This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECE 493 HW #3 Version 1.00 March 18, 2011 Spring 2011 Univ. of Illinois Due Thur, Mar. 17 Prof. Allen Topic of this homework: RanknSpan; Taylor series; Vector fields, Gradient Vector field topics Deliverables: Show your work. Numerical results are not sufficient, expect when specifically requested. General definitions: i , j , k are given in Greenberg on page 689: i i = j j = k k = 1 , i j = j k = i k = 0 , (1) i i = 0 , i j = k , k j = i , . (2) 1. Triple product: Let A = [ a 1 ,a 2 ,a 3 ] T , B = [ b 1 ,b 2 ,b 3 ] T , C = [ c 1 ,c 2 ,c 3 ] T be three vectors in R 3 . (a) Show that A ( B  C ) = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle . Solution: There are several ways of defining a vector that are used, and you need to learn to move between them. It is confusing to write a vector both as a column of three numbers, as Z = [1 , 2 , 3] T , where the script T is transpose of the rowvector to a column, and as Z = i + 2 j + 3 k . They each represent the same thing. The arrow over the top indicates a column vector, but the rules of computation are the same. So you need to switch back and forth between the two ways of doing business....
View
Full
Document
This note was uploaded on 03/28/2011 for the course ECE ECE 493 taught by Professor Jontb.allen during the Spring '11 term at University of Illinois at Urbana–Champaign.
 Spring '11
 JontB.Allen

Click to edit the document details