Generating Nice Linear Systems for Matrix Gaussian Elimination

Autor/in	Homewood, L. James
Titel	Generating Nice Linear Systems for Matrix Gaussian Elimination
Quelle	In: AMATYC Review, 25 (2004) 2, S.29-34 (6 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0740-8404
Schlagwörter	Algebra; Mathematics Instruction; College Mathematics; Community Colleges; Mathematical Concepts; Equations (Mathematics); Matrices; Problem Solving + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Community college; Community College; Equations; Mathematics; Gleichungslehre; Matrizenrechnung; Problemlösen
Abstract	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. (As Provided).
Anmerkungen	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
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10