Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 3 - Determinants - 3.2 Exercises - Page 177: 14

Answer

$20$

Work Step by Step

With a single row exchange, we are fortunate to find that expanding down fourth column of the $4\times 4$ matrix and across the second row of the $3\times 3$ matrix matrix reduces the original determinant of order 4 to a determinant of order 2. $\begin{vmatrix}1&5&4&1\\0&-2&-4&0\\3&5&4&1\\-6&5&5&0\end{vmatrix}=\begin{vmatrix}1&5&4&1\\0&-2&-4&0\\2&0&0&0\\-6&5&5&0\end{vmatrix}=-1\begin{vmatrix}0&-2&-4\\2&0&0\\-6&5&5\end{vmatrix}=- \left [-2\begin{vmatrix}-2&-4\\5&5\end{vmatrix} \right ]=2\cdot 10=20$
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