(Solved): 3. Use the \( z \)-transform properties to (a) (15 points), determine the z-transform, including t ...

3. Use the \( z \)-transform properties to (a) (15 points), determine the z-transform, including the ROC, of the sequence \( x[n]=0.5^{n-3}(u[n]-n u[n-10]) \), (b) (20 points), determine the inverse z-transform of \[ X(z)=\frac{3}{1+z^{-1}-2 z^{-2}} . \]