ef06fk - MAS 3105 Final Exam and Key Prof S Hudson 1[10pts...

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MAS 3105 Dec 13, 2006 Final Exam and Key Prof. S. Hudson 1) [10pts] Solve for X , given XA + C = X and A = 2 1 0 2 C = 0 - 1 1 5 2) [10pts] Use a Wronskian to show that these vectors are LI in C [ - π, π ]: e x , e - x , e 2 x . 3) [10pts] You are a corporate spy hired to investigate student preferences in FIU math classes. After intercepting several encrypted text messages, you discover their coding matrix A , and most of their decoding matrix B . Find the missing entry of B and decode the message: 21 54 42 64 155 106 25 63 38. At the end, as usual, ‘1’ means ‘a’. Also, ‘0’ means ‘blank’, etc [so, 0 thru 26 = blank, abcde fghij klmno pqrst uvwxy z] A = 1 2 1 2 5 3 2 3 2 B = 1 - 1 1 2 0 - 1 - 4 1 4) [10pts] You are given three data points for ( x, y ): (0 , 1) , (3 , 4) and (6 , 5). (You may put these into a chart). Find the best least squares fit by a linear function, y = c 0 + c 1 x . 5) [10pts] Let B = { (1 1 1 1) T , (1 - 1 - 1 1) T , (1 - 1 1 3) T } , and S = span( B ). Use the GS process to find an orthonormal basis of S . Note: the first two vectors are already orthogonal, and both have norm = 2.
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