Linear Algebra : 2HS102

Learning Outcomes: 
Upon completion of this course, students will be able to:
• Understand all basic fundamentals of Matrices and Vectors.
• Prepare him / herself for solving a Linear equation.
• Prepare him/herself for Learning Advance Mathematics in coming semester.
• Apply knowledge of matrices and vectors in various applications of his/her branch.
Syllabus: 
Unit NoTopics
1

Matrix Algebra:

Review of algebra of matrices & elementary transformations, Rank of a matrix, inverse of a matrix by Gauss-Jordan method, normal form of a matrix, Solution of system of algebraic simultaneous equations, Linear dependent and Linear independent vectors. Eigen values and Eigen vectors, Eigen values and Eigen vectors of: Symmetric, Skewsymmetric, Hermitian, Skewhermitian, Unitary and Normal matrix, Algebraic and Geometric multiplicity, Diagonalization, Spectral theorem for real symmetric matrices, Application of Quadratic forms.

2

Vector Space :

Vectors in Rn and its properties, Dot product, Norm and Distance properties in Rn, Pythagorean theorem in Rn ,Definition and Examples of vector spaces, Vectorsubspace, Linear Independence and dependence ,Linear span of set of vectors, Basis of subspaces, Extension to basis.  

3

Linear Transformation :

Definition and basic properties, Types of linear transformation(Rotation,reflection,expansion,contraction,shear,projection),Matrix of linear transformations,Change of basis and similarity, Rank nullity theorem

4

Infinite Series :

Definition, Comparison test, Cauchy’s integral test, ratio test, root test, Leibniz’s rule for alternating series, power series, range of convergence, uniform convergence.

Text Books: 
Name : 
Higher Engineering Mathematics
Author: 
by Dr. B. S. Grewal
Name : 
Vector Calculus and Linear Algebra
Author: 
Dr. A.R.Patel
Dr.H.C.Patel
Reference Books: 
Name: 
Higher Engineering Mathematics Vol. I & II
Author: 
Dr. K. R. Kachot.
Name: 
Advanced Engineering Mathematics
Author: 
Erwin Kreyszig.
Edition: 
5TH
Name: 
Applied mathematics for engineering
Author: 
by Dr. R. C. Shah.
Syllabus PDF: 
AttachmentSize
PDF icon Linear Algebra.pdf173.62 KB
branch: 
CBA
BDA
MA
Cyber Security
Course: 
2018
Stream: 
B.Tech