Linear Algebra: A Modern Introduction

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

Chapter 4 - Eigenvalues and Eigenvectors - 4.2 Determinants - Exercises 4.2 - Page 281: 11



Work Step by Step

By using the cofactor expansion along the first row: $det\begin{vmatrix} a& b&0\\ 0&a &b\\ a&0 &b \end{vmatrix}$ $=a\times det\begin{vmatrix} a&b\\ 0 &b \end{vmatrix}-b\times det\begin{vmatrix} 0 &b\\ a&b \end{vmatrix}+0\times det\begin{vmatrix} 0&a\\ a&0 \end{vmatrix}$ $=a(ab-0)-b(0-ab)+0$ $=a^2b+ab^2$
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