# 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