# Question #2017865: Applications of Linear Algebra

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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