Module: Linear Algebra I

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Linear Algebra I
Module Code	MTH1087
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	7.5

Description

The purpose of this module is to introduce students to matrix algebra and linearity and to the notions of vector space and linear transformation. In this module students will gain a sound grasp of elementary linear algebra, and fundamental computational skills; it lays the foundations for further courses in linear algebra, calculus, probability and statistics.

Learning Outcomes

1. demonstrate computational skills by solving wide range of drill problems involving topics in the indicative syllabus
2. state selected definitions and theorems related to the indicative syllabus
3. solve exercises that test understanding of these definitions and theorems
4. explain arguments used to prove selected theorems in special cases
5. Demonstrate an understanding of the mechanics of change of basis

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	Lecture
Tutorial	12	Tutorial
Independent Study	170	Independent learning
Assignment Completion	2	Final Exam
Total Workload: 220

Section Breakdown
CRN	11806	Part of Term	Semester 1
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Ronan Egan	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	In class test	10%	Week 5
In Class Test	n/a	10%	Week 10
Formal Examination	End of semester Written Exam	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Vectors:
vectors in Euclidean space, linear combinations, dot product, orthogonality, one-dimensional projection, Cauchy-Schwarz Inequality.

Matrices and systems of equations:
Matrices, systems of linear equations, Gauss-Jordan elimination, invertible matrices, elementary matrices

Dimension:
subspaces, linear independence, basis, dimension, Rank-Nullity Theorem

Vector spaces
Abstract vector spaces and linear transformation. General rank-nullity Theorem.

Matrix representations
Coordinates, matrix representations, similarity

Indicative Reading List

Books:

John B. Fraleigh,Raymond A. Beauregard: 1995, Linear Algebra, Addison Wesley, 595, 0201526751
Gilbert Strang: 2023, Introduction to Linear Algebra, Wellesley-Cambridge Press, 0, 1733146679
Howard Anton,Chris Rorres,Anton Kaul: 2019, Elementary Linear Algebra, John Wiley & Sons, 802, 1119282365

Articles:
None

Other Resources

None