(a) Bearing in mind that $Z\left\{a^{n} ight\}=\frac{z}{z-a}$, determine the inverse Z-transform of $$ Z^{-1}\left\{\frac{10 z(z+5)}{(z-1)(z-2)(z+3)} ight\} $$ (b) Solve the linear difference equation $$ u_{n+2}+2 u_{n}=0 \text { given that } u_{0}=1 \text { and } u_{1}=\sqrt{2} $$