**ERIC Number:**EJ875465

**Record Type:**Journal

**Publication Date:**2004

**Pages:**6

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**ISSN-0740-8404

Generating Nice Linear Systems for Matrix Gaussian Elimination

Homewood, L. James

AMATYC Review, v25 n2 p29-34 Spr 2004

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian elimination to introduce their students to algorithms that are capable of handling very large linear systems. Instructors should be able to generate, if they desire, a wide variety of modestly sized nice matrices from which they may choose introductory examples and select exam questions. The formulas for generating nice 2 x 3, 3 x 4, and 4 x 5 augmented matrices are shown in this article, with emphasis on the derivation of the matrix. An instructor may use any of these formulas to generate an augmented matrix representing a "one-solution," a dependent or an inconsistent system. The author has developed TI-83 and TI-86 programs that generate nice augmented matrices.

Descriptors: Algebra, Mathematics Instruction, College Mathematics, Community Colleges, Mathematical Concepts, Equations (Mathematics), Matrices, Problem Solving

American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: amatyc@amatyc.org; Web site: http://www.amatyc.org

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Two Year Colleges

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A