Question

at http://tutorial.math.lamar.edu/Classes/DE/RealEigenvalues.aspx in first example how did the author get 2n_1 +2n_2 = 0 ?

Answer 1

ok got it, he made the augmented matrix in which the second row is zero, am I right?

Answer 2

Do you know how to find the null space of a singular matrix?
that is the most straight-forward approach to find the eigenvectors
you would get vector
\[c \left(\begin{matrix}-1 \\ 1\end{matrix}\right)\]
or simply
\[\left(\begin{matrix}-1 \\ 1\end{matrix}\right)\]

In the example, we know the matrix is singular so one of the rows is dependent. (We could row reduce to set the bottom row to all zeros). So ignore that row.

So he just multiplied the top row times his (n1 n2) vector and set it = 0