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\text { Calculate } A^{n} \mathbf{v} \text { where } A=\left[\begin{array}{cc}

5 & 4 \\

-3 & -3

\end{array}\right] \text { and } \mathbf{v}=\left[\begin{array}{l}

0 \\

2

\end{array}\right] \text {. Use your result to find } A^{10} \mathbf{v} \text { Let } A^{n}=\left[\begin{array}{ll}

a_{n} & b_{n} \\

c_{n} & d_{n}

\end{array}\right] \text {. Calculate } b_{n} \text {. Use your result to find } b_{10} \text {. } For this question, express your answers in as simple a form as possible. If the answer is an integer,provide the integer.

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