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# prove or desprove lenearity..

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#### transgalactic

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

i need to prove lenearity by constant

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

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

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

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#### maxmcp

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

i need to prove lenearity by constant

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

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

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

I think you have to multiply the variable t1 or t2 by a constant. so the RHS has eg. 2*t1 in place of t1, and if the result is equal to 2*y then it is linear.

by addition, I am not too sure and wouldnt want to lead you in the wrong direction, but I think you need to prove that $y(t_1+t_2)= y(t_1)+y(t_2)$, which again I would suggest to do by substitution.

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