Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Appendix E - Exercise Set - Page 1005: 23

Answer

$15$

Work Step by Step

The determinant of the matrix is the same regardless of the row or column you select to expand by. Choosing the first row: The elements of the first row are $1, 0$ and $4$. The first row of the array of signs is $ + , - , +$ . $$\begin{vmatrix} 1 & 0 & 4\\ 1 & -1 & 2\\ 3 & 2&1 \end{vmatrix}=1\begin{vmatrix} -1 & 2 \\ 2 & 1 \end{vmatrix}-0\begin{vmatrix} 1 & 2 \\ 3& 1 \end{vmatrix}+4\begin{vmatrix} 1 & -1 \\ 3& 2 \end{vmatrix}$$ $$=1(-1-4)-0(1-6)+4(2-(-3))=-5-0+20=15$$
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