Prerequisite

Calculus -I

Description and Objective

Linear algebra is the study of 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 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

1. Identify and construct linear transformations of a matrix. 
2. Characterize linear transformations as onto, one-to-one.s
3. Solve linear systems represented as linear transforms and express linear transforms in other forms, such as matrix equations, and vector equations.
4. Characterize a set of vectors and linear systems using the concept of linear independence.

Contents 

1. Representation of linear equations in matrix form
2. Matrices, operations on matrices
3. Solution of linear system, Gauss-Jordan and Gaussian elimination method
4. Permutations and determinants and their computation
5. Definition of Vector space with examples and properties
6. Subspaces, Linear combination and spanning set, Linearly Independent sets
7. Finitely generated vector spaces
8. Bases and dimension of a vector space
9. Intersections, sums and direct sums of subspaces
10. Quotient Spaces, linear mappings, Kernel and image of a linear mapping
11. Rank and nullity, Reflections, projections and homotheties
12. Change of basis, eigen-values and eigenvectors
13. Theorem of Hamilton-Cayley
14. Inner product Spaces with properties, Projection
15. Cauchy inequality, Orthogonal and orthonormal basis
16. Gram Schmidt process and diagonalization.

Recommended Books

1. Anton H., Rorres C., Elementary Linear Algebra: Applications Version, 10th Edition, (John Wiley and sons, 2010.)
2. Herstein I.N. Topics in Algebra, (Xerox Publishing Company, 1975.)

​Suggested Books

1. Curtis C. W. Linear Algebra, (Springer 2004.)
2. Apostol T. Multi Variable Calculus and Linear Algebra, 2nd ed., (John Wiley and sons, 1997.)
3. Grossman S. I. Elementary Linear Algebra, 5th Edition, (Cengage Learning, 2004.)Hussain K.Linear Algebra, 1st edition, (2007).
4. Kolman B., Hill D. R., Introductory Linear Algebra, 7th edition (Pearson Prentice Hall)
5. Malik D.S.Mordeson J.N. Sen M.R. Fundamental of Abstract Algebra, (McGraw Hill companies, Inc. 1987.)

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                                                    09:30 AM-11:00 AM (Reg)                      02:00 PM-03:30 PM (SS)

Tuesday                                                   09:30 AM-11:00 AM (Reg)                      02:00 PM-03:30 PM (SS)

Commencement of Classes                                                   January 13, 2020

Mid Term Examination                                                            March 09-13, 2020

Final Term Examination                                                          May 04-08, 2020

Declaration of Result                                                              May 19, 2020