In Exercises 1–6, determine whether or not the given matrix is stochastic. If so, determine if it is regular, absorbing, or neither.
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Finite Mathematics & Its Applications (12th Edition)
- In Exercises 5–8, use the definition of Ax to write the matrix equation as a vector equation, or vice versa. 5. 5 1 8 4 -2 -7 3 −5 5 -1 3 -2 = -8 - [18] 16arrow_forwardThe bookshop manager at the university has developed a matrix formula for determining the number of Pure and Applied Mathematics textbooks he should order each year. For 2016, the starting point for the formula is the column matrix So. This lists the number of Pure and Applied Mathematies textbooks sold in 2015. 505 Pure 316 Applied Oj is a column matrix listing the number of Mathematics and Physics textbooks to be ordered for 2016. Oj is given by the matrix formula : 01 = A So + B where A= 0.85 0 0.78 80 and B = 75 Determine O1, correct to the nearest integer. a. Given that S, - 499 303 Pure , representing the number of textbooks sold in 2016, b. Applied determine O2 (the numbers of books to be ordered for 2017) using the same matrix equation. The matrix formula above only allows the manager to predict the number of books he should order one year ahead. A new matrix formula enables him to determine the number of books to be ordered two or more years ahead. The new matrix formula is On…arrow_forwardFind the elementary matrix E such that EB = A where 2 3 1 3 6 -8 1 A 4 -3 -2 and B 4 %| 7 -6 7 -6 2 ? ? ? E = ? ? ?arrow_forward
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- A study showed the following migration matrix, which describes the movement of the population of the United States during 1989. In 1989, about 12.2% of the total population lived in State A. What percentage of the total population would eventually live in State Aif the listed migration probabilities were to remain constant over many years? From: State A Rest of U.S. To: 0.9627 0.0059 State A 0.0373 0.9941 Rest of U.S Use technology to determine the approximate percentage of the total U.S population that would evetually live in State A if the migration probabilities remained constant. The percentage of the total U.S. population that would eventually live in State A is %. (Round the final answer to one decimal place as needed. Round all intermediate values to six decimal places as needed.)arrow_forwardSolve each system in Exercises 1–4 by using elementary rowoperations on the equations or on the augmented matrix. Followthe systematic elimination procedure described in this section.arrow_forwardConsider the following system with five components. It operates only if there is a path of functional components from left to the right. The probability that each device functions is as shown. What is the probability that the circuit operates? Assume independence. A. 0.84 B. 0.16 C. 0.035 D. 0.50 E. none of the precedingarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning