Mathematics II Syllabus

System of linear equations, Row reduction and Echelon forms, Vector equations, The matrix

equations Ax = b, Applications of linear system, Linear independence

Introduction to linear transformations, the matrix of a linear Transformation, Linear models in

business, science, and engineering

Matrix operations, The inverse of a matrix, Characterizations of invertible matrices, Partitioned

matrices, Matrix factorization, The Leontief input output model, Subspace of Rn, Dimension and

rank

Introduction, Properties, Cramer’s rule, Volume and linear transformations

Vector spaces and subspaces, Null spaces, Column spaces, and Linear transformations, Linearly

independent sets: Bases, Coordinate systems

Dimension of vector space and Rank, Change of basis, Applications to difference equations,

Applications to Markov Chains

Eigenvectors and Eigenvalues, The characteristic equations, Diagonalization, Eigenvectors and

linear transformations, Complex eigenvalues, Discrete dynamical systems, Applications to

differential equations

Inner product, Length, and orthoganility, Orthogonal sets, Orthogonal projections, The Gram-

Schmidt process, Least squares problems, Application to linear models, Inner product spaces,

Applications of inner product spaces

Binary Operations, Groups, Subgroups, Cyclic Groups

Rings and Fields, Integral domains