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# e408fk - MAS 3105 Quiz 4 and Key Prof S Hudson 1 The matrix...

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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 0 1 2 1 5 U = 1 2 0 3 0 0 1 2 0 0 0 0 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 don’t have the scores from the grader yet, but he estimates that the average was about 35/60. If so, an approx scale is A’s 45-60, B’s 39-44, C’s 33-38, D’s 27-32. He said some students couldn’t write proofs, using the definition of LI for example. You had graded HW on that, so I suppose you know whether this is a problem for you. If

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e408fk - MAS 3105 Quiz 4 and Key Prof S Hudson 1 The matrix...

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