What was the result of Marbury vs. Madison?

In the Marbury v. Madison case, the United States Supreme Court ruled in favor of William Marbury's argument, but his commission was still denied because the court lacked the power to issue a writ of mandamus. The court ruled that President Thomas Jefferson, through his Secretary of State James Madison, was wrong to prohibit Marbury from becoming the Justice of the Peace of Washington County in the District of Columbia.