9. (a) A sequence of numbers is defined by $$\begin{aligned} & u _ { 1 } = 8
& u _ { n + 1 } = 4 u _ { n } - 9 n , \quad n \geqslant 1 \end{aligned}$$ Prove by induction that, for \(n \in \mathbb { Z } ^ { + }\), $$u _ { n } = 4 ^ { n } + 3 n + 1$$ (b) Prove by induction that, for \(m \in \mathbb { Z } ^ { + }\), $$\left( \begin{array} { l l } 3 & - 4
1 & - 1 \end{array} \right) ^ { m } = \left( \begin{array} { c c } 2 m + 1 & - 4 m
m & 1 - 2 m \end{array} \right)$$