prove or desprove lenearity.. - Electronic Circuits Projects Diagrams Free

transgalactic · 3rd November 2009, 10:27 PM

$ y(t)=e^{-t}x(t) $

i need to prove lenearity by constant
and by addition

$ y(t_1)=e^{-t_1}x(t_1) $
$ y(t_2)=e^{-t_2}x(t_2) $
$ y(t_1)+y(t_2)=e^{-t_1}x(t_1)+e^{-t_2}x(t+2) $

$y(t_1+t_2)=e^{-t_1-t_2}x(t_1+t_2)$

i dont know if $y(t_1+t_2)= y(t_1)+y(t_2)$
?

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3rd November 2009, 10:27 PM	#1
transgalactic	prove or desprove lenearity.. $<br /> <br /> y(t)=e^{-t}x(t)<br />$ i need to prove lenearity by constant and by addition $<br /> <br /> y(t_1)=e^{-t_1}x(t_1)<br />$ $<br /> <br /> y(t_2)=e^{-t_2}x(t_2)<br />$ $<br /> <br /> y(t_1)+y(t_2)=e^{-t_1}x(t_1)+e^{-t_2}x(t+2)<br />$ $y(t_1+t_2)=e^{-t_1-t_2}x(t_1+t_2)$ i dont know if $y(t_1+t_2)= y(t_1)+y(t_2)$ ? Last edited by transgalactic; 3rd November 2009 at 10:28 PM.