Linear Algebra: A Modern Introduction

Published by Cengage Learning
ISBN 10: 1285463242
ISBN 13: 978-1-28546-324-7

Chapter 4 - Eigenvalues and Eigenvectors - 4.6 Applications and the Perron-Frobenius Theorem - Exercises 4.6 - Page 359: 2

Answer

Not regular.

Work Step by Step

$A=\begin{bmatrix} 1 &0.5 \\ 0 & 0.5 \end{bmatrix}$ We can see that $A$ is an upper triangular matrix and we know that any power of an upper triangular matrix is also an upper triangular matrix. Thus no power of $A$ has only positive entries, so it cannot be regular.
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