### Description and Aim

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

### Learning Outcomes

After the completion of the course, students will be able to identify and construct linear transformations of a matrix, characterize linear transformations as onto, one-to-one, can solve linear systems represented as linear transforms, can express linear transforms in other forms, such as matrix equations, and vector equations and characterize a set of vectors and linear systems using the concept of linear independence.

Course Outline:

1. System of Linear Equations and Matrices
2. Introduction to system of linear equations ,Matrix form of system of Linear Equations
3. Gaussian Elimination method, Gauss-Jorden Method
4. Consistent and inconsistent systems
5. Homogeneous system of equations Vector Equations
6. Introduction to vector in plane
7. Vector form of straight line
8. Linear Combinations
9. Geometrical interpretation of solution of Homogeneous and Non-homogeneous equations
10. Applications of Linear Systems
11. Applications: Matrices in Engineering, Graphs and Networks, Markov Matrices, Population, and Economics; Linear Programming, Fourier series: Linear Algebra for Functions, Linear Algebra for Statistics and Probability, Computer Graphics.
12. Economic Model Linear transformations
13. Introduction to linear transformations
14. Matrix transformations
15. Domain and range of linear transformations
16. Geometric interpretation of linear transformations
17. Matrix of linear transformations Inverse of a matrix
18. Definition of inverse of a matrix
19. Algorithm to find the inverse of matrices
20. LU factorization Determinants
21. Introduction to determinants, Geometric meaning of determinants
22. Properties of determinants, Crammer Rule
23. Cofactor method for finding the inverse of a matrix Vector Spaces
24. Definition of vector spaces, Subspaces
25. Spanning set
26. Null Spaces and column spaces of linear transformation
27. Linearly Independent sets and basis
28. Bases for Null space and Kernal space
29. Dimension of a vector space Eigen Values and Eigen vectors
30. Introduction to Eigen value and Eigen vectors
31. Computing the Eigen values, Properties of Eigen values
32. Diagonalization, Applications of Eigen values

Suggested Books

1. Linear Algebra by David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron.
2.  Linear Algebra and Its Applications by David C Lay and Steven R Lay.
3. Schaum’s Outline of Theory and Problem of Linear Algebra. Seymour Lipschutz. Mc-Graw Hill.

### 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-9:30 AM (Reg)                        12:30 PM-02:00 PM (SS)

Friday                                                      08:00 AM-9:30 AM (Reg)                         3:30 PM-05:00 PM (SS)

Commencement of Classes                                                   February 22, 2020

Mid Term Examination                                                            April 19 to May 23, 2020

Final Term Examination                                                          June 15-22, 2020

Declaration of Result                                                              July 03, 2020