| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Linear Algebra | MEM233 | 3. Semester | 3 + 0 | 3.0 | 5.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Lectures at the class. |
| Course Coordinator |
Assoc. Prof. Dr. ZAKİR DENİZ |
| Instructors | |
| Assistants | |
| 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. |
| Learning Outcomes |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Systems of linear equations and their solutions. | Verbal Expression |
| 2. Week | Matrices and matrix operations. | Verbal Expression |
| 3. Week | Special Matrices; Identity matrix, diagonal matrix, inverse matrix and their properties. Matrices and Systems of linear equations. | Verbal Expression |
| 4. Week | Echelon Form of a matrix and solutions of systems of linear equations. | Verbal Expression |
| 5. Week | Elementary matrices, calculation of inverse matrix, equivalent matrices. | Verbal Expression |
| 6. Week | Determinants and properties of determinants. | Verbal Expression |
| 7. Week | Cofactors. Adjoint matrix. Cofactor expansion. Calculation of matrix inverses. Cramer's Rule. | Verbal Expression |
| 8. Week | Relation of matrix inverse and matrix determinant with the solution of the system of linear equations. | Verbal Expression |
| 9. Week | Vectors in the plane and in 3 - Space. Definition of vector spaces. | Verbal Expression |
| 10. Week | Subspaces. | Verbal Expression |
| 11. Week | Linear independence. | Verbal Expression |
| 12. Week | Basis and dimensions. | Verbal Expression |
| 13. Week | Coordinates and Isomorphisms. | Verbal Expression |
| 14. Week | Change of basis. Rank of a matrix. | Verbal Expression |
| Leon, Steven J., 2006, “Linear Algebra with Applications”, 7th Edition Prentice Hall, ISBN: 0 - 13 - 200306 - 6. |
| Howard Anton, Chris Rorres, 2005, “Elementary Linear Algera”, John Wiley and Sons. |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Midterm 1 | 1 | 50 | 50 |
| Final | 1 | 77.5 | 77.5 |
| Total Workload | 127.5 | ||
| ECTS Credit of the Course | 5.0 | ||
