Explanation Given Information: The provided matrix is [ 0.2 0.2 0.2 0.3 0.3 0.3 0.5 0.5 0.5 ] . 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 [ 0.2 0.2 0.2 0.3 0.3 0.3 0.5 0.5 0.5 ] . Thus, to calculate the first five powers of the provided matrix. The first power can be calculated using the formula as, A 1 = A = [ 0.2 0.2 0.2 0.3 0.3 0.3 0.5 0.5 0.5 ] Therefore, the first power is A 1 = [ 0.2 0.2 0.2 0.3 0.3 0.3 0.5 0.5 0.5 ] . Now, to calculate the second power using the formula A 2 = A ⋅ A = [ 0.2 0.2 0.2 0.3 0.3 0.3 0.5 0.5 0.5 ] [ 0.2 0.2 0.2 0.3 0.3 0.3 0.5 0.5 0.5 ] = [ 0.04 + 0.06 + 0.10 0.04 + 0.06 + 0.10 0.04 + 0.06 + 0.10 0.06 + 0.09 + 0.15 0.06 + 0.09 + 0.15 0.06 + 0.09 + 0.15 0.10 + 0.15 + 0.25 0.10 + 0.15 + 0.25 0

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ISBN: 9781323788707

Author: Goldstein

Publisher: PEARSON

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Chapter 8.1, Problem 44E

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To calculate: The first five powers of the matrix [.2.2.2.3.3.3.5.5.5].

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Chapter 8.1, Problem 43E

Chapter 8.1, Problem 45E

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Chapter 8 Solutions

FINITE MATHEMATICS & ITS APPLICATIONS

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The first five powers of the matrix [ .2 .2 .2 .3 .3 .3 .5 .5 .5 ] .

Solution Summary: The author calculates the first five powers of the matrix using the formula c1=A =left.

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To calculate: The first five powers of the matrix [.2.2.2.3.3.3.5.5.5].

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Chapter 8 Solutions