Linear Algebra and Its Applications (5th Edition)

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

Chapter 3 - Determinants - 3.1 Exercises - Page 170: 24

Answer

This scaling of row 1 by a constant multiple $k$ multiplies the determinant by $k$.

Work Step by Step

$1\begin{vmatrix}4&-4\\-3&1\end{vmatrix}-0\begin{vmatrix}-3&-4\\2&1\end{vmatrix}+1\begin{vmatrix}-3&4\\2&-3\end{vmatrix}=-8+0+1=-7$ $k\begin{vmatrix}4&-4\\-3&1\end{vmatrix}-0\begin{vmatrix}-3&-4\\2&1\end{vmatrix}+k\begin{vmatrix}-3&4\\2&-3\end{vmatrix}=-8k+0+1k=-7k$
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