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# e208k - MAS 3105 Quiz 2 and Key AM Prof S Hudson Note on...

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MAS 3105 AM: Jan 31, 2008 Quiz 2 and Key Prof. S. Hudson Note on problem 1: ‘Find B ’ means - write out all 9 entries of B . ‘Check’ usually means - show me the calculation on paper. For 1c and 1d, I’ll accept a short proof instead, if you prefer. Parts 1a - 1d are closely related, so do them in order, and you should not need any trial and error. A transpose might help with one part. 1) [10pts each part] 1a) For the matrix A given below, check that A 3 = O . Such a matrix is called nilpotent . A = 0 1 0 0 0 1 0 0 0 1b) Find a nonzero 3x3 matrix B , so that AB = O (for the same A as above). 1c) Find two nonzero 3x3 matrices C and D so that C - D = A . Then, check that CB = DB . 1d) Find nonzero 3x3 matrices E , F and G so that EF = EG . Check. 2) [20pts] Choose ONE of these to prove. Use words and sentences and standard methods to completely explain your reasoning and your formulas. Some of these are just parts of theorems we did in class. If so, you are NOT allowed to simply quote the theorem! You ARE allowed to use previous theorems, definitions and/or previous HW.

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e208k - MAS 3105 Quiz 2 and Key AM Prof S Hudson Note on...

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