Unformatted text preview: A and B are nxn matrices. a) If S = { v 1 ,v 2 ...v n } , then span( S ) is a subspace of V . b) For all nxn matrices, det( AB ) = det( A ) det( B ). c) If A has two identical rows, then det( A ) = 0. (Use induction. Possible +2 bonus for choosing this one!). Answer: Parts a) and b) are in the text, though the proof of b) on page 112 has only minimal explanation. 3c) This is HW 2.110. Don’t include speciﬁc examples. Do include a basis step ( n = 2) and an induction step ( n > 2). You can then expand on row 1 if it is not one of the two identical rows (you cam ”assume” this, but say so). Explain brieﬂy the calculation that leads to 0. 1...
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 Spring '09
 JULIANEDWARDS
 Linear Algebra, Inductive Reasoning, Det, Prof. S. Hudson

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