This preview shows page 1. Sign up to view the full content.
Unformatted text preview: x R n , y R m . (a) Show that x A T y = Ax y . (b) Check this equation with x = 5 3 , A = 1 2 3 1 4 , y = 2 43 . 5. Let A be a 2 2 symmetric matrix, x R 2 . Dene f ( x ) = x Ax . Show that f ( x ) = 2 Ax . 6. For f : R R , assume that f , f 00 , f (3) and f (4) exist and are continuous on the interval ( x *1 , x * + 1). Suppose that f ( x * ) = 0, f 00 ( x * ) = 0, and f (3) ( x * ) = 0, and f (4) ( x * ) < 0 Prove that x * is a strict local maximizer of f ....
View
Full
Document
This note was uploaded on 03/18/2012 for the course MTH 432 taught by Professor Douglasward during the Spring '12 term at Miami University.
 Spring '12
 DouglasWard
 Math

Click to edit the document details