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: 5

Answer

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

Work Step by Step

The first example occurs when the matrix has a pivot in both columns, meaning the second row of the original matrix was not a constant multiple of the first row. The second example occurs when one row is a constant multiple of the other row, but neither has an initial $0$. The third example occurs when one row is a constant multiple of the other row, and they both have an initial $0$.
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