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e209k - MAS 3105 Quiz 2 and Key Prof S Hudson 1 If possible...

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MAS 3105 May 14, 2009 Quiz 2 and Key Prof. S. Hudson 1) If possible, find a nonzero 2x2 matrix A such that A 2 = O (the zero matrix). If it is not possible, explain why not. Note: nonzero means at least one entry of A is not zero. 2) Write v as a linear combination of u and w . For maximum credit, solve this using a reliable method (guessing the answer may only get partial credit). v = 1 2 u = 2 1 w = 1 1 3) Choose ONE of these to prove. You can answer on the back. a) If A is a symmetric nonsingular matrix, then A - 1 is also symmetric [if you know a formula for the transpose of A - 1 , you can use it without proving it]. b) Prove this part of the TFAE theorem: If A is row equivalent to I , then A is 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 = 0 1 0 0 2) [first version] There were two versions of the quiz. The first one shows the correct year,
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