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Unformatted text preview: CME302 Homework 1 Grading Comments October 6, 2009 T&B 2.1 Two common ways to prove this: the way given in the solutions, and by induction. If the second method is used, a formal induction proof is required for full points (3 points otherwise). In particular, you need to identify the base case, induction hypothesis, and perform the induction step. Some students appealed to a more general theorem: A normal u.t. matrix is diagonal. This approach is discouraged (3 points given if no other proof is stated): it defeats the point of the the problem, and you won't get much out of solving it this way. Now, we don't want you to become paranoid about proofs: we accept that 1 + 1 = 2  no need to pull a Whitehead & Russell. But if you find that you can plug a problem into a theorem that you looked up and that we didn't cover in class and thereby complete the problem in one line, you should look for another, quite likely more educational, proof. T&B 2.6 The hardest part of this problem is showing your basis of the null space is complete. One can either derive the null space and show it is complete simultaneously by solving (I + uv )x = 0 for x, or one must show that for all vectors w not parallel to u, Aw = 0. T&B 3.3a,b Some students forgot to determine a vector for which equality is achieved in each case. T&B 5.3a A few students forgot to find U and V with the fewest negative signs. T&B 5.3b If you missed points on this problem, have another look at Fig. 4.1 in T&B. 1 ...
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This document was uploaded on 06/17/2010.
 Fall '09

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