Module Code - Title:
MS4131
-
LINEAR ALGEBRA 1
Year Last Offered:
2025/6
Hours Per Week:
Grading Type:
N
Prerequisite Modules:
Rationale and Purpose of the Module:
The aim of this module is to introduce students to the main ideas of Linear Algebra
and its many applications. The emphasis is on developing the student's ability
to perform calculations on and with matrices, particularly 2x2 and 3x3 matrices,
and on and with vectors in 2 and 3 dimensions.
These ideas are then extended to higher dimensions.
Syllabus:
Matrices: introduction to matrices, matrix algebra, transpose of a matrix, symmetric matrices, invertible matrices and their inverses, determinants.
Vectors in 2 and 3 dimensions: geometric interpretation of vectors, vector arithmetic, Euclidean norm, Euclidean scalar product, angle, orthogonality, projections,
cross product and its uses in the study of lines and planes in 3 dimensions.
Lines and planes in 3-dimensional space: parametric equation of a line,
distance between a point and a line, point-normal form and general form
of the equation of a plane, distance between a point and a plane.
Extension to vectors in n dimensions;
Systems of linear equations and their solution: Gaussian elimination methods
(Gauss, Gauss-Jordan) and inverse matrix method;
Matrices acting on vectors: eigenvalues and eigenvectors particularly
in 2 and 3 dimensions.
Applications: least squares fit, rotation matrices.
Learning Outcomes:
Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)
The student will be able to carry out matrix algebra operations on matrices of any
order including the evaluation of determinants of square matrices and the calculation of eigenvalues and eigenvectors.
The student will be able to apply Gaussian elimination to a system of linear equations in order to determine its solution and use Gaussian elimination to find the inverse of an invertible matrix.
The student will also be able to apply the inverse matrix method to solve linear
systems, where appropriate.
The student will be able to carry out vector space operations on vectors of 2 and 3
dimensions including inner product, cross product and norm calculations.
The student will be able to use vectors to solve problems in 3-dimensional geometry
involving lines and planes.
The student will learn how the concepts learnt can be generalised to n-dimensional
spaces.
The student will be able to use matrices in a variety of applications.
Affective (Attitudes and Values)
N/A
Psychomotor (Physical Skills)
N/A
How the Module will be Taught and what will be the Learning Experiences of the Students:
Normal weekly lectures and tutorials. Mid-term exam(s) and final exam. Graduates, on successful completion of the module, will be well grounded in the foundations of linear algebra and will show confidence in their choice of appropriate method for solving problems and proving basic results in linear algebra. Graduates will be expected to be proactive and collaborative in tackling problems proposed in the tutorials.
Research Findings Incorporated in to the Syllabus (If Relevant):
Prime Texts:
Anton H (2010)
Elementary Linear
Algebra (10ed)
, Wiley
Other Relevant Texts:
Anton, H (2014)
Elementary Linear Algebra: with Supplemental
Applications (11ed)
, Wiley
Strang, G (2009)
Introduction to Linear Algebra (4ed)
, Wellesley-Cambridge Press
Johnson, L.W .et al (2015)
Introduction to Linear Algebra (6ed)
, Pearson
Programme(s) in which this Module is Offered:
BSFIMAUFA - FINANCIAL MATHEMATICS
BSMSCIUFA - MATHEMATICAL SCIENCES
BSMAPHUFA - MATHEMATICS AND PHYSICS
BSPHEDUFA - PHYSICAL EDUCATION
Semester(s) Module is Offered:
Autumn
Module Leader:
kevin.moroney@ul.ie