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Consider a discrete-time system which in response to input sequence $x[n] \;( n$ integer) outputs the sequence $y[n]$ such that
\[y[n]=\left\{\begin{array}{ll}
0, & n=-1,-2,-3, \ldots, \\
\frac{1}{2}(y[n-1]+n x[n]), & n=0,1,2, \ldots
\end{array}\right.\]

Which of the following describes the system?

  1. Linear, time-invariant
  2. Linear, time-variant
  3. Non-linear, time-invariant
  4. Non-linear, time-variant
  5. Cannot be determined from the information given
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