Difference between revisions of "2006 Canadian MO Problems/Problem 3"

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==Problem==
 
==Problem==
In a rectangular array of nonnegative real numbers with <math>m</math> rows andn <math>n</math> columns, each row and each column intersect in a positive element, then the sums of their elements are the same. Prove that <math>m=n</math>.
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In a rectangular array of nonnegative real numbers with <math>m</math> rows andn <math>n</math> columns, if a row and a column intersect in a positive element, then the sums of their elements are the same. Prove that <math>m=n</math>.
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==Solution==
 
==Solution==
 
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Revision as of 11:14, 15 August 2008

Problem

In a rectangular array of nonnegative real numbers with $m$ rows andn $n$ columns, if a row and a column intersect in a positive element, then the sums of their elements are the same. Prove that $m=n$.

Solution

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See also

2006 Canadian MO (Problems)
Preceded by
Problem 2
1 2 3 4 5 Followed by
Problem 4