e107k - and 16 out of 20 The unofficial scale is A’s...

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MAS 3105 Jan 18, 2007 Quiz I and Key Prof. S. Hudson 1) Use Gaussian elimination to put the following system into RREF. You do not have to find the solution set. 1 2 3 0 4 0 5 1 2 3 0 4 1 12 0 0 0 1 4 1 13 2) Answer each part with “True” or “False”. a) If a linear system has at least two solutions, it has infinitely many. b) A 5x3 system cannot have free variables. c) Every 3x5 system has three lead variables. d) Every consistent square system has a unique solution. e) Every consistent underdetermined system has infinitely many solutions. 3) Explain your answer to the last True-False question. Give a reason that it is always true, or give an example to show it can be false. Either way, include a few sentences in your answer. Remarks and Answers: The average among the passing scores was about 50/60, which is a little high even for Quiz 1. The averages for the 3 parts separately were about 19, 15
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Unformatted text preview: and 16 out of 20. The unofficial scale is: A’s 54-60, B’s 48-53, C’s 42-47, D’s 36-41. 1) I meant to draw in a vertical line after column 6, but it’s not really important (see Ch 1.2 problem 1) and this didn’t seem to bother anyone. Answer: 1 2 3 4 5 1 4 6 1 7 2) TFFFT 3) Since it is underdetermined, there are more variables than the number of equations, which is the maximum number of lead variables. So, there is a free variable, and infinitely many solutions. You cannot justify statement 2e with an example, because it says ” Every ...”. Somehow, a few people who answered ”False” gave a pretty good discussion [even with the wrong conclusion], and I gave them a little partial credit. But this is very unusual. 1...
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