Syllabus Fee Structure Demo Classes     UPSC Maths Optional Syllabus For Paper I PAPER – I (1) Linear Algebra:  Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; linear transformations, rank and nullity, matrix of a linear transformation. Algebra of Matrices; row and column reduction, echelon form, congruence and similarity; […]

Home Question Details Exam UPSC Paper Optional Paper  Subject Mathematics 1  Year 2022 More Details Previous Question Next Question Section: A Question:01(a) Prove that any set of (mathrm{n}) linearly independent vectors in a vector space (mathrm{V}) of dimension (mathrm{n}) constitutes a basis for (mathrm{V}). Question:01(b) Let (mathrm{T}: mathbb{R}^2 rightarrow mathbb{R}^3) be a linear transformation such

Home Question Details Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 8 Question Type Exercise More Details Previous Question Next Question Question: Show that the relation (mathrm{R}) in the set (mathrm{A}={1,2,3,4,5}) given by (mathrm{R}={(a, b):|a-b|) is even (}), is an equivalence relation. Show that all

Home Question Details Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 6 Question Type Exercise More Details Previous Question Next Question Show that the relation (R) in the set ({1,2,3}) given by (R={(1,2),(2,1)}) is symmetric but neither reflexive nor transitive. Expert Answer Solution:  [A={1,2,3,}: R={(1,2),(2,1)}](a)

Home Question Details Board CBSE Book NCERT Textbook Class 12 Subject Mathematics Chapter 1 [Relations and Functions] Exercise 1.1 Question No. 7 Question Type Exercise More Details Previous Question Next Question Show that the relation R in the set A of all the books in a library of a college, given by (mathrm{R}={(x, y): x)