SYLLABUS- LINEAR ALGEBRA, Unit-1: Vector spaces and their elementary properties, Subspaces, Linear dependence and independence, Basis and dimension, Direct sum, Quotient space. Unit-2: Linear transformations and their algebra, Range and null space, Rank and nullity, Matrix representation of linear transformations, Change of basis. Unit-3: Linear functionals, Dual space, Bi-dual space, Natural isomorphism, Annihil- ators, Bilinear and quadratic forms, Inner product spaces, Cauchy-Schwarz's inequality, Bessel's inequality and orthogonality