1. The problem statement, all variables and given/known data Solve X' = [ [9, 4, 0], [-6, -1, 0], [6, 4, 3]] * X using eigenvalues. 2. Relevant equations (A - λI) * K = 0 X = eλt 3. The attempt at a solution Set up the characteristic equation to find eigenvalues. I found a root of multiplicity 2 of λ=3 and another distinct root λ=5. When setting up equations to solve for the eigenvectors (setting λ= 3) I found: 6k1 + 4k2 = 0 -6k1 -4k2 = 0 6k1 + 4k2 = 0 So there's only a dependency for k1 and k2. So can't I simply find two linearly independent eigenvectors by substituting different values for k3 such as [2, -3, 1] and [2, -3, 2] and use those as two independent solutions? Or does this mean I still have to walk through the steps of using the Kteλt + Peλt form of the solution to find the second solution for the λ=3 root?