2HS201 Linear Algebra

Learning Outcomes: 
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, Vector subspace, 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: 
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: 
Dr. R. C. Shah
Syllabus PDF: 
AttachmentSize
PDF icon Linear Algebra.pdf186.07 KB
branch: 
CBA
BDA
MA
Course: 
2016
Stream: 
B.Tech