Dick S. answered 08/09/19
Science Tech Eng Math Physics, Simple Explanations, UC Berkeley Grad
given eigenvalues, eigenvectors for matrix A are λ1 = 2, v1 = [-5 1]t and λ2 = 6, v2 = [5 4]t
(t means transpose ... means the row vector is actually a column vector)
Defn of Eigenvector, Eigenvalue:
Avi = λivi for all i, in this case, i = 1, 2
so,
A(v1 + v2) = λ1v1 + λ2v2 = 2[-5 1]t + 6[5 4]t = [-10 2]t + [30 24]t = [20 26]t
and,
A(3v1) = 3Av1 = 3λ1v1 = 3(2)[-5 1]t = [-30 6]t