ABSTRACT
Linear algebra is typically introduced in an introductory engineering mathematics course in the context of solving a set of n linear equations in n unknowns. This chapter briefly reviews some results in the solution of a system of linear equations. It is common to linearize a nonlinear system using Taylor's series expansion; the properties of the linearized system give a good qualitative picture of the behavior of the original nonlinear system. Nonlinear equations and optimization problems may be solved by successively linearizing the system. Linear algebra is also useful for parameter estimation using least squares approach. Eigenvalues and eigenvectors were introduced to solve linear ordinary differential equations (ODEs). The eigenvalue decomposition is the cornerstone of the analysis of linear dynamical systems. In chemical engineering, difference equations are often used in computer-based process control and logistic maps.
