Explanation Given Information: The provided matrix is [ 0.1 0.3 0.9 0.7 ] . Formula used: Multiplication of matrices is given by, A 1 = A A 2 = A ⋅ A A 3 = A 2 ⋅ A A 4 = A 3 ⋅ A And A 5 = A 4 ⋅ A Calculation: The given matrix is [ 0.1 0.3 0.9 0.7 ] . Thus, to calculate the first five powers of the provided matrix. The first power can be calculated using the formula as, A 1 = A = [ 0.1 0.3 0.9 0.7 ] Therefore, the first power is A 1 = [ 0.1 0.3 0.9 0.7 ] . Now, to calculate the second power using the formula A 2 = A ⋅ A = [ 0.1 0.3 0.9 0.7 ] [ 0.1 0.3 0.9 0.7 ] = [ 0.01 + 0.27 0.03 + 0.21 0.09 + 0.63 0.27 + 0.49 ] = [ 0.28 0.24 0.72 0.76 ] Therefore, the second power is A 2 = [ 0.28 0.24 0.72 0.76 ] . Now, to calculate the third power using the formula A 3 = A 2 ⋅ A = [ 0.28 0.24 0.72 0.76 ] [ 0.1 0.3 0.9 0.7 ] = [ 0.028 + 0.216 0.084 + 0.168 0.072 + 0.684 0.216 + 0.532 ] = [ 0.244 0.252 0.756 0.748 ] Therefore, the third power is A 3 ≈ [ 0

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134507125

Author: Goldstein

Publisher: PEARSON

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Chapter 8.1, Problem 41E

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To calculate: The first five powers of the matrix [.1.3.9.7].

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Chapter 8.1, Problem 40E

Chapter 8.1, Problem 42E

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Chapter 8 Solutions

Finite Mathematics & Its Applications (12th Edition)

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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The first five powers of the matrix [ .1 .3 .9 .7 ] .

Solution Summary: The author calculates the first five powers of the matrix left[cc.1& 0.3 0.9&

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To calculate: The first five powers of the matrix [.1.3.9.7].

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Chapter 8 Solutions