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 - Problems - Page 219: 21

Answer

Non-invertible

Work Step by Step

The matrix is non-invertible if and only if $D=0$. Upper A$=\begin{bmatrix} 1 & 2 &-3&5\\ 0 & 4 &-6 &11\\ 0 & 0 &\frac{7}{2} &-\frac{13}{4}\\ 0 & 0 & 0& 0 \end{bmatrix}$ Hence here $D=1.4.\frac{7}{2}.0=0$, thus the matrix is non-invertible.
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