**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:**

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

**Course Outline:**

- System of Linear Equations and Matrices
- Introduction to system of linear equations
- Matrix form of system of Linear Equations
- Gaussian Elimination method
- Gauss-Jorden Method
- Consistent and inconsistent systems
- Homogeneous system of equations Vector Equations
- Introduction to vector in plane
- Vector in RPn
- Vector form of straight line
- Linear Combinations
- Geometrical interpretation of solution of Homogeneous and Non-homogeneous equations
- Applications of Linear Systems
- Traffic Flow Problem
- Electric circuit Problem
- Economic Model Linear transformations
- Introduction to linear transformations
- Matrix transformations
- Domain and range of linear transformations
- Geometric interpretation of linear transformations
- Matrix of linear transformations Inverse of a matrix
- Definition of inverse of a matrix
- Algorithm to find the inverse of matrices
- LU factorization Determinants
- Introduction to determinants
- Geometric meaning of determinants
- Properties of determinants
- Crammer Rule
- Cofactor method for finding the inverse of a matrix Vector Spaces
- Definition of vector spaces
- Subspaces
- Spanning set
- Null Spaces and column spaces of linear transformation
- Linearly Independent sets and basis
- Bases for Null space and Kernal space
- Dimension of a vector space Eigen Values and Eigen vectors
- Introduction to Eigen value and Eigen vectors
- Computing the Eigen values
- Properties of Eigen values
- Diagonalization
- Applications of Eigen values

**Recommended Books: **

- Linear Algebra and its applications by David C. Lay. 4th Edition, Addison Wesley, ISBN 978 0 321 38517 8
- 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