Answer
This addition of a scalar multiple of row 2 to row 1 does not change the determinant.
Work Step by Step
$\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc=(ad-bc)+(kcd-kcd)=(ad+kcd)-(bc+kcd)=\begin{vmatrix}a+kc&b+kd\\c&d\end{vmatrix}$
Linear Algebra and Its Applications (5th Edition)
by Lay, David C.; Lay, Steven R.; McDonald, Judi J.
Published by
Pearson
ISBN 10:
032198238X
ISBN 13:
978-0-32198-238-4
Chapter 3 - Determinants - 3.1 Exercises - Page 170: 20
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