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: 26

Answer

$-3$

Work Step by Step

The elements of the first row are $2, -2$ and $1$. The first row of the array of signs is $ + , - , +$ . $$\begin{vmatrix} 2& -2 & 1\\ 4 & 1 & 3\\ 3 & 1&2 \end{vmatrix}=2\begin{vmatrix} 1& 3 \\ 1 & 2 \end{vmatrix}-(-2)\begin{vmatrix} 4 & 3 \\ 3& 2 \end{vmatrix}+1\begin{vmatrix} 4 & 1 \\ 3& 1 \end{vmatrix}$$ $$=2(2-3)-(-2)(8-9)+1(4-3)=-2-2+1=-3$$
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