real distinct eigenvaluesunder this case well

Question

Real Distinct Eigenvalues

Under this case we'll have the real, distinct eigenvalues l₁ ≠l₂≠l₃ a and their related eigenvectors, ?h₁ , ?h₂ and  ?h₃  are guaranteed to be linearly independent and therefore the three linearly independent solutions we find from this case are,

e^l1t ?h_1,               e^l2t ?h_2,                       e^l3t ?h₃