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math54-fall06-mt1-Voiculescu-soln

# math54-fall06-mt1-Voiculescu-soln - p r i n t your name S...

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print your name: Mark Lqndr, SID: !8672ij2 Signature: , , , Discussion Section : U " z i (I) Math 54 First idt term' Fall 2006 Instructor: D.V. Voiculescu This i s a "closed book" exam, so you may not bring i n or use notes or the textbook. Calculators are not allowed. Please write your name, SID and Discussion Section # on everything you hand in, including this sheet o f paper on which you have t o provide the answers t o Problem I11 (the true or false questions ). For Problems I and I1 you must show the method and calculations you use t o get the answers ( write the solutions t o these i n your blue book ). The Requirementis 20 points. Problem I (5pts). Solve by Gauss elimination the system : x+y = 1, x+z = -1, t+y = 1, t+z-2w = -1 Problem I1 (4pts). Orthogonalize by Gram-Schmidt i n x4 the vectors: (l,l,@,@), (-l,@,l,@),

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