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DEPARTMENT OF MATHEMATICS
SCHOOL OF PHYSICAL AND MATHEMATICAL SCIENCES
FIRST SEMESTER, 2024/2025 ACADEMIC YEAR

COURSE SYLLABUS

Course Code and Title: MATH351 - Linear Algebra

(3 Credits)

Lecture Period and Venue:

Group 1

– Monday 11:30am - 1:20pm (LOT Room 01)

– Wednesday 11:30am - 1:20pm (Dept of Math, Room 05)

Group 2

– Monday 5:30pm - 7:20pm (Dept of Math, Room 05)

– Wednesday 11:30am - 1:20pm (N-Block, Room 3)

Course Instructors:
• Group 1

– Name: Dr Vincent T. Teyekpiti

– Office: Room 25, Department of Mathematics
– Office Hours: Tue 12:00 - 2:00pm, Fri 10:00am - 12:00pm or by appointment
– Email: vteyekpiti@ug.edu.gh

• Group 2

– Name: Mr Felix Ofori

– Office: Room 1, Department of Mathematics
– Office Hours: Tue 10:00am - 12:00pm, Wed 2:00pm - 4:00pm
– Email: fofori006@gmail.com

Instructors: Dr Vincent T. Teyekpiti and Mr Felix Ofori Page 1 of 5

Prerequisite: Math224 (with a pass of at least grade D)

Department Examinations Officer:

• Name and Office: Dr. Vasco B. Normenyor, Room 26, Department of Mathe-
matics

• Email: bvnormenyo@ug.edu.gh

Level 300 Course Advisor:

• Name and Office: Dr Ralph A. Twum, Room 13, Department of Mathematics

• Email: ratwum@ug.edu.gh

Course Description:
The aim of this course is to broaden your knowledge of the fundamental concepts and
techniques of linear algebra. The main ideas and techniques to be covered are used ex-
tensively in engineering, electromagnetism, economics, statistics, computer science and
many other areas of pure and applied mathematics. The course is designed to extend
ideas from Math 224. The course emphasis is on understanding fundamental concepts,
developing concrete understanding and acquiring the ability to solve problems. The pre-
sentation of the course will be in an abstract perspective. The concept of abstraction helps
to reduce the objects of study to their most basic form for easy understanding. Topics
to be covered include vector spaces, linear transformations, eigenvalue and eigenvectors,
diagonalization and normal forms of matrices, quadratic and bilinear forms.

Course Objective:
The course is designed with main emphases on developing a clear understanding of the
fundamental concepts of linear algebras and a range of skills allowing students to apply
such concepts to problems in thermodynamics, physics, engineering, economics, computer
science and information theory. After completing this course, students should gain the
understanding necessary for advanced studies in the physical and mathematical sciences.

Learning Outcomes:
At the end of the course, students should obtain the following learning outcomes defined
in the context of skills, knowledge and general competence. The student should be able
to:
• extend the definitions and terminologies from introductory algebra to linear algebra

• give accurate account of the concepts of vector spaces and give examples of vector
spaces

• determine when a set with the associated operations satisfies the conditions of a
vector space.

• acquire comprehensive understanding of subspaces and determine when a subset

with the associated operations is a subspace of a vector space

• accurately define linear combination, spanning set, linearly dependent and linearly
independent set, basis of a vector space and the dimension of a vector space

Instructors: Dr Vincent T. Teyekpiti and Mr Felix Ofori Page 2 of 5

 • demonstrate the ability to define linear transformations and give examples of such
transformations
• represent a linear transformation by a matrix and determine the rank of a matrix
• find the column space and null space of the matrix representation of a linear trans-
formation
• demonstrate the ability to determine the eigenvalues and eigenvectors of a matrix
• find the characteristic polynomial of a matrix and demonstrate the ability to de-
compose a vector space into eigenspaces
• determine the Jordan normal form of a matrix
• determine the matrix corresponding to a quadratic form
• determine the ”definiteness” of a quadratic form
• formulate real world problems (from relevant areas of applications) in a mathemat-
ical form and perform mathematical analysis of such problems using concepts from
linear algebra

Course Delivery:
The delivery will be largely based on problem solving. There will be an interactive
lecture and tutorial sessions. Lecture materials will be uploaded to the course website and
students are encouraged to read them before attending face-to-face lecture and tutorial
sessions where students will have the opportunity to engage in collaborative learning
activities. Weekly assignments will be given to enhance your understanding of the course.

