UPSC/IAS/CSE-Civil Services Maths/Mathematics Optional Syllabus Paper-1 2022-2023 Section-A (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’s and similarity; Rank of a https://juliusfdvgp.vidublog.com/21428698/helping-the-others-realize-the-advantages-of-upsc-maths-optional-syllabus-2020-pdf