Tracogna_MAT_343_ONLINE_A_Summer_2018.dtangap.Section_5.4_Inner_Product_Spaces.pdf - Derick Tangap Tracogna MAT 343 ONLINE A Summer 2018 Assignment

# Tracogna_MAT_343_ONLINE_A_Summer_2018.dtangap.Section_5.4_Inner_Product_Spaces.pdf

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Derick TangapTracognaMAT343ONLINEASummer2018Assignment Section5.4InnerProductSpaces due 06/14/2018 at 11:59pm MST1.(1 point) Given the vectorx=-3-4-1, find||x||1=||x||=||x||2=Solution:kxk1=|x1|+|x2|+|x3|=|-3|+|-4|+|-1|=3+4+1=8kxk=max(3,4,1) =4kxk2=p(-3)2+(-4)2+(-1)2=26Answer(s) submitted:84sqrt(26)(correct)Correct Answers:845.099019513592782.(1 point) Letx=-6-24andy=363. Compute||x-y||1=||x-y||=||x-y||2=Solution: x-y=-9-81.kx-yk1=|-9|+|-8|+|1|=18kx-yk=max(|-9|,|-8|,|1|) =9kx-yk2=p(-9)2+(-8)2+(1)2=146Answer(s) submitted:189sqrt(146)(correct)Correct Answers:18912.08304597359463.(1 point) Use the inner product<f,g>=Z10f(x)g(x)dxin the vector spaceC0[0,1]to find<f,g>,||f||,||g||, andthe angleθf,gbetweenf(x)andg(x)forf(x) =10x2-3 andg(x) =6x+5.hf,gi=,kfk=,kgk=,θf,gradians.Solution:hf,gi=R10f(x)g(x)dx=R10(10x2-3)(6x+5)dx=R10(60x3+50x2-18x-15)dx=604+503+-182-15=233kfk=phf,fi=qR10f(x)f(x)dx=qR10(10x2-3)2dx=qR10(100x