Finding general solution to linear system

[member 731016]

Homework Statement

Please see below. I am unsure why the example says we cannot choose $v_1 = (0, 0)$.

Relevant Equations

Please see below.

For this problem,

My working is,
$0v_1 + 0v_2 = 0$, however, does someone please know why the example says we cannot choose $v_1 = (0, 0)$ since from $0v_1 + 0v_2 = 0$ $v_1, v_2 \in \mathbb{R}$ i.e there is no restriction on what the vector components could be)?

Thanks!

 

[Hill]

Eigenvectors are non-zero vectors by definition.

Zero vector satisfies $Ax=\lambda x$ for any $A$ and any $\lambda$.