Consider a klh-order difference equation in the fonn of

Chapter , Problem 83

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Consider a klh-order difference equation in the fonn of equation l with a sel of k inilial condilions. and let lhe matrix fonn of the equalion be s., =As,_,, Suppose. furlhcrmorc. thai A has k distincl eigenvalues A A2 .... Ak, and that v 1, v2 .... , Vt are corresponding c igenveclors. (a) Prove thai there exis1 scalars t 1.12 .... . I t such lhat (b) Prove that for any positive inleg

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