Information Package / Course Catalogue
Linear Algebra
Course Code: EK413
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 5
Objectives of the Course

The aim of this course is to give students fundamental knowledge about linear algebra. Creating base information about course content such as vectors, vector spaces, matrices and their applications. Applications of Eigenvalues and Eigenvectors of a matrices in several business problems will be mentioned in this course.

Course Content

Systems of linear equations, matrices, determinants. Vectors, vector spaces, basis and dimension, linear transformations. Eigenvalues, eigenvectors, and quadratic forms.

Name of Lecturer(s)
Learning Outcomes
1.On successful completion of this course unit students will be capable of gained the ability to; perform matrix operations (addition, subtraction,multiplication). Compute the determinant of a given matrix,
2.Solve systems of linear equations by using Gaussian elimination; and apply the basic techniques of matrix algebra, including finding the inverse of an invertible matrix using Gauss-Jordan elimination,
3.Understand the basic ideas of vector algebra: linear dependence and independence; comprehend vector spaces and subspaces,
4.Find the eigenvalues and eigenvectors of a square matrix using the characteristic polynomial,
5.Decompose linear transformations according to their eigenvectors and eigenvalues.
Recommended or Required Reading
1.Gilbert Strang, INTRODUCTION TO LINER ALGEBRA, Wellesley-Cambridge Press
2.Ron Larson, David C. Falvo, ELEMENTARY LINEAR ALGEBRA,
Weekly Detailed Course Contents
Week 1 - Theoretical
Definition of matrix, types of matrix, Equality of Matrices, Addition and subtraction of matrices, matrix multiplication by a scalar, Some properties about them. Multiplying matrices and Some properties about it. Transposes of matrices and properties of the transpose.
Week 2 - Theoretical
Some Special Matrices and matrix applications.(Symmetric Matrix,Anti symmetric matrix, periodic matrix, idempotent matrix, Nilpotent matrix, orthogonal matrix, A conjugate of a matrix and its properties, hermitian matrix,Anti hermitian matrix, regular matrix, singuler matrix, and their applications
Week 3 - Theoretical
Definition of a determinant. Laplace expansion of a matrix. Properties of a determinant.
Week 4 - Theoretical
Rule of Sarrus. The adjoint of a matrix, Using the adjoint matrix to find an inverse matrix and some applications about this.
Week 5 - Theoretical
System of linear equations: solving systems of linear equations with aid of equaivalent matrices, linear homogeneous equations and some applications about this
Week 6 - Theoretical
Cramer’s rule. Using the inverse of a coefficient matrix to solve a linear systems and some applications about this.
Week 7 - Theoretical
Cramer’s rule. Using the inverse of a coefficient matrix to solve a linear systems and some applications about this.
Week 8 - Theoretical
Vectors: Definition of Vectors,The sum of vectors and Subtraction of vectors and Multiplication of vectors, Dot product of two vectors and their properties, Vector product of two vectors(Cross product of vectors ) and their properties, Mixed product of three vectors(Triple product) and their properties, Double vector product(double cross) and their properties and some applications about this.
Week 9 - Theoretical
Vector Spaces: Definition of vector spaces and theorems. Subspaces and their applications.
Week 10 - Theoretical
Vector Spaces: Definition of vector spaces and theorems. Subspaces and their applications.
Week 11 - Theoretical
Span concept and fundamental theorems. Linear dependence and linear independence of vectors and some theorems about linear dependence and linear independence. Some applications about this
Week 12 - Theoretical & Practice
Quiz, Bases and dimension concepts and fundamental theorems. Some applications about this.
Week 13 - Theoretical
Definition of coordinates and transition matrices and some theorems.Some applications about this.
Week 14 - Theoretical
Eigenvalues and eigenvectors: The eigenvalues of a square matrix.Cayley Hamilton Theorem and their applications.
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory144398
Midterm Examination110111
Final Examination114115
TOTAL WORKLOAD (hours)124
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
OÇ-1
5
3
3
3
4
4
4
5
5
OÇ-2
3
3
3
4
4
4
5
5
5
OÇ-3
5
5
5
5
4
4
4
4
4
OÇ-4
3
3
3
3
5
5
5
5
5
OÇ-5
3
3
3
5
4
4
4
5
5
Adnan Menderes University - Information Package / Course Catalogue
2026