e307k

# e307k - The average was about 40/60 The unoﬃcial scale...

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MAS 3105 Feb 20, 2007 Quiz 3 and key Prof. S. Hudson 1) [10pts] Use Cramer’s Rule to solve for x 2 . Show all your work clearly. 2 x 1 + 3 x 2 = 3 3 x 1 + 2 x 2 = 5 2) Short answer problems - 5pts each. a) Solve for X (in terms of A , B - 1 , I , etc), given that 2 X + B = AX . b) Give an example of a pair of 2x2 matrices, A and B , such that no X solves part a). c) Based on your MHW, tell me what you know about magic(24). 3) [20pts] True or False. Let L = { v 1 , v 2 , v 3 , v 4 } = { (1 , 1 , 0) T , (2 , 2 , 0) T , (0 , 1 , 1) T , (0 , 2 , 2) T } . L is a spanning set for R 3 . L ∪ { e 1 } is a spanning set for R 3 . L is linearly independent in R 3 . e 1 , v 1 , v 4 is linearly independent in R 3 . v 1 , v 3 , v 4 is linearly dependent in R 3 . 4) [15pt] Choose ONE, to prove on the back; assuming A and B are nxn. a) det A = det A T (use induction). b) det ( AB ) = det ( A ) det ( B ) (you can assume A is nonsingular). c) Prove that if L V , span( L ) is a subspace of V . Remarks and Answers:
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Unformatted text preview: The average was about 40/60. The unoﬃcial scale starts with A’s = 48 to 60 etc (then, each letter grade is 10 percent (6 points) lower). I also computed the total of your 3 quiz scores, and estimated your semester grade on the upper right corner of your quiz. The average total was 123/180. This does not yet include your HW or MHW grades. I felt the grades were lowest on problem 2. Please practice problems like 2a) [which were also on HW2 and Quiz 2] until you’ve mastered them; these should be easy by now! 1) x 2 = det A 2 / det A =-1 / 5 2) X = ( A-2 I )-1 B ; A = 2 I and any B 6 = O ; It is a singular matrix 3) FTFTT 4) See the text. 1...
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