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solution of linear equations. Suppose A E Rmxn, b exists an a satisfying x > 0, Ax = b ere exists no A with ATA≥0, ATA +0, 6 x ≤ 0. ve the following fact from linear algebra: cx ||

solution of linear equations. Suppose A E Rmxn, b exists an a satisfying x > 0, Ax = b ere exists no A with ATA≥0, ATA +0, 6 x ≤ 0. ve the following fact from linear algebra: cx ||

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Separation theorems and supporting hyperplanes 2.20 Strictly positive solution of linear equations. Suppose A E RmXn, be R", with b e R(A). Show that there exists an x satisfying x > 0, Ax = b if and only if there exists no A with A" A = 0, A" A + 0, Hint. First prove the following fact from linear algebra: cx = d for all x satisfying Ax = b if and only if there is a vector A such that c= AT A, d = b" X.
Transcribed Image Text:Separation theorems and supporting hyperplanes 2.20 Strictly positive solution of linear equations. Suppose A E RmXn, be R", with b e R(A). Show that there exists an x satisfying x > 0, Ax = b if and only if there exists no A with A" A = 0, A" A + 0, Hint. First prove the following fact from linear algebra: cx = d for all x satisfying Ax = b if and only if there is a vector A such that c= AT A, d = b" X.
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