I'm walking through an example of how to calculate the eigenvectors of a matrix, in my course book. But I don't get one step they do, and it isn't explained at all.
How does the top part conclude in the bottom eqautions? (c is any complex constant that is not zero)
PS: Excuse me for the vague question. But I don't know what they are doing, so I don't know how to direct the question.
Since the equation clearly gives $v_1=0\Rightarrow v_2=0$, you pick any nonzero value for $v_1$, say $c$, and calculate what the corresponding value of $v_2$ should be (in this case we obviously use the first equation $-(1+\sqrt{5})v_1+2v_2=0$ to get $v_2=\frac12(1+\sqrt5)v_1=\frac12(1+\sqrt5)c$, which you can check also satisfies the second equation).