Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.7 Exercises - Page 62: 24

Answer

$ \begin{bmatrix} \blacksquare&*\\ 0&0 \end{bmatrix} $ $ \begin{bmatrix} 0&\blacksquare\\ 0&0 \end{bmatrix} $ $ \begin{bmatrix} 0&0\\ 0&0 \end{bmatrix} $

Work Step by Step

The columns of a matrix are linearly dependent if and only if at least one column of does not contain a pivot position. Hence, we can have a pivot position in the first column only, in the second column only, or in neither column.
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