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if I have $$ A= \begin{bmatrix} \hphantom{-}1 & 0 & 0\\ -1 & 1 & 1 \\ -1 & 0 & 2\\ \end{bmatrix} $$ I am given the characteristic values are $$ \lambda_{1}=1 \text{ and } \lambda_{2}=2 \text{ and A is similar to a characteristic polynomial} $$ I have found the spectral decomposition of A. I now need to use this to find $$2^{A}$$ how do I do this?

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    what do you mean $A$ is similar to its characteristic polynomial by the way?2013-06-15

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