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

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> The numbers $\lambda\_1^k$ and $\lambda\_2^k$ satisfy the Fibonacci rule $F\_{k+2}=F\_{k+1} + F\_k$ :
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> $\lambda\_1^{k+2}=\lambda\_1^{k+1} + \lambda\_1^k$ and $\lambda\_2^{k+2}=\lambda\_2^{k+1} + \lambda\_2^k$
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> Prove this by using the original equation for the $\lambda's$ (Multiply it by $\lambda^k$)
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> Then any combination of $\lambda\_1^k$ and $\lambda\_2^k$ satisfies the rule.
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> The combination $F\_k=(\lambda\_1^k-\lambda\_2^k)/(\lambda\_1-\lambda\_2)$ gives the right start of $F\_0=0$ and $F\_1=1$.
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I'm not sure what "the original equation for the $\lambda's$" is, or what I'm supposed to prove. Can someone please help?