Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 3 - Determinants - 3.2 Properties of Determinants - True-False Review - Page 218: e



Work Step by Step

We know that the determinant of a matrix \[ \left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right] \] is $D=ad-bc$. Also, a matrix is non-invertible if $D=0$. here $D=x^2y-xy^2=xy(y-x)$. Thus if it is non-invertible then $x=0$, $y=0$ or $x=y$, thus the statement is false.
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