(a) Show that if A is a real symmetric matrix and n is its largest eigenvalue, then n =max c=0 Acc |c|2 . (b) IfBisanotherrealsymmetricmatrix,Bispositivedenite,and n is thelargestrootofthepolynomialequationdet(AB)=0,showthat n =max c=0 Acc Bcc . [Hint for (b): Use the fact that B has a unique square root that is positive denite symmetric.]

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