 COURSE SUMMARY
Course Title:
Basic Linear Algebra
Course Code:
19MAT104
Year Taught:
2019
Semester:
1
Degree:
School:
School of Engineering
Campus:
Bengaluru
Chennai
Coimbatore
Amritapuri

'Basic Linear Algebra' is a course offered in the first and second semester of  B. Tech. programs at the School of Engineering, Amrita Vishwa Vidyapeetham.

### Objectives

The course is expected to enable the students

• To solve simultaneous algebraic equations using methods of matrix algebra.
• To understand basics of matrix algebra and determinan
• To use vector space methods and diagonalization in practical problems.

Keywords: Euclidean Vector Space, System of Equations, General Vector Spaces, Linear Transformation, Diagonalization.

### Course Outcomes

At the end of the course the student will be able to

CO1: Apply concepts of matrix algebra for solving simultaneous linear algebraic equations.

CO2: Understand the power of mathematical abstraction through introduction and application of concepts like vector spaces, inner product spaces and linear transformations.

CO/PO Mapping

 CO/P O PO 1 PO 2 PO 3 PO 4 PO 5 PO 6 PO 7 PO 8 PO 9 PO1 0 PO1 1 PO1 2 PSO 1 PSO 2 PSO 3 CO1 2 2 2 1 1 1 2 CO2 3 2 1 1 2 2 1

#### SYLLABUS

Vectors in Rn, notion of linear independence and dependence, linear span of a set of vectors, vector subspaces of Rn, basis of a vector subspace.

Linear system of equations, Gauss elimination, Linear independence, Rank of a matrix, row space and column space, existence and uniqueness of system of linear equations, Determinants, Cramer’s’ rule, Inverse of a matrix, Gauss-Jordan elimination.

Vector spaces, subspaces, linear independence, basis, dimension, change of basis, row, column and null spaces, linear transformation, eigen values and eigen vectors, diagonalization, inner product spaces, Gram-Schmidt orthogonalisation.

#### TEXT BOOKS / REFERENCES

Text Book

1. Elementary Linear Algebra, Howard Anton and Chris Rorres, 11th Edition, Wiley, 2015.
2. Linear algebra: A modern introduction, D Poo Cengage Learning,4thEdition 2015.
3. Engineering Mathematics, Srimanta Pal and Subodh C Bhunia, , John Wiley and Sons, 2012, Ninth Edition.