In Problems 5-8, find the pivot element, identify the entering and exiting variables, and perform one pivot operation. x 1 x 2 s 1 s 2 P 1 6 1 0 0 36 3 1 0 1 0 5 − 1 − 2 0 0 1 0
In Problems 5-8, find the pivot element, identify the entering and exiting variables, and perform one pivot operation. x 1 x 2 s 1 s 2 P 1 6 1 0 0 36 3 1 0 1 0 5 − 1 − 2 0 0 1 0
Solution Summary: The author calculates the pivot element, identify the entering and exiting variables, and execute one pivot operation. The pivot column contains most negative indicator in the last row of the simplex tableaux.
Prove let Aand B submodul of M
A is large sub podule A large of B
and B large of M.
SM
B Smale sub module B/A smal of M/A
and As Mallof M.
Give example and expleain caim.
Amonorphism and split
d) Determine the following group: Hom, (Q,Z)
and Ho M₂ (Q, Q) and Hom (2/12, Q) =
Q2: Using the Laplace transform, find the solution for the following equation
y"" +y" = 6et + 6t + 6. Suppose zero initial conditions (y"" (0) = y"(0) = y'(0) = y(0) = 0).
1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
Chapter 6 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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