sol66 - Partial Solution Set, Leon 6.6 6.6.1 Find the...

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: Partial Solution Set, Leon 6.6 6.6.1 Find the matrix associated with each of the quadratic forms. (a) 3 x 2- 5 xy + y 2 (b) 2 x 2 + 3 y 2 + z 2 + xy- 2 xz + 3 yz (c) x 2 + 2 y 2 + z 2 + xy- 2 xz + 3 yz Solution : (a) A = 3- 5 / 2- 5 / 2 1 . (b) A = 2 1 / 2- 1 1 / 2 3 3 / 2- 1 3 / 2 1 . (c) A = 1 1 / 2- 1 1 / 2 2 3 / 2- 1 3 / 2 1 . 6.6.6 Which of the following matrices are positive definite? Negative definite? Indefinite? (a) A = 3 2 2 2 is positive definite. Since it is 2 2, any test will do. (b) A = 3 4 4 1 is indefinite. Its determinant is -13, so it has eigenvalues of both signs. (d) A = - 2 1- 1 1- 2 is negative definite, since- A is positive definite. 6.6.7 For each of the following functions, determine whether the given stationary point corre- sponds to a local minimum, a local maximum, or a saddle point. (d) f ( x, y ) = y x 2 + x y 2 + xy , (1 , 1)....
View Full Document

This note was uploaded on 07/17/2011 for the course MATH 311 taught by Professor Anshelvich during the Spring '08 term at Texas A&M.

Page1 / 2

sol66 - Partial Solution Set, Leon 6.6 6.6.1 Find the...

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