# Linear Algebra (MATH275) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Linear Algebra MATH275 3. Semester 4 0 0 4 6
Pre-requisite Course(s)
None
Course Language English Compulsory Departmental Courses Bachelor’s Degree (First Cycle) 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 Adequate knowledge in mathematics, science and subjects specific to the computer engineering discipline; the ability to apply theoretical and practical knowledge of these areas to complex engineering problems. X
2 The ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose. X
3 The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose.
4 The ability to develop, select and utilize modern techniques and tools essential for the analysis and determination of complex problems in computer engineering applications; the ability to utilize information technologies effectively.
5 The ability to design experiments, conduct experiments, gather data, analyze and interpret results for the investigation of complex engineering problems or research topics specific to the computer engineering discipline.
6 The ability to work effectively in inter/inner disciplinary teams; ability to work individually X
7 Effective oral and writen communication skills in Turkish; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and to receive clear and understandable instructions.
8 The knowledge of at least one foreign language; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and to receive clear and understandable instructions.
9 Recognition of the need for lifelong learning; the ability to access information, to follow recent developments in science and technology.
10 The ability to behave according to ethical principles, awareness of professional and ethical responsibility;
11 Knowledge of the standards utilized in software engineering applications
12 Knowledge on business practices such as project management, risk management and change management;
14 Knowledge on sustainable development
15 Knowledge on the effects of computer engineering applications on the universal and social dimensions of health, environment and safety;
16 Awareness of the legal consequences of engineering solutions
17 An ability to describe, analyze and design digital computing and representation systems. X
18 An ability to use appropriate computer engineering concepts and programming languages in solving computing problems.

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