### Linear Algebra (MATH-122)

Description and Objective:

Linear algebra is the study of matrices, vector spaces and linear transformations. The main objective of this course is to help students learn in rigorous manner, the tools and methods essential for studying the solution spaces of problems in engineering and develop mathematical skills needed to apply these to the problems arising within their field of study; and to various real-world problems.

Pre requisite:

None

Learning Outcomes:

1. Interpret the vector equations and linear transformations.
2. Illustrate how to solve a system of linear equations that appears in different engineering applications.
3. Apply the basic knowledge of vector spaces, eigen value and eigen vectors.
4. Implement key concepts developed in the course using a mathematical simulation software.

Course Outline:

1. System of Linear Equations and Matrices
2. Introduction to system of linear equations
3. Matrix form of system of Linear Equations
4. Gaussian Elimination method
5. Gauss-Jorden Method
6. Consistent and inconsistent systems
7. Homogeneous system of equations Vector Equations
8. Introduction to vector in plane
9. Vector in RPn
10. Vector form of straight line
11. Linear Combinations
12. Geometrical interpretation of solution of Homogeneous and Non-homogeneous equations
13. Applications of Linear Systems
14. Traffic Flow Problem
15. Electric circuit Problem
16. Economic Model Linear transformations
17. Introduction to linear transformations
18. Matrix transformations
19. Domain and range of linear transformations
20. Geometric interpretation of linear transformations
21. Matrix of linear transformations Inverse of a matrix
22. Definition of inverse of a matrix
23. Algorithm to find the inverse of matrices
24. LU factorization Determinants
25. Introduction to determinants
26. Geometric meaning of determinants
27. Properties of determinants
28. Crammer Rule
29. Cofactor method for finding the inverse of a matrix Vector Spaces
30. Definition of vector spaces
31. Subspaces
32. Spanning set
33. Null Spaces and column spaces of linear transformation
34. Linearly Independent sets and basis
35. Bases for Null space and Kernal space
36. Dimension of a vector space Eigen Values and Eigen vectors
37. Introduction to Eigen value and Eigen vectors
38. Computing the Eigen values
39. Properties of Eigen values
40. Diagonalization
41. Applications of Eigen values

Recommended Books:

1. Linear Algebra and its applications by David C. Lay. 4th Edition, Addison Wesley, ISBN 978 0 321 38517 8
2. Linear Algebra and its Applications by Gilbert Strang, 4th Edition, ISBN978-0030105678

Assessment Criteria:

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50

Key Dates and Time of Class Meeting:

Monday                                                    08:00 AM-09:30 AM

Thursday                                                 12:30 PM-02:00 PM

Commencement of Classes                                                   March 02, 2020

Mid Term Examination                                                            April 27 to May 04, 2020

Final Term Examination                                                          June 22-26, 2020

Declaration of Result                                                              July 03, 2020