Coordinate Geometry: Change of axes; Direction Cosines and projections; Pair of Straight line & 2 Degree General Equation; Shortest Distance; Coordinates of a point in space in different systems; Plane; Quadratics.
Linear Algebra: Determinants: Evaluation, Cramer’s Rule. Matrix: operations, different types, Echelon form – elementary row operations, Rank. Linear equation: systems, solution, Gaussian elimination. Vector space: vectors, linear dependency, bases, Euclidian space, inner product, and inner product space, Gram-Schmidt Orthogonalization. Linear transformations: basic concepts, linear operators. Eigenvalue and Eigenvectors: diagonalization, Cayley-Hamilton theorem; Quadratic forms and Hermitian forms.
Matrices: Matrix Operations, The Inverse of a Matrix, Characterizations of Invertible Matrices, Linear Subspaces, Dimension and Rank