pset8 - 18.06 Problem Set 8 Due Wednesday, 23 April 2008 at...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 18.06 Problem Set 8 Due Wednesday, 23 April 2008 at 4 pm in 2-106. 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....
View Full Document

Page1 / 3

pset8 - 18.06 Problem Set 8 Due Wednesday, 23 April 2008 at...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online