(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to prove f(r) =A[itex]\bullet[/itex] (r-kz) is a linear operator, but I don't understand why it is linear.

2. Relevant equations

A function of a vector is called linear if:

f(r1+r2) = f(r1) + f(r2) and f(ar) = af(r)

3. The attempt at a solution

f(r1+r2) =A[itex]\bullet[/itex] (r1+r2-kz) =A[itex]\bullet[/itex]r1+A[itex]\bullet[/itex]r2-A[itex]\bullet[/itex]kz

However, f(r1) + f(r2) =A[itex]\bullet[/itex]r1-A[itex]\bullet[/itex]kz

+A[itex]\bullet[/itex]r2-A[itex]\bullet[/itex]kz

So, I just proved that the function is NOT a linear function, how great... :(

By the way,r= (x,y,z) in this book, if that changes anything.

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# Homework Help: How can I prove this function is a linear function?

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