Explanation Given: The matrix A = [ 0.55 0.45 0 1 ] Explanation: A matrix is said to be regular, if there exists a positive integer such that if the matrix is raised to that positive integer, all the enteries in the matrix are positive. As, the first power of the matrix has a zero, not all enteries are positive. Now, check for the second power. A 2 = A ⋅ A = [ 0.55 0.45 0 1 ] [ 0.55 0.45 0 1 ] = [ 0.3025 0.6975 0 1 ] The second power too has a 0, a nonpositive entry

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ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10.2, Problem 4E

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If the provided matrix is regular.

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If the provided matrix is regular.

Solution Summary: The author explains that a matrix is said to be regular, if there exists an integer such that all the enteries in the matrix are positive.

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