# Linear Algebra

## Applications

Applications of linear algebra have grown rapidly since the introduction of the computer. Finding the inverse of a matrix, especially one that has hundreds or thousands of rows and columns, is a task easily performed by computer in a relatively short time. Virtually any problem that can be translated into the language of linear mathematics can be solved, provided a solution exists. Linear algebra is applied to problems in transportation and communication to route traffic and information; it is used in the fields of biology, sociology, and ecology to analyze and understand huge amounts of data; it is used daily by the business and economics community to maximize profits and optimize purchasing and manufacturing procedures; and it is vital to the understanding of physics, chemistry, and all types of engineering.

## Resources

### Books

Bittinger, Marvin L:, and Davic Ellenbogen. Intermediate Algebra: Concepts and Applications. 6th ed. Reading, MA: Addison-Wesley Publishing, 2001.

Garfunkel, Soloman A., ed. For All Practical Purposes, Introduction to Contemporary Mathematics. New York: W. H. Freeman, 1988.

Larson, Ron. Calculus With Analytic Geometry. Boston: Houghton Mifflin College, 2002.

Swokowski, Earl W. Pre Calculus, Functions, and Graphs. 6th ed. Boston: PWS-KENT Publishing Co., 1990.

Weisstein, Eric W. The CRC Concise Encyclopedia of Mathematics. New York: CRC Press, 1998.

## KEY TERMS

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Linear equation

—A linear equation is one in which no product of variables appears. The graph of a linear equation is a straight line, hence the term linear.

Matrix

—A matrix is a rectangular array of numbers, such as a table, having I rows and j columns.

Simultaneous equations

—When the solution to an equation satisfies two or more equations at the same time, the equations are called simultaneous equations.

Variable

—A variable is a quantity that is allowed to have a changing value, or that represents an unknown quantity.

Vector

—A quantity or term that can be expressed in terms of both magnitude (a number) and a direction.