The $n$vector $c$ represents the daily earnings
of a company over $n$ days,
with negative entries meaning a loss on that day.
Suppose that $n$ is even, and consider the average
earnings in the second half of the period
(i.e., over days $i=n/2+1,\ldots, n$)
minus the average earnings over the first half of the period
(i.e., over days $i=1, \ldots, n/2$). (This quantity gives a
kind of trend in average earnings.) Is this a linear function of $c$?

yes
Correct!

no
Incorrect.