Explanation Given Information: The provided matrix is [ 0 1 1 0 ] . 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 1 0 ] . 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 1 0 ] Therefore, the first power is A 1 = [ 0 1 1 0 ] . Now, to calculate the second power using the formula A 2 = A ⋅ A = [ 0 1 1 0 ] [ 0 1 1 0 ] = [ 0 + 1 0 0 1 + 0 ] = [ 1 0 0 1 ] Therefore, the second power is A 2 = [ 1 0 0 1 ] . Now, to calculate the third power using the formula A 3 = A 2 ⋅ A = [ 1 0 0 1 ] [ 0 1 1 0 ] = [ 0 1 + 0 0 + 1 0 ] = [ 0 1 1 0 ] Therefore, the third power is A 3 = [ 0 1 1 0 ]

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134507125

Author: Goldstein

Publisher: PEARSON

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Chapter 8.1, Problem 42E

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To calculate: The first five powers of the matrix [0110].

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Chapter 8.1, Problem 41E

Chapter 8.1, Problem 43E

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Chapter 8 Solutions

Finite Mathematics & Its Applications (12th Edition)

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The first five powers of the matrix [ 0 1 1 0 ] .

Solution Summary: The author explains how to calculate the first five powers of the matrix: left[cc0& 1 1& 0

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Chapter 8 Solutions