Department of Mathematics and Physics

Course Title Introduction to Linear Algebra

Course Code MAT-125
Section No 9
Semester Summer 2023
Course Dr. Mohammad Monir Uddin (monir.uddin@northsouth.edu)
Coordinator
Instructor & Department Information

Instructor's Name Dr. Atia Afroz

Office Room SAC 1064A
Office Hours ST (4:30PM~5:30PM)
Office Phone
Email Address atia.afroz@northsouth.edu
Links

Marks Distribution:
Attendance 10%
Assignments 10%
Quizzes 20%
Mid-Term 25%
Final Exam 35%

Grading Policy:

Numerical Scores Letter Grade Grade Points

93 & above A 4.0
90 - 92 A- 3.7
87 – 89 B+ 3.3
83 – 86 B 3.0
80 – 82 B- 2.7
77 – 79 C+ 2.3
73- 76 C 2.0
70 – 72 C- 1.7
67 - 69 D+ 1.3
60 - 66 D 1.0
Course Short Description

This is an introductory course in linear algebra. The course will introduce the basic concepts
and techniques of linear algebra, along with the insights of its wide applications in physics,
economics and social sciences, natural sciences, and engineering. The course will require the
development of theoretical results, which will require the use of mathematical rigor, algebraic
manipulation, and geometry.

This course covers, but is not limited to, the study of systems of linear equations, matrices,
determinants, vectors and vector spaces, basis and dimension of vector spaces, linear
transformations, eigenvalues and eigenvectors, and their applications. Computer software will
be used to enhance the learning of the topics and techniques covered.

Course Objectives

1. To understand the fundamental properties of matrices including determinants, inverse

matrices, matrix factorizations, eigenvalues, eigenvectors along with their application,
and linear transformations.
2. Understanding the basic concepts of the system of linear equations, apply the matrix
calculus to solve linear systems of equations.
3. To comprehend the Euclidean n-space, vector spaces, subspaces, linear span, and
determine the basis and dimension of vector spaces.
4. Solving problems using computer programming and graphing calculators to gain an
insight into the applicability of linear algebra.

Course Learning Outcomes

Upon successful completion of this course, students will be able to:

• (CO-1) Demonstrate the ability to understand the basic properties of

matrices including determinants, inverse matrices, matrix
factorizations, eigenvalues, eigenvectors, and linear
transformations, the applications of eigenvectors including the
investigation of the diagonalizability of matrices.
• (CO-2) Explain the fundamental concepts of the system of linear
equations using geometry and graphs; and apply the matrix
calculus to solve linear systems of equations.
• (CO-3) Comprehend the concept of Euclidean n-space, vector spaces,
subspaces, linear span, and determine the basis and dimension of
vector spaces.
• (CO-4) Develop problem solving ability using computer programming
and graphing calculators and have an appreciation of the wide
application of this discipline within the scientific field.
CLOs Course Outcomes (CO) Bloom’s Delivery Assessment
taxonomy methods tools
domain/level and activities
(C: Cognitive
P: Psychomotor
A:Affective)
CO-1 Demonstrate the ability to C1, C2, C3, C4 Lectures, notes Quiz,
understand the basic Assignment,
properties of matrices Midterms,
including determinants, inverse Final Exam
matrices, matrix factorizations,
eigenvalues, eigenvectors, and
linear transformations, the
applications of eigenvectors
including the investigation of
the diagonalizability of
matrices.
CO-2 Explain the fundamental C2, C3, P2 Lecture, notes, Assignment,
concepts of the system of linear group discussion Class
equations using geometry and participation,
graphs; and apply the matrix Quiz,
Midterms
calculus to solve linear systems
of equations.
CO-3 Comprehend the concept of C1, C2, C3 Lecture, notes Discussion,
Euclidean n-space, vector spaces, Quiz,
subspaces, linear span, and Midterms,
determine the basis and Final Exam
dimension of vector spaces.
CO-4 Develop problem solving ability C2, C3, C6, P3 Lecture, notes, Assignment,
using computer programming group discussion Discussion,
and graphing calculators and Class
have an appreciation of the participation
wide application of this
discipline within the scientific
field.
 Article no. Assessment Learning
Lecture Topics in the text tools Outcomes
book

