Examples of Linearity:
Assume y[n] and y(t) are respectively outputs corresponding to input signals
x[n] and x(t)
1) System with description y(t) = t . x(t) is linear.
Consider any two input signals, x1(t) and x2(t), with corresponding outputs y1(t) and y2(t).
a and b are arbitrary constants. The output corresponding to a.x1(t) + b.x2(t) is
= t (a.x1(t) + b.x2(t))
= t.a.x1(t) + t.b.x2(t), which is the same linear combination of y1(t) and y2(t).
Hence proved.
2) The system with description
 is not linear.
See for yourself that the system is neither additive, nor homogenous.
Show for yourself that systems with the following descriptions are linear:
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