Consider a discrete-time system which in response to input sequence $x[n]$ ( $n$ integer) outputs the sequence $y[n]$ such that
\[y[n]=\left\{\begin{array}{ll}
0, & n=-1,-2,-3, \ldots, \\
\alpha y[2 n-1]+\beta y[n-1]+\gamma x[n-1]+x[n]+1, & n=0,1,2, \ldots
\end{array}\right.\]
Which of the below makes the system linear and time-invariant?
- Only $\alpha=\beta=\gamma=0$
- Only $\alpha=\beta=0$ (parameter $\gamma$ can take any value)
- Only $\alpha=0$ (parameters $\beta$ and $\gamma$ can take arbitrary values)
- Always non-linear, but time-invariant only if $\alpha=0$ (parameters $\beta$ and $\gamma$ can take arbitrary values)
- Cannot be determined from the information given
