MAT1041 Linear AlgebraBahçeşehir UniversityDegree Programs CIVIL ENGINEERINGGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
Bachelor TR-NQF-HE: Level 6 QF-EHEA: First Cycle EQF-LLL: Level 6

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT1041 Linear Algebra Fall 3 0 3 6

Basic information

Language of instruction: English
Type of course: Must Course
Course Level: Bachelor’s Degree (First Cycle)
Mode of Delivery: Face to face
Course Coordinator : Instructor MAHMOUD JAFARI SHAH BELAGHI
Course Lecturer(s): Prof. Dr. SÜREYYA AKYÜZ
Recommended Optional Program Components: None
Course Objectives: To define matrix operations such as addition, multiplication, inversion and to prove some of related properties; To teach to solve a system of linear equations by using matrices; To give the definitions of a vector space, subspace, base and dimension and to prove some of related theorems; To introduce the notion of a linear map and the types of linear maps (such as injective, surjective and bijective); To teach the matrix representation of linear mappings and proving some of related properties; To construct the space of linear mappings and to give its structural properties; To define the transpose of a linear functional and to prove related properties.

Learning Outcomes

The students who have succeeded in this course;
1. Solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.
2. Carry out matrix operations, including inverses and determinants.
3. Demonstrate understanding of the concepts of vector space and subspace.
4. Demonstrate understanding of linear independence, span, and basis.
5. Determine eigenvalues and eigenvectors and solve eigenvalue problems.
6. Apply principles of matrix algebra to linear transformations.

Course Content

Systems of linear equations, matrices; Vector spaces, subspaces, base and dimension, coordinate; Linear mappings, kernel and image subspaces; Matrix representations of linear mappings; Linear functional, transpose of a linear mapping. Eigenvalues and eigenvectors, diagonalization of matrices.

Weekly Detailed Course Contents

Week Subject Related Preparation
1) - Introduction to Systems of Linear Equations - Gaussian Elimination and Gauss-Jordan Elimination
2) - Operations with Matrices - Properties of Matrix Operations
3) - The Inverse of a Matrix
4) - The Determinant of a Matrix - Evaluation of a Determinant Using Elementary Operations
5) - Properties of Determinants
6) - Vectors in R^n - Vector Spaces \ review.
7) - Subspaces of Vector Spaces - Spanning Sets and Linear Independence
8) - Basis and Dimension
9) - Rank of a Matrix and Systems of Linear Equations
10) - Introduction to Linear Transformations
11) - The Kernel and Range of a Linear Transformation
12) - Matrices for Linear Transformations - Transition Matrices and Similarity \ review.
13) - Eigenvalues and Eigenvectors - Diagonalization
14) - Symmetric Matrices and Orthogonal Diagonalization


Course Notes / Textbooks: Elementary Linear Algebra, Howard Anton, Wiley Publishing Co. (2000)
References: 1.Lang, S., "Linear Algebra", Addison-Wesley Publishing Company, (1968).
2.Hoffman, K. M., Kunze R. A., "Linear Algebra", Printice Hall, 2. edition, (1971).
3.Koç, C., "Basic Linear Algebra", Matematik Vakfı, (1995).
4. Lipschutz, S., "Linear Algebra, Schaum’s Outline Series", McGraw-Hill, Inc., (1974).
5.Kolman, B., Hill, D. R., "Introductory Algebra with Applications", Prentice Hall

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Midterms 2 % 60
Final 1 % 40
Total % 100
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 7 98
Midterms 2 2 4
Final 1 2 2
Total Workload 146

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
Program Outcomes Level of Contribution
1) Adequate knowledge in mathematics, science and civil engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems. 5
2) Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. 2
3) Ability to design a complex system, process, structural and/or structural members to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
4) Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in civil engineering applications; ability to use civil engineering technologies effectively.
5) Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or civil engineering research topics.
6) Ability to work effectively within and multi-disciplinary teams; individual study skills.
7) Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing.
8) Awareness of the necessity of lifelong learning; ability to access information to follow developments in civil engineering technology.
9) To act in accordance with ethical principles, professional and ethical responsibility; having awareness of the importance of employee workplace health and safety.
10) Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
11) Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of civil engineering solutions.