Unformatted text preview: ± z = ( ?, 1 )( x ,³ ) = ? x + 1 ³ ≥ or ? x ≥ − 1 ³ > x solves Gordan’s system I. 3.241 Let a 1 , a 2 ,..., a ± be a basis for ´ . Let ? = ( a 1 , a 2 ,..., a ± ) be the matrix whose columns are a ³ . To say that ´ contains no positive vector means that the system ? x > has no solution. By Gordan’s theorem, there exists some y ≩ such that ? ? y = that is a ³ y = ya ³ = 0 , µ = 1 , 2 ,...,² so that y ∈ ´ ⊥ . 190...
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 Fall '10
 Dr.DuMond
 Economics, Macroeconomics, Linear Algebra, Determinant, All rights reserved, Gordan

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