Comparing the Temptation of Satan upon Jesus in Matthew and Luke

Why is the ordering of Satan tempting Jesus different in Matthew from Luke?

In Matthew, Jesus is tempted to turn rock into bread then jump off the Temple so angels can catch him and then worship Satan to rule the world.
In Luke, Jesus is tempted to turn rock into bread then rule the world then jump off the Temple.

Throughout these two books Matthew emphasizes Jesus as king whereas Luke emphasizes Jesus as man. Luke was a doctor. Matthew was a tax collector paying homage to the emperor king.

They write from two different perspectives.

Therefore, to finish with Jesus as Lord (a king) is emphasized in Matthew, whereas Luke finishes with the temptation that can affect a person if he jumps off the Temple.

Does anyone have a better answer?