e304k

# e304k - MAS 3105 Quiz 3 Key Feb 16, 2004 Prof. S. Hudson 1)...

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MAS 3105 Feb 16, 2004 Quiz 3 Key Prof. S. Hudson 1) Use Cramer’s Rule to solve for x 2 . Show all your work clearly [and check your answer if you have time]. 2 x 1 + 3 x 2 = 12 3 x 1 + 2 x 2 = 13 2) Suppose that A and B are 3x3 matrices. Answer True or False: If A is row equivalent to B , then det A = det B . If B is row equivalent to a nonsingular matrix, then det ( B ) is nonzero. If det (2 A ) = 8 then det ( A - 1 ) = 1. If det ( A ) = 1 then A - 1 = adj A . The set of 2x2 matrices, denoted R 2 x 2 , is a vector space. 3) Choose ONE of these to prove. Assume A and B are nxn matrices. You can answer on the back. a) If A is square with two identical rows, then det A = 0. [Use induction.] b) State and prove Cramer’s Rule. c) If S = { v 1 ,v 2 ...v n } , then span( S ) is a subspace of V [Mention all 4 parts of the deﬁnition of subspace, and prove parts 3 and 4 carefully]. Key: The average was about 47/60, or about 78 per cent - pretty good. Generally the scores were high on problems 1 and 2.

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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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e304k - MAS 3105 Quiz 3 Key Feb 16, 2004 Prof. S. Hudson 1)...

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