A causal linear and time$-$invariant $($LTI$)$ system produces the output sequence y$($n$)=\{1,0\mathrm{.}9\}$ for $0$ n $1$ when excited by the input sequence x$($n$)=\{1,0\mathrm{.}9,0\mathrm{.}2\}$ for $0$ n $2.$