Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 4 - Vector Spaces - 4.8 Row Space and Column Space - Problems - Page 325: 4

Answer

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Work Step by Step

a) We obtain $\begin{bmatrix} -3\\ 1\\ 1 \end{bmatrix} \approx \begin{bmatrix} -3\\ 0\\ 0 \end{bmatrix}\approx\begin{bmatrix} 1\\ 0\\ 0 \end{bmatrix}$ We notice that there is only one row vector which is equivalent to basis of row space of $A$ with $n=1$. So, the basis for row-space is of $A$ equal to $\{(1)\}$. b) We notice that just one column $A$is dependent $\{(1)\}$ . So, the basis for column-space of $A$ is equal to $\{(-3,1,7)\}$ with $m=3$.
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