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e408fk - MAS 3105 Oct 17, 2008 Quiz 4 and Key Prof. S....

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Unformatted text preview: MAS 3105 Oct 17, 2008 Quiz 4 and Key Prof. S. Hudson 1) The matrix A is row equivalent to U . a) Find a basis for N ( A ), and explain briefly how you know it is a basis. b) Do the same for Col A . A = 1 2- 1 1 2 4- 3 1 2 1 5 U = 1 2 3 1 2 2) Are the following sets subspaces of R 3 ? Explain each answer briefly. a) S = { ( x 1 ,x 2 ,x 3 ) T | x 1 = x 2 and x 3 = 0 } b) S = { ( x 1 ,x 2 ,x 3 ) T | x 1 = x 2 or x 1 = x 3 } 3) Choose ONE of these to prove. You can answer on the back. a) If dim(V)= n > 0 and B = { v 1 ,v 2 ,...,v n } is L.I., then B is a basis of V. b) If U and V are subspaces of W then so is U V . c) If B = { v 1 ,v 2 ,...,v n } V is L.I., then any subset of B is also L.I. Remarks and Answers: I dont have the scores from the grader yet, but he estimates that the average was about 35/60. If so, an approx scale is As 45-60, Bs 39-44, Cs 33-38, Ds 27-32....
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This note was uploaded on 12/26/2011 for the course MAS 3105 taught by Professor Julianedwards during the Spring '09 term at FIU.

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e408fk - MAS 3105 Oct 17, 2008 Quiz 4 and Key Prof. S....

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