SEMESTER – IV, PAPER – V
CBCS/ SEMESTER SYSTEM (w.e.f. 2020-21 Admitted Batch)
B.A./B.Sc. MATHEMATICS
LINEAR ALGEBRA SYLLABUS (75 Hours)
Course Outcomes:
After successful completion of this course, the student will be able to;
- understand the concepts of vector spaces, subspaces, basis, dimension and their properties
- understand the concepts of linear transformations and their properties
- apply Cayley- Hamilton theorem to problems for finding the inverse of a matrix and higher powers of matrices without using routine methods
- learn the properties of inner product spaces and determine orthogonality in inner product
Course Syllabus:
UNIT – I (12 Hours)
Vector Spaces-I:
Vector Spaces, General properties of vector spaces, n-dimensional Vectors, addition and scalar multiplication of Vectors, internal and external composition, Null space, Vector subspaces, Algebra of subspaces, Linear Sum of two subspaces, linear combination of Vectors, Linear span Linear independence and Linear dependence of Vectors.
UNIT –II (12 Hours)
Vector Spaces-II:
Basis of Vector space, Finite dimensional Vector spaces, basis extension, co-ordinates, Dimension of a Vector space.
UNIT –III (12 Hours)
Linear Transformations:
Linear transformations, linear operators, Properties of L.T, sum and product of LTs, Algebra of Linear Operators, Range and null space of linear transformation, Rank and Nullity of linear transformations – Rank – Nullity Theorem.
UNIT –IV (12 Hours)
Matrix:
Matrices, Elementary Properties of Matrices, Rank of Matrix, Linear Equations, Characteristic equations, Characteristic Values & Vectors of square matrix, Cayley – Hamilton Theorem(only problems).
UNIT –V (12 Hours)
Inner product space:
Inner product spaces, Euclidean and unitary spaces, Norm or length of a Vector, Schwartz inequality, Triangle Inequality, Parallelogram law.
Co-Curricular Activities(15 Hours)
Seminar/ Quiz/ Assignments/ Linear algebra and its applications / Problem Solving.
Reference Books :
- Linear Algebra by J.N. Sharma and A.R. Vasista, published by Krishna Prakashan Mandir, Meerut-250002.
- Linear Algebra by Kenneth Hoffman and Ray Kunze, published by Pearson Education (low priced edition), New
- Linear Algebra by Stephen H. Friedberg et al published by Prentice Hall of India Pvt. Ltd. 4th Edition