assignment 1 answers

assignment 1 answers - Math 3C03, A1 Answers, page 1 of 2...

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Math 3C03, A1 Answers, page 1 of 2 Math 3C03, Assignment 1, Answers (due Friday, Sept. 24, 2010 by 3pm) Sec. 9.5, use the Wronskian to test the three functions for linear independence. "ß / ß B/ BB Answer. ââ â â â â â â â â â â â â ab a b a b a b ºº "/ B / " / B/ ! / /  B/ B / œœ / / B / ! / #/  B/ "" B "# B ww w B B B ww ww ww B (everywhere) œ/ #B"B œ/ Á! #B #B These functions are linearly independent (on all of ) _ß_ Þ ___________________________________________________________________ Sec. 9.6, use Gram-Schmidt method to orthogonalize the list of functions over ef 0ß1ß2 the interval where cd !ß " ß 0 B œB ß 1B œBß 2B œBÞ #$ Answer. , @Bœ 0BœB " Ø@ ß @ Ù œ B .B œ ! " # " $ ' @œ1 @ #" Ø@ ß 1Ù Ø@ ß@ Ù " Ø@ ß 1Ù œ B .B œ " ! " $ " % ' @ B œB  BœB  B # ## "Î% "Î$ % $ @œ2 @ @ $" # Ø@ ß2Ù Ø@ ß2Ù Ø@ß@Ù Ø@ ß 2Ù œ B † B .B œ " ! " $ " & ' Ø @ß@Ùœ B B . B B B . B !! #% $ # $$ * %# " ' # '' ˆ‰ ˆ œ œ œ " $ $ "'$!"& " & ) " ') !) ! Ø@ ß2Ù œ B  B B .B œ B  B .B # & % %% ˆ œ œ œ " $ "!* " '# ! ' ! ' ! @BœB B BBœBB BB $ $# $ # "Î& "Î'! "Î$ "Î)! % & $ % % $ œBBB $& Remark. (Not required:) The inner product Ø@ ß @ Ù œ Þ " "&(&
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assignment 1 answers - Math 3C03, A1 Answers, page 1 of 2...

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