a$.$ Consider $g(k)=\{\begin{array}{ccc}{2}^k,& k=0,1,2,& 3\\ 0,& k<mn>0</mn>\end{array},$ find the z$-$transform $G(z)$ using general definition of z$-$transform.

b$.$ Using z$-$transformation obtain the convolution of the two sequences

$u(k)=\{\begin{array}{ccc}3,& k=0,1,& 2\\ ?\end{array}$

$0,k<mn>0</mn>$

$y(k)=\{\begin{array}{ccc}k,& k=0,1,& 2\end{array}$

$0,k<mn>0</mn>$

c$.$ Solve the linear systems governed by the following difference equations:

$x(k)-0\mathrm{.}5x(k-1)+0\mathrm{.}06x(k-2)=e(k)$

Where $e(k)$ is an input, $e(k)=\{\begin{array}{ccc}3,& k=0,& 1\\ 0,& k2\end{array}$