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: 32



Work Step by Step

Since the third column of the matrix is the sum of the first column and two times the second column, we have the following: $ \begin{bmatrix}4&1&6\\-7&5&3\\9&-3&3\end{bmatrix}\begin{bmatrix}1\\2\\-1\end{bmatrix}=1\cdot\begin{bmatrix}4\\-7\\9\end{bmatrix}+2\cdot\begin{bmatrix}1\\5\\-3\end{bmatrix}+(-1)\cdot\begin{bmatrix}6\\3\\3\end{bmatrix}=\begin{bmatrix}0\\0\\0\end{bmatrix} $ Any nonzero constant multiple of this solution will also work as a nontrivial solution to the homogeneous equation.
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