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I'm having difficulty with the following, problem 5.3.7 from Gilbert Strang's "Linear Algebra and its Application".

The numbers $\lambda_1^k$ and $\lambda_2^k$ satisfy the Fibonacci rule $F_{k+2}=F_{k+1} + F_k$ :

$\lambda_1^{k+2}=\lambda_1^{k+1} + \lambda_1^k$ and $\lambda_2^{k+2}=\lambda_2^{k+1} + \lambda_2^k$

Prove this by using the original equation for the $\lambda's$ (Multiply it by $\lambda^k$)

Then any combination of $\lambda_1^k$ and $\lambda_2^k$ satisfies the rule.

The combination $F_k=(\lambda_1^k-\lambda_2^k)/(\lambda_1-\lambda_2)$ gives the right start of $F_0=0$ and $F_1=1$.

I'm not sure what "the original equation for the $\lambda's$" is, or what I'm supposed to prove. Can someone please help?

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    What *is* "the original equation for the $\lambda'$s"? Where did you encounter this problem, and in what context? The more you can tell us about that, the more likely we'll be able to help you.2012-11-11
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    That is the part that also confuses me. It is a problem of the book "linear algebra and its application, 5.3.7", and I'm not sure what the 'original equation' means, also I can't find any 'equation for lambda' in previous pages...2012-11-11
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    Anyway, I can't understand what is the main point of this problem. What should I prove? The above two equations for lambdas? By using the Fibonacci formula?2012-11-11
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    Who would the book's author(s) be? Have you stated the *entire* problem?2012-11-11
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    The author is Gilbert Strang.2012-11-11

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