If X1(t) -> system => y1(t) and X2(t) -> system => y2(t) implies a*X1(t)+ b*X2(t) -> system => a*y1(t) + b*y2(t)

for any complex number a,b

then the system is called linear.


E.g.

y(t)=$ x^2 (t) $ is non-linear


Since a*y1(t) + b*y2(t)=$ (a*X1(t)+ b*X2(t))^2= (a*X1(t))^2+ 2*(a*X1(t)*(b*X2(t)) + (b*X2(t))^2 $


y(t)=2(x)t is linear

Since a*y1(t) + b*y2(t)=2*(a*X1(t)+ b*X2(t))= 2*a*X1(t)+ 2*b*X2(t)

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