Outline of Topics:
1) Vector Spaces
Definition and examples of vector spaces, subspaces of vector spaces and their ex-
amples, spanning sets, linearly independent and linearly dependent sets, bases of
vector spaces, dimension of a vector space
2) Linear Transformations
Definition and examples of linear transformations, elementary properties of linear
transformations, representing a linear transformation by a matrix, matrix repre-
sentation of a linear transformation, kernel and image of a linear transformation,
change of basis, inner product spaces, orthogonality and projections
3) Eigenvalues and Eigenvectors
Determine the eigenvalues and eigenvectors of a matrix, find the characteristic poly-
nomial of a matrix, determinant and trace of a matrix, decompose a vector space
into eigenspaces, diagonalization of a matrix, Jordan normal form of a matrix,
applications to systems of linear differential equations
4) Quadratic and Bilinear Forms
Determine the matrix corresponding to a quadratic form, Determine the de
niteness of a quadratic form

Instructors: Dr Vincent T. Teyekpiti and Mr Felix Ofori Page 3 of 5

Course Delivery Schedule:

Week Topics
1 Definition and examples of vector spaces, subspaces of vector spaces
and their examples
2 spanning sets, linearly independent and linearly dependent sets
3 Bases of vector spaces, dimension of a vector space
4 Definition and examples of linear transformations, elementary prop-
erties of linear transformations, representing a linear transformation
by a matrix
5 Matrix representation of a linear transformation, kernel and image
of a linear transformation, change of basis,
6 Inner product spaces, orthogonality
7 Orthogonality and projections
8 Determine the eigenvalues and eigenvectors of a matrix, find the
characteristic polynomial of a matrix
9 Determinant and trace of a matrix, decompose a vector space into
eigenspaces, diagonalization of a matrix
10 Jordan normal form of a matrix, applications to systems of linear
differential equations
11 Determine the matrix corresponding to a quadratic form, determine
the defi
niteness of a quadratic form
12 Singular Value decomposition, principal component analysis

Assessment and Grading:

Final Exam - - - - - - - - - - - - - - - - - - - - 60% of the final score
Quizzes, Class Tests, Exercises - - - - - - - - 40% of the final score

Please note that the final examination will be written on the UG campus. The date and
venue will be communicated to students by the Academic Affairs Directorate. Timelines
for the continuous assessment tests will be announced in class and on the Sakai course
webpage.

Plagiarism Policy:
UG has an ongoing commitment to nurturing a culture of learning informed by academic
integrity. As a result of this commitment, all UG staff and students have an onerous
responsibility to stick to this principle of academic integrity. Plagiarism is a threat to
academic integrity and is not tolerated at UG. The UG plagiarism policy outlines the
primary obligations of students and is available online at the Academic Quality Assurance
Unit webpage.

Instructors: Dr Vincent T. Teyekpiti and Mr Felix Ofori Page 4 of 5

Grading Scale:
Mark Grade
80 - 100 A
75 - 79 B+
70 - 74 B
65 - 69 C+
60 - 64 C
55 - 59 D+
50 - 54 D
45 - 49 E
0 - 44 F

References
[1] J. Hefferon, Linear Algebra, Department of Mathematics & Applied Mathematics,
Virginia Commonwealth University, 2009. (This is a freely available textbook. A copy
is on the course website.)
[2] D. J. S. Robinson, A Course in Linear Algebra with Applications, Second Edition,
World Scientific, 2006.
[3] G. Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press, 2003.

Disclaimer:
The instructors reserve the right to make changes to the syllabus. Students will be
notified of any changes. Please consult the course website for any updates.

Instructors: Dr Vincent T. Teyekpiti and Mr Felix Ofori Page 5 of 5