Emine ÇELİK

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. The Determinant of a Matrix. Determinants and Elementary operations. Properties of determinants.	Worksheet III
8. Week	Applications of Determinants, Cramer's rule.
9. Week	Vectors, linear independence, bases and transformations.	Worksheet IV.
10. Week	The Scalar Product, inner product spaces, orthonormal bases: Gram-Schmidt Process. QR factorization.
11. Week	Eigenvalues and eigenvectors.
12. Week	The Characteristic function. Cayley-Hamilton Theorem.
13. Week	Diagonalization. Similar Matrices.
14. Week	Eigenvalues and eigenvectors on behaviors of linear systems.
15. Week	Review and problem-solving session.