Hermitian, Skew-Hermitian, Orthogonal and Unitary matrices. Elementary operation on matrices. Inverse of a matrix using Gauss Jordan Method. Linear independence of row and column vectors, Row rank, Column rank and their equivalence. Eigen values, Eigen vectors and the characteristic equation of a matrix, Properties of eigen values for special type of matrices, Diagonalization, Cayley-Hamilton theorem. Consistency of a system of linear equations.
Relations between roots and coefficients of a general polynomial, Transformation of equation. Descartes’ rule of signs, Solution of cubic equations, Biquadratic equations and their solution. De Moivre’s theorem and its application, Direct and inverse circular functions, hyperbolic and logarithmic functions. Summation of Series.