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Determinantal Loci

by Marvin Marcus (University of California, Santa Barbara)

This article originally appeared in:
College Mathematics Journal
January, 1992

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

This article characterizes the points \((x, y)\) in the plane for which the determinant of a matrix of a particular form involving \((x, y)\) is \(0\).  The matrices of interest have the form  \(A+xL+uM\), where \(A\), \(L\), and \(M\) are square matrices, \(L\) and \(M\) are of rank one, and \(L + M\) is of rank two.

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Capsule Course Topic(s):
Linear Algebra | Determinants
Linear Algebra | Geometry
Linear Algebra | Matrix Multiplication
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