1. Let v be a vector space with inner product <.,.>. Let x, y belong to V and define W = span {x}. Let (ŷ) be the projection of y onto W.

a). show that llyll = ll ŷ ll if and only is y belongs to W

b). Use a) to show that l <x,y> l = llxll llyll if and only if y belongs to W.

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