Linear Algebra and Its Applications, 4th Edition

Published by Brooks Cole
ISBN 10: 0030105676
ISBN 13: 978-0-03010-567-8

Chapter 1 - Section 1.2 - The Geometry of Linear Equations - Problem Set: 11

Answer

$a = 2$ or $a = -2$

Work Step by Step

Let's look at the column picture here x$\begin{bmatrix} a \\ 2 \\ \end{bmatrix}$ + y$\begin{bmatrix} 2 \\ a \\ \end{bmatrix}$ = $\begin{bmatrix} 0 \\ 0 \\ \end{bmatrix}$ If $\begin{bmatrix} a \\ 2 \\ \end{bmatrix}$ = k$\begin{bmatrix} 2 \\ a \\ \end{bmatrix}$ where k is any real number, then the entire line $x+ky = 0$ will be the solution set. Therefore $a = 2*k$ and $2 = k*a$ solving these two simultaneously, we get $k = 1$ or $k = -1$ which further translates as $a = 2$ or $a = -2$
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