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6 Nov 2019
Consider this sequence
G_0 = 0, G_1 = 1, and G_k + 2 = (G_A + G_k + 1)/2. (So G_k + 2 is the average of the previous two numbers G_k and G_k + 1) This problem will find the limit of G_k as k rightarrow infinity. a) Find a matrix A which satisfies [G_k + 2 G_k + 1] = A[G_k + 1 G_k] b) Find eigenvalues and eigenvectors of A c) Write A^k = S Lambda^k S^-1 where Lambda is a diagonal matrix. d) Find the limit as k rightarrow infinity of the numbers G_k. Show transcribed image text
Consider this sequence
G_0 = 0, G_1 = 1, and G_k + 2 = (G_A + G_k + 1)/2. (So G_k + 2 is the average of the previous two numbers G_k and G_k + 1) This problem will find the limit of G_k as k rightarrow infinity. a) Find a matrix A which satisfies [G_k + 2 G_k + 1] = A[G_k + 1 G_k] b) Find eigenvalues and eigenvectors of A c) Write A^k = S Lambda^k S^-1 where Lambda is a diagonal matrix. d) Find the limit as k rightarrow infinity of the numbers G_k.
Show transcribed image text Trinidad TremblayLv2
28 Jun 2019