# Linear Algebra (MATH275) Ders Detayları

Course Name Corse Code Dönemi Lecture Hours Uygulama Saati Lab Hours Credit ECTS
Linear Algebra MATH275 3. Semester 4 0 0 4 6
Pre-requisite Course(s)
None
Course Language İngilizce Service Courses Taken From Other Departments Lisans Face To Face Lecture, Question and Answer, Drill and Practice. 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. 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. 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

### Sources

Course Book 1. Elementary Linear Algebra, B. Kolman and D.R. Hill, 9th Edition, Prentice Hall, New Jersey, 2008 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

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 40 100

### Course Category

Core Courses X

### 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.
2 An ability to design and conduct experiments, as well as to analyze and interpret data.
3 An ability to design a system, component, or process to meet desired needs.
4 An ability to function on multi-disciplinary teams.
5 An ability to identify, formulate, and solve engineering problems.
6 An understanding of professional and ethical responsibility.
7 An ability to communicate effectively.
8 The broad education necessary to understand the impact of engineering solutions in a global and societal context.
9 Recognition of the need for, and an ability to engage in life-long learning.
10 Knowledge of contemporary issues.
11 An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.
12 Skills in project management and recognition of international standards and methodologies

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