  # 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:
Author:
Erwin Kreyszig
Edition:
5th
Name:
Applied mathematics for engineering
Author:
Dr. R. C. Shah
Syllabus PDF:
AttachmentSize Linear Algebra.pdf186.07 KB
branch:
CBA
BDA
MA
Course:
2016
Stream:
B.Tech