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final_s09_post - Math 235 Final Exam Spring 2009 NOTE The...

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Math 235 - Final Exam Spring 2009 NOTE: The questions on this exam does not exactly reflect which questions will be on this terms exam. That is, some questions asked on this exam may not be asked on our exam and there may be some questions on our exam not asked here. 1. Short Answer Problems a) By considering the dimensions of the range or null space, determine the rank and the nullity of L : P 2 M (2 , 2) given by L ( ax 2 + bx + c ) = a a c c . b) Let V, W be finite dimensional vectors spaces over R . Give the formula for finding the matrix of a linear transformation L : V W with respect to any basis B for V and any basis C for W . c) Let A be an n × n matrix. Give the definition of an eigenvalue and eigenvector of A . d) State the principal axis theorem. e) State Schur’s theorem. 2. Let y = 5 - 9 5 and let W be the subspace of R 3 spanned by - 3 - 5 1 , - 3 2 1 . a) Find proj W ( y ).
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