Math-I (Linear Algebra)

Course Code: MM 103 | Credits: 3 | Prerequisite: Nil

Unit I:(Matrices) Basic concepts of matrices, multiplication by scalars, addition and multiplication of matrices, transpose, trace and determinant, rank and inverse, and special matrices such as Hermitian and unitary matrices.
Unit II:(Linear Systems and Eigenvalues) Systems of linear equations and their solution by Cramer’s rule; row reduced echelon matrices, existence and general properties of solutions; eigenvalues, eigenvectors, diagonalisation of matrices, functions of matrices and the Cayley-Hamilton theorem.
Unit III:(Complex Numbers and Vectors) Algebra of complex numbers, polar form, the Argand diagram and the triangle inequality; addition of vectors, the dot and cross products and their geometric interpretation, the triple product, and area and volume in terms of vector products.
Unit IV:(Plane Geometry) Coordinate systems, the distance and section formulae, area of a triangle, straight lines, the angle between two lines, concurrent lines, the distance between two lines, and conic sections.
Unit V:(Solid Geometry) Cartesian coordinates in three dimensions, distance between points, direction cosines and ratios and their properties, the equation of a plane from given data, equations of a straight line in various forms, the image of a point in a plane, the distance from a point to a plane along a line, and the equations of a circle and a sphere.

Hoffman, Kenneth and Kunze, Ray. Linear Algebra. Pearson, 1971
Kumaresan, S. Linear Algebra: A Geometric Approach. Prentice Hall of India, 2004
Thomas, George and Finney, Ross. Calculus and Analytic Geometry. Addison-Wesley, 1965