Explanation Given Information: The provided matrix is [ 0.5 0 0.5 1 ] . Stochastic matrices for which some power contains no zero entries are called regular matrices. Consider the given matrix [ 0.5 0 0.5 1 ] . Thus, to check the matrix provided is regular for which some power contains no zero entries. The first power can be calculated as, A 1 = A = [ 0.5 0 0.5 1 ] Therefore, the first power A 1 = [ 0.5 0 0.5 1 ] . Now, the second power can be calculated as, A 2 = A ⋅ A = [ 0.5 0 0.5 1 ] [ 0.5 0 0.5 1 ] = [ 0.25 + 0 0 0.25 + 0.5 1 ] = [ 0

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Author: Larry Goldstein, David Schneider

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Chapter 8.1, Problem 45E

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Whether the given matrix is regular or not, by looking at the first few powers of the matrix [0.500.51].

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Chapter 8.1, Problem 44E

Chapter 8.1, Problem 46E

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Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)

Ch. 8.1 - 1. Is a stochastic matrix? Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E

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Whether the given matrix is regular or not, by looking at the first few powers of the matrix [ 0.5 0 0.5 1 ] .

Solution Summary: The author explains that the given matrix is not regular as all powers have a zero entry in the upper right corner. Stochastic matrices for which some power contains no zero entries are called regular

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Whether the given matrix is regular or not, by looking at the first few powers of the matrix [0.500.51].

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