Linear Algebra (MATH275) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Linear Algebra MATH275 4 0 0 4 6
Pre-requisite Course(s)
Course Language English
Course Type N/A
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Question and Answer, Drill and Practice.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives This course is designed to enrich the knowledge of engineering students in linear algebra, and to teach them the basics and application of the methods for the solution of linear systems occurring in engineering problems.
Course Learning Outcomes The students who succeeded in this course;
  • understand the notion of matrix and perform algebraic operations on matrices, find the inverse of a nonsingular matrix, solve linear systems by using echelon form of matrices, determine the existence and uniquness of the solution and determine infinitely many solutions, if any
  • makes sense of vector spaces, subspaces, linear independence, basis and dimensions and rank of a matrix,
  • comprehend and use inner product, Gram-Schmidt process, orthogonal complements,
  • understand and use linear transformation and associated matrices,
  • evaluate determinants and solve linear systems with unique solution via determinant (Cramer’s Rule),
  • understand and find eigenvalues and eigenvectors, determine if a matrix is diagonalizable, and if it is, diagonalize it.
Course Content Linear equations and matrices, real vector spaces, inner product spaces, linear transformations and matrices, determinants, eigenvalues and eigenvectors.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Systems of Linear Equations, Matrices, Matrix Multiplication, Algebraic Properties of Matrix Operations pp. 1-39
2 Special Types of Matrices and Partitioned Matrices, Echelon Form of a Matrix, Solving Linear Systems pp. 42-49, 86-93, 95-103, 111-113
3 Elementary Matrices; Finding Inverses, Equivalent Matrices pp. 117-124, 126-129
4 Determinants, Properties of Determinants, Cofactor Expansion pp. 141-145, 146-154, 157-163
5 Inverse of a Matrix (via Its Determinant), Other Applications of Determinants (Cramer’s Rule) pp. 165-168, 169-172
6 Vectors in the Plane and In 3-D Space, Vector Spaces, Subspaces pp. 177-186, 188-196, 197-203
7 Span, Linear Independence, Basis and Dimension pp. 209-214, 216-226, 229-241
8 Homogeneous Systems, Coordinates and Isomorphism, Rank of a Matrix pp. 244-250, 253-266, 270-281
9 Inner Product Spaces, Gram-Schmidt Process pp. 290-296, 307-317, 320-329
10 Orthogonal Complements, Linear Transformations and Matrices pp. 332-343, 363-372
11 Kernel and Range of a Linear Transformation pp. 375-387
12 Matrix of a Linear Transformation pp. 389-397
13 Eigenvalues and Eigenvectors pp. 436-449
14 Diagonalization and Similar Matrices, Diagonalization of Symmetric Matrices pp. 453-461, 463-472
15 General Review
16 Final Exam


Course Book 1. Elementary Linear Algebra, B. Kolman and D.R. Hill, 9th Edition, Prentice Hall, New Jersey, 2008
Other Sources 2. Linear Algebra, S. H. Friedberg, A. J. Insel, L. E. Spence, Prentice Hall, New Jersey, 1979
3. Basic Linear Algebra, Cemal Koç, Matematik Vakfı Yay., Ankara, 1996

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 60
Final Exam/Final Jury 1 40
Toplam 3 100
Percentage of Semester Work 60
Percentage of Final Work 40
Total 100

Course Category

Core Courses X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 An ability to apply knowledge of mathematics, science and engineering to Industrial Engineering; an ability to apply theoretical and practical knowledge to model and solve engineering problems. X
2 An ability to identify, formulate and solve complex engineering problems; an ability to select and apply proper analysis and modeling methods. X
3 An ability to design a complex system, process, tool or component to meet desired needs within realistic constraints; an ability to apply modern design.
4 An ability to develop, select and put into practice techniques, skills and modern engineering tools necessary for engineering practice; an ability to use information technology effectively.
5 An ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or disciplinary research topics. X
6 An ability to work individually, on teams, and/or on multidisciplinary teams. X
7 Ability to communicate effectively in Turkish orally and in writing; knowledge of at least one foreign language; effective report writing and understand written reports, preparing design and production reports, making effective presentations, giving and receiving clear and understandable instruction.
8 A recognition of the need for, and an ability to engage in life-long learning; an ability to use information-seeking tools and to follow the improvements in science and technology.
9 An ability to behave according to the ethical principles, an understanding of professional and ethical responsibility. Information on standards used in industrial engineering applications.
10 Knowledge of business applications such as project management, risk management and change management. A recognition of entrepreneurship, innovativeness. Knowledge of sustainable improvement.
11 Information on the effects of industrial engineering practices on health, environment and security in universal and societal dimensions and the information on the problems of the in the field of engineering of the era. Awareness of the legal consequences of engineering solutions.
12 An ability to design, development, implementation and improvement of integrated systems that include human, materials, information, equipment and energy.
13 Knowlede on appropriate analytical, computational and experimental methods to provide system integration.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Special Course Internship
Field Work
Study Hours Out of Class 14 4 56
Presentation/Seminar Prepration
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 10 10
Total Workload 86