e105k - =3 3 Answer each part with “True” or...

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MAS 3105 May 12, 2005 Quiz I Prof. S. Hudson NAME Show all your work and reasoning for maximum credit. If you continue your work on another page, be sure to leave a note. Do not use a calculator, book, or any personal paper. You may ask about any ambiguous questions or for extra paper. If you use extra paper, hand it in with your exam. 1) Two sets of one-way streets intersect as shown [see the textbook, page 21]. The streets are marked with their average hourly volume of traffic, but some are not known. Set this problem up as a linear system of equations in standard form. You do not have to do any GE or solve it. 2) Solve the following system, using α notation (if necessary) in your answer. x 1 + 3 x 2 + x 3 =1 x 2 - x 3
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Unformatted text preview: =3 3) Answer each part with “True” or “False”. a) If A is a 3x5 matrix then A x = b is overdetermined. b) If A is a 3x5 matrix in REF then a 32 = 0. c) Interchanging two equations in a system is a Type I operation. d) If A is nonsingular, then A x = b is consistent. e) A homogeneous system with a nonzero solution has infinitely many solutions. Answers: 1) See the example on page 21, and the matrix at the top of page 22. But your answer should be in equation form, so write x 1-x 2 = 160 etc (4 equations). 2) This is already in REF, and x 3 = α is free. From Back Sub., we get { (-8-4 α, 3 + α, α ) } 3) FTTTT (you can ask me about these, of course). 1...
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