e206fk

e206fk - MAS 3105 Quiz II and Key Sept 27, 2006 Prof. S....

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MAS 3105 Sept 27, 2006 Quiz II and Key Prof. S. Hudson 1) [10pts] Suppose A is a type I matrix (it swaps rows) and B is a type III matrix. What is det( ABBA )? Explain. 2) [20pts] Find 2x2 matrices A , B and C such that: none of them are O (the zero matrix), none are the same, and CA = CB . [This is similar to a HW problem, but that had AC = BC instead]. 3) [10pts] Find three different examples of a 2x2 matrix A such that AA = A . Hint: at least two can be pretty simple, maybe even familiar. 4) [20pts] Choose ONE of these to prove. Use the back if you need more space. Use words and sentences and standard methods to completely ex- plain your reasoning and your formulas. a) If A and B are nonsingular they are row equivalent (you can use facts from the HW to prove this). b) If A is nonsingular then det(A) is nonzero (This part of Thm 2.2.2 - don’t just quote that theorem). c) If A has two identical rows, then det(A) = 0 (use induction). Answers:
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e206fk - MAS 3105 Quiz II and Key Sept 27, 2006 Prof. S....

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