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.
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.
- 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 form of straight line
- Linear Combinations
- Geometrical interpretation of solution of Homogeneous and Non-homogeneous equations
- Applications of Linear Systems
- 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.
- 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
- Linear Algebra by David Cherney, Tom Denton, Rohit Thomas and Andrew Waldron.
- Linear Algebra and Its Applications by David C Lay and Steven R Lay.
- Schaum’s Outline of Theory and Problem of Linear Algebra. Seymour Lipschutz. Mc-Graw Hill.
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