Unformatted text preview: ) denotes the maximum of a and b . (d) Let v 2 V and U = Span( v ). Then dim( U + S ) = dim S + 1. 4. Given three ordered bases for R 3 : E = [ e 1 ; e 2 ; e 3 ], F = [ f 1 ; f 2 ; f 3 ] and H = [ h 1 ; h 2 ; h 3 ], where e 1 ; e 2 ; e 3 form the standard basis, and f 1 = (1 1 1) T ; f 2 = (1 2 2) T ; f 3 = (2 3 4) T ; h 1 = (3 2 5) T ; h 2 = (1 1 2) T ; h 3 = (2 3 2) T : (a) If [ x ] F = (1 ± 1 2) T , ±nd [ x ] E and [ x ] H . (b) Find, by evaluating [ f 1 ] H , [ f 2 ] H , [ f 3 ] H , the transition matrix from F to H . (c) Find the transition matrix from F to H by ±rst evaluating the transition matrices from F to E and from H to E ....
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 Spring '10
 Dr,Li

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