English | 2021 | ASIN: B093DDVP1D | 528 pages | PDF | 7.52 MB
Note: Five questions are to be attempted selecting at least one from section (B).
(A) Linear Algebra (Eight questions)
Vector spaces-vector space, Sub spaces, Linear combinations, Linear spans, Sums and direct sums, linear dependence, Bases and dimensions, Dimensions and subspaces, coordinates and change of bases. Linear transformations-Linear transformations, rank and nullity, Operations with linear transformations, Linear Operators, algebra of linear operators, Invertible linear operators, Matrix of linear transformation, Matrices and linear transformation, Matrix of a linear operator, Change of basis, similarity.
Linear functionals-linear functional, Dual space and dual basis, Double dual space, Annihilators, Transpose of linear transformation. Bilinear, Quadratic and Hermitian forms -bilinear forms, Quadratic forms.
(B) Linear Programming (Two questions)
Linear programming Graphical method, Simplex method, The dual of linear programming problem.