MATH 204 Exam 2, Fall 2002

LEBRARY GE HA GHE Nov. 9,2002 ‘ ( 8 9 10 instructions: 1. Write your name and circle your section number. a 2 Answer,in detail, every part in the space provided for it and circle your final result .Do not mention just the answer. neh + Saye 4, 3.The colored booklet is for scratch work and will not be corrected. Sm, 4 fxg % . 1. The solution to a system of equations b ving the form AX = B can be found ia the matrix A 7 60 multiplication: =X “(3 mh 24 ohh V1 a AY. ao 1.(10%) What is the original system of equations? : e bs. ‘ Ve Ga Ht Ves we briny Hae vest ue ws Ak=6 Ais C4 6) eat He invesse M MH ef ach. a Ke ~) Doe UR ya. Be Ousich AZ = (on za )er K Nowseess ye fa@ FT)... Ma ny phoned ours, AK s# i (As 9/ a)" 4 “ val .(5%) What is the solution ? So Ny Xs “e (sey) 0 xb 7 u I.(10%) The following matrix gives the transition probabilities related to a nfarket dominated by two firms, A and B: rs 0.4 0.6 0.2 08 Assume currently firm Ahas 65% of the market share. 1.(5%) Predict the market share of A in the next period. a y » fort a les Orit, Oe ats ) _ a ose —“ , poe fe sf , yo eee Poe : - Govt : Cob Re yt ee uo) 2 SS { . (0 ha rs . _ - iy ‘a if ; oe rae Ke? bo! y 4 \ ¥ 2:{40%) Assume the transition matrix remains stable, Find the expected equilibrium shares of thet two firms, if they exist. peck YN UNIVERSITY Pp LIBRARY OF BEIRUT ‘ -5 1 -2 Ill.(20%)Given the matrix 4=|-4 0 -2 3-2 -3 1.Calculate || by adding columns. Show your work. . -5S | 3 45 = (co —6-16)~(¢ -Qo +12) 3| 3-9 — 22 +8 =\-147] wa x, 28 2. Use Cramer's rule to solve just for x, inthe system: Al x, |=|—14 [Here Ais the x; -7 given matrix. CLOMmEnSs Cube Sony“ « Xe =| atel [A] we bor and Axa ¢ eo 1.6 te -4 O (4 [3-2 -4| my X2= SKS x2 Aeerccmey fo tome Ba py 3. Find just the 3” column of A, (the matrix of cofactors of A). i. ube f= 0 = ES “=f fee | 32 (0 +4) = on y 4.Determine A? = Ax A oS | «eZ \Gs { 9% ) [ab -4-) (-$ 40+) (to -246), “4 “5 set on 3 73 ‘ Somphe 4 hove Wh. ating val ly 'VERSIT Dy, LiBwary OF fKIRuT * WV,(10%) Find the 33 matrix B for which b, “fn . i inj Mey 35 fits 4 tex r faa yd) “ey Ren de 4 120 o 4 ¢ ang x ai iy = AUial=ey Ss - | of Y 443 =e 220) (Z)26 © AQ )20 2(2@)*(1): z \% 36 -2 a Aes * v\-8h4 te G-4plen] aren Blea) a4 Ags 2(9)(2)226 ane Ayge y-2U(B)alz -Z V.(20%) The table below has been provided by the quality control department of a factory: y Product 1 (P1) | Product 2 (Pz) | Product 3 (Ps) | tetal (A)Acceptable 50 42 78 19qo (B)Unacceptable | 12 8 10 20 Tetof 62 So EB Zoo One item is randomly taken from the batch. Find the following probabilities: 1. P(A) F - We : 2 do 3 5 a . (A ) Se “Ww LL 3 Lo 2. P(AAP,) ; - Oo + $5 x wl zs jor ; . _ BE 20 y —- Lo 3. P(BU P2) - Be $° . 3 = a2 = os¢ | Soo + Feo 7 Wo 6 a 4. P(Ps| A) we = PCPA N A) = Fs/we . 48 2 low F(A | Fo / 206 iy