Explanation Given Information: The provided matrix is [ 1 1 2 0 1 2 ] . 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 [ 1 1 2 0 1 2 ] . Thus, to calculate the first five powers of the provided matrix. The first power can be calculated using the formula as, A 1 = A = [ 1 1 2 0 1 2 ] = [ 1 0.5 0 0.5 ] Therefore, the first power is A 1 = [ 1 0.5 0 0.5 ] . Now, to calculate the second power using the formula, A 2 = A ⋅ A = [ 1 1 2 0 1 2 ] [ 1 1 2 0 1 2 ] = [ 1 + 0 1 2 + 1 4 0 + 0 0 + 1 4 ] = [ 1 3 4 0 1 4 ] Therefore, the second power is A 2 = [ 1 3 4 0 1 4 ] . Now, to calculate the third power using the formula, A 3 = A 2 ⋅ A = [ 1 3 4 0 1 4 ] [ 1 1 2 0 1 2 ] = [ 1 + 0 1 2 + 3 8 0 0 + 1 8 ] = [ 1 7 8 0 1 8 ] Therefore, the third power is A 3 = [ 1 7 8 0 1 8 ]

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ISBN: 9781323788707

Author: Goldstein

Publisher: PEARSON

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Chapter 8.1, Problem 40E

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To calculate: The first five powers of the matrix [112012].

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Chapter 8.1, Problem 39E

Chapter 8.1, Problem 41E

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The first five powers of the matrix [ 1 1 2 0 1 2 ] .

Solution Summary: The author calculates the first five powers of the matrix: left[cc1&

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To calculate: The first five powers of the matrix [112012].

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