of linear equations, Gaussian elimination.
- Matrix algebra: nxm matrices, sums, products, transpose, inverse of an nxn matrix, matrix equations.
- Determinants, cofactor definition of the inverse, proof that detA≠O if and only if A invertible.
- Properties of R^n, subspaces of R^n, span, null space and column space of a matrix.
- Linear independence of vectors in R^n.
- Scalar product and geometrical applications.
- Vector product and applications in R³.
- Linear transformations in R^n, examples in R² and R³.
- Eigenvalues and eigenvectors.
Throughout the module some theorems will be proved.
Learning and Teaching
Teaching and learning methods
Lectures, problem classes and workshops
|Total study time||150|
Resources & Reading list
Lang Serge. Introduction to Linear Algebra. UTM Springer.
Hirst & Singerman (2000). Basic Algebra and Geometry. Pearson Higher Education.
Lay David C -. Linear Algebra and its applications. Pearson International.
Edwards CH & Penney DE. Elementary Linear Algebra. Prentice Hall.
Martin Anthony and Michele Harvey (2012). Linear Algebra: Concepts and Methods. Cambridge University Press.
Leon Steven J. Linear Algebra with Application. Pearson International.
Larson, Edwards, Falvo. Elementary Linear Algebra. (Houghton Mifflin.
This is how we’ll formally assess what you have learned in this module.
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Repeat type: Internal & External