psCharFunct1Qu

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

Info iconThis preview shows pages 1–3. 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: 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....
View Full Document

This note was uploaded on 08/01/2008 for the course ARE 211 taught by Professor Simon during the Fall '07 term at Berkeley.

Page1 / 4

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

This preview shows document pages 1 - 3. Sign up to view the full document.

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