Linear Algebra

GANPAT UNIVERSITY

FACULTY OF ENGINEERING & TECHNOLOGY

Programme

Bachelor of Technology

Branch/Spec.

Computer  Science & Engineering (CSE/CBA/CS/BDA)

Semester

II

Version

1.0.0.1

Effective from Academic Year

2022-23

Effective for the batch Admitted in

June 2022

Subject  code

2HS102

Subject Name

Linear Algebra                                                                  

Teaching scheme

Examination scheme (Marks)

(Per week)

Lecture(DT)

Practical(Lab.)

Total

CE

SEE

Total

L

TU

P

TW

Credit

3

1

0

0

4

Theory

40

60

100

Hours

3

1

0

0

4

Practical

0

0

0

Pre-requisites:

Matrices, Basic Arithmetic operations for Matrices

Learning Outcome:

Upon completion of this course, students will be able to:

• Understand all basic fundamentals of Matrices and Vectors.
• Prepare and extrapolate him/herself to analyse, interpret, construct, and solve a Linear equation.
• Apply the Linear algebra  mathematical techniques to various computation problems.
• Apply knowledge of matrices and vectors in various applications of respective field

Theory syllabus

Unit

Content

Hrs

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

22

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. 

5

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

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.

14

Practical content

Not Applicable

Mooc  Course

Course Name: Introduction to Abstract and Linear Algebra

Link: https://onlinecourses.nptel.ac.in/noc22_ma04

Text Books

1

Higher Engineering Mathematics by Dr. B. S. Grewal

2

Vector Calculus and Linear Algebra by Dr. A.R.Patel & Dr.H.C.Patel

Reference Books

1

Higher Engineering Mathematics Vol. I & II by Dr. K. R. Kachot.

2

Advanced Engineering Mathematics (Fifth Edition), Erwin Kreyszig.

3

Applied mathematics for engineering by Dr. R. C. Shah.

Course Outcomes:

COs

Description

CO1

Understand all basic fundamentals of Matrices and Vectors.

CO2

Prepare and extrapolate him/herself to analyse, interpret, construct, and solve a Linear equation.

CO3

Apply the Linear algebra  mathematical techniques to various computation problems.

CO4

Apply knowledge of matrices and vectors in various applications of respective field

Mapping of CO and PO