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Dr.Öğr.Üyesi

Emine ÇELİK

Fen Fakültesi

Matematik Bölümü

İletişim

eminecelik@sakarya.edu.tr

0264 295 6093

Sosyal Hesaplar

Linear Algebra

MAT 115 - Linear Algebra

Fall 2024 Sakarya University

Linear Algebra (3+0) 3 credits

Course Information

Instructor: Emine Çelik

Email: eminecelik@sakarya.edu.tr

Office: #308 Department of Mathematics

Homepage: https://eminecelik.sakarya.edu.tr

Textbooks

  • [1] David C. Lay, Linear Algebra and Its Applications, Pearson, 2003.
  • [2] Ron Larson, Elementary Linear Algebra, Cengage Learning, 2017.

Student Learning Outcomes

Upon completion of this course, students will be able to:

  • Solve linear systems using various methods.
  • Work with matrices and their operations.
  • Compute the dimension of a vector space, the rank of a matrix, and the span of a collection of vectors.
  • Compute eigenvalues and eigenvectors, determine whether a matrix is diagonalizable, and if possible, diagonalize it.

Tentative Course Schedule

Week Topics Worksheets
1. Week Introduction to systems of linear equations.  
2. Week Vector Equations. The Matrix Equation Ax=b. Row reduction and echelon forms.  
3. Week Gaussian Elimination and Gauss-Jordan Elimination.  Worksheet I
4. Week Operations with Matrices. Properties of Matrix operations.  Worksheet II
5. Week Theory of linear systems, homogeneous and nonhomogeneous systems, rank.  
6. Week The inverse of a matrix. Characterization of invertible matrices.  
7. Week LU factorization.    Worksheet III
8. Week  The Determinant of a Matrix. Determinants and Elementary operations.  
9. Week Properties of determinants.   Worksheet IV.
10. Week  Applications of Determinants, Cramer's rule.  
11. Week  Vectors, linear independence,  
12. Week  bases and transformations.  
13. Week  The Scalar Product.  
14. Week  Eigenvalues and eigenvectors.  
15. Week  Similar Matrices.