Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 10 - Section 10.6 - Determinants and Cramer's Rule - 10.6 Exercises - Page 742: 3

Answer

TRUE

Work Step by Step

The determinate for a square matrix for $m$ columns anfd $n$ rows is defined as: $det(A)= \begin{vmatrix}p&q\\r&s\end{vmatrix}=ps-rq$ Counter Example: $det(A)= \begin{vmatrix}2&3\\2&3\end{vmatrix}=(2)(3)-(3)(2)=6-6=0$ Therefore, the given statement is true that when $det(A)=0$, then the matrix $A$ is not invertible.
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