psCharFunct1Qu

# psCharFunct1Qu - Fall 2007 ARE211 Problem Set#13 Char of...

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Unformatted text preview: Fall 2007 ARE211 Problem Set #13 Char of Functions Problem Set Due date: Dec 11 Problem 1 Show that a function f : X → A is invertible ⇔ f is bijective Problem 2 Which of the following functions is bijective? If it is bijective, give the inverse. a) f : R → R f ( x ) = 2 x + 4 b) f : R → R f ( x ) = | 2 x + 4 | c) f : [- 2 , ∞ ) → R f ( x ) = | - 2 x- 4 | d) f : [- 2 , ∞ ) → [0 , ∞ ) f ( x ) = | - 2 x- 4 | e) f : (0 , ∞ ) → (0 , ∞ ) f ( x ) = 1 /x if x rational x if x irrational 1 2 Problem 3 Let A be a (nxn) matrix. The main diagonal consists of the elements { a ii , i = 1 ..n } . Show that a) A necessary condition for A to be positive definite is that all elements on the main diagonal are strictly positive. b) A necessary condition for A to be negative definite is that all elements on the main diagonal are strictly negative....
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## This note was uploaded on 08/01/2008 for the course ARE 211 taught by Professor Simon during the Fall '07 term at Berkeley.

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psCharFunct1Qu - Fall 2007 ARE211 Problem Set#13 Char of...

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