Quiz-1-Fall-2002-03

# Quiz-1-Fall-2002-03 - ummzu rkrvnksi‘i‘v“? L Ii rs...

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Unformatted text preview: ummzu rkrvnksi‘i‘v“? L Ii rs I<~A\ RAY m1" lilﬁiltilii QUIZ - l — M204. _ I y ‘ Nov. 9,2002 Name::' it'ixiﬁl‘ ‘ ‘ : r 5 6 C7,) 8 9 10 lﬂSfod/bﬂS.‘ ' _ a H4 (3 1. Write your name and circle your section number. X H ' 2 Answerjn detail, every part in the space provided for it and circle your ﬁnal result .Do not 4 mention just the answer. . - ‘2'): 4 .t 33: 1‘. . 3.The colored booklet is for scratch work and will not be corrected. 5‘9: ' -+ c x 2_ 7- . LThe solution to a system of equations ving the form = B can be found by the matrix (R \ . 7 —1 - 60 . I - ,. i I multiplication: X = MyktL/L I 2. ~__ A a 12 —6 —24 1.00%) What is the original system of equations? :7 - s ‘ )_ ‘c: '3 H1...” H‘ «Axill- _ I -'_ ’3] ~— 1 t 3 Que LLJU r\ 'AWA‘U' Ll AIX :3 I: (A. 1 ﬂ ( 13. *6 ) r: s. . iri VERSE "l s c _ ,_ _ a J _ , .l2 c1 fulﬁl H a! 7‘ '13 h , If). '1‘. “U, .53. “.1. I?“ ~ .. 3 C) Q54“; f: ( if ) 1 ' is. ' . I lieutﬁ‘l‘ﬁr’ r=.'._' “‘6 1 l r .5 Fl "7" 75: - ’ " " l 'l l’ g p M 3" 0 (“45’ 9/ 7T 7 q. 2.(5%) What is the solution ? (11. .15..)(72. ) I U‘Li...;.,':)i'{ \ f in“ I a v’\ .r my) 1'» 5H .. li.(iO%)The following matrix gives the transition probabilities related to a market dominated by two ﬁrms, A and B: T = 0.4 0.6 r a 0.2 0.8 r Assume currently ﬁrm A has 65% of the market share. 1.(5%) Predict the market share of A in the next period. .‘J g'.‘ fir: " (M‘ , C.“ q Li‘- 1‘ i‘: [\L r L: ‘;0r}i : l; if 2.619%) Assume the transition matrix remains stable. Find the expected equilibrium shares of / the two ﬁrms, if they exist. ‘. i y.' P. " 2.“\_\~"‘IL"-‘Illar" (. _._u;,,._--——........_._...._ 'JAxrlHu'n I‘VH'EHSIT ‘ LIB NARY 0F BEJBU'I i. 3 — 2 — 3 1.Caiculate |A| by adding columns. Show your work —SI j; A o -_-. (o —6_lé)—(O-§o+’§.) —2 m? 3 —:2 “33 +3‘EYJ._ / x1 28 2. Use Cramer’s rule to solve just for x3 in the system: A[ ]= {— 14]. Here A is the —— 7 ~ ~5 1 -2 |ii.(20%)Giventhematnx A: —4 O —2 givenmatn'x. Cramms Quite was ‘3: X3 =| 'i (xiv) I W“ "-5 r62; avg—w.- MJ my: ng 1% ‘_7‘7i “L1 0 L; r» "ER “,‘ ‘ - 3i] 3. Find just the 3rd celgmn of A (the matrix of cofactors of :1)“ “I \Y a “tth O '- 9‘ = ' ~ﬂ s-{io-sh !) Jl-'§=(o+q);”‘ 4.Determine A2 = A x A s I —1)(—-s I «#2 ) [(52.5-94) (-540-M30ua2-i-6h 2: .2, :2 w w w f; I; r 17M". '~" ' ‘ "H'EHMTM “Emmy 0F mama-r ‘ j-2i+l ; if i=j !V.(10%) Find the 3X3 matrix B for which by = 21'2-j ; if 1' at j - 01.3 with) whim :g Amuzrafmna l3 Bé m3 (Aug-1 s 3-31141: :a‘ﬂh-l Q1;:a(Q)/3 :3 g a“: a”) g, .% “J A31: 1(Q)(2)= Zé anal 0x31"; 3.. 713).}! = — 7. V.(20%)The table below has been provided by the quality control department of a factory — Productl P: Product2 P2 A Accetabne E- B Unaccetable _ ' One item is randomly taken from the batch. Find the following probabilities: 1. PW ,,,_ We) .—. 139.9. :13. :lCM‘BQ earn-«w- ‘Zupo 'w \ A, . -3 / 2. P(AnP1) _ ' — 2 é. “a .1. -: 0.& ’ .a- ' w (4 Ipﬂpsi/' / 3. P(BUP2) ‘ 1 9(1),} 461%,)- €(EﬁPz‘l "1 30 SG 9“ E, I: 7:, 5‘3 C "2'30 4' 2‘20 ‘Zoo A 4* / 4' PM A) .. = PCPg of); «2-. ﬁs/wa 2a : \OrH WA ) rap/22w '90 j ...
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## This note was uploaded on 01/02/2011 for the course MATH 204 taught by Professor Romyarbid during the Three '10 term at Notre Dame AU.

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Quiz-1-Fall-2002-03 - ummzu rkrvnksi‘i‘v“? L Ii rs...

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