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A Direct Proof That Row Rank Equals Column Rank

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.

Old Node ID: 
3719
MSC Codes: 
15A04
Author(s): 
Nicholas Loehr (University of Michigan Flint)
Publication Date: 
Monday, July 18, 2011
Original Publication Source: 
College Mathematics Journal
Original Publication Date: 
September, 2007
Subject(s): 
Algebra and Number Theory
Linear Algebra
Matrix Algebra
Topic(s): 
Linear Algebra
Rank of Matrices
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Publish Page: 
Furnished by JSTOR: 
File Content: 
Rating Count: 
68.00
Rating Sum: 
194.00
Rating Average: 
2.85
Applicable Course(s): 
3.8 Linear/Matrix Algebra
Modify Date: 
Monday, July 18, 2011
Average: 2.9 (68 votes)

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