midterm1sol.pdf - Math 54 First Midterm Exam, Prof....

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Math 54 First Midterm Exam, Prof. SrivastavaSeptember 23, 2016, 4:10pm–5:00pm, 155 Dwinelle Hall.Name:SID:Instructions:Write all answers in the provided space.This exam includes two pagesof scratch paper, which must be submitted but will not be graded.Do not under anycircumstances unstaple the exam. Write your name and SID on every page. Show your work— numerical answers without justification will be considered suspicious.Calculators, phones, cheat sheets, textbooks, and your own scratch paper are not allowed.UC Berkeley Honor Code:As a member of the UC Berkeley community, I act withhonesty, integrity, and respect for others.Sign here:QuestionPoints120212310418Total:60Do not turn over this page until your instructor tells you to do so.
Name and SID:1. (20 points) Circle always true (T) or sometimes false (F) for each of the following. Thereis no need to provide an explanation. Two points each.For parts (a)-(f), assumeAis an arbitrarym×nmatrix andRis the reduced rowechelon form ofA. For parts (g) and (h) assumeAandBare arbitraryn×nsquarematrices.(a)Ais invertible if and only ifRis invertible.TF
(b) The column space ofAis equal to the column space ofR.
(c) The null space ofAis equal to the null space ofR.T
(d) The linear transformationsT(x) =AxandS(x) =Rxare the same.TF

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Term
Spring
Professor
Chorin

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