**Question: **Let A be a linear map of the n-dimensional space (V, F) onto itself. Assume that for some \(\lambda \in F\) and basis \(\left( {{v}_{i}} \right)_{i=1}^{n}\) we have \(A{{v}_{1}}={{v}_{1}}\) and \(A{{v}_{k}}=\lambda {{v}_{k}}+{{v}_{k+1}}\)

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