Introduction to Matrices

A matrix is a 2-dimensional array of numbers arranged in rows and columns. Matrices provide a method of organizing, storing, and working with mathematical information. Matrices have an abundance of applications and uses in the real world. Matrices provide a useful tool for working with models based on systems of linear equations. We’ll use matrices in this chapter to solve systems of linear equations with several variables.

Matrices are used in encryption and in economic modelling. They are also used in optimization problems such as maximizing profit or revenue or minimizing cost. Matrices are used in business for scheduling, routing transportation and shipments, and managing inventory. Just about any application that collects and manages data can apply matrices. Use of matrices has grown as the availability of data in many areas of life and business has increased. They are important tools for organizing data and solving problems in all fields of science, from physics and chemistry, to biology and genetics, to meteorology and economics. In computer science, matrix mathematics lies behind animation of images in movies and video games.

Computer science analyzes diagrams of networks to understand how things are connected to each other, such as relationships between people on a social website, and relationships between online search results and how people link from one website to another. The mathematics to work with network diagrams comprise the field of “graph theory”; it relies on matrices to organize the information in the graphs that diagram connections and associations in a network. For example, if you use Facebook or Linked-In or other social media sites, these sites use network graphs and matrices to organize your relationships with other users.