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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)....
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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.
 Spring '08
 Anshelvich
 Linear Algebra, Algebra

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