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 - 3.1 The Definition of the Determinant - True-False Review - Page 206: f



Work Step by Step

We know that the determinant of a matrix \[ \left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right] \] is $D=ad-bc$. Hence for the matrix a matrix \[ \left[\begin{array}{rr} 1 & 1 \\ 2 &1 \\ \end{array} \right] \] $D=1\cdot1-1\cdot2=1-2=-1$ whereas all the entries are positive. Thus the statement is false.
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