2. The Fibonacci numbers F(0), F(1), F(2),… are defined as follows: F(0) := 0 F(1) := 1 F(n) := F(n − 1) + F(n − 2) Prove by induction that for all n ≥ 1, n>2 F (n − 1) · F(n + 1) − F(n)² = (−1)n

Linear Algebra: A Modern Introduction
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Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
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2. The Fibonacci numbers F(0), F(1), F(2),… are defined as follows:
F(0) := 0
F(1) := 1
F(n) := F(n − 1) + F(n − 2)
Prove by induction that for all n ≥ 1,
n>2
F(n − 1) · F(n + 1) − F(n)² = (−1)″
Transcribed Image Text:2. The Fibonacci numbers F(0), F(1), F(2),… are defined as follows: F(0) := 0 F(1) := 1 F(n) := F(n − 1) + F(n − 2) Prove by induction that for all n ≥ 1, n>2 F(n − 1) · F(n + 1) − F(n)² = (−1)″
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