Linear Algebra ( MA15001 )
F.Y.B. Tech. Semester I (All Branches) 2019-20
Teaching Scheme : Lectures : 2hrs/week + Tutorial : 1 hr / week
Examination Scheme : Continuous evaluation: 40 (20+20) marks, End Sem. Exam : 60 marks
Text book: 1. (Tb1) - Introduction to Linear Algebra (2nd edition) by Serge Lang, Springer.
Unit 1: Matrices and Linear Equations, Vector spaces
Lesson Topic Section nos. and books to
no. be referred
1 Matrices and linear equations: basic properties of Tb1, Chapter II, section1,
matrices section 2
2 Homogeneous linear equations and elimination, Tb1, Chapter II, section 3
Theorem 3.1
3 Row operations and Gauss elimination, Theorem 4.1, Tb1, Chapter II, section 4
Theorem 4.2 , examples
4 Basic concepts in linear algebra: vector spaces, Tb1, Chapter III, section 1
definitions, subspaces
5 Linear Combinations, linear dependence/ independence Tb1, Chapter III, section 2,
of vectors section 4
6 Basis and Dimension Tb1, Chapter III , section 5
7 Row and Column spaces, Rank of the matrix Tb1, Chapter III, section 6
8 * Basic properties of determinants, Theorem 1.1, Tb1, Chapter VII, section
determinants of order n, Theorem 2.1 (SELF STUDY) 1, section 2
9 Theorem 2.2, rank of the matrix and sub-determinants, Tb1, Chapter VII, section 3
Theorem 3.1, corollary 3.2 and examples
10 * Applications to system of linear equations (SELF ( Notes will be provided.)
STUDY)
Unit II: Mappings, Rank, Eigen values and Eigen vectors
Lesson Topic Section no. of text book
no.
1 Mappings: Definition and examples Tb1, Chapter IV, section 1
2 Linear mappings: Examples and properties Tb1, Chapter IV, section 2
3 Co-ordinates of a linear map, Proposition (2.1), The Tb1, Chapter IV, section 2
vector space of linear maps
4 Kernel and images of a linear map, Theorem 3.1 and 3.2 Tb1, Chapter IV, section 3
5 The rank and linear equations, Theorems: 4.1, 4.2, 4.3, Tb1, Chapter IV, section 4
4.4
6 Matrix associated with a linear map, change of bases, Tb1, Chapter IV, section5.
Eigen values and Eigen vectors Chapter VIII, section 1
7 Eigen values, Eigenvectors and their basic properties, Tb1, Chapter VIII, section
The characteristic polynomial, Theorems: 2.1, 2.2 1, section 2
8 Eigen values and eigenvectors of symmetric matrices, Tb1, Chapter VIII, $3
Theorems: 3.1, 3.2, Corollary 3.3, Theorem 3.4
Unit III : Inner product spaces, canonical forms. quadratic forms
Lesson Topic Section no. of text book
no.
1 Scalar products, Theorem 1.1 & 1.2 Tb1, Chapter VI, section 1
2 Theorem 1.3 & 1.4, Orthogonal bases Tb1, Chapter VI, section 1,
section 2
3 Gram-Schmidth process: Theorem 2.1, corollary 2.2 Tb1, Chapter VI, section 2
4 Theorem 2.3 Tb1, Chapter VI, section 2
5 Diagonalization of symmetric linear map and Theorem Tb1, Chapter VIII, section
4.1 and examples 4
6 *Geometric applications of linear transformations ( Notes will be provided.)
(SELF STUDY)
7, 8 Quadratic forms: Positive definiteness Rb1, page no. 348-358
Topics marked with * are self study topics. Questions based on these topics will be
asked in exams.
Reference Books :
(Rb1) - Linear Algebra and its Applications (4th edition) by Gilbert Strang, Cengage
Learning (2006) .
Linear Algebra A geometric approach by S. Kumaresan, Prentice hall of India, New Delhi.
Linear Algebra (3rd edition) by Serge Lang, Springer.
Elementary Linear Algebra (10th edition) by Howard Anton and Chris Rorres, John Wiley
and sons.
Schaum’s outlines of Linear Algebra (5th edition) by Seymour Lipchitz, Marc Lipson,
McGraw-Hill Education (India) Private Limited, New Delhi.
Linear Algebra by Hoffman and Kunze, (2nd edition) Prentice Hall Publication, New
Delhi.
Advanced Engineering Mathematics (10th edition) by Erwin Kreyszig, Wiley eastern Ltd.
Advanced Engineering Mathematics by Chandrika Prasad and Reena Garg, Khanna
Publishing Company Private Limited, New Delhi.
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Important Note :
• Two tests T1 and T2 (Each of 20 marks) and end semester examination will be conducted as
follows.
Exam Day and Date Syllabus
T1 To be announced later Unit 1
T2 To be announced later Unit 2
End Semester Exam To be announced later All Units
• 100% attendance is compulsory.
