Solution Found!
Use Exercise 19 to show that if P is an n × n stochastic
Chapter 4, Problem 20E(choose chapter or problem)
Use Exercise 19 to show that if P is an n × n stochastic matrix, then so is P2Reference:S be the 1 × n row matrix with a 1 in each column, a. Explain why a vector x in is a probability vector if and only if its entries are nonnegative and Sx = 1. (A 1 × 1 matrix such as the product Sx is usually written without the matrix bracket symbols.)b. Let P be an n × n stochastic matrix. Explain why SP = S.c. Let P be an n × n stochastic matrix, and let x be a probability vector. Show that Px is also a probability vector.
Questions & Answers
QUESTION:
Use Exercise 19 to show that if P is an n × n stochastic matrix, then so is P2Reference:S be the 1 × n row matrix with a 1 in each column, a. Explain why a vector x in is a probability vector if and only if its entries are nonnegative and Sx = 1. (A 1 × 1 matrix such as the product Sx is usually written without the matrix bracket symbols.)b. Let P be an n × n stochastic matrix. Explain why SP = S.c. Let P be an n × n stochastic matrix, and let x be a probability vector. Show that Px is also a probability vector.
ANSWER:Solution 19E(a)As the sum of entries of vector is 1 so the entries are not all zeros.Thus, by the def