HW3-sol - ECE 493 HW #3 Version 1.00 March 18, 2011 Spring...

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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: Rank-n-Span; 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 row-vector 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....
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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.

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HW3-sol - ECE 493 HW #3 Version 1.00 March 18, 2011 Spring...

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