## Linear Algebra and Its Applications, 4th Edition

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