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A Direct Proof That Row Rank Equals Column Rank

by Nicholas Loehr (University of Michigan Flint)

This article originally appeared in:
College Mathematics Journal
September, 2007

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

A row (column) of a matrix is called “extraneous” if it is a linear combination of the other rows (columns).  The author shows that deleting an extraneous row or column of a matrix does not affect the row rank or column rank of a matrix.  This fact establishes the theorem in the title.


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Capsule Course Topic(s):
Linear Algebra | Rank of Matrices
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