Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 2 - Matrix Algebra - 2.9 Exercises - Page 160: 9

Answer

$dim\ Col\ A=3$ and $dim\ Nul\ A=1$

Work Step by Step

The basis for Col A include the pivot columns and the basis for Nul A include all other columns. The basis for Col A is $\begin{bmatrix} 1\\ -3\\ 2\\ -4 \end{bmatrix} $, $\begin{bmatrix} 2\\ -1\\ 4\\ 2 \end{bmatrix} $, and $\begin{bmatrix} -4\\ 5\\ -3\\ 7 \end{bmatrix} $ The basis for Nul A is $\begin{bmatrix} -3\\ 9\\ -6\\ 12 \end{bmatrix} $ dim Col A=3 and dim Nul A=1
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