1 Matrices and Matrix Operations, Inverse; 1.3, 1.4, 1.7 Quiz1, CO-1
Rules of Matrix Arithmetic, Discussions
2 Diagonal, Triangular and Symmetric 1.3, 1.4, Quiz 1, CO-1
Matrices, Matrices and Matrix Operations, Discussions
3 Inverse; Rules of Matrix Arithmetic, 1.7 Assignment I, CO-1
Diagonal, Triangular and Symmetric Midterm
Matrices
4 Elementary Matrices and a Method for 1.5 Assignment I, CO-1
Finding inverse of Matrix, Elementary Midterm
Matrices and a Method for Finding inverse
of Matrix
5 2.1 Quiz 1, CO-1
Determinant by Cofactor Expansion
Midterm
6 Evaluating Determinants by Row Reduction 2.2 Midterm CO-1
7 2.3 Midterm, CO-1
Properties of Determinant Function
Assignment I
8 Introduction to System of Linear Equations, 1.1, 1.2 Discussions, CO-2
Gaussian Eliminations
9 Gaussian Eliminations (No solution and 1.2 Midterm, CO-2
Unique solution)
10 Gaussian Eliminations (many 1.2 Midterm, CO-2
solutions),Solution of Homogeneous system
of Linear Equations
11 Further Results on Systems of Equations 1.2 Midterm, CO-2
and Invertibility,
12 Euclidean n-space and properties, Euclidean 1.6 Discussions CO-2, CO-
n-space and Gramsmith Orthogonalization Midterm 3
13 Midterm Exam
14 4.2 Final, CO-1
Linear Transformation
15 Linear Transformation and properties, 4.2 , 4.3 Final, CO-1
General Linear Transformations, Kernel and
Range,
16 Inverse Linear Transformations, Matrices 8.1, 8.2, Final, CO-2, CO-
of General Linear Transformations Assignment II 3
17 Inverse Linear Transformations, Matrices 8.3, 8.4 Final, CO-2, CO-
of General Linear Transformations Assignment II 3
18 5.1 Quiz 2 CO-1
Real Vector Spaces, Subspaces
19 Linear combination,Linear Independence 5.2 Final CO-3
and Dependence

20 Linear combination,Linear Independence 5.3 Final CO-3

and Dependence

21 Basis, Dimension, Solution Space and Null 5.4 Quiz 2, Final CO-3
Space Exam
22 Fundamental Subspace of Linear Algebra 5.5 Quiz 3, Final CO-3
(Row Space, Column Space and Null Space) Exam
23 Fundamental Subspace of Linear Algebra 5.5 Quiz 3, Final CO-3
(Row Space, Column Space and Null Space) Exam
24 Rank and Nullity 5.6 Final Exam CO-3
25 Eigenvalues and Eigenvectors 7.1 Quiz 3 CO-3
29 Diagonalization 7.2 Final Exam CO-3
26 7.2 Final exam, CO-3
Algebraic and Geometric Multiplicity
Assignment II
27 Cheley Hamilton Theorem (CHT) and its 7.3 Final exam, CO-3
applications Quiz3
28 11.2, 11.3 Discussions CO-4
Applications of Linear Algebra
Final exam
29 11.6, 11.7 Discussions CO-4
Applications of Linear Algebra
Final exam
30 11.16 Discussions, CO-4
Applications of Linear Algebra
Final exam
Final Exam (Declared by the Controller of Examinations)
 Mapping of Course Outcomes

Class Schedule

Note: The instructor reserves the right to make changes to the syllabus if necessary.

List of additional readings

• Chapter 3: Vectors in 2-Space and 3-Space: Introduction to Vectors, Norm of a Vector;

Vector Arithmetic, Dot Product; Projections, Lines and Planes in 3-Space
• Chapter 6: Inner Product Spaces: Inner Products, Angle and Orthogonality in Inner
Products, Orthonormal Bases; Gram-Schmidt Process, Orthogonal Matrices; Change of
Basis.

Classroom Rules of Conduct

Please Refer to NSU Student Handbook, Sections: “Disciplinary Actions” and “Procedures
and Guidelines”.

Exams & Make-up Exam Policy

NO makeup for quizzes and NO Formative assessment will be retaken under any
circumstances. If a student misses the Midterm and/or Final exams due to circumstances
beyond their control (official valid documents are required) and is informed beforehand (if
possible), reasonable arrangement may be considered. Please note that the retake exam
questions are generally a bit tricky and critical compare to the regular exam questions.
Students may get the opportunity to see/recheck their midterm and Final exam scripts.
Cell phones are prohibited in exam sessions.

Attendance Policy: As per NSU policy.