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Given the definition of Linear systems

$ \alpha x1(t) + \beta x2(t) <\math> is <math> \alpha y1(t)+ \beta y2(t). $

Consider the following system: $ e^{2jt}\to system\to te^{-2jt} $


         $ e^{-2jt}\to system\to te^{2jt} $

From the given system:

$ x(t)\to system\to tx(-t) $

From Euler's formula $ e^{iy}=cos{y}+i sin{y} $

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett