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# e311k - MAS 3105 Quiz III and Key Prof S Hudson 1[20pt a...

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MAS 3105 Feb 17, 2011 Quiz III and Key Prof. S. Hudson 1) [20pt] a) Find adj( A ). b) Use that to ﬁnd A - 1 . Check your work. A = 1 1 0 0 2 1 0 0 3 2) [20pt each] Choose TWO to prove. Mark them clearly. You can answer on the back. a) Prove that if A is nonsingular and upper triangular, then adj( A ) is also upper triangular. b) Suppose A and B are both nxn. Prove that if AB = I , then A is nonsingular. Do not quote HW here. c) Use induction to prove that if A is upper triangular, then det A = a 11 a 22 ...a nn . d) Thm 3.2.1: Span { v 1 ,v 2 ,...v n } is a subspace of V . [use the def of subspace] e) For every m × n matrix A , N ( A ) is a subspace of R n .[use the def of subspace] Remarks and Answers: The average was approx 40/60. The scale is approx A’s = 49 to 60 B’s = 43 to 48 C’s = 37 to 42 D’s = 33 to 36 Currently the Quiz averages are approx 52, 44, 40 [these ﬂuctuate a little as people drop or change rank] with a combined average of 45. You can estimate your current

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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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e311k - MAS 3105 Quiz III and Key Prof S Hudson 1[20pt a...

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