I need to solve the following problem,
In this problem, the eigenvalues of the coefficient matrix can be found by inspection and factoring. Apply the eigenvalue method to find a general solution of the system.
Now I know how to find the eigenvalues by using the fact that
EDIT: Originally I didn't understand what inspection meant either. After googling it this is what I found. Imagine you have the matrix,
By noticing (or inspecting) that each row sums up to the same value, which is 0, we can easily see that [1, 1, 1] is an eigenvector with the associated eigenvalue of 0.