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Unformatted text preview: MAS 3105 June 22, 2005 Final Exam Prof. S. Hudson Name Show all your work and reasoning for maximum credit. If you continue your work on another page, be sure to leave a note. Do not use a calculator, book, or any personal paper. You may ask about any ambiguous questions or for extra paper. If you use extra paper, hand it in with your exam. 1) [20pts] Set B = { v 1 , v 2 , v 3 , v 4 } = { (1 , , 0) T , (1 , , 1) T , (0 , 1 , 1) T , (0 , , 1) T } . So, B is a set of 4 column vectors in R 3 . Answer, and explain briefly: a) Is B a spanning set of R 3 ? b) Is B linearly independent? c) Let C = { v 1 , v 2 , v 4 } . Is C a basis of R 3 ? d) Let D = { v 1 , v 2 , v 3 } . Show that D is a basis of R 3 . e) Find the transition matrix from D to the standard basis of R 3 . 2) [15 points] Choose ONE of these to prove (you can use the back). a) If an nxn matrix A is diagonalizable, then it has n L.I. eigenvectors....
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 Spring '09
 JULIANEDWARDS
 Linear Algebra, Unitary matrix, Matrix representation, Prof. S. Hudson, squares problem Ax

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