Difference between revisions of "1965 IMO Problems/Problem 2"
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Revision as of 11:43, 16 July 2009
Problem
Consider the system of equations
![\[a_{11}x_1 + a_{12}x_2 + a_{13}x_3 = 0\]](http://latex.artofproblemsolving.com/1/8/a/18adca5a58b5c0fceb009eddd8da54eb3f708e59.png)
![\[a_{21}x_1 + a_{22}x_2 + a_{23}x_3 = 0\]](http://latex.artofproblemsolving.com/d/d/f/ddfcafa461ec4fecf95446f00716e9e501deeb98.png)
![\[a_{31}x_1 + a_{32}x_2 + a_{33}x_3 = 0\]](http://latex.artofproblemsolving.com/d/0/a/d0a1b4632e8b8ba0fce7f094d1288af1bd24a8f1.png)
with unknowns 
, 
, 
. The coefficients satisfy the conditions:
(a) 
, 
, 
are positive numbers;
(b) the remaining coefficients are negative numbers;
(c) in each equation, the sum of the coefficients is positive.
Prove that the given system has only the solution 
.
Solution
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