Ask a dumb question but confuse me long time.
The following is what I know:
1st case
$Ax = b$ is an affine set in $x$,i.e. $\{x | Ax = b\}$, and it is linear in $x$.
2nd case
$ f(x) = Ax + b$ is an affine function. It is not linear because of $b$.But $f(x) = Ax$ is linear in $x$.
My question is I am still confused about both of them, can anyone provide a more mature way to seperate both of them? What is the main difference (or application) between them?