Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
3MAT211Doğrusal Cebir3+0+03612.11.2026
Course Details
Language of Instruction Turkish
Level of Course Unit Bachelor's Degree
Department / Program Industrial Engineering
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course The purpose of this course is to teach students methods for solving systems of linear equations, concepts of matrices and determinants, vector spaces, subspaces, linear independence, basis, and dimension; and to provide theoretical and practical knowledge on linear transformations, eigenvalues, eigenvectors, and diagonalization to enable them to solve engineering problems.
Course Content Systems of linear equations and Gauss-Jordan elimination method. Matrices and matrix operations, inverse matrix. Determinants, Cramer ` s rule, and properties of determinants. Vector spaces, subspaces, linear combinations, span, linear independence, basis, and dimension. Null space, column space, and row space. Linear transformations and their matrix representations. Eigenvalues, eigenvectors, characteristic equation, and diagonalization. Inner product spaces and the Gram-Schmidt orthogonalization process.
Course Methods and Techniques Face-to-face lecture, problem solving, question-answer, and application examples.
Prerequisites and co-requisities None
Course Coordinator Associate Prof.Dr. Serkan Aracı
Name of Lecturers Associate Prof.Dr. SERKAN ARACI
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Vektör uzayları, alt uzaylar, lineer bağımsızlık, taban ve boyut kavramlarını analiz edebilme.
Karakteristik denklemler üzerinden özdeğer ve özvektörleri hesaplayabilme ve uygun matrisleri köşegenleştirebilme.
Howard Anton, Chris Rorres, "Elementary Linear Algebra", 11th Edition, Wiley.
Bernard Kolman, David R. Hill, "Introductory Linear Algebra with Applications", Pearson.
Matris işlemlerini yapabilme, matrisin tersini bulabilme ve determinant özelliklerini uygulamalarda kullanabilme.
Lecture presentation slides and problem solving handouts.
Lineer dönüşümleri matrisler ile temsil edebilme, çekirdek ve görüntü uzaylarını belirleyebilme.
Gilbert Strang, "Introduction to Linear Algebra", 5th Edition, Wellesley-Cambridge Press.
Lineer denklem sistemlerini Gauss ve Gauss-Jordan yöntemlerini kullanarak çözebilme.
Course Notes Lecture presentation slides, practice and problem-solving handouts.

Course Category
Mathematics and Basic Sciences %100

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Mid-terms 1 % 40
Final examination 1 % 60
Total
2
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Course Duration 14 5 70
Hours for off-the-c.r.stud 14 7 98
Mid-terms 1 5 5
Final examination 1 5 5
Total Work Load   Number of ECTS Credits 6 178

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Ability to solve systems of linear equations using Gauss and Gauss-Jordan methods.
2 Ability to perform matrix operations, find inverse matrices, and apply determinant properties in practical problems.
3 Ability to analyze concepts of vector spaces, subspaces, linear independence, basis, and dimension.
4 Ability to represent linear transformations with matrices, and determine kernel and image spaces.
5 Ability to calculate eigenvalues and eigenvectors via characteristic equations and diagonalize suitable matrices.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Systems of linear equations, augmented matrices, and Gauss elimination method Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
2 Gauss-Jordan method, reduced row echelon form (RREF), and solution states Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
3 Matrix operations, properties of matrix algebra, and elementary matrices Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
4 Methods for finding matrix inverse and LU decomposition Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
5 Definition of determinant, cofactor expansion, and properties of determinants Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
6 Adjoint matrix, inverse matrix via determinants, and Cramer ` s rule Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
7 Vector spaces, subspaces, and linear combinations of vectors Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
8 Midterm Exam Reviewing exam topics. Lecture notes.
9 Span, concepts of linear independence and dependence Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
10 Basis, dimension, and matrix spaces (row, column, and null space) Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
11 Linear transformations, kernel, image, and matrix representation Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
12 Eigenvalues, eigenvectors, and characteristic equation Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
13 Diagonalization of matrices and applications Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
14 Inner product spaces, orthogonality, and Gram-Schmidt process Reading the relevant chapters of the textbook. Lecture notes and recommended textbooks.
15 General review and end-of-term evaluation General review of course topics. Lecture notes.

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22 P23 P24
C1 5 5 3 2 1 1 1 1 1 1 1
C2 5 5 3 2 1 1 1 1 1 1 1
C3 5 4 3 2 1 1 1 1 1 1 1
C4 5 4 3 2 1 1 1 1 1 1 1
C5 5 5 4 3 1 1 1 2 1 1 1

  Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant