MAS 3105May 14, 2009Quiz 2 and KeyProf. S. Hudson1) If possible, find a nonzero 2x2 matrixAsuch thatA2=O(the zero matrix). If it isnot possible, explain why not. Note:nonzeromeans at least one entry ofAis not zero.2) Writevas a linear combination ofuandw. For maximum credit, solve this using areliable method (guessing the answer may only get partial credit).v=12u=21w=113) Choose ONE of these to prove. You can answer on the back.a) IfAis a symmetric nonsingular matrix, thenA-1is also symmetric [if you know aformula for the transpose ofA-1, you can use it without proving it].b) Prove this part of the TFAE theorem: IfAis row equivalent toI, thenAis nonsingular.Remarks and Answers:Average 44/60. A’s = 50-60, B’s 44-49, C’s 38-43, D’s 32-37.1) There are many examples (all singular, of course), but several people used this one:A=01002) [first version] There were two versions of the quiz. The first one shows the correct year,
This is the end of the preview.
access the rest of the document.