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**Unformatted text preview: **Math 425 Exam 1 Jerry L. Kazdan March 3, 2011 12:00 – 1:20 Directions This exam has three parts, Part A, short answer, has 1 problem (12 points). Part B has 5 shorter problems (7 points each, so 35 points). Part C has 3 traditional problems (15 points each so 45 points). Total is 92 points. Closed book, no calculators or computers– but you may use one 3 00 × 5 00 card with notes on both sides. Part A: Short Answer (1 problems, 12 points). 1. Let S and T be linear spaces and A : S → T be a linear map. Say V and W are particular solutions of the equations A V = Y 1 and A W = Y 2 , respectively, while Z 6 = 0 is a solution of the homogeneous equation A Z = 0. Answer the following in terms of V , W , and Z . a) Find some solution of A X = 3 Y 1 . b) Find some solution of A X =- 5 Y 2 . c) Find some solution of A X = 3 Y 1- 5 Y 2 . d) Find another solution (other than Z and 0) of the homogeneous equation A X = 0....

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