Linear Algebra and Its Applications (5th Edition)

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

Chapter 3 - Determinants - 3.2 Exercises - Page 177: 4

Answer

Given a square matrix, $A$, if a multiple of one row of $A$ is added to another row to produce a matrix $B$, then det $B$ = det $A$.

Work Step by Step

Given a square matrix, $A$, if a multiple of one row of $A$ is added to another row to produce a matrix $B$, then det $B$ = det $A$. In this case, $-2$ times Row 1 was added to Row 2 in matrix $A$ to get matrix $B$. Thus, det$A$ = det $B$.
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