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: 23

Answer

By Th.8, the columns of K are linearly dependent, and they do not span $\mathbb{R}^{n}$.

Work Step by Step

The statements in Th.8 $\mathrm{b}. \quad A$ is row equivalent to the $n\times n$ identity matrix. $\mathrm{e}.\quad$ The columns of $A$ form a linearly independent set. $\mathrm{h}.\ \quad$The columns of $A$ span $\mathbb{R}^{n}$. are all false when A=K. Thus, the columns of K are linearly dependent, and they do not span $\mathbb{R}^{n}$.
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