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: 3

Answer

Given matrix $A$, if one row of $A$ is multiplied by $k$ to produce $B$, then $det$ $B$ = $k$ $* det$ $A$.

Work Step by Step

Given matrix $A$, if one row of $A$ is multiplied by $k$ to produce $B$, then $det$ $B$ = $k$ $* det$ $A$. In this case, the first row of the matrix on the right was multiplied by 3 to reach the matrix the left. Thus, the determinant of the matrix on the left is three times the determinant of the matrix on the right.
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