Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
11th Edition
ISBN: 9781305283831
Author: Tan
Publisher: Cengage Learning
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Chapter 9.BMO, Problem 2BMO
To determine
To find:
The steady-state vector for the transition matrix
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Find the transition matrix from B to B'.
B = {(1,0) , (0, 1)}, B' = {(1,1), (5, 6)}
-5
[1 5
5
6
6
Let B = {(1,1, 1), (1, – 1, 1), (0,0, 1)}, B' = {(2,2, 0), (0, 1, 1), (1,0, 1)}, and [x]p
[2 3 1]".
(a) Find the transition matrix from B to B'
(b) Find the transition matrix from B' to B
(c) Verify that the two transition matrices from (a) and (b) are inverses of each other.
(d) Find the coordinate matrix [xR
Let B = {(1, 1, 1), (1, −1, 1), (0, 0, 1)}, B′= {(2, 2, 0), (0, 1, 1), (1, 0, 1)}, and [x]B′=[2 3 1]T .(a) Find the transition matrix from B to B′(b) Find the transition matrix from B′to B(c) Verify that the two transition matrices from (a) and (b) are inverses of each other.(d) Find the coordinate matrix [x]B
Chapter 9 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences-Custom Edition
Ch. 9.1 - What is a finite stochastic process? What can you...Ch. 9.1 - Prob. 2CQCh. 9.1 - Consider a transition matrix T for a Markov chain...Ch. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7E
Ch. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - In Exercises 1-10, determine which of the matrices...Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - In Exercises 1518, find X2 the probability...Ch. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Political Polls: Morris Polling conducted a poll 6...Ch. 9.1 - Commuter Trends: In a large metropolitan area, 20...Ch. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - MARKET SHARE OF AUTO MANUFACTURERES In a study of...Ch. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - In Exercises 29 and 30, determine whether the...Ch. 9.1 - Prob. 30ECh. 9.1 - Prob. 1TECh. 9.1 - Prob. 2TECh. 9.1 - Prob. 3TECh. 9.1 - Prob. 4TECh. 9.2 - Prob. 1CQCh. 9.2 - Prob. 2CQCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - COMMUTER TRENDS Within a large metropolitan area,...Ch. 9.2 - Prob. 19ECh. 9.2 - PROFESSIONAL WOMEN From data compiled over a...Ch. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - NETWORK NEWS VIEWERSHIP A television poll was...Ch. 9.2 - Prob. 24ECh. 9.2 - GENETICS In a certain species of roses, a plant...Ch. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 1TECh. 9.2 - Prob. 2TECh. 9.2 - Prob. 3TECh. 9.3 - What is an absorbing stochastic matrix?Ch. 9.3 - Prob. 2CQCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - In Exercises 9-14, rewrite each absorbing...Ch. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - GAME OF CHANCE Refer to Exercise 26. Suppose Diane...Ch. 9.3 - Prob. 28ECh. 9.3 - COLLEGE GRADUATION RATE The registrar of...Ch. 9.3 - Prob. 30ECh. 9.3 - GENETICS Refer to Example 4. If the offspring are...Ch. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.4 - a. What is the maximin strategy for the row player...Ch. 9.4 - Prob. 2CQCh. 9.4 - Prob. 1ECh. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - In Exercises 1-8, determine the maximin and...Ch. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - In Exercises 9-18, determine whether the...Ch. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - GAME OF MATCHING FINGERS Robin and Cathy play a...Ch. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - MARKET SHARE: Rolands Barber Shop and Charleys...Ch. 9.4 - In Exercises 24-26, determine whether the...Ch. 9.4 - Prob. 25ECh. 9.4 - Prob. 26ECh. 9.5 - Prob. 1CQCh. 9.5 - Prob. 2CQCh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - In Exercises 1-6, the payoff matrix and strategies...Ch. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - The payoff matrix for a game is [332311121] a....Ch. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - In Exercises 11-16, find the optimal strategies, P...Ch. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - COIN-MATCHING GAME Consider the coin-matching game...Ch. 9.5 - INVESTMENT STRATEGIES As part of their investment...Ch. 9.5 - INVESTMENT STRATEGIES The Maxwells have decided to...Ch. 9.5 - CAMPAIGN STRATEGIES Bella Robinson and Steve...Ch. 9.5 - MARKETING STRATEGIES Two dentists, Lydia Russell...Ch. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.CRQ - Prob. 1CRQCh. 9.CRQ - Prob. 2CRQCh. 