Linear algebra is the study of linear systems of equations, vector spaces, and linear transformations. Solving systems of linear equations is a basic tool of many mathematical procedures used for solving problems in science and engineering.

**Prerequisite **

To succeed in this course you will need to be comfortable with vectors, matrices, and three-dimensional coordinate systems.

**Learning Outcomes**

At the end of this course the student will be able to:

- Solve linear systems of equations
- Comprehend vector spaces, subspaces and inner product spaces
- Understand fundamental properties of matrices including determinants, inverse matrices, matrix factorizations, eigenvalues, orthogonality and diagonalization
- Have an insight into the applicability of linear algebra
- Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra.

**Contents**

- Matrices: Addition, Multiplication, Transpose.
- Matrices and Systems of Linear Equations.
- Block Matrices. Polynomial in Matrices.
- Invertible Matrices, Complex Matrices.
- Elementary Matrices and Applications.
- Quadratic Forms, Simlarity.
- Vector Spaces, Subspaces.
- Linear Combination, Linear Spans.
- Basis and Dimension.
- Change of Basis.
- Orthogonality.
- Inner Product Spaces, Cauchy-Schwarz Inequality.
- Applications, Porjections, Inner Products and Matrices.
- Normed Vector Spaces.

**Recommended Books**

- . Schaum’s Outline of Theory and Problem of Linear Algebra. Seymour Lipschutz. Mc-Graw Hill.
- Mathematical Methods for Physicists by George Arfken and Hans J. Weber, (6th and onwards editions) Acad Press.
- Advanced Engineering Mathematics, Erwin Kreyszig, (2007).
- Mathematical Physics by E. Butkov, Addison-Wesley London.

**Suggested Books**

- Elementary Linear Algebra and its Applications by Howard Anton and Chris Rorres, 11th Edition.
- David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron
- Linear Algebra and Its Applications by David C Lay and Steven R Lay.

**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*

Wednesday-Thursday 1:00pm-2:00pm

Firday 2:00pm-3:00pm

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