HW3-2 - ECE 493 HW #3 Version 1.00 March 11, 2011 Spring...

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Unformatted text preview: ECE 493 HW #3 Version 1.00 March 11, 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 ....
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