e408k

# e408k - MAS 3105 Quiz 4 and Key AM: Feb 28, 2008 Prof. S....

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MAS 3105 AM: Feb 28, 2008 Quiz 4 and Key Prof. S. Hudson 1) [40 pts] Set B = { v 1 , v 2 , v 3 } = { (1 , 0 , 0) T , (1 , 1 , 0) T , (1 , 0 , 1) T } . So, B is a set of 3 column vectors in R 3 . Answer, and explain brieﬂy: a) Is B a basis of R 3 ? b) Find the transition matrix from B to the standard basis of R 3 . c) Notice that w = (3 , 1 , 0) T is a simple LC of v 1 and v 2 . Find the coordinates of w with respect to B . Write your answer as a column vector. d) Suppose B 2 = { v 3 , v 2 , v 1 } . Find the transition matrix from B 2 to B . e) Find the coordinates of w with respect to B 2 (as in part c). Check your answer to (d) using your answers to (c) and (e). 2) Choose ONE of these to prove. You can answer on the back. a) If the columns of A are LI and Ax = b is consistent, then the system has a unique solution. This is a rephrasing of Thm 3.3.2; so, prove it, don’t just quote it. b) If dim(V)= n > 0 and B = { v 1 ,v 2 ,...,v n } spans V , then B is a basis of V. c) Any two bases of

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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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e408k - MAS 3105 Quiz 4 and Key AM: Feb 28, 2008 Prof. S....

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