### 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 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.

### Contents

1. Vector space, definition, examples and properties
2. Subspaces
3. Linear combination and Linear Span of a set,
4. Linearly Dependent and Linearly Independent sets
5. Basiss of a vector space
6. dimension of a vector space
7. Intersections, sums and direct sums of subspaces
8. Quotient Spaces,
9. Change of basis, Linear transformation
10. Rank and Nullity of linear transformation
11. Eigen values and eigen vectors
12. Dual spaces
13. Inner product Spaces with properties, Projection
14. Cauchy inequality, Orthogonal and orthonormal basis
15. Gram Schmidt process and diagonalization.

### Recommended Books

1. Dar K. H, Linear Algebra, (1st edition, 2007).

2. Kolman B., Hill D. R., Introductory Linear Algebra, (Pearson/Prentice Hall 8th edition, 2005)

### Suggested Books

1. Cherney D., Denton T., Thomas R. and Waldron A. Linear Algebra, (Davis California, 1st edition 2013)

2. Anton H., Rorres C., Elementary Linear Algebra: Applications Version, (John Wiley & Sons, 11th edition 2014.)

3. Grossman S. I. Elementary Linear Algebra, (Cengage Learning, 5th edition, 2004.)

### 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)

Tuesday                                                   09:30 AM-11:00 AM (Reg)                      12:30 PM-02:00 PM (SS)

Wednesday                                              02:00 PM-03:30 PM (SS)

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