Course Overview

Linear algebra is a cornerstone of modern mathematics and has wide-ranging applications in fields such as computer science, engineering, physics, economics, and data science. In this course, we will explore key topics including:

• Vectors and Vector Spaces: Learn about vectors in n-dimensional space, scalar and vector products, and their geometric interpretations. We will also delve into the axioms of vector spaces, subspaces, and the concepts of linear independence and basis.
• Matrices and Determinants: Understand the algebra of matrices, including operations, types of matrices, and the row-reduced echelon form. We will also cover determinants, their properties, and their role in solving systems of linear equations using Cramer's rule.
• Eigenvalues and Eigenvectors:  Discover how to find eigenvalues and eigenvectors, and explore their significance in diagonalizing matrices and understanding linear transformations.
• Linear Transformations: Study the concept of linear transformations, their matrix representations, and how they relate to vector spaces. We will also explore the rank and nullity of transformations and their eigen spaces.

Course Objective

On completion of the course, successful students will be able to:

• identify the basic ideas of vector algebra,

• describe the concept of vector space over a field,

• calculate scalar and vector products,

• understand the basic theory of matrix,

• find Adjoint of a matrix,

• solve system of linear equations,

• determine row reduced echelon forms of a matrix,

• determine the eigenvalues and eigenvectors of a square matrix,

• grasp Gram-Schmidt process, find an orthogonal basis for a vector space,

• invert orthogonal matrix,

• understand the notion of a linear transformation,

• find the linear transformation with respect to two bases,

 Teaching and Learning Strategies

This course will employ a variety of active learning strategies to enhance your understanding:

• Modified Lectures: Engaging video lectures will break down complex concepts into manageable parts.
• Inductive and Deductive Approaches: We will use both theoretical explanations and practical examples to reinforce learning.
• Heuristic Methods: Problem-solving exercises will encourage you to explore and discover solutions on your own.
• Assignments and Quizzes:Regular assignments, tests and quizzes will help you practice and assess your understanding of the material.

Assessment and Grading

Your performance in this course will be evaluated through:

• Assignments (20%): Regular problem sets to reinforce your learning.
• Tests (30%):  successive tests and quizes to assess your progress.
• Final Examination (50%): A comprehensive exam at the end of the semester.

Course Policies

• Attendance: You are expected to attend at least 85% of the course.
• Continuous Assessment: Participation in all assignments and tests is mandatory.
• Final Examination: You must take the final exam to complete the course.
• University Regulations: Please adhere to all rules and regulations set by the university.

References:

1. Lang, S; Linear Algebra

2. Gemeda,D., An Introduction to Linear Algebra, Department of Mathematics, AAu, 2000

3. Lay,D. C., Linear algebra and its applications, Pearson Addison Wesley, 2006

4. Kolman, B. and Hill, D.R., Elementary linear algebra, 8th ed., Prentice Hall, 2004

5. H. Anton, H. and Rorres,C., Elementary linear algebra, John Wiley & Sons, INC.,1994

6. Hoffman, K. & Kunze,R., Linear Algebra, 2nd ed., Prentice Hall INC.1971

7. Lipschutz,S., Theory and problems of linear algebra, 2nd ed. Mc Graw-Hill, 1991

8. Introduction to Linear Algebra by Gilbert Strang, Wellesley Cambridge Press; 4th Edition.