9.CRQ - Fill in the blanks. The probabilities in a Markov...Ch. 9.CRQ - Fill in the blanks. A transition matrix associated...Ch. 9.CRQ - Prob. 5CRQCh. 9.CRQ - Prob. 6CRQCh. 9.CRQ - Prob. 7CRQCh. 9.CRQ - Prob. 8CRQCh. 9.CRQ - Prob. 9CRQCh. 9.CRQ - Prob. 10CRQCh. 9.CRE - Prob. 1CRECh. 9.CRE - Prob. 2CRECh. 9.CRE - Prob. 3CRECh. 9.CRE - Prob. 4CRECh. 9.CRE - Prob. 5CRECh. 9.CRE - Prob. 6CRECh. 9.CRE - In Exercises 7-10, determine whether the matrix is...Ch. 9.CRE - Prob. 8CRECh. 9.CRE - Prob. 9CRECh. 9.CRE - Prob. 10CRECh. 9.CRE - In Exercises 11-14, find the steady-state matrix...Ch. 9.CRE - Prob. 12CRECh. 9.CRE - Prob. 13CRECh. 9.CRE - Prob. 14CRECh. 9.CRE - Prob. 15CRECh. 9.CRE - Prob. 16CRECh. 9.CRE - Prob. 17CRECh. 9.CRE - Prob. 18CRECh. 9.CRE - Prob. 19CRECh. 9.CRE - Prob. 20CRECh. 9.CRE - Prob. 21CRECh. 9.CRE - Prob. 22CRECh. 9.CRE - Prob. 23CRECh. 9.CRE - Prob. 24CRECh. 9.CRE - Prob. 25CRECh. 9.CRE - Prob. 26CRECh. 9.CRE - Prob. 27CRECh. 9.CRE - Prob. 28CRECh. 9.CRE - Prob. 29CRECh. 9.CRE - OPTIMIZING DEMAND The management of a divison of...Ch. 9.BMO - The transition matrix for a Markov process is...Ch. 9.BMO - Prob. 2BMOCh. 9.BMO - Prob. 3BMOCh. 9.BMO - Prob. 4BMOCh. 9.BMO - The payoff matrix for a certain game is A=[213234]...Ch. 9.BMO - Prob. 6BMO
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- Find the transition matrix from B to B'. B = {(-1, 0, 0), (0, 1, 0), (0, 0, −1)}, B' = {(0, 0, 7), (1, 3, 0), (9, 0, 7)} ☐☐☐ ☐ ☐ ☐arrow_forwardLet B = {(1,2), (-1, –1)}, B' = {(-4, 1), (0, 2)} be bases for R?. %3| 2 1 be the matrix for T: R? –→ R² relative to B. 0 -1 Let A = (a) Find the transition matrix P from B' to B. (b) Use the matrices P and A to find [v]B and [T(v)]B where [v]g = [-1 4]". (c) Find P-1 and A' (the matrix for T relative to B'). (d) Find [T(v)]B' two ways.arrow_forward(a) find the transition matrix from B to B′. (b) find the transition matrix from B′ to B.(c) verify that the two transition matrices are inverses of each other.(d) find the coordinate matrix [x]B′, given the coordinate matrix [x]B.B = {(1, 0), (1, −1)}, B′ = {(1, 1), (1, −1)}, [x]B = [2 −2]Tarrow_forward
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- please send step by step complete handwritten solution Q6arrow_forwardLet B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4, 4)} be bases for R², and let [2 A = 23 40 be the matrix for T: R² → R² relative to B. (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [v] and [7(v)]B, where [v] B¹ = [3-4]T. [V] B [T(v)]B = €arrow_forwardLet 8 = {(1, 3), (-2,-2)} and 8' = {(-12, 0), (-4, 4)) be bases for R², and let A = - [83] be the matrix for 7: R² R² relative to 8. (a) Find the transition matrix P from 8' to 8. 6 4 P= 9 4 (b) Use the matrices P and A to find [v] and [7(v)]g, where [v]= [4 -1]. [v]g= Q [7(v)]a = (c) Find A-1 and A' (the matrix for 7 relative to 8'), p-1= - A'= (d) Find [7(v)]g two ways. [7(v)]g = P¹[7(v)]g = [7(v)]g¹ = A'[v]g' =arrow_forward
- According to data collected during one year in a large metropolitan community, 30% of commuters used public transportation to get to work, and this rose by 4% the following year. This is modeled by the transition matrix P P' M= P P' 0.9 0.1 0.1 0.9 , So = [0.3 0.7] where P represents the percentage of people that use public transportation and P' the percentage of people that do not. What percentage of commuters in this communit will use public transportation in the long run? Round the percent to the nearest tenth. O A. 50.0% OB. 37.2% O C. 34.0% O D. 30.0% Carrow_forwardLet 8 = {(1, 3), (-2,-2)} and 8 = {(-12, 0), (-4, 4)) be bases for R2, and let 4 2 A = - [83] 03 be the matrix for T: R2 R² relative to 8. (a) Find the transition matrix P from 8' to 8. P= ↓↑ (b) Use the matrices P and A to find [v] and [7(v)]g, where [v] = [4 -1]7. [7(v)]B (c) Find P-¹ and A' (the matrix for 7 relative to 8'). p-1= ↓1 -88- A'= ↓↑ (d) Find [7(v)]g' two ways. [7(v)] = P¹[7(v)]g = [7(v)]g¹ = A'[v]g' = = [v]8 = = ↓↑ 8 ↓ ↑arrow_forwardLet B= ((1, 3), (-2,-2)) and 8' = ((-12, 0), (-4, 4)) be bases for R2, and let be the matrix for T: R2 R2 relative to B. (a) Find the transition matrix P from B' to B. p= (b) Use the matrices P and A to find [v] and [7(v)le, where [vla [-1 31. [v] = [T(v)18- 11 p-1 11 (c) Find pand A' (the matrix for 7 relative to 8). 41 41 (d) Find [7(vil bwo ways. (7)=P(7) [vila Al- 11 11arrow_forward
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