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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F966fd174-f774-4251-9c7b-7355db0f5142%2F3e371d4a-b5f1-47ed-b040-bd63779a06a4%2Fnqxeveg.png&w=3840&q=75)
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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