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Unformatted text preview: 1 Winter 2010 Math 255 and bounded domain, S , and so has a maximum and minimum on the domain S , the unit sphere. Show that there must be x 1 , x 2 and x 3 , with x 2 1 + x 2 2 + x 2 3 = 1 and a scalar λ 6 = 0 such that for i = 1, 2 and 3, 3 X j =1 a i,j x j = λx i . Remark For those with some linear algebra background, the vector x is called an eigenvector, while the scalar λ is called an eigenvalue. biii) What are the maxima and minima for f on B = { ( x 1 ,x 2 ,x 3 )  x 2 1 + x 2 2 + x 2 3 ≤ 1 } ? Review problem (extra credit) : Give a rigorous proof of the chain rule for a scalar function of one variable. Please give all details and assumptions. 2...
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 Fall '08
 JackWaddell
 Math, Optimization, Linear Algebra Background

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