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: 3

Answer

0

Work Step by Step

First, use cofactor expansion (Theorem 4.1) along the first row: \[ \begin{vmatrix} 1 & -1 & 0\\-1 & 0 & 1\\0 & 1 & -1 \end{vmatrix} = 1 \cdot \begin{vmatrix} 0 & 1\\1 & -1 \end{vmatrix} -(-1) \cdot \begin{vmatrix} -1 & 1\\0 & -1 \end{vmatrix} +0 \] Then simplify the expansion: $=1 \cdot (0-1) + 1 \cdot (1-0)$ $=-1+1$ $=0$
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