Signals & Systems - what's the output?

[Angello90]

Homework Statement

Input and system response is as follow:

$$x[n] = r[n] - 2r[n - 1] + r[n - 2]$$
$$h[n] = \delta[n - 2]$$

The output is:
$$y[n] = u[n - 3]$$

Is that true?

Homework Equations

The Attempt at a Solution

I draw the h[n] and x[n] and they looked as follows:

As for me when these two are multiplied, it will become $$y[n]=0$$.
Am I right?

Thanks

 

[Angello90]

Can anyone give me a tip maybe? Thanks!