Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 3 - Section 3.5 - Determinants and Cramer’s Rule - Exercise Set - Page 240: 31



Work Step by Step

Formula to determine the determinant, $D$ of a $3 \times 3$ matrix is: $D=\begin{vmatrix}a&b&c\\d&e&f\\g&h&i\end{vmatrix}=a \begin{vmatrix}e&f\\h&i\end{vmatrix}-b \begin{vmatrix}d&f\\g&i\end{vmatrix}+c \begin{vmatrix}d&e\\g&h\end{vmatrix}$ Thus, as per question, we have $D=\begin{vmatrix}1&1&1\\2&2&2\\-3&4&-5\end{vmatrix}=2-16+14=0$
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