$11\mathrm{.}16.$ Find the inverse $z-$transform of each given $E(z)$ by the two methods given in Section $11\mathrm{.}5.$

Compare the values of $e(k)$ for $k=0,1,2,$ and $3$ obtained by the two methods.

$*($a$)E(z)=\frac{0\mathrm{.}1z}{(z-1)(z-0\mathrm{.}9)}$

$($b$)E(z)=\frac{0\mathrm{.}1z(z+1)}{(z-1)(z-0\mathrm{.}9)}$

$($c$)E(z)=\frac{0\mathrm{.}1}{(z-1)(z-0\mathrm{.}9)}$

$($d$)E(z)=\frac{0\mathrm{.}1}{z(z-1)(z-0\mathrm{.}9)}$

$($e$)$ Verify the partial fractions using MATLAB.