The exam covers Chapter 5, Sections 5.1, 5.2, 5.3, and Chapter 6, Sections 6.1, and 6.2 except the QR Decomposition. You should be able to prove Theorem 5.5 on p. 289 and Theorem 6.4 on p. 313 using the same arguments as in the text. You should also study all of the homework from these chapters.
No calculators are allowed. Note: I have provided only two sample tests since Test 3 from earlier years covered different material.