In Exercises 9–12, convert the absorbing stochastic matrix to standard form.
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Finite Mathematics & Its Applications (12th Edition)
- In Exercises 13–18, perform each matrix row operation and write the new matrix. -6 4| 10 13. 1 5 -5 3 4 7 -12 6 9 40 3. 14. 1 -4 7|4 2 0 -1 |7 1 3 -3 15. 1 -3R, + R, -2 -1 -9- -9- 16. 3 3 -1 10 -3R + R2 1 3 5 1 -1 1 1 3. 1 -2 -1 17. 2 4| 11 -2R, + R3 5 1 6. -5R, + R4 1 -5 2 -2 4 -3 -1 18. 3 2 -1 -3R + R3 -4 4 2-3 4R, + R4 -len すす 2. 1. 2. 1. 3.arrow_forward[M] In Exercises 37–40, determine if the columns of the matrix span R4.arrow_forwardDetermine whether the matrix is stochastic.arrow_forward
- The 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_forwardProve the ergodic-stochastic transformation.arrow_forwardDetermine which of the matrices in Exercises 1–6 are symmetric. 3.arrow_forward
- Use Cramer’s rule to compute the solutions of the systems in Exercises 1–6.arrow_forwardIn Exercises 29–32, find the elementary row operation that trans- forms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first.arrow_forwardShow the situation in the picture where A is a nxn reversible matrix.arrow_forward
- Compute the steady-state matrix of the stochastic matrix. 1 1 1 0 - 4 3 1 2 0 1 0 3 1 0 0 1 - 4 3 0 0 2 3 0 0 0 0arrow_forwardFind the inverses of the matrices in Exercises 1–4.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_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning