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e108k - Roughly A’s = 55 to 60 B’s = 49 to 54 C’s =...

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MAS 3105 11AM, Jan 17, 2008 Quiz I and Key Prof. S. Hudson 1) Use Gaussian elimination to put the following system into reduced row echelon form. Use matrix notation. Find the solution set, using α notation (if necessary) in your answer. x 1 + x 2 + x 3 =1 2 x 1 + 2 x 2 + x 3 =4 2) Write down the information in this traffic flow diagram as a 2x2 system of linear equa- tions. Then solve it. Any valid method is OK, but remember to show your work. 3) Answer each part with “True” or “False”. a) A 2x3 matrix in RREF must have at least two 1’s . b) An overdetermined system cannot have free variables. c) Any two inconsistent 2x5 systems (involving the same variables) are equivalent. d) An underdetermined system can have a unique solution. e) A homogeneous system in triangular form has only the trivial solution. Remarks and Answers: The average of the top 25 scores was about 51 out of 60 (85 percent). Quiz 1 is easier than most (except maybe the TF), so the scale is a bit higher.
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Unformatted text preview: Roughly, A’s = 55 to 60, B’s = 49 to 54, C’s = 43 to 48, D’s = 37 to 42. This is just an advisory (unofficial) scale; I’ll give you more info on the scale as the term goes on, and decide on the official scale after the final exam. 1) The solution set is S = { (3-α, α,-2) } . You should use this same notation, or something pretty close. I suggest checking your answer (eg set α = 0 and check that (3,0,-2) works. Then maybe α = 1). The RREF (without the vertical line) is: ± 1 1 0 3 0 0 1-2 ² 2) The traffic diagram was on the board and had only two intersections. The first showed IN = x 1 + 230, and OUT = 150 + x 2 . So, the first equation is x 1-x 2 =-80. Similarly, the second simplifies to x 2 = 130. So, x 1 = 50. You can stop there (you’ve solved it), or you can write S = { (50 , 130) } , using the notation of problem 1. 3) FFTFT 1...
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