Prove Scaling Property for Integer & Rational Factors

[dashkin111]

Homework Statement

a system has the following property:
Its response to a sum of inputs is the sum of its responses to the inputs.

(a) Prove that the scaling property holds for any integer scaling factor
(b) Prove that the scaling property holds for any rational scaling factor

Homework Equations

The Attempt at a Solution

y_{n}(t)+...+y_{1}(t)+y_{0}(t) = x_{n}(t)+...+x_{1}(t)+x_{0}(t)


That's basically what it's saying, where y(t) is the response to the x(t). But I don't understand what it means by proving it, isn't it kind of trivial?

 

[EnumaElish]

Isn't it saying y(xn + ... + x0) = y(xn) + ... + y(x0) ?

 

[dashkin111]

Isn't it saying y(xn + ... + x0) = y(xn) + ... + y(x0) ?

Oh yeah, thanks. But still isn't it trivial to prove scaling for it?

 

[HallsofIvy]

Well, sometimes you are given easy problems! If you think it is trivial, go ahead and do it.