e104k - c Every consistent underdetermined system has...

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MAS 3105 Jan 14, 2004 Quiz I and Key Prof. S. Hudson Each problem was worth 20 points, with possible partial credit on 1) and 3). The average was 47/60, or about 75-80 per cent, which is normal for a Quiz I. 1) Use Gaussian elimination to put the following system into row echelon form. If it is consistent, find the solution set. [If there are free variables, use α notation in your answer.] 2 x 1 + 3 x 2 + x 3 =1 x 1 + x 2 + x 3 =3 3 x 1 + 4 x 2 + 2 x 3 =4 Answer: S = { (8 - 2 α, α - 5 , α ) } [see problem 1.2.5e]. It is easy to check your answer by setting α = 0 and/or α = 1. 2) Answer each part with “True” or “False”. a) Every homogeneous linear system is consistent. b) Every system in reduced row echelon form is also in triangular form.
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Unformatted text preview: c) Every consistent underdetermined system has infinitely many solu-tions. d) Every system in triangular form has a unique solution. e) Every system in triangular form has a nontrivial solution. Answers: TFTTF 3) Use the traffic flow diagram [given on the real exam] to make a 2x2 linear system of equations. Do not solve it. Answer: After simplification, x 1-x 2 = 50 and x 1 + x 2 = 850. I gave credit for answers in matrix form, but deducted a few points if the equations were not written in standard form. 1...
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