Solution Found!
Lucas started with L0 = 2 and L1 = 1. The rule Lk+2 = Lk+1 +Lk is the same, so A is
Chapter 5, Problem 5.3.7(choose chapter or problem)
Lucas started with L0 = 2 and L1 = 1. The rule Lk+2 = Lk+1 +Lk is the same, so A is still Fibonaccis matrix. Add its eigenvectors x1 +x2: " 1 1 # + " 2 1 # = " 1 2 (1+ 5) 1 # + " 1 2 (1 5) 1 # = " 1 2 # = " L1 L0 # . Multiplying by A k , the second component is Lk = k 1 + k 2 . Compute the Lucas number L10 slowly by Lk+2 = Lk+1 +Lk , and compute approximately by 10 1 .
Questions & Answers
QUESTION:
Lucas started with L0 = 2 and L1 = 1. The rule Lk+2 = Lk+1 +Lk is the same, so A is still Fibonaccis matrix. Add its eigenvectors x1 +x2: " 1 1 # + " 2 1 # = " 1 2 (1+ 5) 1 # + " 1 2 (1 5) 1 # = " 1 2 # = " L1 L0 # . Multiplying by A k , the second component is Lk = k 1 + k 2 . Compute the Lucas number L10 slowly by Lk+2 = Lk+1 +Lk , and compute approximately by 10 1 .
ANSWER:Step 1 of 7
Fibonacci rule is given by:
Let the Fibonacci matrix be as follows:
