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 - 1.2 Exercises - Page 22: 6

Answer

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

Work Step by Step

This exercise is just like the last one, except that it is not possible for the final row to contain any entries. If it did contain an entry, it would either be in a pivot column and require elimination by row operations (matrix 1 above) or it would be below a row of all zeros and need to be swapped with a previous row (matrices 2 and 3 above).
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