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ERIC Number: EJ875465
Record Type: Journal
Publication Date: 2004
Pages: 6
Abstractor: As Provided
Reference Count: 0
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.
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