Scales and Modes on Guitar.

For the Aeolian mode you can improvise a melody over the chords:

||: Am / / / | Am / / / | E / / / | E / / / :||


To improvise over the Major scale you can use the chords:

||: C / / / | / / / / | FMaj7 / / / | / / / / :||

You could create your own chord progression using any of the above chords then improvise a melody using any of the notes from the Aeolian mode in A, or Major scale in C.