MAT237Y – Multivariable CalculusSummer 2009Assignment # 1 with corrections.Questions are worth 10 marks each.Due Tuesday, May 19, at 6:10pm sharp.1.(a) Using the dot product, show that forx,y∈Rn, the formula2bardblxbardbl2+ 2bardblybardbl2=bardblx+ybardbl2+bardblx−ybardbl2holds.(b) The norm onRncan be defined in terms of the dot product bythe formulabardblxbardbl=√x•x. Show that the reverse is true. That is,find a formula forx•yinvolving the norms of vectors (bardblxbardbl,bardblybardbl,bardblx+ybardbl, andbardblx−ybardblfor example), and without using coordinates.
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