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: 21

Answer

This scaling of row 2 by a constant $k$ multiplies the determinant by $k$.

Work Step by Step

$\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc=\frac{1}{k}(kad-kbc)=\frac{1}{k}\begin{vmatrix}a&b\\kc&kd\end{vmatrix}$, $k\neq 0$ $k=0\implies\begin{vmatrix}a&b\\kc&kd\end{vmatrix}=k(ad-bc)=0=0\begin{vmatrix}a&b\\c&d\end{vmatrix}$
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