For be the projection of into the line spanned by be the projection of into the line spanned by be the projection of into the line spanned by etc., back and forth between the spans of That is, is the projection of into the span of if i + 1 is even, and into the span of if i + 1 is odd. Must that sequence of vectors eventually settle down-must there be a sufficiently large i such that if so, what is the earliest such i?

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a, b e Rn let v