You chose a very interesting case, up until your post I was not familiar with the case. It is even more interesting that it hinged on three issues. First, did Marbury and the other appointees have a right to their commissions? The answer to this question was yes, the rights of the appointees' had been violated by Jefferson when he blocked their commissions, which already had been confirmed and affixed with seals. Second, if they did have a right that had been violated, did federal law provide a remedy? The answer to this question was also yes, Marbury was entitled to sue and seek a legal remedy, and a federal judge could issue a writ ordering Jefferson to comply. Finally, was an order from the U.S. Supreme Court the right remedy to solve the problem? This one was a bit more complicated and I will use a direct quote because I am unsure I can do the explanation justice. (Pun intended!)