In Marbury v. Madison, the Supreme Court established the principle of constitutional review by? I am seconding guessing myself on my answer so can you point me the right direction is it:

claiming that Section 13 of the 1789 Judiciary Act providing that the Supreme Court will issue a writ of mandamus was unconstitutional.

or

lecturing the Jeffersonians on why Marbury was rightfully entitled to his appointment.

I think your first answer is correct.

http://en.wikipedia.org/wiki/Marbury_v._Madison

In Marbury v. Madison, the Supreme Court established the principle of constitutional review by claiming that Section 13 of the 1789 Judiciary Act, which provided that the Supreme Court could issue a writ of mandamus, was unconstitutional.

To arrive at this answer, you can review the background of the case. Marbury v. Madison involved an attempt by President Thomas Jefferson and his administration to prevent the delivery of commissions to several federal justices of the peace, including William Marbury. Marbury filed a lawsuit directly with the Supreme Court, asking them to issue a writ of mandamus to force the new Secretary of State, James Madison, to deliver the commission.

In its ruling, the Supreme Court, under Chief Justice John Marshall, first addressed whether Marbury had a legal right to the commission. The Court determined that Marbury did have a right to the appointment, as his appointment was valid and had been properly signed and sealed.

However, the Court then went on to declare that the provision of the Judiciary Act of 1789, which granted the Court the power to issue a writ of mandamus in this situation, was unconstitutional. The Court reasoned that the Constitution did not grant the Supreme Court the authority to issue such a writ in original jurisdiction cases (cases that originate directly with the Supreme Court). This was a significant decision because it marked the first time the Court used the power of judicial review to declare an act of Congress unconstitutional.

Overall, the correct answer to the question is that the Supreme Court established the principle of constitutional review in Marbury v. Madison by claiming that Section 13 of the Judiciary Act of 1789 was unconstitutional.