منابع مشابه
The real final exam.
Editor’s Note: Every departing Medical Student, Graduate Student, Urology Research Resident, and Post-Doctoral Fellow trained in Dr. Donald S. Coffey’s laboratory or classroom for 4 decades has been given this “real final exam”—in either oral, written, or both forms. Some believe the wisdom in it passed on to the next generations of cancer researchers is as vast and generous and dedicated to th...
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Please answer the following questions in your blue book, one question per blue book. No credit will be awarded for answers without explanations. Calculators are allowed, but no points will be taken o¤ if you are unable to simplify a mathematical expression. Point totals are provided next to each question; the suggested number of minutes to spend on each question roughly corresponds to the point...
متن کاملMath 312 Final Exam
a) What are the possible values for the rank of A? Why? Solution By the Rank-Nullity Theorem 0 ≤ rank (A) ≤ min{6, 4} = 4. b) What are the possible values for the dimension of the kernel of A? Why? Solution Since dim(image(A)) ≤ 4, by the Rank-Nullity Theorem 2 ≤ dim ker(A) ≤ 6. c) Suppose the rank of A is as large as possible. What is the dimension of ker(A)? Explain. Solution Since then dim(i...
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(This can be shown using a basis argument, which would amount to what most of you wrote anyway.) Thus, given S ∈ L(V ) such that imS ⊆ imT , we can define R = (T |W )−1S, from which it follows TR = S. Conversely, if S = TR, then since linear operators preserve inclusion and R(V ) ⊆ V , we have S(V ) = (TR)(V ) ⊆ T (V ); that is, imS ⊆ imT . 2. Let T be a linear operator on V with distinct eigen...
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ژورنال
عنوان ژورنال: Canadian Medical Association Journal
سال: 2008
ISSN: 0820-3946,1488-2329
DOI: 10.1503/cmaj.081611