# Determinantal Loci

by Marvin Marcus (University of California, Santa Barbara)

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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