Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 2 - Matrix Algebra - 2.3 Exercises - Page 117: 6

Answer

$A$ is not an invertible matrix. (Th.8, (a) and (b))

Work Step by Step

Adding $3R_{1}$ to $R_{3}$ $A\sim\left[\begin{array}{lll} 1 & -5 & -4\\ 0 & 3 & 4\\ 0 & -9 & -12 \end{array}\right] $adding $3R_{2}$ to $R_{3}$ $\sim\left[\begin{array}{lll} 1 & -5 & -4\\ 0 & 3 & 4\\ 0 & 0 & 0 \end{array}\right]$ we see that $A$ can not row-reduce to $I_{3}$ So, looking at Th.8, $\mathrm{b}. \quad A$ is row equivalent to the $n\times n$ identity matrix.. is not valid. Then, $\mathrm{a}. \quad A$ is an invertible matrix. is not valid as well $A$ is not an invertible matrix. (Th.8, (a) and (b))
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