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# e306k - MAS 3105 Quiz 3 and Key Prof S Hudson 1 Find det(A...

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MAS 3105 May 25, 2006 Quiz 3 and Key Prof. S. Hudson 1) Find det( A ), if A is 3x3 and it factors into A = LU = 1 0 0 l 21 1 0 l 31 l 32 1 u 11 u 12 u 13 0 u 22 u 23 0 0 u 33 2) Which of these are spanning sets of R 3 ? Justify your answers. a) { (1 , 0 , 0) T , (1 , 1 , 0) T , (1 , 1 , 1) T , (2 , 2 , 2) T } b) { (1 , 1 , 0) T , (2 , 2 , 0) T , (1 , 1 , 1) T , (2 , 2 , 2) T } 3) Choose ONE of these to prove (on the back is OK). Assume A and B are nxn matrices. a) Show that if AB = I , then BA = I . b) If L is a list of vectors in V , then span( L ) is a subspace of V . c) If A has two identical rows, then det ( A ) = 0 (use induction). Bonus (5pt): Suppose A = [1 1 1; 2 2 2; 3 3 3] (notation as in MATLAB, etc). Without doing any numerical work, predict the answer to A * adj A = Remarks + Answers: The average was about 50/60. Problem 1) was pretty easy. Problem 2 was harder, mainly because it came from Ch 3.2, not in HW3. 1) det(
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