e407k - B are also L.D. Answers and Remarks: The average...

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MAS 3105 March 1, 2007 Quiz 4 and Key Prof. S. Hudson 1) Use a Wronskian to determine whether the three vectors 1, e x , e - x are LI in C [0 , 1]: 2) Find the transition matrix representing the change in coordinates from the basis [ x, 1] of P 2 to the basis [3 x - 1 , 3 x + 1]. 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) Two vectors in V are L.D. if and only if one is a scalar multiple of the other. c) Suppose A is 4x4 and is row equivalent to B . Suppose the first three columns of A are L.D. Then the first three columns of
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Unformatted text preview: B are also L.D. Answers and Remarks: The average was about 40/60. As = 48-60, Bs = 42-47, etc. 1) W ( x ) = det 1 e x e-x e x-e-x e x e-x = 2 since e x e-x = 1. Since 2 6 = 0 they are LI. 2) 3 3-1 1 -1 = 1 / 6-1 / 2 1 / 6 1 / 2 3a) See the proof of the 2/3s theorem (show the vectors span V ). 3b) was HW 3c) Basically, repeat our discussion of dependency relations; that the columns of A and B have the same ones. 1...
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