Question: Subspaces. Consider the set of sequences \(\left\{f_{k}\right\}_{k=0}^{\infty}:=\left\{f_{0}, f_{1}, f_{2}, \ldots\right\}\) satisfying \(f_{k}=f_{k-1}+f_{k-2}\) where \(f_{0}\) and \(f_{1}\) are arbitrary real numbers. Is this a subspace in the vector space of all sequences of real numbers over the field of real numbers?

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