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A Tricky Linear Algebra Example

by David Sprows

This article originally appeared in:
College Mathematics Journal
January, 2008

Subject classification(s): Algebra and Number Theory | Linear Algebra | Vector Spaces
Applicable Course(s): 3.8 Linear/Matrix Algebra

In this article a classroom "trick" involving square arrangements of natural numbers is used to motivate a discussion of a special class of matrices. In particular, a basis is obtained for those \(n\) by \(n\) square matrices with the property that if \(n\) entries are selected from the matrix so that no two values are in the same row or the same column, then the sum of these \(n\) entries will always be the same.

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Capsule Course Topic(s):
Linear Algebra | Bases
Linear Algebra | Linear Independence
Linear Algebra | Vector Spaces, Subspaces
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