| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Linear Algebra | MEM233 | Turkish | Compulsory | 3. Semester | 3 + 0 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lectures at the class. |
| Course Coordinator | Doç. Dr. ZAKİR DENİZ |
| Instructor(s) | Doç. Dr. GÜLHAN AYAR (Güz) |
| Goals | 1.To teach matrix algebra and system of linear equations. 2.To teach how to solve a system of linear equations. 3.To teach invertible matrices, inverse of a matrices, the properties of the determinant function. 4.To teach vector spaces, subspaces, span of a set, linear independency of a set, basis, the coordinates of a vector, and the dimension. |
| Course Content | Systems of linear equations and matrices; matrix algebra, special types of matrices, elementary row and column operations, echelon form, elementary matrices, inverses, equivalent matrices. Solutions of systems of linear equations. Determinants; properties of determinants, cofactor and adjoint of a matrix, derivation of inverse matrix, Cramer's rule. Vector Spaces; definition of vector spaces, subspaces, linear independence, bases and dimension, coordinates, change of basis and isomorphisms, rank of a matrix. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Systems of linear equations and their solutions. | Interview |
| 2. Week | Matrices and matrix operations. | Interview |
| 3. Week | Special Matrices; Identity matrix, diagonal matrix, inverse matrix and their properties. Matrices and Systems of linear equations. | Interview |
| 4. Week | Echelon Form of a matrix and solutions of systems of linear equations. | Interview |
| 5. Week | Elementary matrices, calculation of inverse matrix, equivalent matrices. | Interview |
| 6. Week | Determinants and properties of determinants. | Interview |
| 7. Week | Cofactors. Adjoint matrix. Cofactor expansion. Calculation of matrix inverses. Cramer's Rule. | Interview |
| 8. Week | Relation of matrix inverse and matrix determinant with the solution of the system of linear equations. | Interview |
| 9. Week | Vectors in the plane and in 3 - Space. Definition of vector spaces. | Interview |
| 10. Week | Subspaces. | Interview |
| 11. Week | Linear independence. | Interview |
| 12. Week | Basis and dimensions. | Interview |
| 13. Week | Coordinates and Isomorphisms. | Interview |
| 14. Week | Change of basis. Rank of a matrix. | Interview |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Sınavlar |
Midterm 1 | 1 | 50 | 50 |
| Final | 1 | 77.5 | 77.5 | |
| Total Workload | 127.5 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
