(Solved): 7 (15 Points) A discrete system described by the following difference equation: \[ Y_{k}+4 Y_{k-1} ...

7 (15 Points) A discrete system described by the following difference equation: \[ Y_{k}+4 Y_{k-1}-4 Y_{k-2}=\left(\frac{1}{2}\right)^{k}+K\left(\frac{1}{2}\right)^{k} \quad\left\{\begin{array}{l} y_{-1}=0 \\ y_{-2}=1 \end{array}\right. \] a) Find \( Y(Z) \) for this system. b) Find impulse response sequence using inverse \( \mathrm{Z} \) transform of \( \mathrm{H}(\mathrm{z}) \). c) Is this Dytem stable? why?