# MATH 1331 Linear Algebra with Applications

First semester, 2017-2018

Module summary

The module covers a variety of topics in linear algebra and discrete mathematics, with an emphasis on their application to financial problems.

Objectives

On completion of this module students should be able to:

(a) use Gaussian elimination to solve systems of linear equations;
(b) work with the basic concepts of linear algebra: linear independence, bases, dimension, linear independence;
(c) compute the product of matrices;
(d) compute the inverse of a specified invertible matrix; calculate the determinant of a square matrix, with numerical and algebraic entries;
(e) compute the eigenvalues and eigenvectors of a specified matrix; determine whether a specified matrix can be diagonalized;
(f) model and solve problems in linear programming;
(g) use stochastic matrices to determine the limiting behaviour of simple Markov processes.

Syllabus

- Linear equations: manipulation of inequalities, matrices, Gaussian elimination, linear independence, bases, dimension, linear transformations, matrix algebra, inverse matrices, determinants, eigenvalues and eigenvectors, diagonalisation.
- Linear programming: feasible sets, slack resources, the simplex method, marginal analysis.
- Theory of games: games and strategies, mixed strategies, determining optimal mixed strategies.
- Markov processes: transition matrices, stochastic matrices, regular and absorbing stochastic matrices, convergence to stable states.

Recommended book

L. Goldstein, D. Schneider and M. Siegel, Finite Mathematics and its Applications, Prentice Hall, 1998.

Last updated 1st September 2017