Question

8. This exercise is a continuation of the previous one. The Lucas numbers Ln are defined by the same relationship as the Fibonacci numbers. Ln+2 = Ln+1 + Ln. However, we begin with Lo = 2 and L-1, which leads to the sequence 2, 1,3,4,7,11,... 「Ln+1 Ln As before, form the vector as a linear combination of vi and v2, eigenvectors of A. Explain why so that a. Xn+1 = Axn. Express X0 b. -(부).. (뷔 Explain why Ln is the closest integer to фп when n is large, where ф is the golden ratio. Use this observation to find L20. c. d.

Answer 1

メー k- k

rt st

거 Fr