(Solved): A discrete-time system is described by the following difference equation \[ y(k+2)+y(k+1)-2 y(k)=3 ...

A discrete-time system is described by the following difference equation \[ y(k+2)+y(k+1)-2 y(k)=3 u(k) \] with \( \{\mathrm{u}(\mathrm{k})\}=\left\{2^{-\mathrm{k}}, \mathrm{k}=0,1,2, \ldots\right\} \). Determine the output sequence \( \{\mathrm{y}(\mathrm{k})\} \) by \( \mathrm{z} \) transform and inverse z transform for the following case \[ y(1)=0 \text { and } y(0)=0 \]