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 The American Mathematical Association of Two-Year Colleges |
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The American Mathematical Association of Two-Year Colleges |
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L.
James (Jim) Homewood is a member of the fulltime mathematics
faculty at the Downtown Campus of Pima Community College in Tucson,
Arizona. He earned a master’s degree in mathematics at Portland
State University, with two additional years as a graduate associate
in the doctoral program in mathematics at the University of Arizona.
His major interests are analysis and functional analysis. |
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| 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 × 3, 3 × 4, and 4 × 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. |
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