Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
2MMT210Linear Algebra3+2+04618.02.2026

 
Course Details
Language of Instruction Turkish
Level of Course Unit Bachelor's Degree
Department / Program Computer Engineering
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course This course aims to teach the practical application of matrices and determinants and the methods for solving systems of linear equations. It will also develop the ability to effectively use linear algebra knowledge in solving engineering problems.
Course Content Matrix and determinant operations, solving systems of linear equations using matrix and determinant approaches (Gauss and Gauss-Jordan elimination methods, inverse matrices, Cramer's rule), Vectors and vector operations, vector spaces, linear dependence and linear independence, basis and dimension, inner product spaces, orthogonal and orthonormal vectors, Gram-Schmidt method, linear transformations, eigenvalues and eigenvectors of a square matrix, the effect of eigenvalues and eigenvectors on the behavior of linear systems.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator Asist Prof. Fatma Zehra UZEKMEK
Name of Lecturers Asist Prof. Fatma Zehra UZEKMEK
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Prof. Dr. Fethi Çallıalp, Çözümlü Lineer Cebir Problemleri, Birsen Yayınevi, 2005.
Steven J. Leon, 2002, Linear Algebra with Applications, Pearson Education International, ISBN:0-13-035568.
Hacısalihoğlu, H. H., Lineer Cebir I, Bilim Yayınları, Ankara, 2000.
Course Notes 1. Narration
2. Question and Answer
3. Discussion
4. Practice and Application
5. Problem Solving
Exams 1 Ara Sınav, 1 Final Sınavı

Course Category
Mathematics and Basic Sciences %100
Engineering %30

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 % 50
Final examination 1 % 50
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 3 42
Mid-terms 1 2 2
Practice 14 2 28
Final examination 1 2 2
Total Work Load   Number of ECTS Credits 6 144

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Performs matrix and determinant operations by using mathematical and fundamental engineering knowledge, finds the inverse of a matrix, and applies the basic techniques of matrix algebra; thereby enhances analytical thinking, problem-solving, and mathematical analysis competencies.
2 Solves systems of linear equations (using Gauss elimination, Gauss–Jordan elimination, the inverse of the coefficient matrix, the inverse matrix method, and Cramer’s rule) by employing the skills of identifying, formulating, and analyzing complex engineering problems; thereby applies mathematical and fundamental engineering knowledge to enhance analytical thinking and problem-solving competencies.
3 Learns the concepts of vector spaces, linear dependence and independence, basis, dimension, and inner product spaces; comprehends the notions of orthogonal and orthonormal vectors, applies the Gram–Schmidt method, and gains the ability to model engineering problems through this technique.
4 Learns the concept of linear transformation; gains the ability to determine the characteristic polynomial, eigenvalues, and eigenvectors of square matrices. Applies the Cayley–Hamilton theorem to compute the inverse and the nth power of a square matrix, thereby enhancing the competence to apply mathematical and fundamental engineering knowledge in solving complex engineering problems.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Matrix definition, types of matrices, trace of a square matrix, equality of matrices, properties of matrices, matrix multiplication and its properties, transpose of a matrix and its properties.
2 Matrix definition, types of matrices, trace of a square matrix, equality of matrices, properties of matrices, matrix multiplication and its properties, transpose of a matrix and its properties.
3 Some Special Matrices (Symmetric Matrix, Antisymmetric Matrix, Idempotent Matrix, Nilpotent Matrix, Involution Matrix, Orthogonal Matrix), Elementary row and column operations on matrices.
4 Some Special Matrices (Symmetric Matrix, Antisymmetric Matrix, Idempotent Matrix, Nilpotent Matrix, Involution Matrix, Orthogonal Matrix), Elementary row and column operations on matrices.
5 Equivalent matrices, the row-reduced (echelon) form of a matrix, the rank of a matrix, the inverse of a square matrix, and related applications.
6 Solving systems of linear equations using equivalent matrices, Gauss elimination, Gauss-Jordan elimination methods, and related applications.
7 Linear homogeneous equation systems, Cramer's rule, inverse matrix method, and related applications.
8 MIDTERM EXAM
9 Vectors, vector operations and related applications.
10 Definition of vector spaces and related theorems, subspaces, the concept of span, and applications related to the subject.
11 Linear dependence and linear independence of vectors, concepts of basis and dimension, applications related to the subject.
12 Definition of inner product and inner product space and related theorems, orthogonal and orthonormal vectors, Gram-Schmidt method, and related applications.
13 Definition of linear transformation and related theorems, applications related to the subject.
14 Calculating the eigenvalues and eigenvectors of a square matrix, calculating the inverse and power of a square matrix using the Cayley-Hamilton Theorem, applications related to the subject.
15 FINAL EXAM

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11
All 5
C1 5
C2 5
C3 5
C4 5

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