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e109k - MAS 3105 Quiz I and Key May 7 2009 Prof S Hudson 1...

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MAS 3105 May 7, 2009 Quiz I and Key Prof. S. Hudson 1) Find the solution set, using α notation, if necessary. x 1 + 3 x 2 + x 3 =2 x 2 - x 3 =4 2) For each system, label it as underdetermined, overdetermined or square. Also, label it as RREF, REF (but not RREF) or neither. Then describe how many solutions there are, and explain that briefly. [total = 9 answers]. A = 1 2 0 1 | 5 0 0 1 3 | 4 , B = 1 2 0 | 5 0 0 0 | 1 , C = 1 0 | 1 1 1 | 1 A) B) C) 3) Answer each part with “True” or “False”. a) An overdetermined system can be consistent. b) Gaussian elimination can change a consistent system into an inconsistent one. c) Any two consistent 2x5 systems are equivalent. d) Matrix multiplication is associative (eg, the associative property is true in this setting). e) Gaussian elimination can change a non-homogeneous system into a homogeneous one. SMALL BONUS: Justify your answer to the last True-False question; part (e). Answers and Remarks: Quiz I is intended to help you get off to a good quick start in this fast-paced course. The material is relatively easy and the Quiz should not seem very
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