Unit 3 : Linear Algebra

Vector spaces, subspaces, algebra of subspaces, quotient spaces, linear combination of vectors, linear span, linear independence, basis and dimension, existence; extension and replacement theorems for basis of a finite dimensional vector space.

Unit 4

Linear transformations, null space, range space, rank and nullity of a linear transformation, matrix representation of a linear transformation relative to ordered bases, algebra of linear transformations, correspondence between LTs and matrices. Linear transformation is non-singular if its representation matrix is non-singular. Invertibility and isomorphisms, isomorphism theorems, change of coordinate matrix.