A sequence of numbers satisfies the inductive relation 10=0, 21=1, (i) Writing vk = Ik Ik...

 

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A sequence of numbers satisfies the inductive relation 10=0, 21=1, (i) Writing vk = Ik Ik | 1 Tk 12k + 3xk-1 for k>1. find a 2 x 2 matrix A such that vk = Avk 1 for all k = 1, 2,... (ii) Compute the vectors Vk for all k = 1, 2,.... (iii) Using (ii), find a formula for k, for all k = 1,2,3,... A sequence of numbers satisfies the inductive relation 10=0, 21=1, (i) Writing vk = Ik Ik | 1 Tk 12k + 3xk-1 for k>1. find a 2 x 2 matrix A such that vk = Avk 1 for all k = 1, 2,... (ii) Compute the vectors Vk for all k = 1, 2,.... (iii) Using (ii), find a formula for k, for all k = 1,2,3,...