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Exercise 5.2.7

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Diagonalize the matrix $A$ by $Q^{- 1} AQ = D$ with $D = (\begin{matrix} 5 & 0 \\ 0 & - 1 \end{matrix})$ and $Q = (\begin{matrix} 1 & 2 \\ 1 & - 1 \end{matrix})$ . So we know that

A^{n} = Q D^{n} Q^{- 1} = Q (\begin{matrix} 5^{n} & 0 \\ 0 & {(- 1)}^{n} \end{matrix}) Q^{- 1} .

jephianlin

2011-06-27 00:00

Exercise 5.2.7

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