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# e308fk - MAS 3105 October 3, 2008 Quiz 3 and Key Prof. S....

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Unformatted text preview: MAS 3105 October 3, 2008 Quiz 3 and Key Prof. S. Hudson 1) (30 pts) Answer True or False: The set of symmetric 2x2 matrices, denoted R 2 x 2 , is a vector space. If A is row equivalent to B , then det A = det B . adj ( A T ) = (adj A ) T If A is nonsingular, then adj ( A- 1 ) = (adj A )- 1 { ( x 1 ,x 2 ) : x 1 + 3 x 2 = 0 } is a subspace of R 2 . { ( x 1 ,x 2 ) : x 1 } is a subspace of R 2 . 2) (10 pts) Suppose A is singular. What can you say about A adj A ? (explain briefly) What about (adj A ) A ? (explain briefly) 3) (20 pts) Choose ONE of these to prove. Assume A and B are nxn matrices. a) If AB = I , then BA = I . b) Use induction to prove that if A has two identical rows, then det A = 0. c) det( AB ) = det( A ) det( B ) [you can use facts about E s, HW results, and any previous theorems. But prove all the cases/lemmas/etc of Thm 2.2.3] Bonus (about 5 points; from exercise 2.2.19): How many additions are required to compute the determinant of a 5x5 matrix using cofactors ? Explain.the determinant of a 5x5 matrix using cofactors ?...
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## This note was uploaded on 12/26/2011 for the course MAS 3105 taught by Professor Julianedwards during the Spring '09 term at FIU.

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e308fk - MAS 3105 October 3, 2008 Quiz 3 and Key Prof. S....

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