MATH 204 Exam 2, Spring 2002
American University of Beirut · Mathematics for Social Sciences II · 3 pages
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ENIC\N CNECERSIT
LIBEL ARY
OF BELRTT
April 6,2002
5 6 7 8
instructions:
1.Write your name and circle your section number.
2.Answer,in detail, every part in the space provided for it,and circle your final result.Do
not mention just the answer.
3.The colored booklet is for scratch work and will not be corrected.
RESERVED FOR CORRECTOR
Ih.
ile
V,
V.
VI.
QUIZ GRADE:
> |. The solution to a system of equations having the form 4.” = B can be found by
. ae {3522 )
the matrix multiplication: = 4) °F iw
Vid -SA-7
i 1.(5%) What is the original system of equations?
\ 2h, - 2 i= 14
4x Bm, 2-2-
+ xX, - Xe. 4
2\(10%) What is the solution ?
ert + (- 2A)
“te 4KC5 (¥)
dominated by two firms,A and B:
(0.8 0.2)
Talo 0.4)
Assume currently firm A has 30% of the market share.
1.(5%) Predict the market share of A in the next period.
2.(10%} Assume the transition matrix remains stable.Find the expected equilibrium
shares of the two firms if they exist.
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> III.(20%)Given the matrix
{Determine 4°? = 4x A
2.Find just the 2" row of 4, (the matrix of cofactors of 4 }.
3.Use the’result found in part (2)above, to find |.4). (No other method is acceptable).
MERICAS CMIVERSIT
LIBiARY
OF BEIRUT
4, Use Cramer's rule to solve just for x, in the system:
> IV.(10%)} Find the 2x4 matrix B for which
m V.(25%) A box contains eight different business books ,six different statistics books
and three different history books
1.What is the probability that a randomly selected book is a history book?
2.1n how many ways can a student select one book of each type?
dana
AMERICAN UNIS"!
LIBRARY
OF RUIRTY
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