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S be the 1 x n row matrix with a 1 in each column, S = [1 1 a. Explain why a vector x in TR" 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 xn stochastic matrix. Explain why SP = S. 1] c. Let P be an n x n stochastic matrix, and let x be a probability vector. Show that Px is also a probability vector.

S be the 1 x n row matrix with a 1 in each column, S = [1 1 a. Explain why a vector x in TR" 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 xn stochastic matrix. Explain why SP = S. 1] c. Let P be an n x n stochastic matrix, and let x be a probability vector. Show that Px is also a probability vector.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 14EQ
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S be the 1 x n row matrix with a 1 in each column, S = [1 1 a. Explain why a vector x in TR" 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 xn stochastic matrix. Explain why SP = S. 1] c. Let P be an n x n stochastic matrix, and let x be a probability vector. Show that Px is also a probability vector.
Transcribed Image Text:S be the 1 x n row matrix with a 1 in each column, S = [1 1 a. Explain why a vector x in TR" 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 xn stochastic matrix. Explain why SP = S. 1] c. Let P be an n x n stochastic matrix, and let x be a probability vector. Show that Px is also a probability vector.
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