The matrices in Exercises 13–18 are absorbing stochastic matrices in standard form. In each, identify R and S and compute the fundamental matrix and the stable matrix.
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Finite Mathematics & Its Applications (12th Edition)
- 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_forward4 11. 5 3 2 -2 2arrow_forwardEach equation in Exercises 1–4 illustrates a property of determinants. State the property.arrow_forward
- In Exercises 8–19, calculate the determinant of the given matrix. Use Theorem 3 to state whether the matrix is singular or nonsingulararrow_forwardFind the matrix A such that T(x) = Ax.arrow_forwardCompute the determinants in Exercises 1–8 using a cofactor expansion across the first row. In Exercises 1–4, also compute the determinant by a cofactor expansion down the second column.arrow_forward
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