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Unformatted text preview: 18.06 Problem Set 8 Due Wednesday, 23 April 2008 at 4 pm in 2106. Problem 1: Do problem 3 in section 6.5 (pg. 339) in the book. Problem 2: Do problem 6 in section 6.5 (pg. 339). Problem 3: For what numbers c and d are the matrices A and B positive definite? Test the 3 determinants: A = c 2 3 2 c 4 3 4 1 B = 1 2 1 2 d 3 1 3 1 Problem 4: Do problem 15 in section 6.5 (pg. 340). Problem 5: Do problem 28 in section 6.5 (pg. 342). Problem 6: a) Let f 1 ( x, y ) = 1 4 x 4 + x 2 y + y 2 . Find the second derivative matrix A 1 = 2 f/x 2 2 f/xy 2 f/yx 2 f/y 2 A 1 is not positive definite everywhere  find the conditions on x and y for it to be positive definite. (Interesting question: check what happens when both partial derivatives vanish, that is, when f/x = f/y = 0. Is f still positive definite? It turns out that f 1 does attain a minimal value, but not along isolated points. Find the points where it hits a global minimum. This part is not required.)the points where it hits a global minimum....
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 Spring '08
 CHANILLO
 Matrices

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